network problem solving techniques

• Network management and monitoring
• 9 most common network issues and how to solve them

Slow network speeds, weak Wi-Fi signals and damaged cabling are just some of the most common network connection issues that IT departments need to troubleshoot.

• David Jacobs, The Jacobs Group

Business networks are complex, and many things can go wrong that disrupt network performance. End users often complain about what appears to be poor application performance, and there can be many possible reasons for these hiccups. Here are nine of the most common network issues to troubleshoot.

1. Slow network

Users complain the network is too slow. There can be many reasons why a network that provided adequate performance in the past is now frustrating its users. For instance, a new application, such as video conferencing or online training videos , may have been added. A failing switch port or link could cause traffic to route around the failure and overload another link.

In other cases, the network could be part of a larger organizational network. As a result, a change in the larger network has resulted in more traffic through the internet connection point, slowing responses to cloud-resident applications.

Another network speed issue could emerge if employees decide to download high-definition videos while at work because downloading in the office is faster than using their home internet connection. A network monitoring tool helps solve any of these common network issues.

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2. Weak Wi-Fi signal

Wi-Fi signal strength may be adequate almost everywhere, but it could be weak or nonexistent in other areas. Rearranging an office area can result in a weak wireless connection, where signal strength had been adequate before the move. For example, a large metal object, like a file cabinet, can block the Wi-Fi signal.

Devices such as microwave ovens, cordless phones and Bluetooth can interfere with Wi-Fi signals, too. A Wi-Fi network test tool can help identify the source of the problem.

3. Physical connectivity issues

A network connection can suddenly break because of physical connectivity issues. A common problem is when a network cable becomes damaged or knocked loose . Cables might be added or removed from a switch, and one of the other cables might accidentally get disconnected.

Or a cable was damaged when it was pulled around a sharp edge while work was done on the heating or air conditioning pipes. It should be clear from the segment of the network affected which cable was damaged. But finding the problem along a cable stretching across the ceiling may be time-consuming.

4. Excessive CPU usage

Task Manager is the first thing to use to find which application is using a high proportion of system resources, such as CPU, memory or disk space. This basic troubleshooting step may not reveal a problem since some applications may be performing complex calculations, receiving high-speed video or interacting with large databases. A virus may also consume resources, so make sure antivirus software is up to date.

If an application has been running for a long time, it may slowly leak resources. The quickest way to improve performance is to stop and restart the application, although sometimes you may need to stop and restart the entire system. Updating device drivers may also improve performance.

Task Manager also shows applications you didn't know were running in the background. One example would be Windows including games upon system startup. Editing startup files can eliminate this problem.

5. Slow DNS lookups

The DNS matches the common name used to match server or service names with the internet address that routes a network request. For commonly used names, the matchup is probably already stored in the system's DNS cache, and the lookup is quick. For less commonly used names, the matchup may be stored in a more distant cache, such as the root server of the top-level name, such as .com, .org or a national root, such as .uk.

Each DNS server along the path checks its cache before making a request to the next server along the path. The next server then checks its cache, repeating the process. If lookup is slow, there may be a slow link along the path or a slow or overloaded server. To address this issue, your local network administrator can reconfigure local routers to shift requests to a faster chain of servers.

6. Duplicate and static IP addresses

On a network, no two systems can share the same internet address. If there are duplicate internet addresses, neither system can access the network reliably. The addresses for most network devices are assigned when Dynamic Host Configuration Protocol ( DHCP ) boots up the systems on the local network. DHCP maintains a pool of addresses assigned to the local network, assigning a different address from the pool to each system.

Workstations are not assigned permanent addresses but receive one for a limited time from DHCP. Systems re-request before the time runs out and usually receive the same address. If the system shuts down without re-requesting and the time runs out, it loses this address and may receive a different one upon startup.

The DHCP administrator may assign a static IP address to some network devices, such as printers or web servers, because external systems won't be updated if an address changes. One issue is users sometimes set up a private web server to support a hobby, allocating a static address without informing the network administrator. Both share a DHCP server in either an organization or home network. So, if the static address matches one assigned by DHCP, it disrupts the network.

Often, these private web servers are set up to upload and download licensed music or video and consume excessive network bandwidth.

7. Exhausted IP addresses

Internet addresses are in limited supply. Each service provider is given a supply based on the expected number necessary. Most familiar are the IPv4 addresses , which were originally thought to be adequate so every system could be allocated one. But, with the proliferation of cellphones and other devices, it's been necessary to move to IPv6 with 128-bit addresses for some networks.

A widely used method to stretch the supply of addresses is Network Address Translation ( NAT ), a feature often built into routers. Each is assigned a single internet address allocated from the worldwide set of addresses. Its internal DHCP server allocates private addresses to systems on connected local networks -- usually, an Ethernet or wireless network.

Private addresses generally start with either 10 or 192.168 on networks using 32-bit IPv4 addresses. These address ranges can be used many times, which helps to save addresses. The NAT server maps traffic to its global address to communicate with the internet. Responses are mapped back via the private addresses.

8. Can't connect to printer

When users can't connect to a printer, the first step is to check simple things like whether the printer is plugged in, turned on and has paper. Also, make sure the printer appears on Devices and Printers on Windows. If it does, click to check whether the file is queued.

Sometimes, you need to stop and restart the print spooler , the software that stores files until the printer is ready to print them. Also, check the printer vendor's website because some brands have a downloadable app that can diagnose and fix problems.

If the OS was just upgraded, scan for other people with similar problems, or check Microsoft.com to see if the company is aware of a problem. Shut off the printer, and turn it back on. Also, shut down your system, and turn it back on.

Finally, update printer drivers and your OS. In some cases, you may need to temporarily shut down your antivirus software . For a wireless printer, make sure it's connected to the signal.

9. VLAN and VPN problems

Check for virtual LAN (VLAN) misconfiguration issues. Review the configuration on each switch, carefully comparing configurations to ensure compatibility of switch configuration.

The most common VPN problem is a failure to connect . First, check to see if you're successfully logging in to the service, and make sure your account is up to date and you're entering your correct credentials. Next, check firewall settings. You need to open some ports. Check if that is the problem by temporarily shutting down your firewall. Finally, restart your system.

Try accessing the VPN from a different network, such as switching from Wi-Fi to Ethernet to the router. If there is still a problem, refer to the firewall documentation for other solutions, or contact the VPN vendor support.

In sum, networks are complex, and problems do occur. These are just some of the most common types of network problems. When other types of network issues occur, scan the web for help, or contact network service providers or device vendor support.

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What Is Network Troubleshooting?

Network troubleshooting is the act of discovering and correcting problems with connectivity, performance, security, and other aspects of networks.

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What's the value of network troubleshooting?

Fast, effective network troubleshooting is a cornerstone of business resilience. Today's networks perform more mission-critical business tasks than ever. Without robust troubleshooting and speedy resolution of issues, networks can suffer costly downtime.

The cost of downtime includes reduced productivity and the economic impacts of disrupted or underperforming services, data breaches, and malware. These consequences can result in steep costs and cause long-lasting damage to brands.

How do organizations handle troubleshooting?

Of course, troubleshooting isn't just about resetting user passwords or restarting devices. Especially in large organizations, it's about a set of procedures, practices, and tools used to process numerous requests by a complex mix of users and dispersed network assets and infrastructure.

Typically, a large organization has an entire team devoted to network troubleshooting. The team's engineers address problems at various levels: Tier 1 for basic issues such as password resets, Tier 2 for issues that can't be resolved by Tier 1, and Tier 3 for mission-critical issues.

Frequently, Tier 1 troubleshooting is outsourced. An escalation framework is used to route requests efficiently and make sure that upper-level engineers are tasked appropriately.

In recent years, artificial intelligence (AI), machine learning (ML), and automation have been used to bridge skills gaps. These technologies offer guided remediation tools that empower Tier 1 engineers to solve complex network problems more rapidly.

Many organizations have separate network troubleshooting tools, but the addition of these tools may require training and management by IT departments. More commonly, network troubleshooting is embedded in a network management system (NMS).

How do NMSs relate to troubleshooting?

In large organizations, network troubleshooting teams are not simply waiting for users to report issues.

An NMS monitors networks continuously. It sends status updates—and alerts, when needed—on network key performance indicators (KPIs) such as connection speed, bandwidth, latency, users, and access.

The NMS performs monitoring by querying the various parts and nodes of the network to update status, at an interval determined by the IT team. Newer network elements, however, use telemetry to transmit their KPIs automatically.

An essential part of network troubleshooting is tracking and collecting data on network events. A system of IT service management (ITSM) tickets is used for this process. The data aggregated from the tickets can provide insights to identify problem areas and guide network optimization and upgrades.

Network events

An occurrence that triggers a network troubleshooting process is called an event. Some common events are described below.

Connection failures

Such events could be caused by cables and plugs that aren't connected properly.

Security lapses

These events could involve anything from a full-blown malware attack to an unapproved user's being able to connect to Wi-Fi.

KPIs missed

KPIs, when they're well-calibrated, can provide early warnings of network issues before they affect users.

Application failures

For locally hosted applications, a failure could mean an update that wasn't installed or the presence of an obsolete device.

Policy failures

Network performance can suffer when network policies, such as those for security, traffic management, and access control, inadvertently contradict each other.

Endpoint issues

Issues with endpoint connectivity, for example, could be caused by endpoints' lack of proximity to network routers, network interference problems, or issues with a remote worker's local network.

Troubleshooting processes

Once alerts or requests have been received and basic problems such as hardware connections and user connectivity have been ruled out, network troubleshooting typically involves one or more of the following steps.

IP-configuration checks

Problems with IP addresses cause many network issues. Often, assigning a new IP address can resolve an issue if a previous address was incorrect.

Ping and tracert testing

If the IP address is correct, the network issue may be upstream of a modem. To diagnose the problem further, IT teams can use the ping utility or the tracert command to test connections with remote servers and return information about the signal path.

A DNS check will determine whether there's a problem with a server to which networks are trying to connect. When an IT team performs a DNS check and receives results such as "Request timed out" or "No response from server," the problem might originate in the DNS server for the destination.

Service provider checks

Outages do occur, even with major cloud providers and cloud-based services. Providers' status pages report outages that might be affecting network performance.

Virus and malware checks

Viruses and other malware can affect network performance, and often they're not easy to detect. IT teams should use security tools to see whether new attacks have been flagged.

Database logs

Databases that are full or overtaxed can slow performance across the network. A fresh review of database logs will show whether this is the case. 

Command-line tools

The most common command-line tools are ipconfig and nslookup. Numerous others—such as iptables, netstat, tcpdump, route, arp, and dig—can also help identify network issues.

Test environments 

For cases that are especially challenging or that involve sensitive or restricted data, IT teams may need to construct test environments, where they can re-create problems and test solutions.

Troubleshooting software features

Engineers benefit from a network troubleshooting interface that provides a global view of an entire network as well as a view into specific KPIs. As networks become more complex and dispersed, the design and ease of use of this interface become even more important.

Customizable views

The ability to filter network data by location, department, device, or network improves the early stages of diagnosing network problems.

Cross-domain visibility

The idea of viewing the network as a series of interconnected domains is becoming obsolete. The typical enterprise network includes not just local-area networks (LANs) connected to the internet, but also remotely hosted databases, applications, and data processing. Up-to-date troubleshooting tools are designed to manage these new, more complex networks.

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Basic Network Troubleshooting: A Complete Guide

The basics of network troubleshooting have not changed much over the years. When you’re network troubleshooting, a lot can be required to solve the problem. You could be solving many different issues across several different systems on your complex, hybrid network infrastructure. A network observability solution can help speed up and simplify the process.

The Network is the Key

“The network is down!” — I’m sure you heard that before.

Despite your best efforts as a network engineer, network failures happen, and you have to fix them. Hopefully, you’ve implemented a network observability platform in advance, so you should be collecting a wealth of information about your network, making troubleshooting easier.

But what happens when it’s time to activate troubleshooting mode?

In this post, I’m going to talk about the steps to troubleshoot your network. And then I’ll provide some best practices, as well as provide examples of troubleshooting with Kentik’s network observability solutions.

What is Network Troubleshooting?

Network troubleshooting is the process of solving problems that are occurring on your network, using a methodical approach. A simple definition for what can often be a hard task!

When users complain, whether they’re internal or external to your organization — or ideally, before they do — you need to figure out what the cause of their problem is. The goal is to troubleshoot and fix whatever issue underlies the problems.

Troubleshooting requires taking a methodical approach to resolving the issue as quickly as possible. Unfortunately for you, the user doesn’t care what your service-level objective for fixing the problem is. In today’s “gotta have it fast” culture, more often than not, you need to fix it now — or revenue is affected.

Let’s get into some ways you can troubleshoot your network and reduce your mean time to repair (MTTR).

Basic Network Troubleshooting Processes

Identify the problem.

When you’re troubleshooting network issues , complexity and interdependency make it complex to track down the problem. You could be solving many different issues across several different networks and planes (underlay and overlay) in a complex, hybrid network infrastructure.

The first thing you want to do is identify the problem you’re dealing with. Here are some typical network-related problems:

• A configuration change broke something . On a network, configuration settings are constantly changing. Unfortunately, configuration change accidents can happen that bring down parts of the network.
• Interface dropping packets . Interface issues caused by misconfigurations, errors, or queue limits lead to network traffic failing to reach its destination. Packets simply get dropped.
• Physics limitations on connectivity . Sometimes, your connections don’t have enough bandwidth. Or the latency is too much between source and destination. These lead to network congestion, slowness, or timeouts.
• Problems in the cloud . Intra- or inter-cloud connectivity problems can have their own unique set of causes and challenges. Often driven by someone else’s congestion, oversubscription, or software failures.

Find Your Network Troubleshooting Tools

Fixing these kinds of troubleshooting problems needs more than identification. To paraphrase French biologist Louis Pasteur — where observation is concerned, chance favors only the prepared mind.

No network engineer can troubleshoot without being prepared with their tools and telemetry. So once you’ve identified that there is a problem, it’s time to use your network troubleshooting tools.

Ideally, you have tools and telemetry in advance, so your network observability toolchain is using AI to automatically identify problems and linking you to a jumping off point so you can drive down both MTTK (Mean Time to Know) and either MTTR (Mean Time to Repair) or MTTI (Mean Time to Innocence).

Here are a few examples of basic network troubleshooting tools:

• Tracert/ Trace Route
• Ipconfig/ ifconfig
• Pathping/MTR

The First Step — Ping Affected Systems

When your network is down, slow, or suffers from some other problem, your first job is to send packets across the network to validate the complaint. Send these pings using the Internet Control Message Protocol (ICMP) or TCP to one or any of the network devices you believe to be involved.

The ping tool is a utility that’s available on practically every system, be it a desktop, server, router, or switch.

There’s a sports analogy that says “the most important ability is availability” for systems. If you can’t reach it, it’s not available to your users.

Sending some ICMP packets across the network, especially from your users’ side, will help answer that question, if your platform isn’t presenting the path to you automatically. In some cases if ICMP is filtered, you can usually switch to TCP (Transmission Control Protocol) and use tcping, telnet, or another TCP-based method to check for reachability.

Get the Path with Traceroute

If you’re not getting any ping responses, you need to find out where the ping is stopping. You can use another ICMP-based tool to help, and that’s traceroute.

Your ping could be getting stopped because ICMP isn’t allowed on your network or by a specific device. If that’s the case, you should consider TCP Traceroute on Linux, which switches to TCP packets.

From traceroute, since you will see the path of IP-enabled devices your packets take, you will also see where the packets stop and get dropped. Once you have that, you can further investigate why this packet loss is happening. Could it be a misconfiguration issue such as a misconfiguration of IP addresses or subnet mask? A misapplied access list?

Test Your Network with Synthetic Monitoring

Tool such as Kentik Synthetic Monitoring enable you to continuously test network performance (via ICMP, TCP, HTTP, and other tests) so you can uncover and solve network issues before they impact customer experience. Ping and traceroute tests performed continuously with public and/or private agents generate key metrics (latency, jitter, and loss) that are evaluated for network health and performance.

To get ahead of the game, Kentik also allows you to set up autonomous tests, so there’s already test history to your top services and destinations. You can also run these continuously (every second, like the ping command default) for high resolution.

Device Commands and Database Logs

Now that you’ve identified the network device or group of devices that could be the culprit, log into those devices and take a look. Run commands based on your device’s network operating system to see some of the configuration.

Take a look at the running configuration to see what interfaces are configured to get to the destination. You can take a look at system logs that the device has kept for any routing or forwarding errors. You can also look at antivirus logs on the destination systems that could be blocking access.

At this point, you may find yourself unable to get enough detail about the problem. Command line tools are telling you how things should work. What if everything’s working the way it should? What now? Or you might be getting overwhelmed by the amount of log data.

Device Configuration Changes

Many network outages relate to changes that humans made! Another key step on the troubleshooting path is to see if anything changed at about the same time as issues started.

This information can be found in logs of AAA (Authentication, Authorization, and Accounting) events from your devices. Ideally stored centrally, but often also visible by examining the on-device event log history.

Packets and Flows

The old saying about packet captures is that packets don’t lie! That’s also true for flow data, which summarizes packets.

Both packets and flows provide information about the source and destination IP addresses, ports, and protocols.

When getting flow data, you’re not as in the weeds as during a packet capture, but it’s good enough for most operational troubleshooting. Whether it’s with NetFlow, sFlow, or IPFIX , you’ll be able to see who’s talking to whom and how with flow data going to a flow collector for analysis.

Capturing packet data is truly getting into the weeds of troubleshooting your network. If it’s unclear from flow, and often if it’s a router or other system bug, you may need to go to the packets.

Unless you have expensive collection infrastructure, it’s also often more time consuming for you than any of the other tools above. Whether it’s tcpdump, Wireshark, or SPAN port, you’ll be able to get needle-in-the-haystack data with packet captures.

One great middle ground is augmented flow data, which captures many of the elements of packets. This can be great if you can get performance data, but not all network devices can watch performance and embed in flow — in fact, the higher speed the device, the less likely it is to support this kind of enhancement.

Collecting and analyzing packets and flows is where you start to venture into the next step. You’re using a mix of utility tools (tcpdump) and software (Wireshark, flow collector). If you’re expecting to keep a low MTTR, you need to move up the stack to software systems.

Up the Stack

If you can’t find issues using these tools and techniques at the network level, you may need to peek up the stack because it could be an application, compute, or storage issue. We’ll cover more on this cross-stack debugging in a future troubleshooting overview.

Kentik Network Observability

Of course, network performance monitoring (NPM) and network observability solutions such as Kentik can greatly help avoid network downtime, detect network performance issues before they critically impact end-users, and track down the root cause of network problems

In today’s complex and rapidly changing network environments, it’s essential to go beyond reactive troubleshooting and embrace a proactive approach to maintaining your network. Network monitoring and proactive troubleshooting can help identify potential issues early on and prevent them from escalating into more severe problems that impact end users or cause downtime.

Kentik’s Network Observability solutions, including the Network Explorer and Data Explorer, can be invaluable tools in implementing proactive troubleshooting strategies. By providing real-time and historical network telemetry data and easy-to-use visualization and analysis tools, Kentik enables you to stay ahead of potential network issues and maintain high-performing, reliable, and secure network infrastructure.

Network Explorer Solution

Kentik Network Explorer provides an overview of the network with organized, pre-built views of activity and utilization, a Network Map, and other ways to browse your network, including the devices, peers, and interesting patterns that Kentik finds in the traffic.

To make NetOps teams more efficient, Kentik provides troubleshooting and capacity management workflows. These are some of the most basic tasks required to operate today’s complex networks, which span data center, WAN, LAN, hybrid and multi-cloud infrastructures.

The Network Explorer combines flow, routing, performance, and device metrics to build the map and let you easily navigate. And everything is linked to Data Explorer if you need to really turn the query knobs to zoom way in.

Data Explorer Solution

If you can’t find the obvious issue with something unreachable or down, it’s key to look beyond the high level and into the details of your network.

Kentik Data Explorer provides a fast, network-centric, easy-to-use interface to query real-time and historic network telemetry data. Select from dozens of dimensions or metrics, 13 different visualizations and any data sources. Set time ranges and search 45 days or more of retained data. Query results within seconds for most searches.

This lets you see traffic, routing, performance, and device metrics in total, by device, region, customer, application, or any combination of dimensions and filters that you need to zoom in and find underlying issues.

Kentik’s Data Explorer provides graphs or table views of network telemetry useful for all types of troubleshooting tasks.

Software Tools Help Facilitate Network Troubleshooting

Marc Andreessen of Netscape fame once said that, “software is eating the world.” But software has made things a lot easier when it comes to network troubleshooting. It has taken over from the manual tools run from a terminal or network device.

There are software tools that ping not just to one device but multiple devices simultaneously for availability and path. Many are flow and packet data stores with software agents sending network data. All this is done and put on a nice dashboard for you. Network troubleshooting is still hard, but software makes it easier.

However, in this cloud-native and multi-cloud infrastructure era, some software makes it easier than others. For that, you need to move beyond traditional monitoring software because it’s not enough anymore. You need to move to observability software.

With software tools like products from Kentik, you can use the devices to send data to observe the state of your network instead of pulling it from the network.

Network Troubleshooting Best Practices

Whether you’re using network observability tools, or have a network small enough where the other tools are sufficient, here are some best practices you should consider.

Develop a Checklist

You should develop a checklist of steps like what I’ve outlined above when troubleshooting.

In his book The Checklist Manifesto , Dr. Atul Gawande discusses how checklists are used by surgeons, pilots, and other high-stress professionals to help them avoid mistakes. Having a checklist to ensure that you go through your troubleshooting steps promptly and correctly can save your users big headaches. And save you some aggravation.

Over time, this checklist will likely become second nature, and having and following it ensures you’re always on top of your game.

Ready Your Software Tools

You want to have already picked the network troubleshooting tools you need to troubleshoot a network problem before you get an emergency call. That isn’t the time to research the best software tool to use. By then, it’s too late.

If you run into a network troubleshooting problem that took longer than you hoped with one tool, research other tools for the next time. But do this before the next big problem comes along.

Get Documentation

It’s tough to jump on a network troubleshooting call and not know much about the network you’re going to, well, troubleshoot. IT organizations are notorious for not having enough documentation. At times, you know it’s because there aren’t enough of you to go around.

But you have to do what you can. Over time, you should compile what you learn about the network. Document it yourself if you have to, but have some information. Identify who owns what and what is where. Otherwise, you could spend lots of troubleshooting time asking basic questions.

Prepare Your Telemetry

In addition to having the software to move with speed, you’ll need to be already sending, saving, and ideally detecting anomalies over your network telemetry. For more details on network telemetry, see our blog posts “The Network Also Needs to be Observable” and “Part 2: Network Telemetry Sources” .

Follow the OSI

If you closely follow the toolset above, you may have noticed that I’m moving up the stack with each tool.

In some ways, I’m following the Open Systems Interconnection (OSI) stack. When troubleshooting, you want to start at the physical layer and work your way up. If you start by looking at the application, you’ll be masking potential physical connection problems such as interface errors or routing issues happening at layer 3. Or any forwarding problems at layer 2.

So follow the stack, and it won’t steer you wrong.

Preparedness and Network Troubleshooting

And there it is. When the network is down, troubleshooting can be a daunting task, especially in today’s hybrid infrastructure environments .

But if you follow the steps I’ve outlined, you can make things easier on yourself. Create your network troubleshooting checklist, decide on your toolset, and get ready. If it’s not down now, the network will likely be down later today.

Now that you know this about network troubleshooting, you’ll be ready when the network issues affect traffic in the middle of the night. You won’t like it; nobody likes those 1:00 A.M. calls. But you’ll be prepared.

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Network Troubleshooting Methodology and Techniques

Another critical skill that a Network Engineer has to have is network troubleshooting. Network issues often arise wherein we do not even have any idea of what caused it. Network problems are inevitable, and you should be equipped with various network troubleshooting tools and skills to be able to address these issues once they happen.

The Cisco Troubleshooting Methodology

Cisco has developed a troubleshooting model to effectively address network issues that will arise and equip you in handling such problems. An important part of troubleshooting is to know how to divide the tasks needed to resolve the issue in a systematic process of elimination. Cisco has broken down the process into eight methodical steps:

• Define the problem.
• Gather detailed information.
• Consider probable cause for the failure.
• Devise a plan to solve the problem.
• Implement the plan.
• Observe the results of the implementation.
• Repeat the process if the plan does not resolve the problem.
• Document the changes made to solve the problem.

OSI Model Approach

Another method that a network administrator uses when troubleshooting a network problem is by referring to the OSI Model. There are several ways to address a network issue using the OSI model, depending on the situation.

This technique is used by analyzing the problem starting from the top of the OSI model, which is the Application layer, and going down the stack. This kind of network troubleshooting technique usually is chosen when you have reason to believe that the issue is most likely on layer 7 based on your past experiences, new software installations, user interface revisions, or security updates.

This OSI approach starts the network issue analysis from the Physical layer, then work your way up to eliminate more potential causes of the issue that will help you isolate the most probable root cause of the problem. This is usually done when we are experiencing a network-wide issue that affects more users.

The bottom-up approach is very useful because the troubleshooting takes place immediately on the network, so access to clients, servers, or applications is not necessary until the later phase of the troubleshooting process. Most network issues arise because of hardware problems, such as legacy devices used within the network having less priority for support and maintenance. A disadvantage of this technique is that it can get time-consuming, especially on large networks with a lot of end-users.

Divide and Conquer

This approach gives a balance between the two techniques above. This is usually used when you do not have a clear idea of what may have caused the network outage. This is done by starting in the middle of the OSI stack, usually on the Transport layer, and perform ping and traceroute tests to isolate the issue. This method is considered a highly effective technique and arguably one of the most popular troubleshooting approaches used today because regardless of the outcome of the initial tests, this technique is more likely to point what or where the problem is by quickly eliminating the potential root cause.

Troubleshooting Methods

Here are some other troubleshooting methods that can be used to efficiently isolate the root cause of the network issue and immediately implement the best solution to it.

Compare Configurations

A lot of network performance issues are usually caused by human errors, and the initial way to troubleshoot problems is to check if there are configuration changes that have been made in the network. One way of knowing these changes is by implementing the AAA mechanism because such changes are being logged by an AAA server, or you can locally access the logs within the device.

Trace the Path

One of the most used troubleshooting tools is sending a ping to your destination device. There is another ICMP-based tool that shows you where the ICMP packet stopped in the network, and that is the traceroute . Having to know where your ping stops gives you an advantage in knowing where the issue is happening so you can easily isolate the problem and further analyze the best approach to rectifying the issue.

Swap-out Components

Usually, network outages are caused by hardware failures ranging from a simple ethernet cable wear and tear to full-on equipment failure. When this happens, we have no choice but to replace the defective hardware with a new one to keep the network up and running. This approach is also used to check if there is a specific device that causes the issue in the network and monitors what happens once the swap has been made.

Connectivity Troubleshooting Tools

There are various troubleshooting tools that are being used to analyze network connection outages or performance issues. Below are some of the most effective tools that we utilize in troubleshooting and can be helpful if we understand how they function.

arp — Address Resolution Protocol (ARP) is a protocol that connects an Internet Protocol (IP) address to a fixed physical machine address, also known as a media access control (MAC) address, in a local-area network (LAN).

ping – is a tool that is used to test the reachability of the destination host by sending an Internet Control Message Protocol (ICMP) packet towards the destination and providing the round-trip time of the packet, which shows how fast it traverses the network.

traceroute – is a diagnostic command that is used to identify where the ICMP packet stops if ever ping tool was not successful and did not reach the destination host. Traceroute shows where the packet travels, so it can easily help us identify where the problem lies.

route — this command enables manual updating of the routing table. The route command can be used to troubleshoot static routing problems in a network.

Telnet – is a protocol that provides a command-line interface for communication with a remote device or server, sometimes employed for remote management but also for initial device setup like network hardware.

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What is Network Troubleshooting? - The Ultimate Survival Guide

Table of contents.

Are you tired of feeling like a lost sailor on a stormy sea of computer problems? Well, fear not, dear reader, for we are about to embark on a journey to demystify the world of network troubleshooting! Intermittent network problems interrupt your flow of work, frustrate users, and can wreak havoc on your business. Troubleshooting network problems as fast as possible is the key to making sure that doesn’t happen.

In this article, we’re running you through what is network troubleshooting, how to troubleshoot network connectivity issues, and how to troubleshoot networks with Network Monitoring and Network Troubleshooting software. We'll equip you with the tools and knowledge you need to navigate the treacherous waters of network issues and emerge victorious. So grab your life jackets and let's set sail!"

What is Network Troubleshooting?

Network troubleshooting refers to the combined measures and processes used to identify, locate, and resolve network problems located anywhere along a network, from WAN to LAN .

It's a logical process that network engineers or IT professionals use to resolve network problems and improve network performance. Essentially, to fix, you need to troubleshoot them. When troubleshooting a network, many IT pros will use a network troubleshooting software or various network troubleshooting tools to help with the process.

Network troubleshooting involves a range of techniques and tools, such as network performance monitoring , network analyzers, ping and traceroute utilities, and network performance testing tools . Network administrators and technicians use these tools to identify and diagnose network problems , which may include slow network speeds, connectivity problems, security breaches, and other issues.

Some common steps involved in network troubleshooting include identifying the problem, testing the network, isolating the issue, analyzing network logs, and implementing a solution. This process may require collaboration among network administrators, IT support staff, and other stakeholders to identify and resolve the issue.

Effective network troubleshooting is critical for maintaining reliable network performance, minimizing downtime, and ensuring the security of network resources.

What is Network Troubleshooting Used For?

Network troubleshooting is used to identify and resolve issues that can occur in a computer network . Computer networks are complex systems that are made up of various components, such as routers, switches, servers, and cables, that work together to transmit data and enable communication between devices.

When problems occur in a network, they can manifest in many ways, such as slow connection speeds, dropped connections, or complete network outages. Network troubleshooting is used to pinpoint the root cause of these issues, so that they can be resolved quickly and efficiently.

Network troubleshooting involves a range of techniques, including analyzing network traffic, checking hardware and software configurations, and testing network connections. By using these techniques, network administrators can diagnose and resolve issues, ensuring that their networks run smoothly and efficiently.

In summary, network troubleshooting is used to :

• Troubleshoot network issues when a user complains of network or application slowdown or poor connectivity.
• Provides end-to-end visibility to pinpoint the source of a network problem.
• Offers in-depth data about the location, and cause of a problem to quickly provide solutions.

What is Network Performance Troubleshooting?

Now let's take it a bit further with the notion of Network Performance .

Network performance troubleshooting is the process of identifying and resolving issues that affect the speed, reliability, and overall performance of a computer network .

Networks can encompass a wide range of technologies, including local area networks (LANs), wide area networks (WANs), wireless networks, and the Internet. When network performance degrades or problems arise, it can lead to slow data transfer, dropped connections, application errors, and other operational disruptions. Troubleshooting network performance involves identifying the root causes of these issues and implementing solutions to address them.

Contrary to more general network troubleshooting, Network Performance Troubleshooting focuses on more specific network issues affecting network performance. We'll go over the differences in more detail later on in the article.

5 Common Network Troubleshooting Use Cases: What is Network Troubleshooting Used For

Network troubleshooting isn't just for fixing boring old technical glitches. It's also a superhero that saves the day in many different situations! From battling slow speeds to fighting off security breaches, network troubleshooting is the hero we need, but not always the one we deserve. So put on your cape, grab your utility belt, and let's dive into some exciting network troubleshooting use cases!

There are many different use cases for network troubleshooting. Here are a few examples:

• Slow network speeds : When users experience slow network speeds , network troubleshooting can be used to identify the cause of the problem. This could be due to a congested network, a faulty switch, or a misconfigured router.
• Dropped connections : When users experience dropped connections, network troubleshooting can help identify the source of the problem. This could be due to interference from other wireless devices, a faulty network card, or a weak signal.
• Network outages : When the network goes down, network troubleshooting can be used to quickly identify and resolve the issue. This could be due to a power outage, a failed piece of network hardware, or a configuration issue.
• Security breaches : Network troubleshooting can also be used to identify and address security breaches. For example, if a user's computer is infected with malware, network troubleshooting can be used to isolate the infected device and prevent the malware from spreading to other devices on the network.
• Software compatibility issues : When new software is installed on a network, compatibility issues can arise. Network troubleshooting can help identify and resolve these issues, ensuring that the new software works as intended and does not cause any network problems.

Experience the Power of Network Troubleshooting for IT Pros with Obkio!

Ready to troubleshoot your network like a pro? Say goodbye to the guessing game and hello to Obkio! With Obkio, you'll be able to easily identify and resolve network issues, without any hocus-pocus or magic spells. So, what are you waiting for?

Let's get your network back in tip-top shape and unleash your inner network wizard!

• 14-day free trial of all premium features
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• Monitor performance in all key network locations
• Measure real-time network metrics
• Identify and troubleshoot live network problems

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What is Proactive Network Troubleshooting?

Troubleshooting network problems so they stop affecting your users is important. But, what's even better is if you identify and troubleshoot network problems before they affect your end-users. This is what we call proactive network troubleshooting.

Proactive network troubleshooting involves anticipating and addressing potential network issues before they occur, rather than simply reacting to problems as they arise and is done through Continuous Network Monitoring. It typically involves using network monitoring tools to identify performance trends and potential issues, as well as regularly auditing network configurations and implementing best practices to prevent problems.

It is important because it gives you a real-time overview of your network at all times, so you can identify, locate, and solve issues before they start affecting end-users, therefore before you receive complaints, and (for Service Providers especially) before it hurts your reputation. By taking a proactive approach to network troubleshooting, organizations can reduce downtime, improve network performance , and enhance overall network security.

Why Network Troubleshooting?

With the increasing complexity of technology and network infrastructures, Network Monitoring has become an integral part of any business that needs to ensure the proper functioning of their network, devices, and applications.

Network Monitoring is generally used for three main purposes:

• Network Assessments
• Network Troubleshooting (like we talk about in this article)
• Continuous Network Monitoring .

The longer network problems exist in your network infrastructure, the more disruptions they cause. Which is why network troubleshooting is essential.

Because so many businesses depend on high-functioning networks that can span across several locations, poor network performance can impact a number of different factors like:

1.IT Services:

• Poor VoIP Quality causing choppy voice and video calls
• Slow Internet performance
• Slowdown of critical applications such as ERP (Netsuite, Microsoft Dynamics or SAP performance issues ), CRM (Microsoft Dynamics, Salesforce performance ), finance, and ecommerce systems.
• VPN connection problems
• Failing Citrix, RDP or Terminal Server sessions
• Low transfer rate

2. Business Affairs:

• Wasted time and productivity
• Overworked IT infrastructure
• Increased operating costs
• Damaged reputation
• Loss of income

3. Clients and Users:

• Lost productivity
• Frustration and disengagement
• Increased user complaints

Bad customer experience

Becuase of that, network troubleshooting is important for several reasons:

• Downtime Reduction : Network downtime can be costly for businesses, causing lost productivity, revenue, and customer dissatisfaction. By quickly identifying and resolving network issues, network troubleshooting can help minimize downtime and keep business operations running smoothly.
• Increased Network Performance : Network troubleshooting helps identify performance bottlenecks, configuration issues, and security vulnerabilities, which can all negatively impact network performance. By addressing these issues, network troubleshooting can help improve network performance and enhance the end-user experience.
• Cost Savings : Network troubleshooting can help businesses save money by preventing unnecessary hardware replacement, reducing the need for expensive IT support, and optimizing network resources. By identifying and resolving issues quickly, network troubleshooting can help minimize the costs associated with network downtime.
• Enhanced Security : Network troubleshooting can help identify security vulnerabilities, such as malware infections, unauthorized access, or weak passwords. By addressing these issues, network troubleshooting can help prevent security breaches and protect sensitive data from unauthorized access.
• Improved User Experience : Network troubleshooting can help ensure that end-users have a positive experience when using network resources. By optimizing network performance, resolving connectivity issues, and preventing downtime, network troubleshooting can help enhance the end-user experience and increase user satisfaction.

In summary, network troubleshooting is important for maintaining a reliable, secure, and high-performing network, which is critical for businesses of all sizes and industries.

Discover the superheroes of network monitoring tools in our comprehensive guide. Unveil the perfect type of network monitoring tool for your business.

Network Troubleshooting Steps: Steps to Troubleshoot a Network

Network troubleshooting is a vital process for maintaining optimal network performance, regardless of the type of network or the specific issues you may be encountering. Whether you're dealing with slow network speeds, intermittent connectivity, high latency, or other network-related problems, a systematic approach can help you identify and resolve these issues efficiently.

Step 1. Set Up End-to-End Network Monitoring

Obkio's network monitoring tool offers valuable insights into your network's performance, allowing you to diagnose problems and implement effective solutions. Below are general steps to guide you through the process of troubleshooting a network using Obkio's tool, adaptable to various network types and issues.

Make sure you have Obkio's network monitoring agents installed at key locations within your network. These agents will continuously exchange synthetic traffic to collect data and provide insights into your network's performance.

Step 2. Identify the Network Issue

Before diving into the intricacies of network troubleshooting, it's essential to establish a clear understanding of the problem you're trying to solve. Network issues can manifest in various ways, and each type of problem requires a unique approach to resolution. Here are some common network issues you might encounter:

• Slow Network Performance: Users are experiencing slow network performance including sluggish Internet speeds or delays when accessing resources. This could be caused by congestion, bandwidth limitations, or other factors.
• Intermittent Connectivity : Users are reporting sporadic disconnections from the network. Intermittent network connectivity could stem from issues with wireless connectivity, signal interference, or unstable network components.
• High Latency : Applications and services are responding slowly due to delays in data transmission. High latency can result from network congestion, long distances, or inefficient routing.
• Packet Loss : Data packets are being dropped, leading to retransmissions and degraded performance. Packet loss can be caused by network congestion, hardware faults, or poor quality connections.
• Jitter : Variability in latency, also called jitter , is causing inconsistent performance, particularly in real-time applications like VoIP or video conferencing.
• Network Outages : Network outages cause the entire network or specific segments to be inaccessible, causing a complete loss of connectivity. Less severe, but temporary loss of connectivity, like network brownouts or Internet brownouts , can also cause an impact.
• Security Breaches : Suspicious activity or unauthorized access is detected, indicating a potential security breach.

Taking the time to accurately define the problem you're facing is a foundational step in successful network troubleshooting. By clearly understanding the symptoms and challenges at hand, you'll set the stage for a more focused and effective investigation, ultimately leading to quicker resolution and improved network performance.

Are you a network admin or IT pro looking to identify and troubleshoot network performance issues in your business network, or a remote worker trying to solve network performance issues in your home network? Whether you need to troubleshoot large networks or single-user workstations, Obkio's Network Monitoring Tool has plans tailored for you. Find the right plan to help you detect and troubleshoot network issues with ease.

Step 3. Access the Network Performance Dashboard

After you've identified the specific issue you're facing and gathered relevant information, the next step is to log in to your Obkio account and access the dashboard. The dashboard serves as a centralized hub where you can monitor and analyze various metrics related to your network's performance.

Here's what you can expect to find on the dashboard:

• Real-Time Metrics : The dashboard typically displays real-time data, allowing you to observe the current state of your network. Network metrics such as latency, packet loss, throughput, and more are presented in a format that's easy to understand.
• Historical Data : In addition to real-time metrics, the dashboard often provides historical data. This historical perspective enables you to identify trends, patterns, and anomalies over time, helping you uncover recurring issues or gradual changes in network behavior.
• Visualizations : Graphs, charts, and visual representations of data make it easier to comprehend complex network information at a glance. Visualizations help you spot sudden spikes, drops, or irregularities in network metrics.
• Alarms and Alerts : The dashboard may include an alerting system that notifies you when predefined thresholds are exceeded. This allows you to respond promptly to abnormal network conditions and take action before issues escalate.
• Network Segments : If you have multiple network segments or locations equipped with Obkio agents, the dashboard might allow you to toggle between different segments for a comprehensive view of the entire network.

Using the Dashboard for Troubleshooting:

• Spotting Abnormalities : Examine the real-time metrics to identify any current anomalies. Sudden increases in latency, packet loss, or other metrics might correlate with reported issues.
• Comparing Historical Data : Look for patterns in historical data that coincide with the reported problems. This can help you understand whether the issues are intermittent or consistent and if they occur during specific times.
• Diagnosing Bottlenecks : Analyze throughput metrics to determine if network congestion is causing slowdowns. Identify which links or segments are experiencing high network utilization .
• Validating Changes : If you've implemented changes to address network issues, monitor the dashboard to ensure that those changes are having the desired effect on performance.
• Data-Driven Decision-Making : Base your troubleshooting decisions on concrete data from the dashboard. Avoid making assumptions and instead rely on the information presented.

Step 4. Monitor Key Network Metrics

Checking key metrics is a fundamental step in troubleshooting a network using Obkio's network monitoring tool. These metrics provide critical insights into various aspects of your network's performance, helping you pinpoint issues and identify areas that require attention.

Here are some of the key network metrics you should be looking at:

Latency : Latency refers to the time it takes for data to travel from the source to the destination. It directly impacts how quickly data packets reach their intended recipients. High latency can lead to delays in data transmission and affect the responsiveness of applications and services.

Packet Loss : Packet loss occurs when data packets do not reach their destination. This can result in data retransmissions, which slow down the network and degrade performance. Identifying and addressing packet loss is crucial for maintaining data integrity and efficient network communication.

Throughput : Throughput measures the amount of data that can be transmitted over the network in a given period. It reflects the network's capacity to handle data. Monitoring throughput helps you identify if the network is operating at its expected capacity. Low throughput could indicate congestion or other limitations.

Jitter : Jitter refers to the variability in the latency of data packets. Inconsistent latency can lead to disruptions in real-time applications. Monitoring jitter is especially important for applications that require consistent data delivery, such as voice and video conferencing.

Round-Trip Time (RTT) : RTT measures the time it takes for a data packet to travel from the source to the destination and back. It provides insights into the time taken for data to make a round trip. Elevated RTT values can indicate issues with network congestion, long distances, or inefficient routing.

Network Health Metrics: These metrics offer an overall assessment of the network's health and performance. They might include indicators such as uptime percentage and overall network response time . Network health metrics provide a high-level overview of how well the network is functioning and whether it meets performance expectations.

I. Interpreting Metrics for Troubleshooting:

• Baseline Comparison : Compare current metrics with historical baseline data. Deviations from the baseline can highlight abnormal behavior and indicate potential issues.
• Thresholds and Alarms : Obkio's monitoring tool might allow you to set thresholds for each metric. When a threshold is breached, the tool can trigger alarms or alerts, notifying you of issues in real time.
• Correlation : Look for correlations between different metrics. For example, high latency might coincide with high packet loss. Identifying these patterns can help you uncover underlying causes.
• Segment-Specific Analysis : If you're monitoring multiple network segments or locations, analyze metrics for each segment individually. This can help you identify whether issues are localized or widespread.
• Investigate Spikes : Sudden spikes or drops in metrics can indicate transient network issues. Investigate the timing and potential causes of these spikes to take appropriate action.

Checking key metrics through Obkio's network monitoring tool provides you with valuable insights into the performance of your network. By understanding the nuances of latency, packet loss, throughput, jitter, RTT , and other vital metrics, you can diagnose issues, make informed decisions, and implement targeted solutions to optimize your network's performance, reliability, and overall user experience.

Step 5. Identify Network Segments

In larger and more complex networks, it's common to have multiple segments, links, or locations interconnected to form a cohesive network infrastructure. When troubleshooting issues, it's important to identify which specific network segment is experiencing problems. This isolation process allows you to focus your efforts on the area where the issue originates and streamline your troubleshooting approach.

Steps to Identify and Isolate Network Segments :

• Network Topology Understanding : Gain a thorough understanding of your network's topology, including routers, switches, access points, and the connections between them. This understanding will help you visualize how data flows within your network.
• Review Monitoring Data : Use Obkio's network monitoring tool to review the metrics and data for each network segment. Identify any irregularities or performance issues that stand out.
• Compare Metrics : Compare the performance metrics of different network segments. Look for significant discrepancies in latency, packet loss, throughput, and other relevant metrics.
• Focus on Affected Users : If users in specific locations or segments are reporting issues, prioritize investigating those areas first. Their feedback can provide valuable insights into the scope of the problem.
• Test Individual Segments : Use Obkio's testing capabilities to run synthetic tests on individual segments. By simulating network traffic, you can pinpoint whether a specific segment is causing the issue.
• Network Flow Analysis : Analyze the flow of network traffic using passive monitoring tools. This can help you identify if a particular segment is receiving unusually high traffic or experiencing congestion.
• Traceroute and Path Analysis : Utilize traceroute tools to map the path that network packets take from source to destination. This can help you identify hops that might be causing delays or issues.
• Collaborate with Network Teams : If your network is managed by different teams or departments, collaborate with them to gain insights into the configuration and performance of specific segments.

Identifying network segments and isolating problematic areas is an essential step in troubleshooting network issues. By focusing your efforts on specific segments, you can streamline your investigation, diagnose issues more effectively, and implement targeted solutions to restore optimal network performance. Obkio's network monitoring tool can provide valuable data and insights to support your efforts in this process.

Step 6. Run Network Tests

Network testing using Obkio's network monitoring tool is a proactive approach to troubleshooting network issues. These tests allow you to simulate network activity and gather valuable data to identify bottlenecks, weaknesses, and areas requiring optimization.

Here's are some network tests to consider:

1. Active Network Monitoring Tests :

• Synthetic Traffic Generation : Active tests involve generating synthetic traffic on the network to measure its performance. Obkio's tool continuously generated synthetic UDP traffic through Monitoring Agents to simulate various types of network activities, such as data transfers, VoIP calls, or video streaming in different network locations.
• Test Goals : The purpose of active tests is to assess how well the network can handle different types of traffic. You can identify bandwidth limitations, latency issues, and performance degradation under varying conditions.

2. Passive Network Monitoring Tests :

• Analyzing Traffic Flows : Passive tests involve analyzing the actual network traffic without injecting synthetic traffic. This approach provides insights into how real-world applications and users are utilizing the network.
• Test Goals : Passive tests help you understand traffic patterns, identify unexpected sources of congestion, and detect potential security or bandwidth misuse issues.

Running tests using Obkio's network monitoring tool is an active and valuable method of troubleshooting network issues. Whether you're generating synthetic traffic or analyzing real traffic flows, these tests help you identify bottlenecks, diagnose performance problems, and make informed decisions to optimize your network's performance, responsiveness, and reliability.

Discover the differences, benefits, and implementation strategies of active network monitoring vs passive network monitoring.

Step 7. Review Network Performance Notifications and Alerts

Reviewing notifications and alerts generated by Obkio's network monitoring tool is crucial for timely response to abnormal network conditions. These alerts serve as early warnings for potential issues, allowing you to take proactive measures to address them.

• Setting Up Alerts : Configure network monitoring alerts within Obkio's tool based on predefined thresholds . These thresholds are values that, when exceeded, trigger an alert. Common metrics for which alerts can be set include latency, packet loss, throughput, and jitter.
• Understand Alert Context : Each alert will provide information about the metric that triggered it, the threshold that was breached, and the specific time the breach occurred. This information helps you understand the severity and nature of the issue.
• Response Time : Quickly respond to alerts to prevent issues from escalating. Some network problems, if left unattended, can worsen and impact user experience or even lead to downtime.
• Correlation with Other Data : Correlate alert notifications with other data available on the dashboard. For example, if you receive an alert about high latency, cross-reference it with throughput and packet loss metrics to gain a fuller picture of the issue.
• Escalation Process : Have a clear process in place for escalating alerts to the appropriate individuals or teams. Ensure that the responsible parties are aware of the alerts and know how to respond.

Reviewing notifications and alerts generated by Obkio's network monitoring tool is an essential step in network troubleshooting. By promptly responding to alerts, you can take proactive measures to prevent disruptions or network disconnections , ensure optimal network performance, and provide a better user experience for individuals relying on your network services.

Step 8. Compare with Baseline Network Performance

Comparing current performance metrics with a baseline of normal network behavior is a valuable technique for identifying anomalies and deviations that could indicate network issues. Baseline comparisons provide context for understanding whether the observed metrics are within expected ranges or if they signify potential problems.

What is a Baseline?

A baseline is a set of historical data that represents the expected or typical performance of your network under normal conditions. It's essentially a reference point that helps you distinguish between regular fluctuations and abnormal behavior.

• Contextual Analysis : A baseline offers context for understanding whether current metrics are typical or unusual. Without a baseline, it's challenging to determine if the observed values are problematic.
• Anomaly Detection : Deviations from the baseline can indicate issues that need attention. When metrics consistently fall outside the baseline range, it's a strong indication that something is amiss.
• Data-Driven Troubleshooting : Baseline comparisons provide an objective basis for making decisions and taking action. They reduce guesswork and help you focus on actual anomalies.

Steps to Compare with Baseline :

• Create a Baseline : Start by establishing a baseline of typical network performance during periods of stability. Collect historical data across key metrics like latency, packet loss, throughput, and more. Obkio's Network Monitoring tool will automatically do this for you!
• Set Thresholds : Define acceptable ranges or thresholds for each metric based on the baseline. These thresholds represent the upper and lower limits of normal behavior.
• Regular Monitoring : Continuously monitor your network's performance using Obkio's tool. Regularly compare current metrics against the baseline thresholds.
• Identify Deviations : If the current metrics consistently deviate from the established baseline, investigate further to understand the cause of the deviation.
• Analyze Patterns : Look for patterns in the deviations. Are there specific times of day, days of the week, or usage scenarios when deviations are more pronounced?
• Cross-Reference Metrics : Cross-reference deviations in one metric with other related metrics. For example, if latency increases, check if packet loss also increases during the same periods.
• Trigger Alerts : Configure alerts in Obkio's tool to notify you when metrics breach baseline thresholds. Alerts prompt quick action when anomalies occur.

Step 9. Check External Factors

Checking external factors is a critical step in troubleshooting network issues. Many network problems can originate outside of your control, such as issues with your Internet Service Provider (ISP) or external attacks like Distributed Denial of Service (DDoS).

It's important to rule out these possibilities before dedicating resources solely to internal network configurations. Here's an expanded explanation of this step:

• ISP Communication : Contact your ISP to inquire about any ongoing maintenance, outages, or known issues. They can provide valuable information about the status of their network.
• Route Analysis : Use tools to analyze network routes and trace paths that data takes from source to destination. Identify if there are any unexpected routing changes or bottlenecks.
• Ping Tests : Conduct ping tests to external servers or websites. Consistently high latency or packet loss in these tests might indicate broader connectivity issues.
• Geographical Outages : Use online services that track global network outages to see if your area or your ISP's region is experiencing connectivity problems.
• DDoS Detection : Monitor network traffic patterns for signs of a DDoS attack. Sudden spikes in traffic or unusual behavior might indicate malicious activity.
• Collaboration with ISP : Work with your ISP to identify the source of any issues affecting your connection. They can provide assistance in resolving connectivity problems.

Checking external factors is a critical step in troubleshooting network issues. By ruling out ISP problems, route anomalies, DDoS attacks, and other external factors, you can confidently focus on optimizing your internal network configurations and addressing issues within your control. This approach leads to more efficient troubleshooting, reduced downtime, and a better overall user experience.

Step 10. Implement Network Optimizations

This step involves making adjustments to your network configuration to optimize network performance and address the identified problems and improve overall performance. Obkio's network monitoring tool can provide valuable insights and recommendations to guide your changes.

Steps to Implement Changes :

• Root Cause Identification : Based on your analysis of metrics, alerts, and tests, pinpoint the specific areas or components causing network issues.
• Network Configuration Changes : Adjust network configurations, such as router settings, firewall rules, or Quality of Service (QoS) policies, to address identified problems.
• Network Optimization Strategies : Depending on the issues, apply optimization techniques such as load balancing , traffic shaping, or upgrading hardware components.
• Documentation : Keep detailed records of the changes you implement, the reasoning behind them, and the expected outcomes. Documentation helps in future troubleshooting and knowledge sharing.
• Testing After Changes : After implementing changes, run tests and monitor metrics to verify if the changes have had the desired effect on network performance.

Utilizing Obkio's Recommendations :

• Data-Driven Insights : Leverage recommendations provided by Obkio's tool to make informed decisions. These recommendations are often based on patterns in collected data.
• Validation : If the tool suggests specific adjustments or configurations, validate these recommendations against your analysis and network requirements.
• Prioritization : If the tool highlights multiple areas for improvement, prioritize changes based on the severity of the issues and potential impact on network performance.

Implementing optimizations based on analysis is a critical step in troubleshooting network issues. Whether addressing configurations, optimizing components, or following tool recommendations, the goal is to resolve problems, optimize performance, and create a more reliable network environment. The combination of analytical insights and recommendations from tools like Obkio enables you to make informed and impactful changes that enhance your network's overall functionality.

Learn to use network optimization and monitoring to optimize network performance, improve your end-user experience, and compare performance from the past.

Step 11. Monitor Network Performance After Changes

After implementing changes, continue to monitor the network using Obkio to ensure that the issues have been resolved and that the performance has improved. Monitoring the network after implementing changes is a crucial step to ensure the effectiveness of your troubleshooting efforts and to validate that the changes have indeed resolved the identified issues. Continuous monitoring helps you maintain a stable and high-performing network environment.

Importance of Post-Change Monitoring :

• Validation : Post-change monitoring confirms whether the implemented changes have had the desired impact on network performance and have resolved the issues.
• Adaptation : Sometimes, changes might not produce immediate results or could inadvertently introduce new issues. Monitoring allows you to identify such scenarios and make necessary adjustments.
• Continuous Optimization : Monitoring after changes is a part of the iterative optimization process. It helps you fine-tune configurations and ensure sustained network efficiency.

Steps to Monitor After Changes :

• Baseline Comparison : Compare post-change metrics to the baseline data collected before implementing the changes. This comparison helps you understand the magnitude of improvement.
• Stability and Consistency : Monitor for stability and consistency in network performance with network stability testing . Changes should result in reduced latency, improved throughput, and fewer instances of packet loss.
• Alerts and Notifications : Configure alerts and notifications in Obkio's tool to be informed of any unusual behavior or deviations from the expected post-change performance.
• Regular Analysis : Regularly review the metrics and data on the dashboard to identify any anomalies or trends that might indicate ongoing or new issues.
• User Feedback : Gather feedback from users to understand their experience after the changes. Their observations can provide valuable insights into real-world improvements.
• Iterative Approach : If the network's performance isn't meeting expectations post-change, consider an iterative approach. Adjust configurations based on new insights and retest.

Monitoring the network after implementing changes is a vital step in the troubleshooting process. By comparing post-change metrics to baseline data, analyzing performance, and staying vigilant for anomalies, you can ensure that your network remains stable, performs optimally, and delivers a consistent and satisfactory experience for users. Obkio's network monitoring tool continues to be a valuable resource in this phase by providing real-time and historical data for ongoing assessment.

7 Network Troubleshooting Techniques to Take Control Of Your Network!

Ready to add some new tricks to your network troubleshooting toolbox? Get ready to tap into your inner network ninja with these network troubleshooting techniques! From ping and traceroute to port scanning and packet analysis, these techniques will help you become a master of network problem-solving. So sharpen your sword, don your ninja outfit, and let's dive into the exciting world of network troubleshooting techniques!

There are many different network troubleshooting techniques that can be used to identify and resolve network issues. Here are a few examples:

Network Troubleshooting Technique #1: Network Monitoring

This complete, end-to-end network troubleshooting technique involves the use of network monitoring software, like Obkio to identify issues and monitor network performance in real-time. This technique is particularly useful for identifying issues such as congestion, bandwidth issues, and security threats, and is a valuable network troubleshooting technique that involves the continuous monitoring of network performance and activity to identify and resolve issues.

Network monitoring allows network administrators to:

• Detect issues early : Network monitoring helps detect issues as soon as they occur, allowing administrators to quickly address them before they escalate into bigger problems.
• Identify performance issues : Network monitoring can help identify performance issues such as slow network speeds , packet loss, and high latency.
• Track network activity : Network monitoring can help track network activity, including which devices are connected to the network, what applications are being used, and how much bandwidth is being consumed.
• Alert administrators : Network monitoring tools can alert administrators of issues through notifications, emails, or text messages, allowing for quick resolution.
• Analyze historical data : Network monitoring software can store and analyze historical data, allowing administrators to identify long-term trends and patterns and plan for future network upgrades and changes.

Network monitoring is especially useful for troubleshooting issues related to network congestion, bandwidth usage, and security threats. By monitoring network traffic, administrators can identify abnormal activity and quickly address any security threats or breaches.

In summary, network monitoring is a powerful network troubleshooting technique that allows administrators to detect and resolve issues in real-time, analyze historical data, and improve overall network performance and security.

Network Troubleshooting Technique #2: Ping

Ping is a basic network troubleshooting technique that sends a small packet of data to a device on the network to verify if it's reachable. The ping tool measures the round-trip time for the data packet to be sent from the source device to the destination device and back. If the destination device responds to the ping request, it indicates that the device is reachable and there is no issue with network connectivity.

Ping is a useful troubleshooting tool because it can help identify several network issues, such as:

• Network connectivity issues : Ping can help identify whether a device is reachable on the network, which can be useful in troubleshooting network connectivity issues .
• [DNS issues](/blog/how-to-identify-dns-issues/ : If the ping fails to resolve a domain name into an IP address, it can indicate a problem with the DNS configuration.
• Firewall issues : Ping can help identify firewall issues by determining whether the firewall is blocking incoming or outgoing traffic to a specific device.
• Network latency : The round-trip time reported by ping can help identify network latency issues, which can impact network performance.

Ping is a quick and easy network troubleshooting tool, but it does have limitations. For example, if a device is configured to block incoming ping requests, the tool may report that the device is not reachable even though it is functioning normally. Additionally, the tool does not provide detailed information about the nature of network issues.

In summary, while ping is a simple and useful network troubleshooting tool, it should be used in conjunction with other techniques for a more comprehensive analysis of network issues.

Network Troubleshooting Technique #3: Traceroute

Traceroute is a network troubleshooting technique that helps identify the path that network packets take from the source device to the destination device. It works by sending a series of packets to the destination device, with each packet having a different time-to-live (TTL) value. Each router along the path to the destination device decrements the TTL value, and if it reaches zero, it discards the packet and sends an ICMP "Time Exceeded" message back to the source device.

Traceroute uses the ICMP protocol to identify the routers along the path to the destination device, and it reports the IP address, hostname, and response time of each router. This information helps network administrators identify the location of network issues and diagnose latency or connectivity problems.

Some of the uses of traceroute as a network troubleshooting technique include:

• Identifying network routing issues : Traceroute helps identify routing issues by reporting the IP address and hostname of each router along the path to the destination device.
• Identifying network latency issues : The response time reported by traceroute helps identify latency issues and can help identify where delays are occurring along the path to the destination device.
• Diagnosing connectivity issues : Traceroute can help diagnose connectivity issues by identifying where packets are dropping or being lost along the path to the destination device.

Traceroute is a valuable network troubleshooting technique that can help administrators identify and resolve network issues. However, it does have limitations. For example, some routers are configured to block ICMP packets, which can result in incomplete traceroute reports. Additionally, traceroute only reports the path taken by network packets and does not provide detailed information about the nature of network issues.

In summary, traceroute is a powerful network troubleshooting technique that helps identify network routing and latency issues, as well as diagnose connectivity issues. It should be used in conjunction with other network troubleshooting tools for a comprehensive analysis of network issues.

Network Troubleshooting Technique #4: Port Scanning

While port scanning is often used as a reconnaissance tool by hackers, it can also be used as a network troubleshooting technique by network administrators. A port scanner is a software tool that scans a range of network ports on a device to determine which ports are open and accepting incoming connections. This information is useful for network administrators who need to verify that their devices are properly configured and secure.

Here are some ways that port scanning can be used as a network troubleshooting technique:

• Identifying open ports : Port scanning can be used to identify which ports are open on a device, which is useful for verifying that services are running and accessible.
• Verifying firewall rules : Port scanning can be used to verify that firewall rules are configured correctly and that the necessary ports are open to allow traffic to flow.
• Checking for rogue devices : Port scanning can be used to identify any unauthorized devices on the network that may be accepting incoming connections on unsecured ports.
• Checking for vulnerabilities : Port scanning can be used to identify any vulnerabilities in the network by identifying open ports that are commonly exploited by attackers.

It's important to note that port scanning can also be used by attackers to identify potential vulnerabilities on a network, so it should be used carefully and with appropriate security precautions in place.

In summary, port scanning can be a useful network troubleshooting technique for network administrators to identify open ports, verify firewall rules, check for rogue devices, and identify potential vulnerabilities. However, it should be used with caution and appropriate security measures in place to avoid unintended consequences.

Network Troubleshooting Technique #5: Configuration Auditing

Configuration auditing is a network troubleshooting technique that involves reviewing and verifying the configuration settings of network devices to ensure that they are properly configured and compliant with organizational policies and industry best practices. It is an important technique for ensuring the security, reliability, and performance of network devices .

Here are some ways that configuration auditing can be used as a network troubleshooting technique:

• Identifying configuration errors : Configuration auditing can be used to identify configuration errors that may be causing network issues or security vulnerabilities. For example, misconfigured network settings can cause devices to not function properly, resulting in connectivity issues.
• Verifying compliance : Configuration auditing can be used to verify that network devices are configured in compliance with organizational policies and industry best practices. For example, it can ensure that devices have been configured with appropriate security settings and that they are using the latest software updates and patches.
• Improving performance : Configuration auditing can be used to optimize network device configurations to improve network performance. For example, it can identify unused or unnecessary services that can be disabled to improve device performance.
• Enhancing security : Configuration auditing can be used to identify security vulnerabilities in network devices, such as weak passwords or open ports that can be exploited by attackers. It can also identify configuration settings that may increase the risk of security breaches, such as unnecessary services running on devices.

Configuration auditing can be performed manually or using automated tools that can scan and analyze device configurations. Automated tools are often preferred because they can perform configuration audits more quickly and thoroughly than manual methods.

In summary, configuration auditing is a valuable network troubleshooting technique that can help identify configuration errors, verify compliance with organizational policies and industry best practices, improve network performance, and enhance security. By using configuration auditing, network administrators can ensure that their devices are properly configured and functioning optimally.

Network Troubleshooting Technique #6: Packet Analysis

Packet analysis is a network troubleshooting technique that involves capturing and analyzing network traffic to identify issues with the network. It is a powerful tool for diagnosing and resolving network issues because it provides detailed information about how data is flowing through the network.

Here are some ways that packet analysis can be used as a network troubleshooting technique:

• Identifying network bottlenecks : Packet analysis can be used to identify where network traffic is being slowed down or congested, which can help network administrators pinpoint where network bottlenecks are occurring.
• Diagnosing application issues : Packet analysis can help diagnose application issues by providing detailed information about how data is flowing between applications and network devices. For example, it can identify issues with application protocols or data formats that may be causing problems.
• Analyzing security incidents : Packet analysis can be used to analyze security incidents, such as malware infections or network intrusions. By examining network traffic, network administrators can identify the source of the incident and determine how it spread throughout the network.
• Verifying network configurations : Packet analysis can be used to verify that network devices are configured correctly and that traffic is flowing as expected. For example, it can confirm that network policies are being enforced and that network devices are properly configured to handle different types of traffic.

Packet analysis requires specialized tools that can capture and analyze network traffic. These tools can provide detailed information about packet headers, payload data, and protocol information. They can also generate graphs and charts that help visualize network traffic and identify patterns.

In summary, packet analysis is a powerful network troubleshooting technique that can help identify network bottlenecks, diagnose application issues, analyze security incidents, and verify network configurations. By using packet analysis, network administrators can ensure that their networks are functioning optimally and securely.

Network Troubleshooting Technique #7: Firmware Updates

Firmware updates are a network troubleshooting technique that involves updating the software that controls the hardware components of network devices. Firmware updates can be used to fix bugs, address security vulnerabilities, and improve device performance.

Here are some ways that firmware updates can be used as a network troubleshooting technique:

• Addressing software bugs : Firmware updates can be used to address software bugs that may be causing network issues. For example, a firmware update can fix a bug that causes a network device to crash or behave unpredictably.
• Patching security vulnerabilities : Firmware updates can be used to patch security vulnerabilities that may be present in network devices. For example, a firmware update can address a vulnerability that allows attackers to gain unauthorized access to a network device.
• Improving device performance : Firmware updates can be used to improve device performance by adding new features or improving existing ones. For example, a firmware update can add support for new networking protocols or improve the speed of data transfer.
• Enhancing compatibility : Firmware updates can be used to enhance compatibility with other network devices or software. For example, a firmware update can add support for a new type of network card or improve interoperability with a specific software application.

Firmware updates can be performed manually or using automated tools that can scan and analyze network devices to identify outdated firmware versions. Automated tools are often preferred because they can perform firmware updates more quickly and thoroughly than manual methods.

In summary, firmware updates are an important network troubleshooting technique that can help address software bugs, patch security vulnerabilities, improve device performance, and enhance compatibility. By keeping their network devices up-to-date with the latest firmware versions, network administrators can ensure that their networks are functioning optimally and securely.

How to Troubleshoot Networks with Network Monitoring

Even the best designed networks are not immune to problems. With the growing complexity of network infrastructures, problems are bound to happen, but just harder to pinpoint. All IT managers generally agree on one thing: it’s not about whether there will be network problems, but rather when they will occur and how to solve them as soon as possible.

Are you tired of constantly putting out fires on your network? Want to take a proactive approach to network troubleshooting? Look no further than network monitoring!

In order to troubleshoot a network as efficiently and painlessly as possible, it’s important to have some best practices or steps in mind that you can follow every time. For this tutorial, we're going to show you how to perform network troubleshooting using the Network Monitoring Technique!

Not only does it provide a real-time view of network activity, but it also enables you to detect and resolve issues quickly, allocate resources more effectively, and enhance network security. Say goodbye to network headaches and hello to smooth sailing with network monitoring!

Network Troubleshooting Step 1. Deploy a Network Troubleshooting Tool

Most businesses don’t have time to manually assess every part of their network to find the cause of a problem. When you have a flood of user complaints and the executive team breathing down your, it can be overwhelming to try to find the problem, let alone fix it.

Luckily, there are several network troubleshooting tools available in the vault of a network administrator or IT specialist - the most important being Network Monitoring. A great network monitoring software, like Obkio Network Performance Monitoring software will provide continuous end-to-end monitoring of your network performance, to identify problems and collect the information you need to troubleshoot, all with one tool!

Obkio continuously monitors end-to-end network performance with synthetic traffic using Network Monitoring Agents . The Agents exchange synthetic traffic to measure network metrics, like packet loss, between each other, identify network issues, and collect the information to help you troubleshoot.

Network Troubleshooting Step 2. Collect Network Performance Metrics

Issues can arise at numerous points along the network. To start troubleshooting a network, you want to have a clear understanding of what the problem is, how it happened, who it’s affecting, when it occurred, and how long it’s been going on.

Once you’ve deployed Obkio Monitoring Agents in your key network locations, they will start measuring key network metrics like jitter, packet loss, and latency and displaying them on Obkio’s Network Response Time Graph .

By gathering the right information and clarifying the problem, you’ll have a much better chance of resolving the issue quickly, without wasting time trying unnecessary fixes. Network troubleshooting helps you get all the information you need about:

• What network problems are affecting your network or application performance.
• Where the network issues are located anywhere along your network.
• Who the owner of the problem is (user, application, network, or ISP), and who is responsible for fixing it.
• How to solve problems for a quick and smooth fix.

Network Troubleshooting Step 3. Isolate the Network Problem

To begin the network troubleshooting process, you've got to catch and isolate the network problem.

To do this, compare the monitoring sessions you created from deploying Obkio's NPM tool.

A. If’s Not a Network Issue

As a reference, below is an example of a Network Session with no network problems.

If you're not experiencing a network problem, it might be a user issue. In this case, you can troubleshoot by installing a Monitoring Agent directly on a user’s workstation (the user who is experiencing the performance problems) to see the issue from their point-of-view.

If you still don’t find that it’s a network problem at this point, it may just be a problem that IT specialists can troubleshoot and resolve directly on the user's workstation or on the remote destination. The problem could be several other hardware-intensive videoconferencing systems, which use up a lot of resources (CPU, RAM).

Obkio monitors these other resource metrics as well.

B. Check for A Network Problem On 2 Network Sessions

In the screenshot below is an example of a network problem on both network sessions.

In this case, the network problem is on a network segment that is common to both network sessions. This means that the problem is:

• Broader and not exclusive to a single network path or destination.
• Affects all services and applications dependent on the network.
• Could be happening in LAN , the firewall or the local loop Internet connection.

C. Check for A Network Problem On 1 Session

In the screenshot below is an example of a network problem on only one network session.

This means that the network problem is happening specifically towards that specific location on the Internet and that the problem is further away.

Network Troubleshooting Step 4. Compare with Network Device Monitoring

If the network problem is on both network sessions, compare that data using Obkio’s Device Monitoring feature to further understand if the network issue is happening on your end, or over the Internet, in your Service Provider’s network.

A. Check your Network Hardware

Believe it or not, many network problems may be caused by faulty hardware, bad physical connections, or incorrect configurations. When you begin the troubleshooting process, check all your hardware to make sure it’s correctly connected, turned on, and working.

If a cord has come loose or has broken, or somebody has switched off an important router, this could be the problem behind your network issues. There’s no point in going through the process of troubleshooting network issues if all you need to do is replace a cord, so make sure all switches are in the correct positions and haven’t been bumped accidentally.

Here are some general network troubleshooting steps for network hardware that can help you identify and resolve network issues :

• Check physical connections : Ensure that all physical connections are secure and correctly plugged in. Loose or damaged cables can cause network connectivity issues.
• Restart devices : Power cycle the affected devices, including the router, switch, and modem. Sometimes, this can resolve the issue by resetting the devices and clearing out any temporary network configurations.
• Check network settings : Verify that the network settings, including IP addresses, subnet masks, and default gateways, are correctly configured. Misconfigured network settings can cause connectivity issues.
• Update firmware and software : Ensure that the devices and software used in the network are updated to the latest versions. Newer versions can contain bug fixes and performance improvements that can resolve network issues.

Going through to check every cord one-by-one can be tiresome and a gigantic loss of time. Thankfully, a network performance monitoring software like Obkio monitors problems within your network interface that are commonly caused by hardware!

B. Check for CPU or Bandwidth Issues

When you compare your previous data with Device Monitoring metrics, you may find CPU or Bandwidth issues. These resource issues likely means that the network issue is on your end and you need to troubleshoot internally.

Here are a few network troubleshooting suggestions got CPU or bandwidth issues:

Traffic Analysis : Examine your firewall logs to determine if the traffic passing through your network is legitimate. This will help identify potential security breaches such as data exfiltration or improper data backup during business hours.

Firewall Management : Prioritize important traffic in order to reduce congestion during periods of high traffic. This ensures that traffic to and from critical applications is given priority and is less likely to cause network congestion.

Bandwidth Upgrade : Contact your Internet Service Provider (ISP) to upgrade your bandwidth if you are experiencing bandwidth constraints.

Resource Investigation : Investigate the reason for missing resources and high CPU usage on your device. This may be due to a software issue, firmware update requirement, buggy software update, or simply inadequate resources, which can be resolved by upgrading to a more powerful device.

C. Check for Internet Problems on Your ISP’s End

If you don’t see any resource issues from your devices, this is a sign that the network problem is actually on your Service Provider’s end.

If you suspect that the issue is with your ISP, you should open a service ticket and provide as much information as possible to support your claim. This will help to quickly escalate the issue past the first level of support. Additionally, Obkio's app can serve as a valuable tool to aid in this process.

The data you can provide is that from your dashboard in the previous steps, as well as your Traceroutes in the next step.

Network Troubleshooting Step 5. Troubleshoot using Traceroutes

The next step in the network troubleshooting process is to collect the last bit of data to help you pinpoint exactly where the network problem is located so you can share that information with your Service Provider.

To do this, we’ll be using Obkio Vision , Obkio’s free Visual Traceroute tool that runs continuously to interpret Traceroute results to identify network problems in your WAN and over the Internet.

Note : If the network problem happening only on your end, you don’t need to do this step. It’ll just give you the same results.

Use Traceroutes, the Network Map, and the Quality Matrix to identify if:

A. The network issue is happening specifically towards a specific location over the Internet. So only one specific site is being affected.

B. The network issue is on your ISP’s side. At this point, open a service ticket with as much information as you can collect.

Network Troubleshooting Step 6. Contact Your Service Provider

If you encounter an issue, it is recommended to contact your Service Provider (MSP or ISP) for assistance with troubleshooting. However, this time, you won't have to deal with first-level support simply instructing you to "reboot your modem." Armed with the data collected using Obkio, you can hold your Service Provider accountable and provide them with all the necessary information to effectively troubleshoot the issue.

• Contact your ISP to get technical support using the screenshots of Monitoring Sessions, Dashboards or Traceroutes in Vision.
• Share results of Live Traceroutes with your ISP using a public link.
• If your ISP wants to analyze your data further, you can create a temporary Read-Only User in your Obkio account for them.

By sharing traceroute results, ISP network engineers can see the problem, change the traceroute options and validate that their changes are fixing the issue without having to get back to you.

Your ISP will then be able to confirm if your analysis is good or not, and if they can fix the issue at hand. If you have the chance to have a good ISP, they will also explain why your analysis is wrong if this is the case.

Network Troubleshooting Step 7. Perform a DNS Check

At this point, if you're still ensure of the cause of the issue, one last thing you can do it perform a DNS check.

DNS, which stands for Domain Name System , is a directory for the Internet (and every internet-connected device) that matches domain names with IP addresses. Every single website has its own IP address on the web, and computers can connect to other computers via the Internet and look up websites using their IP address.

Use the “nslookup” command to determine whether there’s a problem with the server you’re trying to connect to. If you perform a DNS check on, for example, google.com and receive results such as “Timed Out,” “Server Failure,” “Refused,” “No Response from Server,” or “Network Is Unreachable,” it may indicate the problem originates in the DNS server for your destination. (You can also use nslookup to check your own DNS server.)

With Obkio’s Application Performance Monitoring (APM) for HTTP URLs feature , users can now monitor DNS performance! DNS is key to URL monitoring, and is one of the five steps to download the content of a single URL.

Network Troubleshooting Step 8. Continue to Monitor Network Performance

Continuing to monitor network performance is a crucial step in network troubleshooting. After implementing a fix, it's essential to ensure that the network is operating optimally and that the issue is resolved.

Here's why continuing to monitor network performance is important:

• Verify that the issue is resolved : Continuing to monitor the network performance can help you ensure that the issue is resolved. If the issue persists, you may need to investigate further and implement additional fixes.
• Identify new issues : Even if the original issue is resolved, new issues may arise. Continuously monitoring the network performance can help you identify any new issues and address them proactively.
• Optimize network performance : Monitoring the network performance can help you identify areas of the network that can be optimized for better performance. For example, you may find that some devices or applications are using an excessive amount of bandwidth, causing performance issues for other devices on the network.
• Ensure network security : Monitoring the network performance can help you identify potential security threats and breaches. You can set up alerts to notify you of any suspicious network activity and take action to prevent security breaches.

In summary, continuing to monitor network performance after troubleshooting helps you ensure that the network is operating optimally and proactively address any new issues that may arise.

A Network Troubleshooting Use Case

We’re running you through an example of when and how network troubleshooting can help you resolve networks problems!

A. The Problem

Let’s say that users in your company start reporting intermittent network performance and slowness issues, like choppy VoIP Quality and lagginess which makes voice calls incomprehensible.

VoIP Quality is highly reliant on network performance, which means that many network problems like packet loss , latency , and jitter can cause high levels of VoIP degradation.

If you’re a member of the IT team, you’re definitely the first person that users come to with their complaints. Which means that you now need to solve the problems fast because employees are wasting time and the executive team is breathing down your neck.

B. The Solution

When you're looking into how to troubleshoot network connectivity problems, deploy a network monitoring and network troublshooting tool that measures end-to-end network performance to pinpoint network issues located within your business’ LAN, Firewalls, or internet infrastructure.

Get a 360-degree view of network and application performance to help you identify network performance issues you never would have had visibility of before.

C. The Gain

Monitoring network performance using a network performance monitoring software continuously measures the most critical network performance metrics to find issues, even before your users experience them.

That means that you can stay on top of problems by proactively identifying if problems are related to the network, where they are located and when they occurred, even if they happened in the past.

With information about what, where, how, and when network problems occurred, you can drastically improve the time it takes you to troubleshoot and solve problems!

Network Troubleshooting vs. Network Performance Troubleshooting

Network Troubleshooting and Network Performance Troubleshooting are related but distinct aspects of managing and maintaining computer networks. Let's break down the differences between the two:

I. Network Troubleshooting:

Network troubleshooting involves identifying and resolving issues related to network connectivity, functionality, and communication problems. This can encompass a wide range of problems, including devices not being able to connect to the network, intermittent connectivity issues, slow response times, and more. The primary focus of network troubleshooting is to ensure that devices can communicate effectively within the network and with other networks. It's about making sure the network is operational and that devices can connect and communicate as intended.

Common network troubleshooting tasks include :

• Diagnosing and fixing physical connectivity issues like faulty cables or connectors.
• Identifying and resolving IP address conflicts.
• Troubleshooting DNS (Domain Name System) resolution problems.
• Resolving issues with DHCP (Dynamic Host Configuration Protocol) configuration.
• Investigating and addressing firewall or security rule conflicts.

II. Network Performance Troubleshooting:

Network performance troubleshooting, on the other hand, is specifically concerned with addressing problems related to the speed, efficiency, and overall performance of the network. The focus here is not just on whether devices can communicate, but on how well they can do so. Performance issues can manifest as slow data transfer speeds, high latency, bottlenecks, and uneven distribution of network resources. The goal is to optimize the network to ensure smooth and efficient data transfer and application performance.

Common network performance troubleshooting tasks include :

• Identifying and mitigating network congestion points.
• Analyzing bandwidth usage and optimizing traffic flows.
• Detecting and addressing packet loss or jitter issues.
• Investigating the causes of high latency.
• Fine-tuning Quality of Service (QoS) settings to prioritize critical applications.
• Optimizing the configuration of routers, switches, and other network devices to enhance performance.

In summary, network troubleshooting deals with ensuring basic network connectivity and functionality, while network performance troubleshooting goes a step further by focusing on optimizing the efficiency, speed, and quality of data transfer and communication within the network. Both aspects are crucial for maintaining a reliable and high-performing network environment.

How to Troubleshoot Network Performance: Network Performance Troubleshooting Steps

When it comes to Network Performance Troubleshooting, Obkio's Network Performance Monitoring tool is your secret weapon! Obkio is designed to help network administrators and IT teams monitor, optimize and troubleshoot network performance.

It provides insights and data that can be invaluable during the network performance troubleshooting process. Here's how the key steps of network performance troubleshooting can be enhanced with Obkio's NPM tool:

Identifying the Problem: Obkio's tool helps IT pros identify network performance issues and trends by providing real-time data on network metrics such as latency, packet loss, and throughput. These insights can aid in understanding when and where performance issues are occurring.

Isolating the Issue: Obkio's network visualization techniques, including dashboards, Chord Diagram, Visual Traceroute tool , and Network Device Monitoring feature can help pinpoint which specific devices, links, or applications are affected by the performance issues, making it easier to isolate the problem.

Gathering Data: Obkio's monitoring tool continuously collects and presents performance data, enabling administrators to gather detailed information about network behavior over time. This data is crucial for accurate analysis.

Analyzing Network Components: With Obkio's tool, administrators can monitor the health and performance of individual network components like routers, switches, and access points. It provides visibility into how each component contributes to overall performance.

Testing Connectivity: Obkio's active monitoring capabilities allow for real-time testing of connectivity between network locations, helping to identify any issues with routing, packet loss , or latency.

Analyzing Network Traffic: Obkio uses synthetic monitoring and synthetic traffic to simulate real-user traffic and provide detailed insights into network traffic patterns. This helps troubleshooters identify congestion points, and potential bottlenecks that could impact performance, even when there's no real user traffic.

Testing Applications: By monitoring application performance and response times, Obkio can help determine whether performance issues are related to specific applications or the network itself.

Checking for Security Issues: Obkio's network performance data can be used to identify any unusual traffic patterns or unexpected network behaviour that might indicate security-related issues affecting performance.

Updating Firmware and Software: Monitoring performance after firmware or software updates using Obkio's tool can help assess whether these updates have positively or negatively impacted network performance.

Implementing Solutions: Obkio's real-time data and insights can help IT pros implement targeted solutions to help businesses troubleshoot network performance efficiently and effectively. Using tools like Traceroutes and Network Device Monitoring, businesses can understand if network problems are happening locally, or in their MSP network or ISP network . They can then implement solutions interally or reach out to their MSP/ ISP for support with proof from Obkio's app.

Monitoring and Validation: Obkio continuousnetwork monitoring capabilities help network admins validate that their business' network performance has been successfully improved and and optimized and remains stable over time. With continuous network monitoring, IT pros can be sure that, in the future, they can proactively identify network issues and troubleshoot network performance.

Documentation: Obkio's tool provides historical data and reports that can be included in the documentation of the troubleshooting process, helping to track the progression of issues and solutions.

Incorporating Obkio's Network Performance Monitoring tool into the network performance troubleshooting process enhances visibility and data-driven decision-making, ultimately leading to quicker and more effective resolution of network performance issues.

You've Mastered The Art - Start Your Network Troubleshooting Process Now!

Congratulations, network troubleshooters! You've made it to the end of the ultimate survival guide for network troubleshooting. Armed with the knowledge of network troubleshooting techniques, steps, and tools, you're ready to tackle any network issue that comes your way.

Remember, network troubleshooting is not just about fixing problems, but also about optimizing network performance and ensuring network security. By following the network troubleshooting steps and using the appropriate tools, you can quickly identify the root cause of network issues and implement the necessary fixes to ensure optimal performance.

And let's not forget the importance of monitoring network performance even after fixing an issue. By continuing to monitor the network, you can ensure that the issue is resolved, identify any new issues, optimize network performance, and ensure network security.

As mentioned earlier, the easiest and most accurate way to troubleshoot networks is by using a Network Monitoring and Network Troubleshooting software, like Obkio.

Obkio is a simple Network Monitoring software for Enterprises and service providers that allows users to continuously monitor end-to-end performance of their network and core business applications to identify network issues, collect data on network performance, and improve the end-user experience!

Obkio is the ultimate network troubleshooting survival tool.

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The Best Network Troubleshooting & Diagnostics Tools

Network troubleshooting and diagnostic tools help network administrators and technicians identify and resolve issues.

These tools are designed to analyze network performance, identify problems, and provide insights into the functioning of the network.

Network analysis can show you the leading causes of network problems such as; slow speeds, network connection problems, packet loss on overloaded network devices or missing information in your routing table and other system databases.

Here’s our list of the best network diagnostic tools and troubleshooting software:

• Datadog Network Performance Monitoring EDITOR’S CHOICE A cloud-based network monitoring and management service that includes autodiscovery, topology mapping, performance alerts, and troubleshooting tools Start a 15-day free trial .
• ManageEngine OpManager Plus (FREE TRIAL) This bundle of seven ManageEngine tools provides full network monitoring and analysis capabilities. Installs on Windows Server and Linux. Start a 30-day free trial .
• Site24x7 Network Monitoring (FREE TRIAL) A cloud-based service that monitors network devices, tracks traffic patterns, provides capacity planning support, and offers troubleshooting tools. Start a 30-day free trial .
• Paessler Network Troubleshooting with PRTG Infrastructure management system that includes port monitoring.
• SolarWinds Network Configuration Manager An essential system security and administration tool that automatically checks on device settings. The NCM will gather all device configurations, allow the creation of standard settings, and ensure that any unauthorized changes are immediately rolled back.
• N-able N-sight A remote monitoring and management tool that enables central IT departments to manage networks on several remote sites.
• Ping Simple command-line utility that checks on the speed of connections.
• Tracert Free command-line utility that lists the probable hops to a network or internet destination address.
• Ipconfig This command-line tool reports the IPv4 and IPv6 addresses, subnets, and default gateways for all network adapters on a PC.
• Netstat This tool displays active connections on your computer.
• Nslookup Available for Windows, Unix, Linux, and Mac OS, this tool gives you DNS server diagnostics.
• Uptrends Uptime Monitor A free online tool that will make repeated checks on the availability of a website.
• Sysinternals Set of Microsoft tools for Windows that help troubleshoot and configure Active Directory.
• Wireshark Free packet sniffer that will help you analyze traffic flows.
• Nmap Network security and monitoring tool that needs a companion utility, Zenmap, as a user interface.

The best network diagnostics tools & troubleshooting software

When curating this list, we considered the reliability of the tool in use in diverse situations, ease of setting up and use, documentation and support, and how up to date the diagnostic software is kept.

Our methodology for selecting a network diagnostic tool

We reviewed the market for network diagnostic tools and analyzed the options based on the following criteria:

• A package of several useful tools accessible through a single interface
• Methods to reconcile addressing issues with DHCP and DNS servers
• Connection testing systems
• A system of alerts that allow technicians to get on with other tasks if not notified of problems
• Automated system sweeps or useful tests that can be launched on a schedule
• A free tool or a trial period for risk-free assessment
• Value for money from paid tools and worthwhile functions from free tools

Five of the tools in our list ( ping , tracert , ipconfig , netstat , & nslookup ) can be executed directly from a Windows command prompt (cmd.exe) without installing any additional programs for advanced troubleshooting. The rest of the network analysis tools can be used alone or in combination for network discovery.

1. Datadog Network Performance Monitoring (FREE TRIAL)

Datadog is a cloud-based monitoring system for IT resources that is available as a menu of modules. The base package of the service is an Infrastructure module that covers network monitoring. However, this service can be enhanced by adding on the Network Performance Monitoring module.

Key Features:

• Network Traffic Monitor: Measures throughput per link
• Connection Testing: On the network and across the Internet
• Live Traffic Flow: Visualizes speed per link
• Bottleneck Identification: Spots traffic chokepoints
• Protocol Analysis: Identifies the top talkers

Why do we recommend it?

Datadog Network Performance Monitoring is a SaaS package that provides device discovery, network mapping, and traffic analysis. This tool can be slotted together with a Network Device Monitoring service to get full, automated network monitoring. Infrastructure and application monitoring tools on the platform provide the opportunity to create a full-stack monitoring system.

The Network Performance Monitoring module of Datadog adds on analytical functions to the Infrastructure package and includes capacity planning and troubleshooting utilities. While the Infrastructure module looks at device statuses, the Network Performance Monitoring service examines traffic flows .

The Datadog system uses agent software on-site, but all processing and data storage is implemented on the Datadog server. Systems administrators access the Network Performance Monitoring console through any browser in order to see live statistics on current traffic flows on the network. Given that the service is based in the cloud, it can easily monitor remote networks, just as long as that network has the agent module installed on it.

The service doesn’t just display live network traffic data. It also stores that information for analysis . Administrators can trace the journey of a packet, view conversations between endpoints, segment traffic statistics per application or per origin or source, and identify the major bandwidth hogs on the network. The service can unify both onsite, cloud-based, and remote networks to give a complete picture of all network traffic generated by the business. The tool includes live network maps with traffic flows shown on them and it is also possible to see overloaded links or bottlenecks.

Who is it recommended for?

Datadog Network Monitoring is reasonably priced and so accessible to any business. The service is charged for by subscription and there is no setup fee. Charges are levied per host, so even the smallest business will be able to afford this package.

• Network-Wide Performance Tracking: Live throughput volumes
• Equipment Assessments: Examine load balancer and firewall performance
• Services Tracking: Assess DNS accuracy and availability
• Time-Series Traffic Throughput Graphs: Identify the causes of traffic surges
• Automated Monitoring: Alerts for delivery delays
• Doesn’t Include Discovery: Requires a subscription to Datadog Infrastructure

Datadog has a single plan level for its Network Performance Monitoring module. Charges are levied per host per month with a discount for paying annually in advance. The service is available for a 15-day free trial .

EDITOR'S CHOICE

Datadog Network Performance Monitoring is our top pick for a network diagnostic and troubleshooting tool because it includes a lot of automated activity tracking that takes care of performance analysis for you. The system maps all devices and shows live statuses in the topology layout so you can instantly see where problems are arising. A system of alerts also draws your attention to problematic devices and cuts down the time it would otherwise take you to work out why the network is not operating at peak performance.

Download: Get 15-day FREE Trial

Official Site: www.datadoghq.com/free-datadog-trial/

OS: Cloud-based

2. ManageEngine OpManager Plus (FREE TRIAL)

ManageEngine OpManager Plus gives you all the tools you need to monitor networks and servers. These tasks are complex and could involve tracking the statuses of containers, virtualization, file storage servers, firewalls, and IP address-related issues. OpManager Plus takes care of all of those tasks and also adds on an application performance monitor to provide the full stack of IT services.

• Self Setup: Network discovery
• SNMP-Based System: Device monitoring
• Flow Protocols: Traffic analysis

ManageEngine OpManager Plus combines automated monitoring for networks and servers. The tool is also a good choice for its VM monitoring capabilities. Troubleshooting tools in the software include troubleshooting tools, such as NetFlow and other packet data extraction protocols.

The OpManager Plus system gives you the tools to scrutinize and manage network devices. The system automatically detects all devices connected to the network, logs them, and then maps the network . The system then provides constant performance monitoring through SNMP .

You also get a bandwidth analyzer with this bundle. You can see live throughput statistics per link and get the system to assess utilization of full capacity. Performance thresholds will generate alerts if tripped. You can channel these through email, SMS, or a service desk ticketing system. The package lets you run tests to ensure constant system availability.

Device management services include an IP address manager that integrates a DHCP and DNS server. You also get a switch port mapper so that you can see exactly how many ports are occupied on each device. A configuration manager lets you standardize the settings of all of your devices, restoring stored configurations automatically in the case of unauthorized tampering.

There are five editions for OpManager Plus and these include a Free edition. This monitors networks with only three devices, which could only be for the very smallest businesses. Large organizations and multi-site businesses would benefit from the OpManager Plus system. There is also an edition built for MSPs.

• System Information Management: Log collection and analysis
• Network Device Protection: Includes network configuration management
• Network Address Management: IP address management and port scanning
• Very Large System: Includes many non-network management systems, such as application monitoring

The software for ManageEngine OpManager Plus installs on Windows Server or Linux . The bundle offers a lot of services and so you will spend a lot of time learning all of its functions. You can perform that investigation for free with a 30-day free trial .

ManageEngine OpManager Plus Start a 30-day FREE Trial

See also: Network Configuration & Backup Tools

3. Site24x7 Network Monitoring (FREE TRIAL)

Site24x7 Network Monitoring discovers all of the devices on a network, creates a hardware inventory, and draws up a network topology map. The package implements continuous device performance monitoring and also records traffic patterns to guard against system overloads.

• SNMP-Based System: Network discovery
• Automated System Documentation: Inventory and mapping
• Netflow Protocols: Traffic analysis

Site24x7 Network Monitoring uses the Simple Network Management Protocol to identify all devices and create a map. The inventory and map help with troubleshooting but the package goes further, offering alerts when problems are detected, allowing time to fix problems and identifying where the issue lies. The bundle also provides Ping and Traceroute utilities to test connections.

The device agents scan each switch and router and raise alarms when faults are discovered. These alarms get translated into alerts in the Site24x7 dashboard. A traffic monitoring unit in the Site24x7 package will also generate alerts if traffic volumes rise close to the full capacity of a switch interface. The Site24x7 system can be set up to forward alerts as notifications to technicians by SMS, voice call, email, or Slack message.

The alerts of the Site24x7 Network Monitoring service provide immediate root cause analysis if network problems arise, so many times, there won’t be any need for troubleshooting. However, the package also includes Ping and Traceroute utilities.

Site24x7 offers SaaS packages and all of them include the network monitoring system. You can’t subscribe to just the Network Monitoring unit by itself. Other utilities in the plans include server and application monitoring systems and also network configuration management and log management.

The Site24x7 platform is accessible for any size of business. Plans are offered in a base package with capacity expansions available. The based package is sized and priced to be suitable for small businesses but the expansion upgrades make it suitable for larger companies as well.

• Automated Status Tracking: Constant SNMP-based device monitoring
• Bandwidth Analysis: Traffic  flow protocols
• Device Protection: Network configuration management
• Deceptively Low Prices: Base packages are suitable for small businesses and larger companies have to pay for capacity expansions

The Site24x7 plans offer different capacities of each module but all editions include all of the modules on the platform. There is even a plan for use by managed service providers. You can experience Site24x7 with a 30-day free trial .

Site24x7 Network Monitoring Start a 30-day FREE Trial

4. Paessler Network Troubleshooting with PRTG

Paessler’s PRTG is a complete monitoring system. It can help you with troubleshooting because it can diagnose network issues right down the protocol stack and identify the root of the problem. Port monitoring is one of the network diagnostics techniques that you can use with this tool.

• Flexible Package: Buyer decides which services to activate
• SNMP-Based Monitoring: Automated device status detection
• Traffic Flow Protocols: Bandwidth monitoring

Paessler PRTG is a very large package of monitors that include network, server, and application monitors and has sensors for network troubleshooting including Ping implementations and a TraceRoute facility.

The PRTG system includes two port monitoring sensors . One homes in on a specified port on a particular device, the other will check a range of port numbers. This tool only monitors TCP ports. The port range sensor has one extra feature that the single port sensor does not have. You can set it to check the port with TLS protection. Both sensors report on the response time of the port and whether it is open or closed.

PRTG includes network traffic analysis tools to help you troubleshoot delivery speeds. The tool includes a range of traffic monitoring techniques including route tracing to a destination with Traceroute and a Ping sweep , which will give you the response times to each node on your network. A packet-sniffing utility can tell you which applications and endpoints are producing excessive traffic and you can query the health of the network devices to see which are congested to the point of queuing.

Paessler built a tool that covers servers and applications as well as network statuses, port response times, and services to monitor all conditions that can cause software performance issues. If you’ve got VMs on your network, PRTG can sort through their underlying connections, services, servers, and operating software. That monitoring is constant, so you will be able to trace back through events to spot the source of any performance issues.

PRTG is a flexible package. All customers get the same software bundle containing thousands of monitoring tools, which are called “sensors.” Each buyer decides how many sensors to turn on and the price for the package is levied as an allowance of sensors. This is a good package for large businesses and small companies can use the system for free if they only turn on 100 sensors.

• Free for Small Businesses: No charge for 100 sensors
• System Documentation: Network discovery inventory creation, and mapping
• Uptime Monitoring: Device availability checks
• Device Protection Shortfall: No network configuration management

Paessler delivers PRTG as a cloud service or you can install the diagnostic software on your premises. The tool installs on Windows Server environments. You can use the system for free for up to 100 sensors.

5. SolarWinds Network Configuration Manager

The SolarWinds Network Configuration Manager offers the opportunity to automate system troubleshooting and problem resolution. Busy systems managers often overlook the settings of network devices. The network could be performing badly because you don’t have all of the settings of your devices coordinated. The Network Configuration Manager saves you time by seeking out all devices, the network device health, importing their settings into a central manager, and allowing you to create a standard configuration for each device type and make .

• Network Discovery: Access network devices
• Device Protection: Extracts configuration image
• Archiving: Stores configurations
• Device Security Monitoring: Checks for unauthorized configuration changes

SolarWinds Network Configuration Manager scans a network and identifies all devices. It then enables the network manager to create a standard setup for each type of device and then roll that out. Those authorized configurations are stored by the Network Configuration Manager and then the tool performs constant checks on devices. If any changes occur to settings, the system automatically restores the standard configuration by applying the stored image.

The configuration manager rolls out the standard configurations that you write into the central dashboard. This standardization should fix a lot of the problems that you experience on your network because it will wipe out inappropriate settings for network devices, such as routers and switches that might be slowing down data transfers. Once the standard configurations have been stored, they can only be changed through the password-protected dashboard of the Network Configuration Manager.

This system configuration troubleshooter is an important security tool. Unauthorized intruders can be traced or blocked through the network devices of the network , so altering settings is a common intrusion strategy. The Network Configuration Manager constantly monitors the configurations of all network devices and automatically restores the authorized settings, stored as images, should any change be detected.

SolarWinds produces a range of IT whole infrastructure monitoring and network management tools, and many of these are created on a common platform, called Orion. This makes it possible for the independent tools to interact, and the Network Configuration Manager is one of these Orion-based utilities. The central network monitoring tool in the suite is the Network Performance Monitor and this is usually the lead utility in any monitoring system, which is complemented by the Network Configuration Manager. However, SolarWinds NCM can also be used as a standalone tool.

This is an on-premises package for Windows Server. There isn’t a scaled down version for small businesses. So, the Network Configuration Manager would be suitable for larger businesses.

• Blocks Hackers: A security service to block network device tampering
• Switch Management: Allows all configurations to be standardized
• Physical Intrusion Detection: Scans for all devices, spotting rogue equipment
• Uptime Monitoring: Continuous network device availability tests
• Runs on Windows Server: No Linux version

The Network Configuration Manager is a paid tool. However, SolarWinds makes it available on a 30-day free trial .

The Network Configuration Manager is also part of a super-bundle offered by SolarWinds, called the Network Automation Manager . It includes all of the provider’s network monitoring and management tools. The other modules in the bundle are Network Performance Monitor, Netflow Traffic Analyzer, User Device Tracker, VoIP & Network Quality Manager, IP Address Manager, and SolarWinds High Availability. All of these systems appear in a single console that runs on Windows Server . SolarWinds provides a 30-day free trial of this package.

6. N-able N-sight

N-able N-sight is a cloud-based remote monitoring and management software package. As this system monitors the network, it also stores metrics for analysis. Having access to all aspects of a system, including endpoints and servers, N-able has many channels of data for diagnostics and troubleshooting.

• An RMM Package: Monitoring and system management features
• Automated Network Monitoring: Reduces technician wage bill
• Full Stack Observability: Networks, servers, and software
• Unattended Monitoring: Alerts for performance problems

N-able N-sight is a cloud-based service that provides remote monitoring systems for networks, servers, and applications. This service includes a troubleshooting guide that identifies security problems and other issues with networks, endpoints, and software.

Among the benefits offered by N-able N-sight is a service called LOGICcards . This is a data source for a wide range of diagnostic projects. The main value of these feeds lies in security. However, they also give insights into how to improve efficiency and avoid system management mistakes.

LOGICcards gathers data from 5,000,000 endpoints on 4,000,000 networks. Comparing the data extracted from these studies, the LOGICcard system analyzes a network and is able to point out factors and settings that are missing from that system, compared to the organization of the majority of other networks.

Another LOGICcard service is a feed of warnings to look out for, such as patches that cause problems and should be held off or new internet-based scams. A guidance aspect to this service also identifies errors to avoid in network configuration and tips on how to optimize bandwidth usage. Furthermore, the topics covered by a LOGICcard feed adapt according to your responses to past advice.

The dashboard for N-able N-sight is resident on the cloud. It doesn’t require any special equipment to use the service – any standard web browser will do and there is also a N-able N-sight mobile app available.

The N-able brand produces tools for managed service providers (MSPs). The company has two remote monitoring and management (RMM) tools and N-able is one of those. N-able is marketed as a suitable package for small and mid-sized MSPs.

• SNMP-Based System: Network device discovery and constant performance monitoring
• Multi-Tenanted Architecture: Designed for use by managed service providers
• Technician Efficiency Optimization: Task automation scripts
• Device Management Shortfall: No network configuration management

N-able N-sight is a subscription service. This is a great attraction for startups because there are no upfront costs for getting set up. There are no setup fees and there is no need to fork out for a software package Instead, the subscribing company pays a little each month. Interested potential customers can access a 30-day free trial of N-able N-sight.

Ping is the ideal command to use when you need to confirm network connectivity, at the IP level, between two hosts, or to confirm the TCP/IP stack is working on your local machine. A successful ping confirms network connectivity between the two hosts and it also gives reports on packet loss.

• Availability Monitoring: Connectivity test
• Connection Quality: Jitter indicators
• Connection Speed: Roundtrip time

Ping is built into every operating system and it is the basis of many of the network monitoring and troubleshooting systems on this list. The utility can tell you the time a packet takes to get to a specific destination across a network or across the internet. It will also give you information on jitter and packet loss.

Using Ping with Examples

Below is an example of a successful run of the ping command to the “google.com” remote host.

In addition to confirming IP connectivity to “google.com”, these results confirm that we are able to properly resolve domain names (i.e. DNS is working on the local machine).

That Loss figure that you see in the last line of the ping output is the number of lost packets followed by the packet loss rate in brackets.

A few pro-tips for working with the ping command for advanced troubleshooting:

• Use ping –t to ping a host continuously. For example:

would continue to ping google.com until the ping was interrupted. Press control-c (the “CTRL” and “C” keys) to end a continuous ping.

• If you cannot ping domain names like google.com, but you can ping IP addresses on the Internet like 8.8.8.8 (Google’s DNS servers), you may have a DNS-related problem.
• If you cannot ping IP addresses on the Internet like 8.8.8.8, but you can ping hosts on your Local Area Network (LAN), you may have a problem with your default gateway.
• You can use “ping localhost”, “ping::1”, or “ping 127.0.0.1” to test the TCP/IP stack on your local machine. “localhost” is a name that resolves to one of the loopback addresses of a local machine, “::1” is an IPv6 loopback address, and “127.0.0.1” is an IPv4 loopback address.

Ping is a part of every network engineer’s toolkit. It is free to use and provides quick answers.

• Familiar to Many: Commonly-used network tester
• Cost Saver: Free to use
• Variants Available:  Provide repeated tests or range tests
• Basic Display: A command line tool without graphics

Tracert is similar to ping, except it leverages Time To Live (TTL) values to show how many “hops” there are between two hosts. This makes it a helpful tool in determining where a network connectivity breakdown is occurring. Basically, tracert helps you understand if the router or network that is down between your computer and a remote host is one you control or not.

• Traceroute: Implemented as the tracert command
• Path Tests: Exploits the Border Gateway Protocol
• Local and Global Tests: Network or internet testing

Tracert is the Command Prompt implementation of TraceRoute and it provides a list of nodes across the internet to a given destination. While this can’t tell you the exact path that previous transmissions have taken, it follows the path that routing algorithms currently use to reach a destination and shows the transmission times to each node.

Using tracert with examples

Again using google.com as an example, we can see there were 10 hops between our PC and google.com.

TraceRoute is available on all operating systems. While it is implemented by the tracert command on Windows, it is called traceroute on Linux, macOS, and Unix. The tool is free to use and accessible to all network managers.

• End-to-End Testing: Checks a path to a given destination
• Connection Speed: Shows transmission time to each node
• Spots Rerouting: Identifies problematic devices
• Doesn’t Repeat History: Can’t guarantee to exactly trace a previously used path

9. Ipconfig

Determining the IP settings on your computer is an essential part of network troubleshooting. The ipconfig command helps you do just that. Entering ipconfig at a command prompt will return IPv4 and IPv6 addresses, subnets, and default gateways for all network adapters on a PC. This can help determine if your computer has the right IP configuration. Additionally, ipconfig can be used to change or update selected IP settings.

• Quick Command: Show interface settings
• Network Addressing: DHCP controls
• Service Tests: DNS management

Ipconfig is another widely-used free command line utility for troubleshooting networks. The tool shows the addressing information for each network interface on the computer. It will also show the gateway address and the address for the network’s DHCP and DNS servers.

Pro-tips for working with ipconfig:

• If ipconfig returns an IP address that starts with 169.254 (e.g. 169.254.0.5), your PC is likely configured for DHCP but was unable to receive an IP address from a DHCP server.
• Use ipconfig /all to get the full TCP/IP configuration information for all network adapters and interfaces.
• Use ipconfig /release to release the current DHCP assigned network parameters.
• Use ipconfig /renew to renew the current DHCP assigned network parameters.
• Use ipconfig /flushdns to clear the DNS cache when troubleshooting name resolution issues.

Ipconfig is free to use and already installed on your computer. On Linux, macOS, and Unix, it is called ifconfig.

• No Cost: A free utility to show and update IP addresses
• Basic Controls: Can reset address allocations
• Service Verification: Checks on DNS records
• Basic Display: No graphical interface

10. Netstat

Netstat allows you to display active connections on your local machine. This can be helpful when determining why users are unable to connect to a given application on a server or to determine what connections are made to remote hosts from a computer. Entering netstat at the command prompt will display all active TCP connections. Adding parameters to the netstat command will extend or alter the functionality.

• Transmission Control: Port statuses
• Path Analysis: IP routing table
• Dual Stack: IPv4 and IPv6

Netstat lists all the connections that are currently live on the computer on which the command is run. The output show every TCP and UDP port that is currently active, even though the connection might be in a closed state.

netstat commands & example

Here are a few helpful netstat commands and what they do:

• netstat –a displays all active TCP connections and the TCP and UDP ports a computer is listening on.
• netstat –n displays all active TCP connections just like the netstat command, but it does not attempt to translate addresses or port numbers to names and just displays the numerical values.
• netstat –o displays all active TCP connections and includes the process ID (PID) for the process using each connection.

You can combine different parameters to extend the functionality of netstat. For example,

would display all active TCP connections and the TCP and UDP ports a computer is listening on, use numerical values, and report the PID associated with the connections.

Every network administrator will probably use this tool at some point in time. The tool is free to use and it is built into the operating system for Windows, Linux, macOS, and Unix.

• No Cost: Free utility
• Command Line Options: Filterable results
• Constant Monitoring: Can run continuously
• Command Line Tool: No graphical interface

11. Nslookup

nslookup is a useful command-line utility that enables DNS troubleshooting and diagnostics. Nslookup is available on Windows and *nix operating systems. There are a variety of use cases for this flexible utility and it can be run in interactive mode or by entering commands directly at the command prompt.

To help you get started, we’ll review some nslookup commands that are helpful in three of the most common use cases: finding an IP address based on a domain name, finding a domain name based on an IP address, and looking up email servers for a domain.

• Service Testing: Queries DNS records
• Basic Display: Command line tool
• No Cost: Free to use

Nslookup is a command for DNS checks – the name is short for “name server lookup.” With this tool, you can identify the mapping between hostnames and IP addresses on a local network. By entering a remote IP address or Web domain, you can see details from the global DNS service.

Below are examples of how to do each from a Windows command prompt.

Finding an IP address based on a domain name with nslookup:

The output above shows us that the DNS server used on our local machine was ns2.dns.mydns.net and since ns2.dns.mydns.net is not an authoritative name server on Google’s domain, we get a “Non-authoritative answer”. If we wanted to specify a different DNS server in our query, we simply add the DNS server’s domain name or IP address after the command, like this (using the 1.1.1.1 DNS server from CloudFlare ).

Finding a domain name based on an IP address with nslookup

Finding a domain name based on an IP address is similar to the previous process, you simply use an IP address instead of the domain name after the “nslookup” command. For example to find out what the fully-qualified domain name (FQDN) for the IP address 8.8.8.8 is we would use the command below:

Based on the output, we can see that the FQDN associated with 8.8.8.8 is “google-public-dns-a.google.com” which makes sense given 8.8.8.8 is one of the two popular public DNS servers available from Google .

Looking up email servers for a domain with nslookup

Sometimes you may need to determine what email servers are available on a domain. To do that, we simply need to specify that we are looking for MX records using the –ty switch. In the example below, we’ll check what mail servers are returned for gmail.com:

Here, five mail servers were returned along with an MX preference value. The lower the MX preference value, the higher the priority of that server (i.e. those servers should be used first).

Network managers would use nslookup to ensure that the local DNS server is working and also to test for DNS entry errors for Wen properties. The free tool is built into the operating system for Windows, Linux, macOS, and Unix.

• Domain Name Resolution: Shows the domain name for an IP address
• Run for Research: Interactive mode
• Network and Internet: Local or Web domains
• Limited Functionality: Not a full system monitoring package

12. Uptrends Uptime Monitor

Uptrends offers a menu of website monitoring and testing services from its cloud platform. The Uptrends Uptime Monitor is a free service that can be accessed at the Uptrends website.

The free Uptime Monitor offers a choice of locations from which your site can be tested. It is possible to opt for tests to be run from all of the locations that Uptrends offers.

• Great for Small Businesses: Free on-demand website test
• Multiple Launch Sites: Tests from 40 locations
• Extensive Service: 233 servers around the globe

Uptrends Uptime Monitor is a testing service for internet connections. It specifically takes a Web domain as input, so its checks also extend to DNS testing. You can use this tool for free for on-demand availability tests, which can be launched from a long list of locations. You can get the tests to run recursively every minute if you sign up for a paid account.

The free tool is an on-demand testing system and will give you the status of your site from many locations at that moment. It is possible to remind yourself to rerun the test and keep hitting the button. However, it is more practical to get the Uptrends service to repeat its tests automatically.

Uptrends provides automated testing that will launch every minute. The automated service is not free. You can leave that tool to make constant checks on your site’s availability – it will send you an alert if it encounters problems.

If you run a website, you will need to know if it is available, so it is worth going for the paid account. This will notify you if the site goes offline. The tests launch from different locations around the globe, which is a necessary service for websites that use caching servers for delivery speed optimization or content delivery networks.

• Quick Uptime Check: Free single launch test
• Long-Term Uptime Monitoring: Paid repetitive availability tests
• Automated Reporting: Alerts for failed tests
• Reporting Limits: Doesn’t provide page load speeds

The paid packages of Uptrends include internal server monitoring as well as uptime tests. You also get real user monitoring that tracks the responses of your site and its services to visitors. The system is offered in five plans: Starter , Premium , Professiona l, Business , and Enterprise . Each higher plan has more features. You can try all of the features of Uptrends on a 30-day free trial .

13. Sysinternals

The Sysinternals networking utilities suite from Microsoft offers advanced network diagnostic and troubleshooting tools to Windows administrators that require advanced network diagnostic and troubleshooting tools. The Sysinternals utilities include tools that can help troubleshoot and configure Active Directory (AD), like AD Explorer and AD Insight .

• Handy Tools: A suite of utilities
• Connectivity Tests: PowerShell Ping
• Web Research: Whois lookup

Sysinternals is a large package of useful system management utilities for Windows. This is a useful free bundle of tools that are versions of systems that you can get elsewhere, such as Ping and Whois. However, it’s nice to have a package that has all of these tools in one place.

Other tools can help measure network performance ( PsPing ), scan file shares ( ShareEnum ), list or run processes remotely ( PsTools ), and more. If you only require one or a few of the Sysinternals utilities, you can install them separately as opposed to downloading the entire Sysinternals Suite.

Systems administrators will like this package, not just network managers because the bundle includes some nice utilities for managing Active Directory as well as tools to troubleshoot networks.

• No Cost: A free package of system administration tools
• Access Rights Management: Utilities for Active Directory queries
• System Performance: Process examiner
• Not a Full Network Monitoring Package: Only one network troubleshooting tool

14. Wireshark

Wireshark is a protocol analyzer and one of the go-to networking tools for organizations of all sizes when network issues need to be troubleshot with a high level of granularity.

The benefit of using Wireshark to analyze network traffic is that you will be able to view the raw network packets, and this will often allow you to identify the root cause of an issue. This can be especially helpful in situations where it is unclear which application is not doing what it is supposed to or when you try to reverse engineer the functionality of a poorly-documented program.

• Traffic Analysis: Packet capture
• Data Selection: Filtering and query language
• Easy to Read: Color-coded packet display

Wireshark is an iconic packet sniffer and analyzer. Any network engineering course includes a section on the use of Wireshark. This system includes its own filter language that can be applied to packet collection to reduce the large volume of data that it extracts. The same filter language can be applied to search through packet data.

The tradeoff here is that you will have a lot of data to parse through, so some technical knowledge may be required to drill down and identify the important information.

You can download Wireshark for free here .

On Windows operating systems, link-layer packet captures with WireShark are often made possible using Winpcap (either Winpcap or Npcap is required). In addition to enabling WireShark on Windows, Winpcap can enable the powerful Windump command line utility which is Windows answer to the popular tcpdump program found on many *nix operating systems. For a deeper dive on Winpcap, Windump, and tcpdump, check out our recent article on packet sniffers and network analyzers and download the tcpdump cheat sheet .

Wireshark is an excellent tool for processing packet data. However, it’s analytical features are limited. There are a number of other tools that work well with Wireshark to create an even better data analysis system. The data search system Elasticsearch is free to use and it comes with complementary modules for logfile management and data display. Together this suite is called the Elastic Stack .

The illustration below shows how the Elastic Stack can be used with Wireshark to create an improved data analysis system from components that cost nothing.

Although this setup looks complicated, all of the tools shown in this diagram are designed to work together and the Elasticsearch website includes guides on how to put this system together.

Any network manager that doesn’t already know about Wireshark should download it and learn it because this is an essential tool and experience in using it is career-enhancing. The tool is available for Windows, macOS, Linux, and Unix.

• Multiple OSs: Available for Windows, macOS, and Linux
• Two-Way Tracing: Can trace a conversation
• Use with Caution: Can generate very large files

Nmap is a popular security auditing and network exploration tool released under a custom open source license based on GPLv2. While the most popular use cases for nmap are security scans and penetration testing, it can prove quite helpful as a network troubleshooting tool as well.

• Research Tool: Network discovery
• Identification: Endpoint fingerprinting
• Security Monitor: Port scanning

Nmap is another classic that has a long history and so has a lot of fans. It is known to be used by hackers as well as network managers to explore a network and discover all devices. The tool is a command line utility and is a little difficult to use. Get the GUI Zenmap add-on to see a graphical network map.

For example, if you are dealing with an unfamiliar app and want to find out what services are running and which ports are open, nmap can help. Nmap itself uses a command-line interface (CLI), but that doesn’t mean you are out of luck if you prefer a graphical user interface (GUI). Zenmap is the official nmap GUI and is a good way for beginners to start working with nmap.

Nmap doesn’t just map a network, it also performs monitoring. It can be a good tool for checking on all devices, spotting rogue devices, and identifying those that are offline. The tool is free to use. However, getting the free PRTG gives you a much better discovery and mapping service than Zenmap and Nmap offer.

• Network Management Service: Useful for security auditing
• Issue Investigations: Network probing and troubleshooting
• Service Verification: DNS searching
• Command Line Tool: Needs Zenmap for a graphical display

For more on Zenmap and a deeper dive on nmap, check out our Best Free Port Checkers article.

Choosing a network diagnostics & troubleshooting tool

The tools we discussed here are great to have in your network troubleshooting toolbox and we recommend giving some of them a try the next time you find yourself dealing with a head-scratching network troubleshooting scenario. Did you try out our Editor’s choice – SolarWinds Network Configuration Manager ? Did we leave any of your favorite network troubleshooting tools out, or do you have questions about the tools we mentioned here? Let us know in the comments section below.

Related post: PingPlotter Alternatives

Network Diagnostics & Troubleshooting FAQs

What are the six steps of the troubleshooting process.

Follow a formalized routine when troubleshooting networks:

• Identify the problem.
• Make an educated guess of the possible cause of the problem.
• Explore the system to check whether your idea is valid.
• Identify system elements in error; plan and implement remediation steps.
• Check that the solution worked and change procedures to prevent the problem from happening again.
• Document the problem, the solution, and recommendations for procedural change.

Steps 2 and 3 might need to be carried out recursively until you hit the problem. The documentation step is ongoing throughout the troubleshooting process with note-taking to contribute to an accurate record once the entire process is complete.

What causes intermittent network connection issues?

There are many possible causes for intermittent network connection issues:

• Unreliable power source
• Environmental interference
• Queueing on a network device
• A network device overloaded
• A faulty network device
• IP address renewal
• IP address duplication
• DNS server errors
• Firewall software hanging
• Network software jamming
• Hacker attack
• Automatic update of firmware taking a device offline
• Interruption of external networks, e.g., the internet
• Loose cable plug in an endpoint or network device
• Damaged network cable
• Loose wiring
• Multiple domain server clashes
• Lack of storage space on devices for traffic processing or logging
• Security software blocking activity

Which utility or LAN command do you feel was the most useful for network troubleshooting?

Ping and Traceroute are the two LAN commands most often used for network troubleshooting. Ping shows whether an endpoint is contactable. Traceroute shows the most likely path to that endpoint. These two commonly used network utilities are usually integrated into most network monitors.

What are the most common issues that affect network performance and reliability?

The most common issues that affect network performance are:

• Power source problems
• Network device faults
• Network cable faults
• Defective cable connectors
• System overloading
• QoS prioritization
• Incompatible network settings on different devices
• Addressing issues
• Security software
• Hacker or intruder activity
• Network Diagnostics and Troubleshooting

2 Comments Leave a comment

I know this was written a few months ago, but what do you think of PingPlotter Pro? Why did it not make the list of best network troubleshooting software?

Just curious . . .

Hi Ben, Thanks for the reply. The simple answer is: I’ve never used PingPlotter Pro. Topically, it looks like a useful monitoring tool that can also have some troubleshooting benefits. What use cases do you think it is best for?

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This site uses Akismet to reduce spam. Learn how your comment data is processed .

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Network Engineer Skills

Learn about the skills that will be most essential for Network Engineers in 2024.

Getting Started as a Network Engineer

• What is a Network Engineer
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Find the important skills for any job.

Types of Skills for Network Engineers

Technical proficiency and network design, problem-solving and analytical abilities, cybersecurity expertise, automation and scripting, communication and collaboration, continuous learning and adaptability, top hard skills for network engineers.

Essential skills for robust network management, from advanced routing to security, ensuring optimal performance and cutting-edge connectivity solutions.

• Advanced Routing and Switching Techniques
• Network Security Protocols and Firewalls
• Cloud Networking and Virtualization

Wireless and Mobile Networking

• Network Troubleshooting and Diagnostic Tools
• Internet Protocols (IPv4/IPv6)

Software-Defined Networking (SDN)

• Network Automation and Orchestration
• Data Center Networking Technologies
• Understanding of Network Operating Systems (NOS)

Top Soft Skills for Network Engineers

Empowering network solutions through teamwork, adaptability, and a relentless commitment to clear communication and continuous skill enhancement.

• Effective Communication and Articulation
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• Master Emerging Networking Technologies: Keep abreast of new technologies such as 5G, Wi-Fi 6, and software-defined networking (SDN) by pursuing specialized training and certifications.
• Deepen Your Cybersecurity Knowledge: As security threats evolve, understanding cybersecurity best practices and tools is essential for protecting network infrastructure.
• Embrace Automation and Orchestration Tools: Learn to use network automation tools like Ansible, Terraform, or Cisco NSO to increase efficiency and reduce human error.
• Participate in Professional Networking Groups: Join groups like the IEEE or local meetups to exchange knowledge, stay informed about industry trends, and connect with peers.
• Advance Your Cloud Skills: Gain expertise in cloud services and architectures, including public, private, and hybrid cloud, to support the shift towards cloud-based solutions.
• Develop Programming Abilities: Acquire programming skills in languages such as Python or PowerShell to write scripts and automate network tasks.
• Engage in Continuous Learning: Utilize online platforms like Pluralsight, edX, or vendor-specific training to keep your skills sharp and up-to-date.
• Obtain Vendor-Specific Certifications: Validate your expertise and commitment to the profession by achieving certifications from vendors like Cisco, Juniper, or VMware.
• Focus on Soft Skills: Enhance communication, problem-solving, and project management abilities to better collaborate with IT teams and stakeholders.
• Experiment in a Lab Environment: Set up a home lab or use virtual labs to practice and experiment with network configurations and scenarios.

Skill FAQs for Network Engineers

What are the emerging skills for network engineers today, how can network engineers effectivley develop their soft skills, how important is technical expertise for network engineers.

Network Engineer Education

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Brain Power

5 steps (and 4 techniques) for effective problem solving.

Problem solving is the process of reviewing every element of an issue so you can get to a solution or fix it. Problem solving steps cover multiple aspects of a problem that you can bring together to find a solution. Whether that’s in a group collaboratively or independently, the process remains the same, but the approach and the steps can differ.

To find a problem solving approach that works for you, your team, or your company, you have to take into consideration the environment you’re in and the personalities around you.

Knowing the characters in the room will help you decide on the best approach to try and ultimately get to the best solution.

Table of Contents

5 problem solving steps, 4 techniques to encourage problem solving, the bottom line.

No matter what the problem is, to solve it, you nearly always have to follow these problem solving steps. Missing any of these steps can cause the problem to either resurface or the solution to not be implemented correctly.

Once you know these steps, you can then get creative with the approach you take to find the solutions you need.

1. Define the Problem

You must define and understand the problem before you start, whether you’re solving it independently or as a group. If you don’t have a single view of what the problem is, you could be fixing something that doesn’t need fixing, or you’ll fix the wrong problem.

Spend time elaborating on the problem, write it down, and discuss everything, so you’re clear on why the problem is occurring and who it is impacting.

Once you have clarity on the problem, you then need to start thinking about every possible solution . This is where you go big and broad, as you want to come up with as many alternative solutions as possible. Don’t just take the first idea; build out as many as you can through active listening, as the more you create, the more likely you’ll find a solution that has the best impact on the team.

3. Decide on a Solution

Whichever solution you pick individually or as a team, make sure you think about the impact on others if you implement this solution. Ask questions like:

• How will they react to this change?
• Will they need to change anything?
• Who do we need to inform of this change?

4. Implement the Solution

At this stage of problem solving, be prepared for feedback, and plan for this. When you roll out the solution, request feedback on the success of the change made.

5. Review, Iterate, and Improve

Making a change shouldn’t be a one time action. Spend time reviewing the results of the change to make sure it’s made the required impact and met the desired outcomes.

Make changes where needed so you can further improve the solution implemented.

Each individual or team is going to have different needs and may need a different technique to encourage each of the problem solving steps. Try one of these to stimulate the process.

1-2-4 All Approach + Voting

The 1-2-4-All is a good problem solving approach that can work no matter how large the group is. Everyone is involved, and you can generate a vast amount of ideas quickly.

Ideas and solutions are discussed and organized rapidly, and what is great about this approach is the attendees own their ideas, so when it comes to implementing the solutions, you don’t have more work to gain buy-in.

As a facilitator, you first need to present the group with a question explaining the problem or situation. For example, “What actions or ideas would you recommend to solve the company’s lack of quiet working areas?”

With the question clear for all to see, the group then spends 5 minutes to reflect on the question individually. They can jot down their thoughts and ideas on Post-Its.

Now ask the participants to find one or two other people to discuss their ideas and thoughts with. Ask the group to move around to find a partner so they can mix with new people.

Ask the pairs to spend 5 minutes discussing their shared ideas and thoughts.

Next, put the group into groups of two or three pairs to make groups of 4-6. Each group shouldn’t be larger than six as the chances of everyone being able to speak reduces.

Ask the group to discuss one interesting idea they’ve heard in previous rounds, and each group member shares one each.

The group then needs to pick their preferred solution to the problem. This doesn’t have to be voted on, just one that resonated most with the group.

Then ask for three actions that could be taken to implement this change.

Bring everyone back together as a group and ask open questions like “What is the one thing you discussed that stood out for you?” or “Is there something you now see differently following these discussions?”

By the end of the session, you’ll have multiple approaches to solve the problem, and the whole group will have contributed to the future solutions and improvements.

The Lightning Decision Jam

The Lightning Decision Jam is a great way to solve problems collaboratively and agree on one solution or experiment you want to try straight away. It encourages team decision making, but at the same time, the individual can get their ideas and feedback across. [1]

If, as a team, you have a particular area you want to improve upon, like the office environment, for example, this approach is perfect to incorporate in the problem solving steps.

The approach follows a simple loop.

Make a Note – Stick It on The Wall – Vote – Prioritize

Using sticky notes, the technique identifies major problems, encourages solutions, and opens the group up for discussion. It allows each team member to play an active role in identifying both problems and ways to solve them.

Mind Mapping

Mind mapping is a fantastic visual thinking tool that allows you to bring problems to life by building out the connections and visualizing the relationships that make up the problem.

You can use a mind map to quickly expand upon the problem and give yourself the full picture of the causes of the problem, as well as solutions [2] .

The goal of a mind map is to simplify the problem and link the causes and solutions to the problem.

To create a mind map, you must first create the central topic (level 1). In this case, that’s the problem.

Next, create the linked topics (level 2) that you place around and connect to the main central topic with a simple line.

If the central topic is “The client is always changing their mind at the last minute,” then you could have linked topics like:

• How often does this happen?
• Why are they doing this?
• What are they asking for?
• How do they ask for it?
• What impact does this have?

Adding these linking topics allows you to start building out the main causes of the problem as you can begin to see the full picture of what you need to fix. Once you’re happy that you’ve covered the breadth of the problem and its issues, you can start to ideate on how you’re going to fix it with the problem solving steps.

Now, start adding subtopics (level 3) linking to each of the level 2 topics. This is where you can start to go big on solutions and ideas to help fix the problem.

For each of the linked topics (level 2), start to think about how you can prevent them, mitigate them, or improve them. As this is just ideas on paper, write down anything that comes to mind, even if you think the client will never agree to it!

The more you write down, the more ideas you’ll have until you find one or two that could solve the main problem.

Once you run out of ideas, take a step back and highlight your favorite solutions to take forward and implement.

The 5 Why’s

The five why’s can sound a little controversial, and you shouldn’t try this without prepping the team beforehand.

Asking “why” is a great way to go deep into the root of the problem to make the individual or team really think about the cause. When a problem arises, we often have preconceived ideas about why this problem has occurred, which is usually based on our experiences or beliefs.

Start with describing the problem, and then the facilitator can ask “Why?” fives time or more until you get to the root of the problem. It’s tough at first to keep being asked why, but it’s also satisfying when you get to the root of the problem [3] .

As a facilitator, although the basic approach is to ask why, you need to be careful not to guide the participant down a single route.

To help with this, you can use a mind map with the problem at the center. Then ask a why question that will result in multiple secondary topics around the central problem. Having this visual representation of the problem helps you build out more useful why questions around it.

Once you get to the root of the problem, don’t forget to be clear in the actions to put a fix in place to resolve it.

Learn more about how to use the five why’s here .

To fix a problem, you must first be in a position where you fully understand it. There are many ways to misinterpret a problem, and the best way to understand them is through conversation with the team or individuals who are experiencing it.

Once you’re aligned, you can then begin to work on the solutions that will have the greatest impact through effective problem solving steps.

For the more significant or difficult problems to solve, it’s often advisable to break the solution up into smaller actions or improvements.

Trial these improvements in short iterations, and then continue the conversations to review and improve the solution. Implementing all of these steps will help you root out the problems and find useful solutions each time.

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Key Philosophy I: Fluid Progress, Like Water

Key Philosophy II: Pragmatic Priorities

Key Philosophy III: Sustainable Momentum

Key Philosophy IV: Three Goal Focus

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How to improve your problem solving skills and build effective problem solving strategies

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• 18 Free Facilitation Resources We Think You’ll Love

Effective problem solving is all about using the right process and following a plan tailored to the issue at hand. Recognizing your team or organization has an issue isn’t enough to come up with effective problem solving strategies. 

To truly understand a problem and develop appropriate solutions, you will want to follow a solid process, follow the necessary problem solving steps, and bring all of your problem solving skills to the table.   We’ll forst look at what problem solving strategies you can employ with your team when looking for a way to approach the process. We’ll then discuss the problem solving skills you need to be more effective at solving problems, complete with an activity from the SessionLab library you can use to develop that skill in your team.

Let’s get to it! 

Problem solving strategies

What skills do i need to be an effective problem solver, how can i improve my problem solving skills.

Problem solving strategies are methods of approaching and facilitating the process of problem-solving with a set of techniques , actions, and processes. Different strategies are more effective if you are trying to solve broad problems such as achieving higher growth versus more focused problems like, how do we improve our customer onboarding process?

Broadly, the problem solving steps outlined above should be included in any problem solving strategy though choosing where to focus your time and what approaches should be taken is where they begin to differ. You might find that some strategies ask for the problem identification to be done prior to the session or that everything happens in the course of a one day workshop.

The key similarity is that all good problem solving strategies are structured and designed. Four hours of open discussion is never going to be as productive as a four-hour workshop designed to lead a group through a problem solving process.

Good problem solving strategies are tailored to the team, organization and problem you will be attempting to solve. Here are some example problem solving strategies you can learn from or use to get started.

Use a workshop to lead a team through a group process

Often, the first step to solving problems or organizational challenges is bringing a group together effectively. Most teams have the tools, knowledge, and expertise necessary to solve their challenges – they just need some guidance in how to use leverage those skills and a structure and format that allows people to focus their energies.

Facilitated workshops are one of the most effective ways of solving problems of any scale. By designing and planning your workshop carefully, you can tailor the approach and scope to best fit the needs of your team and organization. 

Problem solving workshop

• Creating a bespoke, tailored process
• Tackling problems of any size
• Building in-house workshop ability and encouraging their use

Workshops are an effective strategy for solving problems. By using tried and test facilitation techniques and methods, you can design and deliver a workshop that is perfectly suited to the unique variables of your organization. You may only have the capacity for a half-day workshop and so need a problem solving process to match. 

By using our session planner tool and importing methods from our library of 700+ facilitation techniques, you can create the right problem solving workshop for your team. It might be that you want to encourage creative thinking or look at things from a new angle to unblock your groups approach to problem solving. By tailoring your workshop design to the purpose, you can help ensure great results.

One of the main benefits of a workshop is the structured approach to problem solving. Not only does this mean that the workshop itself will be successful, but many of the methods and techniques will help your team improve their working processes outside of the workshop. 

We believe that workshops are one of the best tools you can use to improve the way your team works together. Start with a problem solving workshop and then see what team building, culture or design workshops can do for your organization!

Run a design sprint

Great for: 

• aligning large, multi-discipline teams
• quickly designing and testing solutions
• tackling large, complex organizational challenges and breaking them down into smaller tasks

By using design thinking principles and methods, a design sprint is a great way of identifying, prioritizing and prototyping solutions to long term challenges that can help solve major organizational problems with quick action and measurable results.

Some familiarity with design thinking is useful, though not integral, and this strategy can really help a team align if there is some discussion around which problems should be approached first. 

The stage-based structure of the design sprint is also very useful for teams new to design thinking.  The inspiration phase, where you look to competitors that have solved your problem, and the rapid prototyping and testing phases are great for introducing new concepts that will benefit a team in all their future work. 

It can be common for teams to look inward for solutions and so looking to the market for solutions you can iterate on can be very productive. Instilling an agile prototyping and testing mindset can also be great when helping teams move forwards – generating and testing solutions quickly can help save time in the long run and is also pretty exciting!

Break problems down into smaller issues

Organizational challenges and problems are often complicated and large scale in nature. Sometimes, trying to resolve such an issue in one swoop is simply unachievable or overwhelming. Try breaking down such problems into smaller issues that you can work on step by step. You may not be able to solve the problem of churning customers off the bat, but you can work with your team to identify smaller effort but high impact elements and work on those first.

This problem solving strategy can help a team generate momentum, prioritize and get some easy wins. It’s also a great strategy to employ with teams who are just beginning to learn how to approach the problem solving process. If you want some insight into a way to employ this strategy, we recommend looking at our design sprint template below!

Use guiding frameworks or try new methodologies

Some problems are best solved by introducing a major shift in perspective or by using new methodologies that encourage your team to think differently.

Props and tools such as Methodkit , which uses a card-based toolkit for facilitation, or Lego Serious Play can be great ways to engage your team and find an inclusive, democratic problem solving strategy. Remember that play and creativity are great tools for achieving change and whatever the challenge, engaging your participants can be very effective where other strategies may have failed.

LEGO Serious Play

• Improving core problem solving skills
• Thinking outside of the box
• Encouraging creative solutions

LEGO Serious Play is a problem solving methodology designed to get participants thinking differently by using 3D models and kinesthetic learning styles. By physically building LEGO models based on questions and exercises, participants are encouraged to think outside of the box and create their own responses. 

Collaborate LEGO Serious Play exercises are also used to encourage communication and build problem solving skills in a group. By using this problem solving process, you can often help different kinds of learners and personality types contribute and unblock organizational problems with creative thinking. 

Problem solving strategies like LEGO Serious Play are super effective at helping a team solve more skills-based problems such as communication between teams or a lack of creative thinking. Some problems are not suited to LEGO Serious Play and require a different problem solving strategy.

Card Decks and Method Kits

• New facilitators or non-facilitators 
• Approaching difficult subjects with a simple, creative framework
• Engaging those with varied learning styles

Card decks and method kids are great tools for those new to facilitation or for whom facilitation is not the primary role. Card decks such as the emotional culture deck can be used for complete workshops and in many cases, can be used right out of the box. Methodkit has a variety of kits designed for scenarios ranging from personal development through to personas and global challenges so you can find the right deck for your particular needs.

Having an easy to use framework that encourages creativity or a new approach can take some of the friction or planning difficulties out of the workshop process and energize a team in any setting. Simplicity is the key with these methods. By ensuring everyone on your team can get involved and engage with the process as quickly as possible can really contribute to the success of your problem solving strategy.

Source external advice

Looking to peers, experts and external facilitators can be a great way of approaching the problem solving process. Your team may not have the necessary expertise, insights of experience to tackle some issues, or you might simply benefit from a fresh perspective. Some problems may require bringing together an entire team, and coaching managers or team members individually might be the right approach. Remember that not all problems are best resolved in the same manner.

If you’re a solo entrepreneur, peer groups, coaches and mentors can also be invaluable at not only solving specific business problems, but in providing a support network for resolving future challenges. One great approach is to join a Mastermind Group and link up with like-minded individuals and all grow together. Remember that however you approach the sourcing of external advice, do so thoughtfully, respectfully and honestly. Reciprocate where you can and prepare to be surprised by just how kind and helpful your peers can be!

Mastermind Group

• Solo entrepreneurs or small teams with low capacity
• Peer learning and gaining outside expertise
• Getting multiple external points of view quickly

Problem solving in large organizations with lots of skilled team members is one thing, but how about if you work for yourself or in a very small team without the capacity to get the most from a design sprint or LEGO Serious Play session? 

A mastermind group – sometimes known as a peer advisory board – is where a group of people come together to support one another in their own goals, challenges, and businesses. Each participant comes to the group with their own purpose and the other members of the group will help them create solutions, brainstorm ideas, and support one another. 

Mastermind groups are very effective in creating an energized, supportive atmosphere that can deliver meaningful results. Learning from peers from outside of your organization or industry can really help unlock new ways of thinking and drive growth. Access to the experience and skills of your peers can be invaluable in helping fill the gaps in your own ability, particularly in young companies.

A mastermind group is a great solution for solo entrepreneurs, small teams, or for organizations that feel that external expertise or fresh perspectives will be beneficial for them. It is worth noting that Mastermind groups are often only as good as the participants and what they can bring to the group. Participants need to be committed, engaged and understand how to work in this context. 

Coaching and mentoring

• Focused learning and development
• Filling skills gaps
• Working on a range of challenges over time

Receiving advice from a business coach or building a mentor/mentee relationship can be an effective way of resolving certain challenges. The one-to-one format of most coaching and mentor relationships can really help solve the challenges those individuals are having and benefit the organization as a result.

A great mentor can be invaluable when it comes to spotting potential problems before they arise and coming to understand a mentee very well has a host of other business benefits. You might run an internal mentorship program to help develop your team’s problem solving skills and strategies or as part of a large learning and development program. External coaches can also be an important part of your problem solving strategy, filling skills gaps for your management team or helping with specific business issues. 

Now we’ve explored the problem solving process and the steps you will want to go through in order to have an effective session, let’s look at the skills you and your team need to be more effective problem solvers.

Problem solving skills are highly sought after, whatever industry or team you work in. Organizations are keen to employ people who are able to approach problems thoughtfully and find strong, realistic solutions. Whether you are a facilitator , a team leader or a developer, being an effective problem solver is a skill you’ll want to develop.

Problem solving skills form a whole suite of techniques and approaches that an individual uses to not only identify problems but to discuss them productively before then developing appropriate solutions.

Here are some of the most important problem solving skills everyone from executives to junior staff members should learn. We’ve also included an activity or exercise from the SessionLab library that can help you and your team develop that skill. 

If you’re running a workshop or training session to try and improve problem solving skills in your team, try using these methods to supercharge your process!

Active listening

Active listening is one of the most important skills anyone who works with people can possess. In short, active listening is a technique used to not only better understand what is being said by an individual, but also to be more aware of the underlying message the speaker is trying to convey. When it comes to problem solving, active listening is integral for understanding the position of every participant and to clarify the challenges, ideas and solutions they bring to the table.

Some active listening skills include:

• Paying complete attention to the speaker.
• Removing distractions.
• Avoid interruption.
• Taking the time to fully understand before preparing a rebuttal.
• Responding respectfully and appropriately.
• Demonstrate attentiveness and positivity with an open posture, making eye contact with the speaker, smiling and nodding if appropriate. Show that you are listening and encourage them to continue.
• Be aware of and respectful of feelings. Judge the situation and respond appropriately. You can disagree without being disrespectful.   
• Observe body language. 
• Paraphrase what was said in your own words, either mentally or verbally.
• Remain neutral. 
• Reflect and take a moment before responding.
• Ask deeper questions based on what is said and clarify points where necessary.   

Active Listening   #hyperisland   #skills   #active listening   #remote-friendly   This activity supports participants to reflect on a question and generate their own solutions using simple principles of active listening and peer coaching. It’s an excellent introduction to active listening but can also be used with groups that are already familiar with it. Participants work in groups of three and take turns being: “the subject”, the listener, and the observer.

Analytical skills

All problem solving models require strong analytical skills, particularly during the beginning of the process and when it comes to analyzing how solutions have performed.

Analytical skills are primarily focused on performing an effective analysis by collecting, studying and parsing data related to a problem or opportunity. 

It often involves spotting patterns, being able to see things from different perspectives and using observable facts and data to make suggestions or produce insight. 

Analytical skills are also important at every stage of the problem solving process and by having these skills, you can ensure that any ideas or solutions you create or backed up analytically and have been sufficiently thought out.

Nine Whys   #innovation   #issue analysis   #liberating structures   With breathtaking simplicity, you can rapidly clarify for individuals and a group what is essentially important in their work. You can quickly reveal when a compelling purpose is missing in a gathering and avoid moving forward without clarity. When a group discovers an unambiguous shared purpose, more freedom and more responsibility are unleashed. You have laid the foundation for spreading and scaling innovations with fidelity.

Collaboration

Trying to solve problems on your own is difficult. Being able to collaborate effectively, with a free exchange of ideas, to delegate and be a productive member of a team is hugely important to all problem solving strategies.

Remember that whatever your role, collaboration is integral, and in a problem solving process, you are all working together to find the best solution for everyone. 

Marshmallow challenge with debriefing   #teamwork   #team   #leadership   #collaboration   In eighteen minutes, teams must build the tallest free-standing structure out of 20 sticks of spaghetti, one yard of tape, one yard of string, and one marshmallow. The marshmallow needs to be on top. The Marshmallow Challenge was developed by Tom Wujec, who has done the activity with hundreds of groups around the world. Visit the Marshmallow Challenge website for more information. This version has an extra debriefing question added with sample questions focusing on roles within the team.

Communication  

Being an effective communicator means being empathetic, clear and succinct, asking the right questions, and demonstrating active listening skills throughout any discussion or meeting. 

In a problem solving setting, you need to communicate well in order to progress through each stage of the process effectively. As a team leader, it may also fall to you to facilitate communication between parties who may not see eye to eye. Effective communication also means helping others to express themselves and be heard in a group.

Bus Trip   #feedback   #communication   #appreciation   #closing   #thiagi   #team   This is one of my favourite feedback games. I use Bus Trip at the end of a training session or a meeting, and I use it all the time. The game creates a massive amount of energy with lots of smiles, laughs, and sometimes even a teardrop or two.

Creative problem solving skills can be some of the best tools in your arsenal. Thinking creatively, being able to generate lots of ideas and come up with out of the box solutions is useful at every step of the process. 

The kinds of problems you will likely discuss in a problem solving workshop are often difficult to solve, and by approaching things in a fresh, creative manner, you can often create more innovative solutions.

Having practical creative skills is also a boon when it comes to problem solving. If you can help create quality design sketches and prototypes in record time, it can help bring a team to alignment more quickly or provide a base for further iteration.

The paper clip method   #sharing   #creativity   #warm up   #idea generation   #brainstorming   The power of brainstorming. A training for project leaders, creativity training, and to catalyse getting new solutions.

Critical thinking

Critical thinking is one of the fundamental problem solving skills you’ll want to develop when working on developing solutions. Critical thinking is the ability to analyze, rationalize and evaluate while being aware of personal bias, outlying factors and remaining open-minded.

Defining and analyzing problems without deploying critical thinking skills can mean you and your team go down the wrong path. Developing solutions to complex issues requires critical thinking too – ensuring your team considers all possibilities and rationally evaluating them. 

Agreement-Certainty Matrix   #issue analysis   #liberating structures   #problem solving   You can help individuals or groups avoid the frequent mistake of trying to solve a problem with methods that are not adapted to the nature of their challenge. The combination of two questions makes it possible to easily sort challenges into four categories: simple, complicated, complex , and chaotic .  A problem is simple when it can be solved reliably with practices that are easy to duplicate.  It is complicated when experts are required to devise a sophisticated solution that will yield the desired results predictably.  A problem is complex when there are several valid ways to proceed but outcomes are not predictable in detail.  Chaotic is when the context is too turbulent to identify a path forward.  A loose analogy may be used to describe these differences: simple is like following a recipe, complicated like sending a rocket to the moon, complex like raising a child, and chaotic is like the game “Pin the Tail on the Donkey.”  The Liberating Structures Matching Matrix in Chapter 5 can be used as the first step to clarify the nature of a challenge and avoid the mismatches between problems and solutions that are frequently at the root of chronic, recurring problems.

Data analysis 

Though it shares lots of space with general analytical skills, data analysis skills are something you want to cultivate in their own right in order to be an effective problem solver.

Being good at data analysis doesn’t just mean being able to find insights from data, but also selecting the appropriate data for a given issue, interpreting it effectively and knowing how to model and present that data. Depending on the problem at hand, it might also include a working knowledge of specific data analysis tools and procedures. 

Having a solid grasp of data analysis techniques is useful if you’re leading a problem solving workshop but if you’re not an expert, don’t worry. Bring people into the group who has this skill set and help your team be more effective as a result.

Decision making

All problems need a solution and all solutions require that someone make the decision to implement them. Without strong decision making skills, teams can become bogged down in discussion and less effective as a result. 

Making decisions is a key part of the problem solving process. It’s important to remember that decision making is not restricted to the leadership team. Every staff member makes decisions every day and developing these skills ensures that your team is able to solve problems at any scale. Remember that making decisions does not mean leaping to the first solution but weighing up the options and coming to an informed, well thought out solution to any given problem that works for the whole team.

Lightning Decision Jam (LDJ)   #action   #decision making   #problem solving   #issue analysis   #innovation   #design   #remote-friendly   The problem with anything that requires creative thinking is that it’s easy to get lost—lose focus and fall into the trap of having useless, open-ended, unstructured discussions. Here’s the most effective solution I’ve found: Replace all open, unstructured discussion with a clear process. What to use this exercise for: Anything which requires a group of people to make decisions, solve problems or discuss challenges. It’s always good to frame an LDJ session with a broad topic, here are some examples: The conversion flow of our checkout Our internal design process How we organise events Keeping up with our competition Improving sales flow

Dependability

Most complex organizational problems require multiple people to be involved in delivering the solution. Ensuring that the team and organization can depend on you to take the necessary actions and communicate where necessary is key to ensuring problems are solved effectively.

Being dependable also means working to deadlines and to brief. It is often a matter of creating trust in a team so that everyone can depend on one another to complete the agreed actions in the agreed time frame so that the team can move forward together. Being undependable can create problems of friction and can limit the effectiveness of your solutions so be sure to bear this in mind throughout a project. 

Team Purpose & Culture   #team   #hyperisland   #culture   #remote-friendly   This is an essential process designed to help teams define their purpose (why they exist) and their culture (how they work together to achieve that purpose). Defining these two things will help any team to be more focused and aligned. With support of tangible examples from other companies, the team members work as individuals and a group to codify the way they work together. The goal is a visual manifestation of both the purpose and culture that can be put up in the team’s work space.

Emotional intelligence

Emotional intelligence is an important skill for any successful team member, whether communicating internally or with clients or users. In the problem solving process, emotional intelligence means being attuned to how people are feeling and thinking, communicating effectively and being self-aware of what you bring to a room. 

There are often differences of opinion when working through problem solving processes, and it can be easy to let things become impassioned or combative. Developing your emotional intelligence means being empathetic to your colleagues and managing your own emotions throughout the problem and solution process. Be kind, be thoughtful and put your points across care and attention. 

Being emotionally intelligent is a skill for life and by deploying it at work, you can not only work efficiently but empathetically. Check out the emotional culture workshop template for more!

Facilitation

As we’ve clarified in our facilitation skills post, facilitation is the art of leading people through processes towards agreed-upon objectives in a manner that encourages participation, ownership, and creativity by all those involved. While facilitation is a set of interrelated skills in itself, the broad definition of facilitation can be invaluable when it comes to problem solving. Leading a team through a problem solving process is made more effective if you improve and utilize facilitation skills – whether you’re a manager, team leader or external stakeholder.

The Six Thinking Hats   #creative thinking   #meeting facilitation   #problem solving   #issue resolution   #idea generation   #conflict resolution   The Six Thinking Hats are used by individuals and groups to separate out conflicting styles of thinking. They enable and encourage a group of people to think constructively together in exploring and implementing change, rather than using argument to fight over who is right and who is wrong.

Flexibility 

Being flexible is a vital skill when it comes to problem solving. This does not mean immediately bowing to pressure or changing your opinion quickly: instead, being flexible is all about seeing things from new perspectives, receiving new information and factoring it into your thought process.

Flexibility is also important when it comes to rolling out solutions. It might be that other organizational projects have greater priority or require the same resources as your chosen solution. Being flexible means understanding needs and challenges across the team and being open to shifting or arranging your own schedule as necessary. Again, this does not mean immediately making way for other projects. It’s about articulating your own needs, understanding the needs of others and being able to come to a meaningful compromise.

The Creativity Dice   #creativity   #problem solving   #thiagi   #issue analysis   Too much linear thinking is hazardous to creative problem solving. To be creative, you should approach the problem (or the opportunity) from different points of view. You should leave a thought hanging in mid-air and move to another. This skipping around prevents premature closure and lets your brain incubate one line of thought while you consciously pursue another.

Working in any group can lead to unconscious elements of groupthink or situations in which you may not wish to be entirely honest. Disagreeing with the opinions of the executive team or wishing to save the feelings of a coworker can be tricky to navigate, but being honest is absolutely vital when to comes to developing effective solutions and ensuring your voice is heard. 

Remember that being honest does not mean being brutally candid. You can deliver your honest feedback and opinions thoughtfully and without creating friction by using other skills such as emotional intelligence. 

Explore your Values   #hyperisland   #skills   #values   #remote-friendly   Your Values is an exercise for participants to explore what their most important values are. It’s done in an intuitive and rapid way to encourage participants to follow their intuitive feeling rather than over-thinking and finding the “correct” values. It is a good exercise to use to initiate reflection and dialogue around personal values.

Initiative 

The problem solving process is multi-faceted and requires different approaches at certain points of the process. Taking initiative to bring problems to the attention of the team, collect data or lead the solution creating process is always valuable. You might even roadtest your own small scale solutions or brainstorm before a session. Taking initiative is particularly effective if you have good deal of knowledge in that area or have ownership of a particular project and want to get things kickstarted.

That said, be sure to remember to honor the process and work in service of the team. If you are asked to own one part of the problem solving process and you don’t complete that task because your initiative leads you to work on something else, that’s not an effective method of solving business challenges.

15% Solutions   #action   #liberating structures   #remote-friendly   You can reveal the actions, however small, that everyone can do immediately. At a minimum, these will create momentum, and that may make a BIG difference.  15% Solutions show that there is no reason to wait around, feel powerless, or fearful. They help people pick it up a level. They get individuals and the group to focus on what is within their discretion instead of what they cannot change.  With a very simple question, you can flip the conversation to what can be done and find solutions to big problems that are often distributed widely in places not known in advance. Shifting a few grains of sand may trigger a landslide and change the whole landscape.

Impartiality

A particularly useful problem solving skill for product owners or managers is the ability to remain impartial throughout much of the process. In practice, this means treating all points of view and ideas brought forward in a meeting equally and ensuring that your own areas of interest or ownership are not favored over others. 

There may be a stage in the process where a decision maker has to weigh the cost and ROI of possible solutions against the company roadmap though even then, ensuring that the decision made is based on merit and not personal opinion. 

Empathy map   #frame insights   #create   #design   #issue analysis   An empathy map is a tool to help a design team to empathize with the people they are designing for. You can make an empathy map for a group of people or for a persona. To be used after doing personas when more insights are needed.

Being a good leader means getting a team aligned, energized and focused around a common goal. In the problem solving process, strong leadership helps ensure that the process is efficient, that any conflicts are resolved and that a team is managed in the direction of success.

It’s common for managers or executives to assume this role in a problem solving workshop, though it’s important that the leader maintains impartiality and does not bulldoze the group in a particular direction. Remember that good leadership means working in service of the purpose and team and ensuring the workshop is a safe space for employees of any level to contribute. Take a look at our leadership games and activities post for more exercises and methods to help improve leadership in your organization.

Leadership Pizza   #leadership   #team   #remote-friendly   This leadership development activity offers a self-assessment framework for people to first identify what skills, attributes and attitudes they find important for effective leadership, and then assess their own development and initiate goal setting.

In the context of problem solving, mediation is important in keeping a team engaged, happy and free of conflict. When leading or facilitating a problem solving workshop, you are likely to run into differences of opinion. Depending on the nature of the problem, certain issues may be brought up that are emotive in nature. 

Being an effective mediator means helping those people on either side of such a divide are heard, listen to one another and encouraged to find common ground and a resolution. Mediating skills are useful for leaders and managers in many situations and the problem solving process is no different.

Conflict Responses   #hyperisland   #team   #issue resolution   A workshop for a team to reflect on past conflicts, and use them to generate guidelines for effective conflict handling. The workshop uses the Thomas-Killman model of conflict responses to frame a reflective discussion. Use it to open up a discussion around conflict with a team.

Planning 

Solving organizational problems is much more effective when following a process or problem solving model. Planning skills are vital in order to structure, deliver and follow-through on a problem solving workshop and ensure your solutions are intelligently deployed.

Planning skills include the ability to organize tasks and a team, plan and design the process and take into account any potential challenges. Taking the time to plan carefully can save time and frustration later in the process and is valuable for ensuring a team is positioned for success.

3 Action Steps   #hyperisland   #action   #remote-friendly   This is a small-scale strategic planning session that helps groups and individuals to take action toward a desired change. It is often used at the end of a workshop or programme. The group discusses and agrees on a vision, then creates some action steps that will lead them towards that vision. The scope of the challenge is also defined, through discussion of the helpful and harmful factors influencing the group.

Prioritization

As organisations grow, the scale and variation of problems they face multiplies. Your team or is likely to face numerous challenges in different areas and so having the skills to analyze and prioritize becomes very important, particularly for those in leadership roles.

A thorough problem solving process is likely to deliver multiple solutions and you may have several different problems you wish to solve simultaneously. Prioritization is the ability to measure the importance, value, and effectiveness of those possible solutions and choose which to enact and in what order. The process of prioritization is integral in ensuring the biggest challenges are addressed with the most impactful solutions.

Impact and Effort Matrix   #gamestorming   #decision making   #action   #remote-friendly   In this decision-making exercise, possible actions are mapped based on two factors: effort required to implement and potential impact. Categorizing ideas along these lines is a useful technique in decision making, as it obliges contributors to balance and evaluate suggested actions before committing to them.

Project management

Some problem solving skills are utilized in a workshop or ideation phases, while others come in useful when it comes to decision making. Overseeing an entire problem solving process and ensuring its success requires strong project management skills. 

While project management incorporates many of the other skills listed here, it is important to note the distinction of considering all of the factors of a project and managing them successfully. Being able to negotiate with stakeholders, manage tasks, time and people, consider costs and ROI, and tie everything together is massively helpful when going through the problem solving process. 

Record keeping

Working out meaningful solutions to organizational challenges is only one part of the process.  Thoughtfully documenting and keeping records of each problem solving step for future consultation is important in ensuring efficiency and meaningful change. 

For example, some problems may be lower priority than others but can be revisited in the future. If the team has ideated on solutions and found some are not up to the task, record those so you can rule them out and avoiding repeating work. Keeping records of the process also helps you improve and refine your problem solving model next time around!

Personal Kanban   #gamestorming   #action   #agile   #project planning   Personal Kanban is a tool for organizing your work to be more efficient and productive. It is based on agile methods and principles.

Research skills

Conducting research to support both the identification of problems and the development of appropriate solutions is important for an effective process. Knowing where to go to collect research, how to conduct research efficiently, and identifying pieces of research are relevant are all things a good researcher can do well. 

In larger groups, not everyone has to demonstrate this ability in order for a problem solving workshop to be effective. That said, having people with research skills involved in the process, particularly if they have existing area knowledge, can help ensure the solutions that are developed with data that supports their intention. Remember that being able to deliver the results of research efficiently and in a way the team can easily understand is also important. The best data in the world is only as effective as how it is delivered and interpreted.

Customer experience map   #ideation   #concepts   #research   #design   #issue analysis   #remote-friendly   Customer experience mapping is a method of documenting and visualizing the experience a customer has as they use the product or service. It also maps out their responses to their experiences. To be used when there is a solution (even in a conceptual stage) that can be analyzed.

Risk management

Managing risk is an often overlooked part of the problem solving process. Solutions are often developed with the intention of reducing exposure to risk or solving issues that create risk but sometimes, great solutions are more experimental in nature and as such, deploying them needs to be carefully considered. 

Managing risk means acknowledging that there may be risks associated with more out of the box solutions or trying new things, but that this must be measured against the possible benefits and other organizational factors. 

Be informed, get the right data and stakeholders in the room and you can appropriately factor risk into your decision making process. 

Decisions, Decisions…   #communication   #decision making   #thiagi   #action   #issue analysis   When it comes to decision-making, why are some of us more prone to take risks while others are risk-averse? One explanation might be the way the decision and options were presented.  This exercise, based on Kahneman and Tversky’s classic study , illustrates how the framing effect influences our judgement and our ability to make decisions . The participants are divided into two groups. Both groups are presented with the same problem and two alternative programs for solving them. The two programs both have the same consequences but are presented differently. The debriefing discussion examines how the framing of the program impacted the participant’s decision.

Team-building 

No single person is as good at problem solving as a team. Building an effective team and helping them come together around a common purpose is one of the most important problem solving skills, doubly so for leaders. By bringing a team together and helping them work efficiently, you pave the way for team ownership of a problem and the development of effective solutions. 

In a problem solving workshop, it can be tempting to jump right into the deep end, though taking the time to break the ice, energize the team and align them with a game or exercise will pay off over the course of the day.

Remember that you will likely go through the problem solving process multiple times over an organization’s lifespan and building a strong team culture will make future problem solving more effective. It’s also great to work with people you know, trust and have fun with. Working on team building in and out of the problem solving process is a hallmark of successful teams that can work together to solve business problems.

9 Dimensions Team Building Activity   #ice breaker   #teambuilding   #team   #remote-friendly   9 Dimensions is a powerful activity designed to build relationships and trust among team members. There are 2 variations of this icebreaker. The first version is for teams who want to get to know each other better. The second version is for teams who want to explore how they are working together as a team.

Time management 

The problem solving process is designed to lead a team from identifying a problem through to delivering a solution and evaluating its effectiveness. Without effective time management skills or timeboxing of tasks, it can be easy for a team to get bogged down or be inefficient.

By using a problem solving model and carefully designing your workshop, you can allocate time efficiently and trust that the process will deliver the results you need in a good timeframe.

Time management also comes into play when it comes to rolling out solutions, particularly those that are experimental in nature. Having a clear timeframe for implementing and evaluating solutions is vital for ensuring their success and being able to pivot if necessary.

Improving your skills at problem solving is often a career-long pursuit though there are methods you can use to make the learning process more efficient and to supercharge your problem solving skillset.

Remember that the skills you need to be a great problem solver have a large overlap with those skills you need to be effective in any role. Investing time and effort to develop your active listening or critical thinking skills is valuable in any context. Here are 7 ways to improve your problem solving skills.

Share best practices

Remember that your team is an excellent source of skills, wisdom, and techniques and that you should all take advantage of one another where possible. Best practices that one team has for solving problems, conducting research or making decisions should be shared across the organization. If you have in-house staff that have done active listening training or are data analysis pros, have them lead a training session. 

Your team is one of your best resources. Create space and internal processes for the sharing of skills so that you can all grow together. 

Ask for help and attend training

Once you’ve figured out you have a skills gap, the next step is to take action to fill that skills gap. That might be by asking your superior for training or coaching, or liaising with team members with that skill set. You might even attend specialized training for certain skills – active listening or critical thinking, for example, are business-critical skills that are regularly offered as part of a training scheme.

Whatever method you choose, remember that taking action of some description is necessary for growth. Whether that means practicing, getting help, attending training or doing some background reading, taking active steps to improve your skills is the way to go.

Learn a process 

Problem solving can be complicated, particularly when attempting to solve large problems for the first time. Using a problem solving process helps give structure to your problem solving efforts and focus on creating outcomes, rather than worrying about the format. 

Tools such as the seven-step problem solving process above are effective because not only do they feature steps that will help a team solve problems, they also develop skills along the way. Each step asks for people to engage with the process using different skills and in doing so, helps the team learn and grow together. Group processes of varying complexity and purpose can also be found in the SessionLab library of facilitation techniques . Using a tried and tested process and really help ease the learning curve for both those leading such a process, as well as those undergoing the purpose.

Effective teams make decisions about where they should and shouldn’t expend additional effort. By using a problem solving process, you can focus on the things that matter, rather than stumbling towards a solution haphazardly. 

Create a feedback loop

Some skills gaps are more obvious than others. It’s possible that your perception of your active listening skills differs from those of your colleagues. 

It’s valuable to create a system where team members can provide feedback in an ordered and friendly manner so they can all learn from one another. Only by identifying areas of improvement can you then work to improve them. 

Remember that feedback systems require oversight and consideration so that they don’t turn into a place to complain about colleagues. Design the system intelligently so that you encourage the creation of learning opportunities, rather than encouraging people to list their pet peeves.

While practice might not make perfect, it does make the problem solving process easier. If you are having trouble with critical thinking, don’t shy away from doing it. Get involved where you can and stretch those muscles as regularly as possible. 

Problem solving skills come more naturally to some than to others and that’s okay. Take opportunities to get involved and see where you can practice your skills in situations outside of a workshop context. Try collaborating in other circumstances at work or conduct data analysis on your own projects. You can often develop those skills you need for problem solving simply by doing them. Get involved!

Use expert exercises and methods

Learn from the best. Our library of 700+ facilitation techniques is full of activities and methods that help develop the skills you need to be an effective problem solver. Check out our templates to see how to approach problem solving and other organizational challenges in a structured and intelligent manner.

There is no single approach to improving problem solving skills, but by using the techniques employed by others you can learn from their example and develop processes that have seen proven results. 

Try new ways of thinking and change your mindset

Using tried and tested exercises that you know well can help deliver results, but you do run the risk of missing out on the learning opportunities offered by new approaches. As with the problem solving process, changing your mindset can remove blockages and be used to develop your problem solving skills.

Most teams have members with mixed skill sets and specialties. Mix people from different teams and share skills and different points of view. Teach your customer support team how to use design thinking methods or help your developers with conflict resolution techniques. Try switching perspectives with facilitation techniques like Flip It! or by using new problem solving methodologies or models. Give design thinking, liberating structures or lego serious play a try if you want to try a new approach. You will find that framing problems in new ways and using existing skills in new contexts can be hugely useful for personal development and improving your skillset. It’s also a lot of fun to try new things. Give it a go!

Encountering business challenges and needing to find appropriate solutions is not unique to your organization. Lots of very smart people have developed methods, theories and approaches to help develop problem solving skills and create effective solutions. Learn from them!

Books like The Art of Thinking Clearly , Think Smarter, or Thinking Fast, Thinking Slow are great places to start, though it’s also worth looking at blogs related to organizations facing similar problems to yours, or browsing for success stories. Seeing how Dropbox massively increased growth and working backward can help you see the skills or approach you might be lacking to solve that same problem. Learning from others by reading their stories or approaches can be time-consuming but ultimately rewarding.

A tired, distracted mind is not in the best position to learn new skills. It can be tempted to burn the candle at both ends and develop problem solving skills outside of work. Absolutely use your time effectively and take opportunities for self-improvement, though remember that rest is hugely important and that without letting your brain rest, you cannot be at your most effective. 

Creating distance between yourself and the problem you might be facing can also be useful. By letting an idea sit, you can find that a better one presents itself or you can develop it further. Take regular breaks when working and create a space for downtime. Remember that working smarter is preferable to working harder and that self-care is important for any effective learning or improvement process.

Want to design better group processes?

Over to you

Now we’ve explored some of the key problem solving skills and the problem solving steps necessary for an effective process, you’re ready to begin developing more effective solutions and leading problem solving workshops.

Need more inspiration? Check out our post on problem solving activities you can use when guiding a group towards a great solution in your next workshop or meeting. Have questions? Did you have a great problem solving technique you use with your team? Get in touch in the comments below. We’d love to chat!

James Smart is Head of Content at SessionLab. He’s also a creative facilitator who has run workshops and designed courses for establishments like the National Centre for Writing, UK. He especially enjoys working with young people and empowering others in their creative practice.

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Going from a mere idea to a workshop that delivers results for your clients can feel like a daunting task. In this piece, we will shine a light on all the work behind the scenes and help you learn how to plan a workshop from start to finish. On a good day, facilitation can feel like effortless magic, but that is mostly the result of backstage work, foresight, and a lot of careful planning. Read on to learn a step-by-step approach to breaking the process of planning a workshop into small, manageable chunks.  The flow starts with the first meeting with a client to define the purposes of a workshop.…

Effective online tools are a necessity for smooth and engaging virtual workshops and meetings. But how do you choose the right ones? Do you sometimes feel that the good old pen and paper or MS Office toolkit and email leaves you struggling to stay on top of managing and delivering your workshop? Fortunately, there are plenty of great workshop tools to make your life easier when you need to facilitate a meeting and lead workshops. In this post, we’ll share our favorite online tools you can use to make your life easier and run better workshops and meetings. In fact, there are plenty of free online workshop tools and meeting…

How does learning work? A clever 9-year-old once told me: “I know I am learning something new when I am surprised.” The science of adult learning tells us that, in order to learn new skills (which, unsurprisingly, is harder for adults to do than kids) grown-ups need to first get into a specific headspace.  In a business, this approach is often employed in a training session where employees learn new skills or work on professional development. But how do you ensure your training is effective? In this guide, we'll explore how to create an effective training session plan and run engaging training sessions. As team leader, project manager, or consultant,…

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Effective Problem-Solving Techniques in Business

Problem solving is an increasingly important soft skill for those in business. The Future of Jobs Survey by the World Economic Forum drives this point home. According to this report, complex problem solving is identified as one of the top 15 skills that will be sought by employers in 2025, along with other soft skills such as analytical thinking, creativity and leadership.

Dr. Amy David , clinical associate professor of management for supply chain and operations management, spoke about business problem-solving methods and how the Purdue University Online MBA program prepares students to be business decision-makers.

Why Are Problem-Solving Skills Essential in Leadership Roles?

Every business will face challenges at some point. Those that are successful will have people in place who can identify and solve problems before the damage is done.

“The business world is constantly changing, and companies need to be able to adapt well in order to produce good results and meet the needs of their customers,” David says. “They also need to keep in mind the triple bottom line of ‘people, profit and planet.’ And these priorities are constantly evolving.”

To that end, David says people in management or leadership need to be able to handle new situations, something that may be outside the scope of their everyday work.

“The name of the game these days is change—and the speed of change—and that means solving new problems on a daily basis,” she says.

The pace of information and technology has also empowered the customer in a new way that provides challenges—or opportunities—for businesses to respond.

“Our customers have a lot more information and a lot more power,” she says. “If you think about somebody having an unhappy experience and tweeting about it, that’s very different from maybe 15 years ago. Back then, if you had a bad experience with a product, you might grumble about it to one or two people.”

David says that this reality changes how quickly organizations need to react and respond to their customers. And taking prompt and decisive action requires solid problem-solving skills.

What Are Some of the Most Effective Problem-Solving Methods?

David says there are a few things to consider when encountering a challenge in business.

“When faced with a problem, are we talking about something that is broad and affects a lot of people? Or is it something that affects a select few? Depending on the issue and situation, you’ll need to use different types of problem-solving strategies,” she says.

Using Techniques

There are a number of techniques that businesses use to problem solve. These can include:

• Five Whys : This approach is helpful when the problem at hand is clear but the underlying causes are less so. By asking “Why?” five times, the final answer should get at the potential root of the problem and perhaps yield a solution.
• Gap Analysis : Companies use gap analyses to compare current performance with expected or desired performance, which will help a company determine how to use its resources differently or adjust expectations.
• Gemba Walk : The name, which is derived from a Japanese word meaning “the real place,” refers to a commonly used technique that allows managers to see what works (and what doesn’t) from the ground up. This is an opportunity for managers to focus on the fundamental elements of the process, identify where the value stream is and determine areas that could use improvement.
• Porter’s Five Forces : Developed by Harvard Business School professor Michael E. Porter, applying the Five Forces is a way for companies to identify competitors for their business or services, and determine how the organization can adjust to stay ahead of the game.
• Six Thinking Hats : In his book of the same name, Dr. Edward de Bono details this method that encourages parallel thinking and attempting to solve a problem by trying on different “thinking hats.” Each color hat signifies a different approach that can be utilized in the problem-solving process, ranging from logic to feelings to creativity and beyond. This method allows organizations to view problems from different angles and perspectives.
• SWOT Analysis : This common strategic planning and management tool helps businesses identify strengths, weaknesses, opportunities and threats (SWOT).

“We have a lot of these different tools,” David says. “Which one to use when is going to be dependent on the problem itself, the level of the stakeholders, the number of different stakeholder groups and so on.”

Each of the techniques outlined above uses the same core steps of problem solving:

• Identify and define the problem
• Consider possible solutions
• Evaluate options
• Choose the best solution
• Implement the solution
• Evaluate the outcome

Data drives a lot of daily decisions in business and beyond. Analytics have also been deployed to problem solve.

“We have specific classes around storytelling with data and how you convince your audience to understand what the data is,” David says. “Your audience has to trust the data, and only then can you use it for real decision-making.”

Data can be a powerful tool for identifying larger trends and making informed decisions when it’s clearly understood and communicated. It’s also vital for performance monitoring and optimization.

How Is Problem Solving Prioritized in Purdue’s Online MBA?

The courses in the Purdue Online MBA program teach problem-solving methods to students, keeping them up to date with the latest techniques and allowing them to apply their knowledge to business-related scenarios.

“I can give you a model or a tool, but most of the time, a real-world situation is going to be a lot messier and more valuable than what we’ve seen in a textbook,” David says. “Asking students to take what they know and apply it to a case where there’s not one single correct answer is a big part of the learning experience.”

Make Your Own Decision to Further Your Career

An online MBA from Purdue University can help advance your career by teaching you problem-solving skills, decision-making strategies and more. Reach out today to learn more about earning an online MBA with Purdue University .

If you would like to receive more information about pursuing a business master’s at the Mitchell E. Daniels, Jr. School of Business, please fill out the form and a program specialist will be in touch!

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• Network Theory Tutorial
• Network Theory - Home

Network Theory - Overview

• Example Problems

Network Theory - Active Elements

Network theory - passive elements, network theory - kirchhoff’s laws, electrical quantity division principles, network theory - nodal analysis, network theory - mesh analysis, network theory - equivalent circuits, equivalent circuits example problem.

• Delta to Star Conversion
• Star to Delta Conversion

Network Theory - Network Topology

Network topology matrices.

• Superposition Theorem
• Thevenin’s Theorem

Network Theory - Norton’s Theorem

Maximum power transfer theorem.

• Response of DC Circuits
• Response of AC Circuits

Network Theory - Series Resonance

• Parallel Resonance

Network Theory - Coupled Circuits

• Two-Port Networks

Two-Port Parameter Conversions

Network theory - filters.

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Network Theory - Quick Guide

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• Network Theory - Discussion
• Selected Reading
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• Computer Glossary

Network theory is the study of solving the problems of electric circuits or electric networks. In this introductory chapter, let us first discuss the basic terminology of electric circuits and the types of network elements.

Basic Terminology

In Network Theory, we will frequently come across the following terms −

Electric Circuit

Electric network.

So, it is imperative that we gather some basic knowledge on these terms before proceeding further. Let’s start with Electric Circuit.

An electric circuit contains a closed path for providing a flow of electrons from a voltage source or current source. The elements present in an electric circuit will be in series connection, parallel connection , or in any combination of series and parallel connections.

An electric network need not contain a closed path for providing a flow of electrons from a voltage source or current source. Hence, we can conclude that "all electric circuits are electric networks" but the converse need not be true.

The current "I" flowing through a conductor is nothing but the time rate of flow of charge. Mathematically, it can be written as

$$I = \frac{dQ}{dt}$$

Q is the charge and its unit is Coloumb.

t is the time and its unit is second.

As an analogy, electric current can be thought of as the flow of water through a pipe. Current is measured in terms of Ampere .

In general, Electron current flows from negative terminal of source to positive terminal, whereas, Conventional current flows from positive terminal of source to negative terminal.

Electron current is obtained due to the movement of free electrons, whereas, Conventional current is obtained due to the movement of free positive charges. Both of these are called as electric current .

The voltage "V" is nothing but an electromotive force that causes the charge (electrons) to flow. Mathematically, it can be written as

$$V = \frac{dW}{dQ}$$

W is the potential energy and its unit is Joule.

As an analogy, Voltage can be thought of as the pressure of water that causes the water to flow through a pipe. It is measured in terms of Volt .

The power "P" is nothing but the time rate of flow of electrical energy. Mathematically, it can be written as

$$P = \frac{dW}{dt}$$

W is the electrical energy and it is measured in terms of Joule .

t is the time and it is measured in seconds.

We can re-write the above equation a

$$P = \frac{dW}{dt} = \frac{dW}{dQ} \times \frac{dQ}{dt} = VI$$

Therefore, power is nothing but the product of voltage V and current I . Its unit is Watt .

Types of Network Elements

We can classify the Network elements into various types based on some parameters. Following are the types of Network elements −

Active Elements and Passive Elements

Linear Elements and Non-linear Elements

Bilateral Elements and Unilateral Elements

We can classify the Network elements into either active or passive based on the ability of delivering power.

Active Elements deliver power to other elements, which are present in an electric circuit. Sometimes, they may absorb the power like passive elements. That means active elements have the capability of both delivering and absorbing power. Examples : Voltage sources and current sources.

Passive Elements can’t deliver power (energy) to other elements, however they can absorb power. That means these elements either dissipate power in the form of heat or store energy in the form of either magnetic field or electric field. Examples : Resistors, Inductors, and capacitors.

Linear Elements and Non-Linear Elements

We can classify the network elements as linear or non-linear based on their characteristic to obey the property of linearity.

Linear Elements are the elements that show a linear relationship between voltage and current. Examples : Resistors, Inductors, and capacitors.

Non-Linear Elements are those that do not show a linear relation between voltage and current. Examples : Voltage sources and current sources.

Network elements can also be classified as either bilateral or unilateral based on the direction of current flows through the network elements.

Bilateral Elements are the elements that allow the current in both directions and offer the same impedance in either direction of current flow. Examples : Resistors, Inductors and capacitors.

The concept of Bilateral elements is illustrated in the following figures.

In the above figure, the current (I) is flowing from terminals A to B through a passive element having impedance of Z Ω. It is the ratio of voltage (V) across that element between terminals A & B and current (I).

In the above figure, the current (I) is flowing from terminals B to A through a passive element having impedance of Z Ω. That means the current (–I) is flowing from terminals A to B. In this case too, we will get the same impedance value, since both the current and voltage having negative signs with respect to terminals A & B.

Unilateral Elements are those that allow the current in only one direction. Hence, they offer different impedances in both directions.

Network Theory - Example Problems

We discussed the types of network elements in the previous chapter. Now, let us identify the nature of network elements from the V-I characteristics given in the following examples.

The V-I characteristics of a network element is shown below.

Step 1 − Verifying the network element as linear or non-linear .

From the above figure, the V-I characteristics of a network element is a straight line passing through the origin. Hence, it is a Linear element .

Step 2 − Verifying the network element as active or passive .

The given V-I characteristics of a network element lies in the first and third quadrants.

In the first quadrant , the values of both voltage (V) and current (I) are positive. So, the ratios of voltage (V) and current (I) gives positive impedance values.

Similarly, in the third quadrant , the values of both voltage (V) and current (I) have negative values. So, the ratios of voltage (V) and current (I) produce positive impedance values.

Since, the given V-I characteristics offer positive impedance values, the network element is a Passive element .

Step 3 − Verifying the network element as bilateral or unilateral .

For every point (I, V) on the characteristics, there exists a corresponding point (-I, -V) on the given characteristics. Hence, the network element is a Bilateral element .

Therefore, the given V-I characteristics show that the network element is a Linear, Passive , and Bilateral element .

From the above figure, the V-I characteristics of a network element is a straight line only between the points (-3A, -3V) and (5A, 5V). Beyond these points, the V-I characteristics are not following the linear relation. Hence, it is a Non-linear element .

The given V-I characteristics of a network element lies in the first and third quadrants. In these two quadrants, the ratios of voltage (V) and current (I) produce positive impedance values. Hence, the network element is a Passive element .

Consider the point (5A, 5V) on the characteristics. The corresponding point (-5A, -3V) exists on the given characteristics instead of (-5A, -5V). Hence, the network element is a Unilateral element .

Therefore, the given V-I characteristics show that the network element is a Non-linear, Passive , and Unilateral element .

Active Elements are the network elements that deliver power to other elements present in an electric circuit. So, active elements are also called as sources of voltage or current type. We can classify these sources into the following two categories −

Independent Sources

Dependent sources.

As the name suggests, independent sources produce fixed values of voltage or current and these are not dependent on any other parameter. Independent sources can be further divided into the following two categories −

Independent Voltage Sources

Independent current sources.

An independent voltage source produces a constant voltage across its two terminals. This voltage is independent of the amount of current that is flowing through the two terminals of voltage source.

Independent ideal voltage source and its V-I characteristics are shown in the following figure.

The V-I characteristics of an independent ideal voltage source is a constant line, which is always equal to the source voltage (VS) irrespective of the current value (I). So, the internal resistance of an independent ideal voltage source is zero Ohms.

Hence, the independent ideal voltage sources do not exist practically , because there will be some internal resistance.

Independent practical voltage source and its V-I characteristics are shown in the following figure.

There is a deviation in the V-I characteristics of an independent practical voltage source from the V-I characteristics of an independent ideal voltage source. This is due to the voltage drop across the internal resistance (R S ) of an independent practical voltage source.

An independent current source produces a constant current. This current is independent of the voltage across its two terminals. Independent ideal current source and its V-I characteristics are shown in the following figure.

The V-I characteristics of an independent ideal current source is a constant line, which is always equal to the source current (I S ) irrespective of the voltage value (V). So, the internal resistance of an independent ideal current source is infinite ohms.

Hence, the independent ideal current sources do not exist practically , because there will be some internal resistance.

Independent practical current source and its V-I characteristics are shown in the following figure.

There is a deviation in the V-I characteristics of an independent practical current source from the V-I characteristics of an independent ideal current source. This is due to the amount of current flows through the internal shunt resistance (R S ) of an independent practical current source.

As the name suggests, dependent sources produce the amount of voltage or current that is dependent on some other voltage or current. Dependent sources are also called as controlled sources . Dependent sources can be further divided into the following two categories −

Dependent Voltage Sources

Dependent current sources.

A dependent voltage source produces a voltage across its two terminals. The amount of this voltage is dependent on some other voltage or current. Hence, dependent voltage sources can be further classified into the following two categories −

• Voltage Dependent Voltage Source (VDVS)
• Current Dependent Voltage Source (CDVS)

Dependent voltage sources are represented with the signs ‘+’ and ‘-’ inside a diamond shape. The magnitude of the voltage source can be represented outside the diamond shape.

A dependent current source produces a current. The amount of this current is dependent on some other voltage or current. Hence, dependent current sources can be further classified into the following two categories −

• Voltage Dependent Current Source (VDCS)
• Current Dependent Current Source (CDCS)

Dependent current sources are represented with an arrow inside a diamond shape. The magnitude of the current source can be represented outside the diamond shape.

We can observe these dependent or controlled sources in equivalent models of transistors.

Source Transformation Technique

We know that there are two practical sources, namely, voltage source and current source . We can transform (convert) one source into the other based on the requirement, while solving network problems.

The technique of transforming one source into the other is called as source transformation technique . Following are the two possible source transformations −

Practical voltage source into a practical current source

Practical current source into a practical voltage source.

The transformation of practical voltage source into a practical current source is shown in the following figure

Practical voltage source consists of a voltage source (V S ) in series with a resistor (R S ). This can be converted into a practical current source as shown in the figure. It consists of a current source (I S ) in parallel with a resistor (R S ).

The value of IS will be equal to the ratio of V S and R S . Mathematically, it can be represented as

$$I_S = \frac{V_S}{R_S}$$

The transformation of practical current source into a practical voltage source is shown in the following figure.

Practical current source consists of a current source (I S ) in parallel with a resistor (R S ). This can be converted into a practical voltage source as shown in the figure. It consists of a voltage source (V S ) in series with a resistor (R S ).

The value of V S will be equal to the product of I S and R S . Mathematically, it can be represented as

$$V_S = I_S R_S$$

In this chapter, we will discuss in detail about the passive elements such as Resistor, Inductor, and Capacitor. Let us start with Resistors.

The main functionality of Resistor is either opposes or restricts the flow of electric current. Hence, the resistors are used in order to limit the amount of current flow and / or dividing (sharing) voltage.

Let the current flowing through the resistor is I amperes and the voltage across it is V volts. The symbol of resistor along with current, I and voltage, V are shown in the following figure.

According to Ohm’s law , the voltage across resistor is the product of current flowing through it and the resistance of that resistor. Mathematically , it can be represented as

$V = IR$ Equation 1

$\Rightarrow I = \frac{V}{R}$ Equation 2

Where, R is the resistance of a resistor.

From Equation 2, we can conclude that the current flowing through the resistor is directly proportional to the applied voltage across resistor and inversely proportional to the resistance of resistor.

Power in an electric circuit element can be represented as

$P = VI$ Equation 3

Substitute, Equation 1 in Equation 3.

$P = (IR)I$

$\Rightarrow P = I^2 R$ Equation 4

Substitute, Equation 2 in Equation 3.

$P = V \lgroup \frac{V}{R} \rgroup$

$\Rightarrow P = \frac{V^2}{R}$ Equation 5

So, we can calculate the amount of power dissipated in the resistor by using one of the formulae mentioned in Equations 3 to 5.

In general, inductors will have number of turns. Hence, they produce magnetic flux when current flows through it. So, the amount of total magnetic flux produced by an inductor depends on the current, I flowing through it and they have linear relationship.

Mathematically , it can be written as

$$\Psi \: \alpha \: I$$

$$\Rightarrow \Psi = LI$$

Ψ is the total magnetic flux

L is the inductance of an inductor

Let the current flowing through the inductor is I amperes and the voltage across it is V volts. The symbol of inductor along with current I and voltage V are shown in the following figure.

According to Faraday’s law , the voltage across the inductor can be written as

$$V = \frac{d\Psi}{dt}$$

Substitute Ψ = LI in the above equation.

$$V = \frac{d(LI)}{dt}$$

$$\Rightarrow V = L \frac{dI}{dt}$$

$$\Rightarrow I = \frac{1}{L} \int V dt$$

From the above equations, we can conclude that there exists a linear relationship between voltage across inductor and current flowing through it.

We know that power in an electric circuit element can be represented as

Substitute $V = L \frac{dI}{dt}$ in the above equation.

$$P = \lgroup L \frac{dI}{dt}\rgroup I$$

$$\Rightarrow P = LI \frac{dI}{dt}$$

By integrating the above equation, we will get the energy stored in an inductor as

$$W = \frac{1}{2} LI^2$$

So, the inductor stores the energy in the form of magnetic field.

In general, a capacitor has two conducting plates, separated by a dielectric medium. If positive voltage is applied across the capacitor, then it stores positive charge. Similarly, if negative voltage is applied across the capacitor, then it stores negative charge.

So, the amount of charge stored in the capacitor depends on the applied voltage V across it and they have linear relationship. Mathematically, it can be written as

$$Q \: \alpha \: V$$

$$\Rightarrow Q = CV$$

Q is the charge stored in the capacitor.

• C is the capacitance of a capacitor.

Let the current flowing through the capacitor is I amperes and the voltage across it is V volts. The symbol of capacitor along with current I and voltage V are shown in the following figure.

We know that the current is nothing but the time rate of flow of charge . Mathematically, it can be represented as

Substitute $Q = CV$ in the above equation.

$$I = \frac{d(CV)}{dt}$$

$$\Rightarrow I = C \frac{dV}{dt}$$

$$\Rightarrow V = \frac{1}{C} \int I dt$$

From the above equations, we can conclude that there exists a linear relationship between voltage across capacitor and current flowing through it.

Substitute $I = C \frac{dV}{dt}$ in the above equation.

$$P = V \lgroup C \frac{dV}{dt} \rgroup$$

$$\Rightarrow P = CV \frac{dV}{dt}$$

By integrating the above equation, we will get the energy stored in the capacitor as

$$W = \frac{1}{2}CV^2$$

So, the capacitor stores the energy in the form of electric field.

Network elements can be either of active or passive type. Any electrical circuit or network contains one of these two types of network elements or a combination of both.

Now, let us discuss about the following two laws, which are popularly known as Kirchhoff’s laws .

Kirchhoff’s Current Law

Kirchhoff’s voltage law.

Kirchhoff’s Current Law (KCL) states that the algebraic sum of currents leaving (or entering) a node is equal to zero.

A Node is a point where two or more circuit elements are connected to it. If only two circuit elements are connected to a node, then it is said to be simple node. If three or more circuit elements are connected to a node, then it is said to be Principal Node .

Mathematically , KCL can be represented as

$$\displaystyle\sum\limits_{m=1}^M I_m = 0$$

I m is the m th branch current leaving the node.

M is the number of branches that are connected to a node.

The above statement of KCL can also be expressed as "the algebraic sum of currents entering a node is equal to the algebraic sum of currents leaving a node". Let us verify this statement through the following example.

Write KCL equation at node P of the following figure.

In the above figure, the branch currents I 1 , I 2 and I 3 are entering at node P. So, consider negative signs for these three currents.

In the above figure, the branch currents I 4 and I 5 are leaving from node P. So, consider positive signs for these two currents.

The KCL equation at node P will be

$$- I_1 - I_2 - I_3 + I_4 + I_5 = 0$$

$$\Rightarrow I_1 + I_2 + I_3 = I_4 + I_5$$

In the above equation, the left-hand side represents the sum of entering currents, whereas the right-hand side represents the sum of leaving currents.

In this tutorial, we will consider positive sign when the current leaves a node and negative sign when it enters a node. Similarly, you can consider negative sign when the current leaves a node and positive sign when it enters a node. In both cases, the result will be same .

Note − KCL is independent of the nature of network elements that are connected to a node.

Kirchhoff’s Voltage Law (KVL) states that the algebraic sum of voltages around a loop or mesh is equal to zero.

A Loop is a path that terminates at the same node where it started from. In contrast, a Mesh is a loop that doesn’t contain any other loops inside it.

Mathematically, KVL can be represented as

$$\displaystyle\sum\limits_{n=1}^N V_n = 0$$

V n is the n th element’s voltage in a loop (mesh).

N is the number of network elements in the loop (mesh).

The above statement of KVL can also be expressed as "the algebraic sum of voltage sources is equal to the algebraic sum of voltage drops that are present in a loop." Let us verify this statement with the help of the following example.

Write KVL equation around the loop of the following circuit.

The above circuit diagram consists of a voltage source, V S in series with two resistors R 1 and R 2 . The voltage drops across the resistors R 1 and R 2 are V 1 and V 2 respectively.

Apply KVL around the loop.

$$V_S - V_1 - V_2 = 0$$

$$\Rightarrow V_S = V_1 + V_2$$

In the above equation, the left-hand side term represents single voltage source VS. Whereas, the right-hand side represents the sum of voltage drops . In this example, we considered only one voltage source. That’s why the left-hand side contains only one term. If we consider multiple voltage sources, then the left side contains sum of voltage sources.

In this tutorial, we consider the sign of each element’s voltage as the polarity of the second terminal that is present while travelling around the loop. Similarly, you can consider the sign of each voltage as the polarity of the first terminal that is present while travelling around the loop. In both cases, the result will be same .

Note − KVL is independent of the nature of network elements that are present in a loop.

In this chapter, let us discuss about the following two division principles of electrical quantities.

Current Division Principle

Voltage division principle.

When two or more passive elements are connected in parallel, the amount of current that flows through each element gets divided (shared) among themselves from the current that is entering the node.

Consider the following circuit diagram .

The above circuit diagram consists of an input current source I S in parallel with two resistors R 1 and R 2 . The voltage across each element is V S . The currents flowing through the resistors R 1 and R 2 are I 1 and I 2 respectively.

$$I_S = I_1 + I_2$$

Substitute $I_1 = \frac{V_S}{R_1}$ and $I_2 = \frac{V_S}{R_2}$ in the above equation.

$$I_S = \frac{V_S}{R_1} + \frac{V_S}{R_2} = V_S \lgroup \frac {R_2 + R_1 }{R_1 R_2} \rgroup$$

$$\Rightarrow V_S = I_S \lgroup \frac{R_1R_2}{R_1 + R_2} \rgroup$$

Substitute the value of V S in $I_1 = \frac{V_S}{R_1}$.

$$I_1 = \frac{I_S}{R_1}\lgroup \frac{R_1 R_2}{R_1 + R_2} \rgroup$$

$$\Rightarrow I_1 = I_S\lgroup \frac{R_2}{R_1 + R_2} \rgroup$$

Substitute the value of V S in $I_2 = \frac{V_S}{R_2}$.

$$I_2 = \frac{I_S}{R_2} \lgroup \frac{R_1 R_2}{R_1 + R_2} \rgroup$$

$$\Rightarrow I_2 = I_S \lgroup \frac{R_1}{R_1 + R_2} \rgroup$$

From equations of I 1 and I 2 , we can generalize that the current flowing through any passive element can be found by using the following formula.

$$I_N = I_S \lgroup \frac{Z_1\rVert Z_2 \rVert...\rVert Z_{N-1}}{Z_1 + Z_2 + ... + Z_N}\rgroup$$

This is known as current division principle and it is applicable, when two or more passive elements are connected in parallel and only one current enters the node.

I N is the current flowing through the passive element of N th branch.

I S is the input current, which enters the node.

Z 1 , Z 2 , …,Z N are the impedances of 1 st branch, 2 nd branch, …, N th branch respectively.

When two or more passive elements are connected in series, the amount of voltage present across each element gets divided (shared) among themselves from the voltage that is available across that entire combination.

The above circuit diagram consists of a voltage source, V S in series with two resistors R 1 and R 2 . The current flowing through these elements is I S . The voltage drops across the resistors R 1 and R 2 are V 1 and V 2 respectively.

The KVL equation around the loop will be

$$V_S = V_1 + V_2$$

Substitute V 1 = I S R 1 and V 2 = I S R 2 in the above equation

$$V_S = I_S R_1 + I_S R_2 = I_S(R_1 + R_2)$$

$$I_S = \frac{V_S}{R_1 + R_2}$$

Substitute the value of I S in V 1 = I S R 1 .

$$V_1 = \lgroup \frac {V_S}{R_1 + R_2} \rgroup R_1$$

$$\Rightarrow V_1 = V_S \lgroup \frac {R_1}{R_1 + R_2} \rgroup$$

Substitute the value of I S in V 2 = I S R 2 .

$$V_2 = \lgroup \frac {V_S}{R_1 + R_2} \rgroup R_2$$

$$\Rightarrow V_2 = V_S \lgroup \frac {R_2}{R_1 + R_2} \rgroup$$

From equations of V 1 and V 2 , we can generalize that the voltage across any passive element can be found by using the following formula.

$$V_N = V_S \lgroup \frac {Z_N}{Z_1 + Z_2 +....+ Z_N}\rgroup$$

This is known as voltage division principle and it is applicable, when two or more passive elements are connected in series and only one voltage available across the entire combination.

V N is the voltage across N th passive element.

V S is the input voltage, which is present across the entire combination of series passive elements.

Z 1 , Z 2 , …, Z 3 are the impedances of 1 st passive element, 2 nd passive element, …, N th passive element respectively.

There are two basic methods that are used for solving any electrical network: Nodal analysis and Mesh analysis . In this chapter, let us discuss about the Nodal analysis method.

In Nodal analysis, we will consider the node voltages with respect to Ground. Hence, Nodal analysis is also called as Node-voltage method .

Procedure of Nodal Analysis

Follow these steps while solving any electrical network or circuit using Nodal analysis.

Step 1 − Identify the principal nodes and choose one of them as reference node . We will treat that reference node as the Ground.

Step 2 − Label the node voltages with respect to Ground from all the principal nodes except the reference node.

Step 3 − Write nodal equations at all the principal nodes except the reference node. Nodal equation is obtained by applying KCL first and then Ohm’s law.

Step 4 − Solve the nodal equations obtained in Step 3 in order to get the node voltages.

Now, we can find the current flowing through any element and the voltage across any element that is present in the given network by using node voltages.

Find the current flowing through 20 Ω resistor of the following circuit using Nodal analysis .

Step 1 − There are three principle nodes in the above circuit. Those are labelled as 1, 2, and 3 in the following figure.

In the above figure, consider node 3 as reference node (Ground).

Step 2 − The node voltages, V 1 and V 2 , are labelled in the following figure.

In the above figure, V 1 is the voltage from node 1 with respect to ground and V 2 is the voltage from node 2 with respect to ground.

Step 3 − In this case, we will get two nodal equations , since there are two principal nodes, 1 and 2, other than Ground. When we write the nodal equations at a node, assume all the currents are leaving from the node for which the direction of current is not mentioned and that node’s voltage as greater than other node voltages in the circuit.

The nodal equation at node 1 is

$$\frac{V_1 - 20}{5} + \frac{V_1}{10} + \frac{V_1 - V_2}{10} = 0$$

$$\Rightarrow \frac{2 V_1 - 40 + V_1 + V_1 - V_2}{10} = 0$$

$$\Rightarrow 4V_1 - 40 - V_2 = 0$$

$\Rightarrow V_2 = 4V_1 - 40$ Equation 1

The nodal equation at node 2 is

$$-4 + \frac{V_2}{20} + \frac{V_2 - V_1}{10} = 0$$

$$\Rightarrow \frac{-80 + V_2 + 2V_2 - 2V_2}{20} = 0$$

$\Rightarrow 3V_2 − 2V_1 = 80$ Equation 2

Step 4 − Finding node voltages, V 1 and V 2 by solving Equation 1 and Equation 2.

Substitute Equation 1 in Equation 2.

$$3(4 V_1 - 40) - 2 V_1 = 80$$

$$\Rightarrow 12 V_1 - 120 - 2V_1 =80$$

$$\Rightarrow 10 V_1 = 200$$

$$\Rightarrow V_1 = 20V$$

Substitute V 1 = 20 V in Equation1.

$$V_2 = 4(20) - 40$$

$$\Rightarrow V_2 = 40V$$

So, we got the node voltages V 1 and V 2 as 20 V and 40 V respectively.

Step 5 − The voltage across 20 Ω resistor is nothing but the node voltage V 2 and it is equal to 40 V. Now, we can find the current flowing through 20 Ω resistor by using Ohm’s law.

$$I_{20 \Omega} = \frac{V_2}{R}$$

Substitute the values of V 2 and R in the above equation.

$$I_{20 \Omega} = \frac{40}{20}$$

$$\Rightarrow I_{20 \Omega} = 2A$$

Therefore, the current flowing through 20 Ω resistor of given circuit is 2 A .

Note − From the above example, we can conclude that we have to solve ‘n’ nodal equations, if the electric circuit has ‘n’ principal nodes (except the reference node). Therefore, we can choose Nodal analysis when the number of principal nodes (except reference node) is less than the number of meshes of any electrical circuit.

In Mesh analysis, we will consider the currents flowing through each mesh. Hence, Mesh analysis is also called as Mesh-current method .

A branch is a path that joins two nodes and it contains a circuit element. If a branch belongs to only one mesh, then the branch current will be equal to mesh current.

If a branch is common to two meshes, then the branch current will be equal to the sum (or difference) of two mesh currents, when they are in same (or opposite) direction.

Procedure of Mesh Analysis

Follow these steps while solving any electrical network or circuit using Mesh analysis.

Step 1 − Identify the meshes and label the mesh currents in either clockwise or anti-clockwise direction.

Step 2 − Observe the amount of current that flows through each element in terms of mesh currents.

Step 3 − Write mesh equations to all meshes. Mesh equation is obtained by applying KVL first and then Ohm’s law.

Step 4 − Solve the mesh equations obtained in Step 3 in order to get the mesh currents .

Now, we can find the current flowing through any element and the voltage across any element that is present in the given network by using mesh currents.

Find the voltage across 30 Ω resistor using Mesh analysis .

Step 1 − There are two meshes in the above circuit. The mesh currents I 1 and I 2 are considered in clockwise direction. These mesh currents are shown in the following figure.

Step 2 − The mesh current I 1 flows through 20 V voltage source and 5 Ω resistor. Similarly, the mesh current I 2 flows through 30 Ω resistor and -80 V voltage source. But, the difference of two mesh currents, I 1 and I 2 , flows through 10 Ω resistor, since it is the common branch of two meshes.

Step 3 − In this case, we will get two mesh equations since there are two meshes in the given circuit. When we write the mesh equations, assume the mesh current of that particular mesh as greater than all other mesh currents of the circuit.

The mesh equation of first mesh is

$$20 - 5I_1 -10(I_1 - I_2) = 0$$

$$\Rightarrow 20 - 15I_1 + 10I_2 = 0$$

$$\Rightarrow 10I_2 = 15I_1 - 20$$

Divide the above equation with 5.

$$2I_2 = 3I_1 - 4$$

Multiply the above equation with 2.

$4I_2 = 6I_1 - 8$ Equation 1

The mesh equation of second mesh is

$$-10(I_2 - I_1) - 30I_2 + 80 = 0$$

Divide the above equation with 10.

$$-(I_2 - I_1) - 3I_2 + 8 = 0$$

$$\Rightarrow -4I_2 + I_1 + 8 = 0$$

$4I_2 = I_1 + 8$ Equation 2

Step 4 − Finding mesh currents I 1 and I 2 by solving Equation 1 and Equation 2.

The left-hand side terms of Equation 1 and Equation 2 are the same. Hence, equate the right-hand side terms of Equation 1 and Equation 2 in order find the value of I 1 .

$$6I_1 - 8 = I_1 + 8$$

$$\Rightarrow 5I_1 = 16$$

$$\Rightarrow I_1 = \frac{16}{5} A$$

Substitute I 1 value in Equation 2.

$$4I_2 = \frac{16}{5} + 8$$

$$\Rightarrow 4I_2 = \frac{56}{5}$$

$$\Rightarrow I_2 = \frac{14}{5} A$$

So, we got the mesh currents I 1 and I 2 as $\mathbf{\frac{16}{5}}$ A and $\mathbf{\frac{14}{5}}$ A respectively.

Step 5 − The current flowing through 30 Ω resistor is nothing but the mesh current I 2 and it is equal to $\frac{14}{5}$ A. Now, we can find the voltage across 30 Ω resistor by using Ohm’s law.

$$V_{30 \Omega} = I_2 R$$

Substitute the values of I 2 and R in the above equation.

$$V_{30 \Omega} = \lgroup \frac{14}{5} \rgroup 30$$

$$\Rightarrow V_{30 \Omega} = 84V$$

Therefore, the voltage across 30 Ω resistor of the given circuit is 84 V .

Note 1 − From the above example, we can conclude that we have to solve ‘m’ mesh equations, if the electric circuit is having ‘m’ meshes. That’s why we can choose Mesh analysis when the number of meshes is less than the number of principal nodes (except the reference node) of any electrical circuit.

Note 2 − We can choose either Nodal analysis or Mesh analysis, when the number of meshes is equal to the number of principal nodes (except the reference node) in any electric circuit.

If a circuit consists of two or more similar passive elements and are connected in exclusively of series type or parallel type, then we can replace them with a single equivalent passive element. Hence, this circuit is called as an equivalent circuit .

In this chapter, let us discuss about the following two equivalent circuits.

Series Equivalent Circuit

Parallel equivalent circuit.

If similar passive elements are connected in series , then the same current will flow through all these elements. But, the voltage gets divided across each element.

It has a single voltage source (V S ) and three resistors having resistances of R 1 , R 2 and R 3 . All these elements are connected in series. The current IS flows through all these elements.

The above circuit has only one mesh. The KVL equation around this mesh is

$$V_S = V_1 + V_2 + V_3$$

Substitute $V_1 = I_S R_1, \: V_2 = I_S R_2$ and $V_3 = I_S R_3$ in the above equation.

$$V_S = I_S R_1 + I_S R_2 + I_S R_3$$

$$\Rightarrow V_S = I_S(R_1 + R_2 + R_3)$$

The above equation is in the form of $V_S = I_S R_{Eq}$ where,

$$R_{Eq} = R_1 + R_2 + R_3$$

The equivalent circuit diagram of the given circuit is shown in the following figure.

That means, if multiple resistors are connected in series, then we can replace them with an equivalent resistor . The resistance of this equivalent resistor is equal to sum of the resistances of all those multiple resistors.

Note 1 − If ‘N’ inductors having inductances of L 1 , L 2 , ..., L N are connected in series, then the equivalent inductance will be

$$L_{Eq} = L_1 + L_2 + ... + L_N$$

Note 2 − If ‘N’ capacitors having capacitances of C 1 , C 2 , ..., C N are connected in series, then the equivalent capacitance will be

$$\frac{1}{C_{Eq}} = \frac{1}{C_1} + \frac{1}{C_2} + ... + \frac{1}{C_N}$$

If similar passive elements are connected in parallel , then the same voltage will be maintained across each element. But, the current flowing through each element gets divided.

It has a single current source (I S ) and three resistors having resistances of R 1 , R 2 , and R 3 . All these elements are connected in parallel. The voltage (V S ) is available across all these elements.

The above circuit has only one principal node (P) except the Ground node. The KCL equation at this principal node (P) is

$$I_S = I_1 + I_2 + I_3$$

Substitute $I_1 = \frac{V_S}{R_1}, \: I_2 = \frac{V_S}{R_2}$ and $I_3 = \frac{V_S}{R_3}$ in the above equation.

$$I_S = \frac{V_S}{R_1} + \frac{V_S}{R_2} + \frac{V_S}{R_3}$$

$$\Rightarrow I_S = V_S \lgroup \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} \rgroup$$

$$\Rightarrow V_S = I_S\left [ \frac{1}{\lgroup \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} \rgroup} \right ]$$

The above equation is in the form of V S = I S R Eq where,

$$R_{Eq} = \frac{1}{\lgroup \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} \rgroup}$$

$$\frac{1}{R_{Eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}$$

That means, if multiple resistors are connected in parallel, then we can replace them with an equivalent resistor. The resistance of this equivalent resistor is equal to the reciprocal of sum of reciprocal of each resistance of all those multiple resistors.

Note 1 − If ‘N’ inductors having inductances of L 1 , L 2 , ..., L N are connected in parallel, then the equivalent inductance will be

$$\frac{1}{L_{Eq}} = \frac{1}{L_1} + \frac{1}{L_2} + ... + \frac{1}{L_N}$$

Note 2 − If ‘N’ capacitors having capacitances of C 1 , C 2 , ..., C N are connected in parallel, then the equivalent capacitance will be

$$C_{Eq} = C_1 + C_2 + ... + C_N$$

In the previous chapter, we discussed about the equivalent circuits of series combination and parallel combination individually. In this chapter, let us solve an example problem by considering both series and parallel combinations of similar passive elements.

Let us find the equivalent resistance across the terminals A & B of the following electrical network.

We will get the equivalent resistance across terminals A & B by minimizing the above network into a single resistor between those two terminals. For this, we have to identify the combination of resistors that are connected in series form and parallel form and then find the equivalent resistance of the respective form in every step.

The given electrical network is modified into the following form as shown in the following figure.

In the above figure, the letters, C to G, are used for labelling various terminals.

Step 1 − In the above network, two 6 Ω resistors are connected in parallel . So, the equivalent resistance between D & E will be 3 Ω. This can be obtained by doing the following simplification.

$$R_{DE} = \frac{6 \times 6}{6 + 6} = \frac{36}{12} = 3 \Omega$$

In the above network, the resistors 4 Ω and 8 Ω are connected in series . So, the equivalent resistance between F & G will be 12 Ω. This can be obtained by doing the following simplification.

$$R_{FG} = 4 + 8 = 12 \Omega$$

Step 2 − The simplified electrical network after Step 1 is shown in the following figure.

In the above network, two 3 Ω resistors are connected in series . So, the equivalent resistance between C & E will be 6 Ω . This can be obtained by doing the following simplification.

$$R_{CE} = 3 + 3 = 6 \Omega$$

Step 3 − The simplified electrical network after Step 2 is shown in the following figure.

In the above network, the resistors 6 Ω and 12 Ω are connected in parallel . So, the equivalent resistance between C & B will be 4 Ω. This can be obtained by doing the following simplification.

$$R_{CB} = \frac{6 \times 12}{6 + 12} = \frac{72}{18} = 4 \Omega$$

Step 4 − The simplified electrical network after Step 3 is shown in the following figure.

In the above network, the resistors 2 Ω and 4 Ω are connected in series between the terminals A & B. So, the equivalent resistance between A & B will be 6 Ω. This can be obtained by doing the following simplification.

$$R_{AB} = 2 + 4 = 6 \Omega$$

Therefore, the equivalent resistance between terminals A & B of the given electrical network is 6 Ω .

Network Theory - Delta to Star Conversion

In the previous chapter, we discussed an example problem related equivalent resistance. There, we calculated the equivalent resistance between the terminals A & B of the given electrical network easily. Because, in every step, we got the combination of resistors that are connected in either series form or parallel form.

However, in some situations, it is difficult to simplify the network by following the previous approach. For example, the resistors connected in either delta (δ) form or star form. In such situations, we have to convert the network of one form to the other in order to simplify it further by using series combination or parallel combination. In this chapter, let us discuss about the Delta to Star Conversion .

Delta Network

Consider the following delta network as shown in the following figure.

The following equations represent the equivalent resistance between two terminals of delta network, when the third terminal is kept open.

$$R_{AB} = \frac{(R_1 + R_3)R_2}{R_1 + R_2 + R_3}$$

$$R_{BC} = \frac{(R_1 + R_2)R_3}{R_1 + R_2 + R_3}$$

$$R_{CA} = \frac{(R_2 + R_3)R_1}{R_1 + R_2 + R_3}$$

Star Network

The following figure shows the equivalent star network corresponding to the above delta network.

The following equations represent the equivalent resistance between two terminals of star network, when the third terminal is kept open.

$$R_{AB} = R_A + R_B$$

$$R_{BC} = R_B + R_C$$

$$R_{CA} = R_C + R_A$$

Star Network Resistances in terms of Delta Network Resistances

We will get the following equations by equating the right-hand side terms of the above equations for which the left-hand side terms are same.

$R_A + R_B = \frac{(R_1 + R_3)R_2}{R_1 + R_2 + R_3}$ Equation 1

$R_B + R_C = \frac{(R_1 + R_2)R_3}{R_1 + R_2 + R_3}$ Equation 2

$R_C + R_A = \frac{(R_2 + R_3)R_1}{R_1 + R_2 + R_3}$ Equation 3

By adding the above three equations, we will get

$$2(R_A + R_B + R_C) = \frac{2(R_1 R_2 + R_2 R_3 + R_3 R_1)}{R_1 + R_2 + R_3}$$

$\Rightarrow R_A + R_B + R_C = \frac{R_1 R_2 + R_2 R_3 + R_3 R_1}{R_1 + R_2 + R_3}$ Equation 4

Subtract Equation 2 from Equation 4.

$R_A + R_B + R_C - (R_B + R_C) = \frac{R_1 R_2 + R_2 R_3 + R_3 R_1}{R_1 + R_2 + R_3} - \frac{(R_1 + R_2)R_3}{R_1 + R_2 + R_3}$

$$R_A = \frac{R_1 R_2}{R_1 + R_2 + R_3}$$

By subtracting Equation 3 from Equation 4, we will get

$$R_B = \frac{R_2 R_3}{R_1 + R_2 + R_3}$$

By subtracting Equation 1 from Equation 4, we will get

$$R_C = \frac{R_3 R_1}{R_1 + R_2 + R_3}$$

By using the above relations, we can find the resistances of star network from the resistances of delta network. In this way, we can convert a delta network into a star network .

Let us calculate the resistances of star network , which are equivalent to that of delta network as shown in the following figure.

Given the resistances of delta network as R 1 = 10 Ω, R 2 = 60 Ω and R 3 = 30 Ω.

We know the following relations of the resistances of star network in terms of resistances of delta network.

Substitute the values of R 1 , R 2 and R 3 in the above equations.

$$R_A = \frac{10 \times 60}{10 +60+30} = \frac{600}{100} = 6\Omega$$

$$R_B = \frac{60 \times 30}{10 +60+30} = \frac{1800}{100} = 18\Omega$$

$$R_C = \frac{30 \times 10}{10 +60+30} = \frac{300}{100} = 3\Omega$$

So, we got the resistances of star network as R A = 6 Ω, R B = 18 Ω and R C = 3 Ω , which are equivalent to the resistances of the given delta network.

Network Theory - Star to Delta Conversion

In the previous chapter, we discussed about the conversion of delta network into an equivalent star network. Now, let us discuss about the conversion of star network into an equivalent delta network. This conversion is called as Star to Delta Conversion .

In the previous chapter, we got the resistances of star network from delta network as

$R_A = \frac{R_1 R_2}{R_1 + R_2 + R_3}$ Equation 1

$R_B = \frac{R_2 R_3}{R_1 + R_2 + R_3}$ Equation 2

$R_C = \frac{R_3 R_1}{R_1 + R_2 + R_3}$ Equation 3

Delta Network Resistances in terms of Star Network Resistances

Let us manipulate the above equations in order to get the resistances of delta network in terms of resistances of star network.

Multiply each set of two equations and then add .

$$R_A R_B + R_B R_C + R_C R_A = \frac{R_1 R_2^2 R_3 + R_2 R_3^2 R_1 + R_3 R_1^2 R_2}{(R_1 + R_2 + R_3)^2}$$

$$\Rightarrow R_A R_B + R_B R_C + R_C R_A = \frac{R_1 R_2 R_3(R_1 + R_2 + R_3)}{(R_1 + R_2 + R_3)^2}$$

$\Rightarrow R_A R_B + R_B R_C + R_C R_A = \frac{R_1 R_2 R_3}{R_1 + R_2 + R_3}$ Equation 4

By dividing Equation 4 with Equation 2, we will get

$$\frac{R_A R_B + R_B R_C + R_C R_A}{R_B} = R_1$$

$$\Rightarrow R_1 = R_C + R_A + \frac{R_C R_A}{R_B}$$

By dividing Equation 4 with Equation 3, we will get

$$R_2 = R_A + R_B + \frac{R_A R_B}{R_C}$$

By dividing Equation 4 with Equation 1, we will get

$$R_3 = R_B + R_C + \frac{R_B R_C}{R_A}$$

By using the above relations, we can find the resistances of delta network from the resistances of star network. In this way, we can convert star network into delta network .

Let us calculate the resistances of delta network , which are equivalent to that of star network as shown in the following figure.

Given the resistances of star network as R A = 6 Ω, R B = 18 Ω and R C = 3 Ω .

We know the following relations of the resistances of delta network in terms of resistances of star network.

$$R_1 = R_C + R_A + \frac{R_C R_A}{R_B}$$

Substitute the values of R A , R B and R C in the above equations.

$$R_1 = 3 + 6 + \frac{3 \times 6}{18} = 9 + 1 = 10 \Omega$$

$$R_2 = 6 + 18 + \frac{6 \times 18}{3} = 24 + 36 = 60 \Omega$$

$$R_3 = 18 + 3 + \frac{18 \times 3}{6} = 21 + 9 = 30 \Omega$$

So, we got the resistances of delta network as R 1 = 10 Ω, R 2 = 60 Ω and R 3 = 30 Ω , which are equivalent to the resistances of the given star network.

Network topology is a graphical representation of electric circuits. It is useful for analyzing complex electric circuits by converting them into network graphs. Network topology is also called as Graph theory .

Basic Terminology of Network Topology

Now, let us discuss about the basic terminology involved in this network topology.

Network graph is simply called as graph . It consists of a set of nodes connected by branches. In graphs, a node is a common point of two or more branches. Sometimes, only a single branch may connect to the node. A branch is a line segment that connects two nodes.

Any electric circuit or network can be converted into its equivalent graph by replacing the passive elements and voltage sources with short circuits and the current sources with open circuits. That means, the line segments in the graph represent the branches corresponding to either passive elements or voltage sources of electric circuit.

Let us consider the following electric circuit .

In the above circuit, there are four principal nodes and those are labelled with 1, 2, 3, and 4. There are seven branches in the above circuit, among which one branch contains a 20 V voltage source, another branch contains a 4 A current source and the remaining five branches contain resistors having resistances of 30 Ω, 5 Ω, 10 Ω, 10 Ω and 20 Ω respectively.

An equivalent graph corresponding to the above electric circuit is shown in the following figure.

In the above graph, there are four nodes and those are labelled with 1, 2, 3 & 4 respectively. These are same as that of principal nodes in the electric circuit. There are six branches in the above graph and those are labelled with a, b, c, d, e & f respectively.

In this case, we got one branch less in the graph because the 4 A current source is made as open circuit, while converting the electric circuit into its equivalent graph.

From this Example, we can conclude the following points −

The number of nodes present in a graph will be equal to the number of principal nodes present in an electric circuit.

The number of branches present in a graph will be less than or equal to the number of branches present in an electric circuit.

Types of Graphs

Following are the types of graphs −

Connected Graph

Unconnected graph, directed graph, undirected graph.

Now, let us discuss these graphs one by one.

If there exists at least one branch between any of the two nodes of a graph, then it is called as a connected graph . That means, each node in the connected graph will be having one or more branches that are connected to it. So, no node will present as isolated or separated.

The graph shown in the previous Example is a connected graph . Here, all the nodes are connected by three branches.

If there exists at least one node in the graph that remains unconnected by even single branch, then it is called as an unconnected graph . So, there will be one or more isolated nodes in an unconnected graph.

Consider the graph shown in the following figure.

In this graph, the nodes 2, 3, and 4 are connected by two branches each. But, not even a single branch has been connected to the node 1 . So, the node 1 becomes an isolated node . Hence, the above graph is an unconnected graph .

If all the branches of a graph are represented with arrows, then that graph is called as a directed graph . These arrows indicate the direction of current flow in each branch. Hence, this graph is also called as oriented graph .

In the above graph, the direction of current flow is represented with an arrow in each branch. Hence, it is a directed graph .

If the branches of a graph are not represented with arrows, then that graph is called as an undirected graph . Since, there are no directions of current flow, this graph is also called as an unoriented graph .

The graph that was shown in the first Example of this chapter is an unoriented graph , because there are no arrows on the branches of that graph.

Subgraph and its Types

A part of the graph is called as a subgraph . We get subgraphs by removing some nodes and/or branches of a given graph. So, the number of branches and/or nodes of a subgraph will be less than that of the original graph. Hence, we can conclude that a subgraph is a subset of a graph.

Following are the two types of subgraphs.

Tree is a connected subgraph of a given graph, which contains all the nodes of a graph. But, there should not be any loop in that subgraph. The branches of a tree are called as twigs .

Consider the following connected subgraph of the graph, which is shown in the Example of the beginning of this chapter.

This connected subgraph contains all the four nodes of the given graph and there is no loop. Hence, it is a Tree .

This Tree has only three branches out of six branches of given graph. Because, if we consider even single branch of the remaining branches of the graph, then there will be a loop in the above connected subgraph. Then, the resultant connected subgraph will not be a Tree.

From the above Tree, we can conclude that the number of branches that are present in a Tree should be equal to n - 1 where ‘n’ is the number of nodes of the given graph.

Co-Tree is a subgraph, which is formed with the branches that are removed while forming a Tree. Hence, it is called as Complement of a Tree. For every Tree, there will be a corresponding Co-Tree and its branches are called as links or chords. In general, the links are represented with dotted lines.

The Co-Tree corresponding to the above Tree is shown in the following figure.

This Co-Tree has only three nodes instead of four nodes of the given graph, because Node 4 is isolated from the above Co-Tree. Therefore, the Co-Tree need not be a connected subgraph. This Co-Tree has three branches and they form a loop.

The number of branches that are present in a co-tree will be equal to the difference between the number of branches of a given graph and the number of twigs. Mathematically, it can be written as

$$l = b - (n - 1)$$

$$l = b - n + 1$$

• l is the number of links.
• b is the number of branches present in a given graph.
• n is the number of nodes present in a given graph.

If we combine a Tree and its corresponding Co-Tree, then we will get the original graph as shown below.

The Tree branches d, e & f are represented with solid lines. The Co-Tree branches a, b & c are represented with dashed lines.

In the previous chapter, we discussed how to convert an electric circuit into an equivalent graph. Now, let us discuss the Network Topology Matrices which are useful for solving any electric circuit or network problem by using their equivalent graphs.

Matrices Associated with Network Graphs

Following are the three matrices that are used in Graph theory.

Incidence Matrix

Fundamental loop matrix.

• Fundamental Cut set Matrix

An Incidence Matrix represents the graph of a given electric circuit or network. Hence, it is possible to draw the graph of that same electric circuit or network from the incidence matrix .

We know that graph consists of a set of nodes and those are connected by some branches. So, the connecting of branches to a node is called as incidence. Incidence matrix is represented with the letter A. It is also called as node to branch incidence matrix or node incidence matrix .

If there are ‘n’ nodes and ‘b’ branches are present in a directed graph , then the incidence matrix will have ‘n’ rows and ‘b’ columns. Here, rows and columns are corresponding to the nodes and branches of a directed graph. Hence, the order of incidence matrix will be n × b .

The elements of incidence matrix will be having one of these three values, +1, -1 and 0.

If the branch current is leaving from a selected node, then the value of the element will be +1.

If the branch current is entering towards a selected node, then the value of the element will be -1.

If the branch current neither enters at a selected node nor leaves from a selected node, then the value of element will be 0.

Procedure to find Incidence Matrix

Follow these steps in order to find the incidence matrix of directed graph.

Select a node at a time of the given directed graph and fill the values of the elements of incidence matrix corresponding to that node in a row.

Repeat the above step for all the nodes of the given directed graph.

Consider the following directed graph .

The incidence matrix corresponding to the above directed graph will be

$$A = \begin{bmatrix}-1 & 1 & 0 & -1 & 0 & 0\\0 & -1 & 1 & 0 & 1 & 0\\1 & 0 & -1 & 0 & 0 & 1 \\0 & 0 & 0 & 1 & -1 & -1 \end{bmatrix}$$

The rows and columns of the above matrix represents the nodes and branches of given directed graph. The order of this incidence matrix is 4 × 6.

By observing the above incidence matrix, we can conclude that the summation of column elements of incidence matrix is equal to zero. That means, a branch current leaves from one node and enters at another single node only.

Note − If the given graph is an un-directed type, then convert it into a directed graph by representing the arrows on each branch of it. We can consider the arbitrary direction of current flow in each branch.

Fundamental loop or f-loop is a loop, which contains only one link and one or more twigs. So, the number of f-loops will be equal to the number of links. Fundamental loop matrix is represented with letter B. It is also called as fundamental circuit matrix and Tie-set matrix. This matrix gives the relation between branch currents and link currents.

If there are ‘n’ nodes and ‘b’ branches are present in a directed graph , then the number of links present in a co-tree, which is corresponding to the selected tree of given graph will be b-n+1.

So, the fundamental loop matrix will have ‘b-n+1’ rows and ‘b’ columns. Here, rows and columns are corresponding to the links of co-tree and branches of given graph. Hence, the order of fundamental loop matrix will be (b - n + 1) × b .

The elements of fundamental loop matrix will be having one of these three values, +1, -1 and 0.

The value of element will be +1 for the link of selected f-loop.

The value of elements will be 0 for the remaining links and twigs, which are not part of the selected f-loop.

If the direction of twig current of selected f-loop is same as that of f-loop link current, then the value of element will be +1.

If the direction of twig current of selected f-loop is opposite to that of f-loop link current, then the value of element will be -1.

Procedure to find Fundamental Loop Matrix

Follow these steps in order to find the fundamental loop matrix of given directed graph.

Select a tree of given directed graph.

By including one link at a time, we will get one f-loop. Fill the values of elements corresponding to this f-loop in a row of fundamental loop matrix.

Repeat the above step for all links.

Take a look at the following Tree of directed graph , which is considered for incidence matrix.

The above Tree contains three branches d, e & f. Hence, the branches a, b & c will be the links of the Co-Tree corresponding to the above Tree. By including one link at a time to the above Tree, we will get one f-loop . So, there will be three f-loops , since there are three links. These three f-loops are shown in the following figure.

In the above figure, the branches, which are represented with colored lines form f-loops. We will get the row wise element values of Tie-set matrix from each f-loop. So, the Tieset matrix of the above considered Tree will be

$$B = \begin{bmatrix}1 & 0 & 0 & -1 & 0 & -1\\0 & 1 & 0 & 1 & 1 & 0\\0 & 0 & 1 & 0 & -1 & 1 \end{bmatrix}$$

The rows and columns of the above matrix represents the links and branches of given directed graph. The order of this incidence matrix is 3 × 6.

The number of Fundamental loop matrices of a directed graph will be equal to the number of Trees of that directed graph. Because, every Tree will be having one Fundamental loop matrix.

Fundamental Cut-set Matrix

Fundamental cut set or f-cut set is the minimum number of branches that are removed from a graph in such a way that the original graph will become two isolated subgraphs. The f-cut set contains only one twig and one or more links. So, the number of f-cut sets will be equal to the number of twigs.

Fundamental cut set matrix is represented with letter C. This matrix gives the relation between branch voltages and twig voltages.

If there are ‘n’ nodes and ‘b’ branches are present in a directed graph , then the number of twigs present in a selected Tree of given graph will be n-1. So, the fundamental cut set matrix will have ‘n-1’ rows and ‘b’ columns. Here, rows and columns are corresponding to the twigs of selected tree and branches of given graph. Hence, the order of fundamental cut set matrix will be (n-1) × b .

The elements of fundamental cut set matrix will be having one of these three values, +1, -1 and 0.

The value of element will be +1 for the twig of selected f-cutset.

The value of elements will be 0 for the remaining twigs and links, which are not part of the selected f-cutset.

If the direction of link current of selected f-cut set is same as that of f-cutset twig current, then the value of element will be +1.

If the direction of link current of selected f-cut set is opposite to that of f-cutset twig current, then the value of element will be -1.

Procedure to find Fundamental Cut-set Matrix

Follow these steps in order to find the fundamental cut set matrix of given directed graph.

Select a Tree of given directed graph and represent the links with the dotted lines.

By removing one twig and necessary links at a time, we will get one f-cut set. Fill the values of elements corresponding to this f-cut set in a row of fundamental cut set matrix.

Repeat the above step for all twigs.

Consider the same directed graph , which we discussed in the section of incidence matrix. Select the branches d, e & f of this directed graph as twigs. So, the remaining branches a, b & c of this directed graph will be the links.

The twigs d, e & f are represented with solid lines and links a, b & c are represented with dotted lines in the following figure.

By removing one twig and necessary links at a time, we will get one f-cut set. So, there will be three f-cut sets, since there are three twigs. These three f-cut sets are shown in the following figure.

We will be having three f-cut sets by removing a set of twig and links of C 1 , C 2 and C 3 . We will get the row wise element values of fundamental cut set matrix from each f-cut set. So, the fundamental cut set matrix of the above considered Tree will be

$$C = \begin{bmatrix}1 & -1 & 0 & 1 & 0 & 0\\0 & -1 & 1 & 0 & 1 & 0\\1 & 0 & -1 & 0 & 0 & 1 \end{bmatrix}$$

The rows and columns of the above matrix represents the twigs and branches of given directed graph. The order of this fundamental cut set matrix is 3 × 6.

The number of Fundamental cut set matrices of a directed graph will be equal to the number of Trees of that directed graph. Because, every Tree will be having one Fundamental cut set matrix.

Network Theory - Superposition Theorem

Superposition theorem is based on the concept of linearity between the response and excitation of an electrical circuit. It states that the response in a particular branch of a linear circuit when multiple independent sources are acting at the same time is equivalent to the sum of the responses due to each independent source acting at a time.

In this method, we will consider only one independent source at a time. So, we have to eliminate the remaining independent sources from the circuit. We can eliminate the voltage sources by shorting their two terminals and similarly, the current sources by opening their two terminals.

Therefore, we need to find the response in a particular branch ‘n’ times if there are ‘n’ independent sources. The response in a particular branch could be either current flowing through that branch or voltage across that branch.

Procedure of Superposition Theorem

Follow these steps in order to find the response in a particular branch using superposition theorem.

Step 1 − Find the response in a particular branch by considering one independent source and eliminating the remaining independent sources present in the network.

Step 2 − Repeat Step 1 for all independent sources present in the network.

Step 3 − Add all the responses in order to get the overall response in a particular branch when all independent sources are present in the network.

Find the current flowing through 20 Ω resistor of the following circuit using superposition theorem .

Step 1 − Let us find the current flowing through 20 Ω resistor by considering only 20 V voltage source . In this case, we can eliminate the 4 A current source by making open circuit of it. The modified circuit diagram is shown in the following figure.

There is only one principal node except Ground in the above circuit. So, we can use nodal analysis method. The node voltage V 1 is labelled in the following figure. Here, V 1 is the voltage from node 1 with respect to ground.

$$\frac{V_1 - 20}{5} + \frac{V_1}{10} + \frac{V_1}{10 + 20} = 0$$

$$\Rightarrow \frac{6V_1 - 120 + 3V_1 + V_1}{30} = 0$$

$$\Rightarrow 10V_1 = 120$$

$$\Rightarrow V_1 = 12V$$

The current flowing through 20 Ω resistor can be found by doing the following simplification.

$$I_1 = \frac{V_1}{10 + 20}$$

Substitute the value of V 1 in the above equation.

$$I_1 = \frac{12}{10 + 20} = \frac{12}{30} = 0.4 A$$

Therefore, the current flowing through 20 Ω resistor is 0.4 A , when only 20 V voltage source is considered.

Step 2 − Let us find the current flowing through 20 Ω resistor by considering only 4 A current source . In this case, we can eliminate the 20 V voltage source by making short-circuit of it. The modified circuit diagram is shown in the following figure.

In the above circuit, there are three resistors to the left of terminals A & B. We can replace these resistors with a single equivalent resistor . Here, 5 Ω & 10 Ω resistors are connected in parallel and the entire combination is in series with 10 Ω resistor.

The equivalent resistance to the left of terminals A & B will be

$$R_{AB} = \lgroup \frac{5 \times 10}{5 + 10} \rgroup + 10 = \frac{10}{3} + 10 = \frac{40}{3} \Omega$$

The simplified circuit diagram is shown in the following figure.

We can find the current flowing through 20 Ω resistor, by using current division principle .

$$I_2 = I_S \lgroup \frac{R_1}{R_1 + R_2} \rgroup$$

Substitute $I_S = 4A,\: R_1 = \frac{40}{3} \Omega$ and $R_2 = 20 \Omega$ in the above equation.

$$I_2 = 4 \lgroup \frac{\frac{40}{3}}{\frac{40}{3} + 20} \rgroup = 4 \lgroup \frac{40}{100} \rgroup = 1.6 A$$

Therefore, the current flowing through 20 Ω resistor is 1.6 A , when only 4 A current source is considered.

Step 3 − We will get the current flowing through 20 Ω resistor of the given circuit by doing the addition of two currents that we got in step 1 and step 2. Mathematically, it can be written as

$$I = I_1 + I_2$$

Substitute, the values of I 1 and I 2 in the above equation.

$$I = 0.4 + 1.6 = 2 A$$

Therefore, the current flowing through 20 Ω resistor of given circuit is 2 A .

Note − We can’t apply superposition theorem directly in order to find the amount of power delivered to any resistor that is present in a linear circuit, just by doing the addition of powers delivered to that resistor due to each independent source. Rather, we can calculate either total current flowing through or voltage across that resistor by using superposition theorem and from that, we can calculate the amount of power delivered to that resistor using $I^2 R$ or $\frac{V^2}{R}$.

Network Theory - Thevenin’s Theorem

Thevenin’s theorem states that any two terminal linear network or circuit can be represented with an equivalent network or circuit, which consists of a voltage source in series with a resistor. It is known as Thevenin’s equivalent circuit. A linear circuit may contain independent sources, dependent sources, and resistors.

If the circuit contains multiple independent sources, dependent sources, and resistors, then the response in an element can be easily found by replacing the entire network to the left of that element with a Thevenin’s equivalent circuit .

The response in an element can be the voltage across that element, current flowing through that element, or power dissipated across that element.

This concept is illustrated in following figures.

Thevenin’s equivalent circuit resembles a practical voltage source. Hence, it has a voltage source in series with a resistor.

The voltage source present in the Thevenin’s equivalent circuit is called as Thevenin’s equivalent voltage or simply Thevenin’s voltage, V Th .

The resistor present in the Thevenin’s equivalent circuit is called as Thevenin’s equivalent resistor or simply Thevenin’s resistor, R Th .

Methods of Finding Thevenin’s Equivalent Circuit

There are three methods for finding a Thevenin’s equivalent circuit. Based on the type of sources that are present in the network, we can choose one of these three methods. Now, let us discuss two methods one by one. We will discuss the third method in the next chapter.

Follow these steps in order to find the Thevenin’s equivalent circuit, when only the sources of independent type are present.

Step 1 − Consider the circuit diagram by opening the terminals with respect to which the Thevenin’s equivalent circuit is to be found.

Step 2 − Find Thevenin’s voltage V Th across the open terminals of the above circuit.

Step 3 − Find Thevenin’s resistance R Th across the open terminals of the above circuit by eliminating the independent sources present in it.

Step 4 − Draw the Thevenin’s equivalent circuit by connecting a Thevenin’s voltage V Th in series with a Thevenin’s resistance R Th .

Now, we can find the response in an element that lies to the right side of Thevenin’s equivalent circuit.

Find the current flowing through 20 Ω resistor by first finding a Thevenin’s equivalent circuit to the left of terminals A and B.

Step 1 − In order to find the Thevenin’s equivalent circuit to the left side of terminals A & B, we should remove the 20 Ω resistor from the network by opening the terminals A & B . The modified circuit diagram is shown in the following figure.

Step 2 − Calculation of Thevenin’s voltage V Th .

There is only one principal node except Ground in the above circuit. So, we can use nodal analysis method. The node voltage V 1 and Thevenin’s voltage V Th are labelled in the above figure. Here, V 1 is the voltage from node 1 with respect to Ground and V Th is the voltage across 4 A current source.

$$\frac{V_1 - 20}{5} + \frac{V_1}{10} - 4 = 0$$

$$\Rightarrow \frac{2V_1 - 40 + V_1 - 40}{10} = 0$$

$$\Rightarrow 3V_1 - 80 = 0$$

$$\Rightarrow V_1 = \frac{80}{3}V$$

The voltage across series branch 10 Ω resistor is

$$V_{10 \Omega} = (-4)(10) = -40V$$

There are two meshes in the above circuit. The KVL equation around second mesh is

$$V_1 - V_{10 \Omega} - V_{Th} = 0$$

Substitute the values of $V_1$ and $V_{10 \Omega}$ in the above equation.

$$\frac{80}{3} - (-40) - V_{Th} = 0$$

$$V_{Th} = \frac{80 + 120}{3} = \frac{200}{3}V$$

Therefore, the Thevenin’s voltage is $V_{Th} = \frac{200}{3}V$

Step 3 − Calculation of Thevenin’s resistance R Th .

Short circuit the voltage source and open circuit the current source of the above circuit in order to calculate the Thevenin’s resistance R Th across the terminals A & B. The modified circuit diagram is shown in the following figure.

The Thevenin’s resistance across terminals A & B will be

$$R_{Th} = \lgroup \frac{5 \times 10}{5 + 10} \rgroup + 10 = \frac{10}{3} + 10 = \frac{40}{3} \Omega$$

Therefore, the Thevenin’s resistance is $\mathbf {R_{Th} = \frac{40}{3} \Omega}$.

Step 4 − The Thevenin’s equivalent circuit is placed to the left of terminals A & B in the given circuit. This circuit diagram is shown in the following figure.

The current flowing through the 20 Ω resistor can be found by substituting the values of V Th , R Th and R in the following equation.

$$l = \frac{V_{Th}}{R_{Th} + R}$$

$$l = \frac{\frac{200}{3}}{\frac{40}{3} + 20} = \frac{200}{100} = 2A$$

Therefore, the current flowing through the 20 Ω resistor is 2 A .

Follow these steps in order to find the Thevenin’s equivalent circuit, when the sources of both independent type and dependent type are present.

Step 1 − Consider the circuit diagram by opening the terminals with respect to which, the Thevenin’s equivalent circuit is to be found.

Step 3 − Find the short circuit current I SC by shorting the two opened terminals of the above circuit.

Step 4 − Find Thevenin’s resistance R Th by using the following formula.

$$R_{Th} = \frac{V_{Th}}{I_{SC}}$$

Step 5 − Draw the Thevenin’s equivalent circuit by connecting a Thevenin’s voltage V Th in series with a Thevenin’s resistance R Th .

Now, we can find the response in an element that lies to the right side of the Thevenin’s equivalent circuit.

Norton’s theorem is similar to Thevenin’s theorem. It states that any two terminal linear network or circuit can be represented with an equivalent network or circuit, which consists of a current source in parallel with a resistor. It is known as Norton’s equivalent circuit . A linear circuit may contain independent sources, dependent sources and resistors.

If a circuit has multiple independent sources, dependent sources, and resistors, then the response in an element can be easily found by replacing the entire network to the left of that element with a Norton’s equivalent circuit .

The response in an element can be the voltage across that element, current flowing through that element or power dissipated across that element.

Norton’s equivalent circuit resembles a practical current source. Hence, it is having a current source in parallel with a resistor.

The current source present in the Norton’s equivalent circuit is called as Norton’s equivalent current or simply Norton’s current I N .

The resistor present in the Norton’s equivalent circuit is called as Norton’s equivalent resistor or simply Norton’s resistor R N .

Methods of Finding Norton’s Equivalent Circuit

There are three methods for finding a Norton’s equivalent circuit. Based on the type of sources that are present in the network, we can choose one of these three methods. Now, let us discuss these three methods one by one.

Follow these steps in order to find the Norton’s equivalent circuit, when only the sources of independent type are present.

Step 1 − Consider the circuit diagram by opening the terminals with respect to which, the Norton’s equivalent circuit is to be found.

Step 2 − Find the Norton’s current I N by shorting the two opened terminals of the above circuit.

Step 3 − Find the Norton’s resistance R N across the open terminals of the circuit considered in Step1 by eliminating the independent sources present in it. Norton’s resistance R N will be same as that of Thevenin’s resistance R Th .

Step 4 − Draw the Norton’s equivalent circuit by connecting a Norton’s current IN in parallel with Norton’s resistance R N .

Now, we can find the response in an element that lies to the right side of Norton’s equivalent circuit.

Follow these steps in order to find the Norton’s equivalent circuit, when the sources of both independent type and dependent type are present.

Step 1 − Consider the circuit diagram by opening the terminals with respect to which the Norton’s equivalent circuit is to be found.

Step 2 − Find the open circuit voltage V OC across the open terminals of the above circuit.

Step 3 − Find the Norton’s current I N by shorting the two opened terminals of the above circuit.

Step 4 − Find Norton’s resistance R N by using the following formula.

$$R_N = \frac{V_{OC}}{I_N}$$

Step 5 − Draw the Norton’s equivalent circuit by connecting a Norton’s current I N in parallel with Norton’s resistance R N .

This is an alternate method for finding a Norton’s equivalent circuit.

Step 1 − Find a Thevenin’s equivalent circuit between the desired two terminals. We know that it consists of a Thevenin’s voltage source, V Th and Thevenin’s resistor, R Th .

Step 2 − Apply source transformation technique to the above Thevenin’s equivalent circuit. We will get the Norton’s equivalent circuit. Here,

Norton’s current,

$$I_N = \frac{V_{Th}}{R_{Th}}$$

Norton’s resistance,

$$R_N = R_{Th}$$

This concept is illustrated in the following figure.

Now, we can find the response in an element by placing Norton’s equivalent circuit to the left of that element.

Note − Similarly, we can find the Thevenin’s equivalent circuit by finding a Norton’s equivalent circuit first and then apply source transformation technique to it. This concept is illustrated in the following figure.

This is the Method 3 for finding a Thevenin’s equivalent circuit.

Find the current flowing through 20 Ω resistor by first finding a Norton’s equivalent circuit to the left of terminals A and B.

Let us solve this problem using Method 3 .

Step 1 − In previous chapter, we calculated the Thevenin’s equivalent circuit to the left side of terminals A & B. We can use this circuit now. It is shown in the following figure.

Here, Thevenin’s voltage, $V_{Th} = \frac{200}{3} V$ and Thevenin’s resistance, $R_{Th} = \frac{40}{3} \Omega$

Step 2 − Apply source transformation technique to the above Thevenin’s equivalent circuit. Substitute the values of V Th and R Th in the following formula of Norton’s current .

$$I_N = \frac{\frac{200}{3}}{\frac{40}{3}} = 5A$$

Therefore, Norton’s current I N is 5 A .

We know that Norton’s resistance, R N is same as that of Thevenin’s resistance R Th .

$$\mathbf {R_N = \frac{40}{3} \Omega}$$

The Norton’s equivalent circuit corresponding to the above Thevenin’s equivalent circuit is shown in the following figure.

Now, place the Norton’s equivalent circuit to the left of the terminals A & B of the given circuit.

By using current division principle , the current flowing through the 20 Ω resistor will be

$$I_{20 \Omega} = 5 \lgroup \frac{\frac{40}{3}}{\frac{40}{3} + 20} \rgroup$$

$$I_{20 \Omega} = 5 \lgroup \frac{40}{100} \rgroup = 2A$$

The amount of power received by a load is an important parameter in electrical and electronic applications. In DC circuits, we can represent the load with a resistor having resistance of R L ohms. Similarly, in AC circuits, we can represent it with a complex load having an impedance of Z L ohms.

Maximum power transfer theorem states that the DC voltage source will deliver maximum power to the variable load resistor only when the load resistance is equal to the source resistance.

Similarly, Maximum power transfer theorem states that the AC voltage source will deliver maximum power to the variable complex load only when the load impedance is equal to the complex conjugate of source impedance.

In this chapter, let us discuss about the maximum power transfer theorem for DC circuits.

Proof of Maximum Power Transfer Theorem

Replace any two terminal linear network or circuit to the left side of variable load resistor having resistance of R L ohms with a Thevenin’s equivalent circuit. We know that Thevenin’s equivalent circuit resembles a practical voltage source.

The amount of power dissipated across the load resistor is

$$P_L = I^2 R_L$$

Substitute $I = \frac{V_{Th}}{R_{Th} + R_L}$ in the above equation.

$$P_L = \lgroup \frac{V_{Th}}{(R_{Th} + R_L)} \rgroup ^2 R_L$$

$\Rightarrow P_L = {V_{Th}}^2 \lbrace \frac{R_L}{(R_{Th} + R_L)^2} \rbrace$ Equation 1

Condition for Maximum Power Transfer

For maximum or minimum, first derivative will be zero. So, differentiate Equation 1 with respect to R L and make it equal to zero.

$$\frac{dP_L}{dR_L} = {V_{Th}}^2 \lbrace \frac{(R_{Th} + R_L)^2 \times 1 - R_L \times 2(R_{Th} + R_L)}{(R_{Th} + R_L)^4} \rbrace = 0$$

$$\Rightarrow (R_{Th} + R_L)^2 -2R_L(R_{Th} + R_L) = 0$$

$$\Rightarrow (R_{Th} + R_L)(R_{Th} + R_L - 2R_L) = 0$$

$$\Rightarrow (R_{Th} - R_L) = 0$$

$$\Rightarrow R_{Th} = R_L\:or\:R_L = R_{Th}$$

Therefore, the condition for maximum power dissipation across the load is $R_L = R_{Th}$. That means, if the value of load resistance is equal to the value of source resistance i.e., Thevenin’s resistance, then the power dissipated across the load will be of maximum value.

The value of Maximum Power Transfer

Substitute $R_L = R_{Th}\:\&\:P_L = P_{L, Max}$ in Equation 1.

$$P_{L, Max} = {V_{Th}}^2 \lbrace \frac{R_{Th}}{(R_{Th} + R_{Th})^2} \rbrace$$

$$P_{L, Max} = {V_{Th}}^2 \lbrace \frac{R_{Th}}{4 {R_{Th}}^2} \rbrace$$

$$\Rightarrow P_{L, Max} = \frac{{V_{Th}}^2}{4 R_{Th}}$$

$$\Rightarrow P_{L, Max} = \frac{{V_{Th}}^2}{4 R_{L}}, \: since \: R_{L} = R_{Th}$$

Therefore, the maximum amount of power transferred to the load is

$$P_{L, Max} = \frac{{V_{Th}}^2}{4R_{L}} = \frac{{V_{Th}}^2}{4R_{Th}}$$

Efficiency of Maximum Power Transfer

We can calculate the efficiency of maximum power transfer, $\eta_{Max}$ using following formula.

$\eta_{Max} = \frac{P_{L, Max}}{P_S}$ Equation 2

$P_{L, Max}$ is the maximum amount of power transferred to the load.

$P_S$ is the amount of power generated by the source.

The amount of power generated by the source is

$$P_S = I^2 R_{Th} + I^2 R_L$$

$$\Rightarrow P_S = 2 I^2 R_{Th},\:since\:R_{L} = R_{Th}$$

Substitute $I = \frac{V_{Th}}{2 R_{Th}}$ in the above equation.

$$P_S = 2\lgroup \frac{V_{Th}}{2 R_{Th}} \rgroup ^2 R_{Th}$$

$$\Rightarrow P_S = 2\lgroup \frac{{V_{Th}}^2}{4 {R_{Th}}^2} \rgroup R_{Th}$$

$$\Rightarrow P_S = \frac{{V_{Th}}^2}{2 R_{Th}}$$

Substitute the values of $P_{L, Max}$ and $P_S$ in Equation 2.

$$\eta_{Max} = \frac{\lgroup \frac{{V_{Th}}^2}{4R_{Th}} \rgroup}{\lgroup \frac{{V_{Th}}^2}{2R_{Th}}\rgroup}$$

$$\Rightarrow \eta_{Max} = \frac{1}{2}$$

We can represent the efficiency of maximum power transfer in terms of percentage as follows −

$$\% \eta_{Max} = \eta_{Max} \times 100\%$$

$$\Rightarrow \% \eta_{Max} = \lgroup \frac{1}{2} \rgroup \times 100\%$$

$$\Rightarrow \% \eta_{Max} = 50\%$$

Therefore, the efficiency of maximum power transfer is 50 % .

Find the maximum power that can be delivered to the load resistor R L of the circuit shown in the following figure.

Step 1 − In Thevenin’s Theorem chapter, we calculated the Thevenin’s equivalent circuit to the left side of terminals A & B. We can use this circuit now. It is shown in the following figure.

Here, Thevenin’s voltage $V_{Th} = \frac{200}{3}V$ and Thevenin’s resistance $R_{Th} = \frac{40}{3} \Omega$

Step 2 − Replace the part of the circuit, which is left side of terminals A & B of the given circuit with the above Thevenin’s equivalent circuit. The resultant circuit diagram is shown in the following figure.

Step 3 − We can find the maximum power that will be delivered to the load resistor, R L by using the following formula.

$$P_{L, Max} = \frac{{V_{Th}}^2}{4 R_{Th}}$$

Substitute $V_{Th} = \frac{200}{3}V$ and $R_{Th} = \frac{40}{3} \Omega$ in the above formula.

$$P_{L, Max} = \frac{\lgroup \frac{200}{3} \rgroup ^ 2}{4 \lgroup \frac{40}{3}\rgroup } $$

$$P_{L, Max} = \frac{250}{3} W$$

Therefore, the maximum power that will be delivered to the load resistor RL of the given circuit is $\mathbf {\frac{250}{3}}$ W

Network Theory - Response of DC Circuits

If the output of an electric circuit for an input varies with respect to time, then it is called as time response . The time response consists of following two parts.

Transient Response

Steady state response.

In this chapter, first let us discuss about these two responses and then observe these two responses in a series RL circuit, when it is excited by a DC voltage source.

After applying an input to an electric circuit, the output takes certain time to reach steady state. So, the output will be in transient state till it goes to a steady state. Therefore, the response of the electric circuit during the transient state is known as transient response .

The transient response will be zero for large values of ‘t’. Ideally, this value of ‘t’ should be infinity. But, practically five time constants are sufficient.

Presence or Absence of Transients

Transients occur in the response due to sudden change in the sources that are applied to the electric circuit and / or due to switching action. There are two possible switching actions. Those are opening switch and closing switch.

The transient part will not present in the response of an electrical circuit or network, if it contains only resistances. Because resistor is having the ability to adjust any amount of voltage and current.

The transient part occurs in the response of an electrical circuit or network due to the presence of energy storing elements such as inductor and capacitor . Because they can’t change the energy stored in those elements instantly.

Inductor Behavior

Assume the switching action takes place at t = 0. Inductor current does not change instantaneously, when the switching action takes place. That means, the value of inductor current just after the switching action will be same as that of just before the switching action.

Mathematically, it can be represented as

$$i_L (0^+) = i_L (0^-)$$

Capacitor Behavior

The capacitor voltage does not change instantaneously similar to the inductor current, when the switching action takes place. That means, the value of capacitor voltage just after the switching action will be same as that of just before the switching action.

$$v_c (0^+) = v_c (0^-)$$

The part of the time response that remains even after the transient response has become zero value for large values of ‘t’ is known as steady state response . This means, there won’t be any transient part in the response during steady state.

If the independent source is connected to the electric circuit or network having one or more inductors and resistors (optional) for a long time, then that electric circuit or network is said to be in steady state. Therefore, the energy stored in the inductor(s) of that electric circuit is of maximum and constant.

$W_L = \frac{L {i_L}^2}{2} = $ Maximum & constant

$\Rightarrow i_L = $ Maximum & constant

Therefore, inductor acts as a constant current source in steady state.

The voltage across inductor will be

$$V_L = L \frac{di_{L}}{dt} = 0V$$

So, the inductor acts as a short circuit in steady state.

If the independent source is connected to the electric circuit or network having one or more capacitors and resistors (optional) for a long time, then that electric circuit or network is said to be in steady state. Therefore, the energy stored in the capacitor(s) of that electric circuit is of maximum and constant.

$W_c = \frac{C{v_c}^2}{2} = $ Maximum & constant

$\Rightarrow v_c = $ Maximum & constant

Therefore, capacitor acts as a constant voltage source in steady state.

The current flowing through the capacitor will be

$$i_c = C\frac{dv_c}{dt} = 0A$$

So, the capacitor acts as an open circuit in steady state.

Finding the Response of Series RL Circuit

Consider the following series RL circuit diagram.

In the above circuit, the switch was kept open up to t = 0 and it was closed at t = 0. So, the DC voltage source having V volts is not connected to the series RL circuit up to this instant. Therefore, there is no initial current flows through inductor.

The circuit diagram, when the switch is in closed position is shown in the following figure.

Now, the current i flows in the entire circuit, since the DC voltage source having V volts is connected to the series RL circuit.

Now, apply KVL around the loop.

$$V = Ri + L \frac{di}{dt}$$

$\frac{di}{dt} + \lgroup \frac{R}{L} \rgroup i = \frac{V}{L}$ Equation 1

The above equation is a first order differential equation and it is in the form of

$\frac{dy}{dt} + Py = Q$ Equation 2

By comparing Equation 1 and Equation 2, we will get the following relations.

$$P = \frac{R}{L}$$

$$Q = \frac{V}{L}$$

The solution of Equation 2 will be

$ye^{\int p dx} = \int Q e^{\int p dx} dx + k$ Equation 3

Where, k is the constant.

Substitute, the values of x, y, P & Q in Equation 3.

$ie^{\int {\lgroup \frac{R}{L} \rgroup}dt} = \int (\frac{V}{L}) \lgroup e^{\int {\lgroup \frac{R}{L} \rgroup}dt} \rgroup dt + k$

$\Rightarrow ie^{\lgroup \frac{R}{L} \rgroup t} = \frac{V}{L} \int e^{\lgroup \frac{R}{L} \rgroup t} dt + k$

$\Rightarrow ie^{\lgroup \frac{R}{L} \rgroup t} = \frac{V}{L} \lbrace \frac{e^{\lgroup \frac{R}{L} \rgroup}t}{\frac{R}{L}} \rbrace + k$

$\Rightarrow i = \frac{V}{R} + k e^{-\lgroup \frac{R}{L} \rgroup}t$ Equation 4

We know that there is no initial current in the circuit. Hence, substitute, t = 0 and 𝑖 = 0 in Equation 4 in order to find the value of the constant k .

$$0 = \frac{V}{R} + ke^{-\lgroup \frac{R}{L} \rgroup(0)}$$

$$0 = \frac{V}{R} + k(1)$$

$$k = - \frac{V}{R}$$

Substitute, the value of k in Equation 4.

$$i = \frac{V}{R} + \lgroup - \frac{V}{R} \rgroup e^{-\lgroup \frac{R}{L} \rgroup t}$$

$$i = \frac{V}{R} - \frac{V}{R}e^{-\lgroup \frac{R}{L} \rgroup t}$$

Therefore, the current flowing through the circuit is

$i = - \frac{V}{R}e^{-\lgroup \frac{R}{L} \rgroup t} + \frac{V}{R}$ Equation 5

So, the response of the series RL circuit, when it is excited by a DC voltage source, has the following two terms.

The first term $-\frac{V}{R}e^{-\lgroup \frac{R}{L} \rgroup t}$ corresponds with the transient response .

The second term $\frac{V}{R}$ corresponds with the steady state response . These two responses are shown in the following figure.

We can re-write the Equation 5 as follows −

$i = \frac{V}{R} \lgroup 1 - e^{-\lgroup \frac{R}{L} \rgroup t} \rgroup$

$\Rightarrow i = \frac{V}{R} \lgroup 1 - e^{-\lgroup \frac{t}{\tau} \rgroup} \rgroup$ Equation 6

Where, τ is the time constant and its value is equal to $\frac{L}{R}$.

Both Equation 5 and Equation 6 are same. But, we can easily understand the above waveform of current flowing through the circuit from Equation 6 by substituting a few values of t like 0, τ, 2τ, 5τ, etc.

In the above waveform of current flowing through the circuit, the transient response will present up to five time constants from zero, whereas the steady state response will present from five time constants onwards.

Network Theory - Response of AC Circuits

In the previous chapter, we discussed the transient response and steady state response of DC circuit. In this chapter, let us discuss the response of AC circuit . The concepts of both transient response and steady state response, which we discussed in the previous chapter, will be useful here too.

In the above circuit, the switch was kept open up to t = 0 and it was closed at t = 0 . So, the AC voltage source having a peak voltage of V m volts is not connected to the series RL circuit up to this instant. Therefore, there is no initial current flows through the inductor.

The circuit diagram, when the switch is in closed position, is shown in the following figure.

Now, the current i(t) flows in the entire circuit, since the AC voltage source having a peak voltage of V m volts is connected to the series RL circuit.

We know that the current i(t) flowing through the above circuit will have two terms, one that represents the transient part and other term represents the steady state.

$i(t) = i_{Tr}(t) + i_{ss}(t)$ Equation 1

$i_{Tr}(t)$ is the transient response of the current flowing through the circuit.

$i_{ss}(t)$ is the steady state response of the current flowing through the circuit.

In the previous chapter, we got the transient response of the current flowing through the series RL circuit. It is in the form of $Ke^{-\lgroup \frac{t}{\tau} \rgroup}$.

Substitute $i_{Tr}(t) = Ke^{-\lgroup \frac{t}{\tau} \rgroup}$ in Equation 1.

$i(t) = Ke^{-\lgroup \frac{t}{\tau} \rgroup} + i_{ss}(t)$ Equation 2

Calculation of Steady State Current

If a sinusoidal signal is applied as an input to a Linear electric circuit, then it produces a steady state output, which is also a sinusoidal signal . Both the input and output sinusoidal signals will be having the same frequency, but different amplitudes and phase angles.

We can calculate the steady state response of an electric circuit, when it is excited by a sinusoidal voltage source using Laplace Transform approach .

The s-domain circuit diagram, when the switch is in closed position, is shown in the following figure.

In the above circuit, all the quantities and parameters are represented in s-domain . These are the Laplace transforms of time-domain quantities and parameters.

The Transfer function of the above circuit is

$$H(s) = \frac{I(s)}{V(s)}$$

$$\Rightarrow H(s) = \frac{1}{Z(s)}$$

$$\Rightarrow H(s) = \frac{1}{R + sL}$$

Substitute $s = j \omega$ in the above equation.

$$H(j \omega) = \frac{1}{R + j \omega L}$$

Magnitude of $\mathbf{\mathit{H(j \omega)}}$ is

$$|H(j \omega)| = \frac{1}{\sqrt{R^2 + {\omega}^2}L^2}$$

Phase angle of $\mathbf{\mathit{H(j \omega)}}$ is

$$\angle H(j \omega) = -tan^{-1} \lgroup \frac{\omega L}{R} \rgroup$$

We will get the steady state current $i_{ss}(t)$ by doing the following two steps −

Multiply the peak voltage of input sinusoidal voltage and the magnitude of $H(j \omega)$.

Add the phase angles of input sinusoidal voltage and $H(j \omega)$.

The steady state current $i_{ss}(t)$ will be

$$i_{ss}(t) = \frac{V_m}{\sqrt{R^2 +{\omega}^2 L^2}} sin \lgroup \omega t + \varphi - tan^{-1} \lgroup \frac {\omega L}{R}\rgroup \rgroup$$

Substitute the value of $i_{ss}(t)$ in Equation 2.

$i(t) = Ke^{-\lgroup \frac{t}{\tau} \rgroup} + \frac{V_m}{\sqrt{R^2 +{\omega}^2 L^2}} sin \lgroup \omega t + \varphi - tan^{-1} \lgroup \frac {\omega L}{R}\rgroup \rgroup$ Equation 3

We know that there is no initial current in the circuit. Hence, substitute t = 0 & i(t) = 0 in Equation 3 in order to find the value of constant, K.

$$0 = Ke^{-\lgroup \frac{0}{\tau} \rgroup} + \frac{V_m}{\sqrt{R^2 +{\omega}^2 L^2}} sin \lgroup \omega (0) + \varphi - tan^{-1} \lgroup \frac {\omega L}{R}\rgroup \rgroup$$

$$\Rightarrow 0 = K + \frac{V_m}{\sqrt{R^2 +{\omega}^2 L^2}} sin \lgroup \varphi - tan^{-1} \lgroup \frac {\omega L}{R}\rgroup \rgroup$$

$$\Rightarrow K = - \frac{V_m}{\sqrt{R^2 +{\omega}^2 L^2}} sin \lgroup \varphi - tan^{-1} \lgroup \frac {\omega L}{R}\rgroup \rgroup$$

Substitute the value of K in Equation 3.

$i(t) = - \frac{V_m}{\sqrt{R^2 +{\omega}^2 L^2}} sin \lgroup \varphi - tan^{-1} \lgroup \frac {\omega L}{R}\rgroup \rgroup e^{-\lgroup \frac{t}{\tau} \rgroup} + \frac{V_m}{\sqrt{R^2 +{\omega}^2 L^2}} sin \lgroup \omega t + \varphi - tan^{-1} \lgroup \frac {\omega L}{R}\rgroup \rgroup$ Equation 4

Equation 4 represents the current flowing through the series RL circuit, when it is excited by a sinusoidal voltage source. It is having two terms. The first and second terms represent the transient response and steady state response of the current respectively.

We can neglect the first term of Equation 4 because its value will be very much less than one. So, the resultant current flowing through the circuit will be

$$i(t) = \frac{V_m}{\sqrt{R^2 +{\omega}^2 L^2}} sin \lgroup \omega t + \varphi - tan^{-1} \lgroup \frac {\omega L}{R}\rgroup \rgroup$$

It contains only the steady state term . Hence, we can find only the steady state response of AC circuits and neglect transient response of it.

Resonance occurs in electric circuits due to the presence of energy storing elements like inductor and capacitor. It is the fundamental concept based on which, the radio and TV receivers are designed in such a way that they should be able to select only the desired station frequency.

There are two types of resonances, namely series resonance and parallel resonance. These are classified based on the network elements that are connected in series or parallel. In this chapter, let us discuss about series resonance.

Series Resonance Circuit Diagram

If the resonance occurs in series RLC circuit, then it is called as Series Resonance . Consider the following series RLC circuit , which is represented in phasor domain.

Here, the passive elements such as resistor, inductor and capacitor are connected in series. This entire combination is in series with the input sinusoidal voltage source.

$$V - V_R - V_L - V_C = 0$$

$$\Rightarrow V - IR - I(j X_L) - I(-j X_C) = 0$$

$$\Rightarrow V = IR + I(j X_L) + I(-j X_C)$$

$\Rightarrow V = I[R + j(X_L - X_C)]$ Equation 1

The above equation is in the form of V = IZ .

Therefore, the impedance Z of series RLC circuit will be

$$Z = R + j(X_L - X_C)$$

Parameters & Electrical Quantities at Resonance

Now, let us derive the values of parameters and electrical quantities at resonance of series RLC circuit one by one.

Resonant Frequency

The frequency at which resonance occurs is called as resonant frequency f r . In series RLC circuit resonance occurs, when the imaginary term of impedance Z is zero, i.e., the value of $X_L - X_C$ should be equal to zero.

$$\Rightarrow X_L = X_C$$

Substitute $X_L = 2 \pi f L$ and $X_C = \frac{1}{2 \pi f C}$ in the above equation.

$$2 \pi f L = \frac{1}{2 \pi f C}$$

$$\Rightarrow f^2 = \frac{1}{(2 \pi)^2 L C}$$

$$\Rightarrow f = \frac{1}{(2 \pi) \sqrt{LC}}$$

Therefore, the resonant frequency f r of series RLC circuit is

$$f_r = \frac{1}{(2 \pi) \sqrt{LC}}$$

Where, L is the inductance of an inductor and C is the capacitance of a capacitor.

The resonant frequency f r of series RLC circuit depends only on the inductance L and capacitance C . But, it is independent of resistance R .

We got the impedance Z of series RLC circuit as

Substitute $X_L = X_C$ in the above equation.

$$Z = R + j(X_C - X_C)$$

$$\Rightarrow Z = R + j(0)$$

$$\Rightarrow Z = R$$

At resonance, the impedance Z of series RLC circuit is equal to the value of resistance R , i.e., Z = R .

Current flowing through the Circuit

Substitute $X_L - X_C = 0$ in Equation 1.

$$V = I[R + j(0)]$$

$$\Rightarrow V = IR$$

$$\Rightarrow I = \frac{V}{R}$$

Therefore, current flowing through series RLC circuit at resonance is $\mathbf{\mathit{I = \frac{V}{R}}}$.

At resonance, the impedance of series RLC circuit reaches to minimum value. Hence, the maximum current flows through this circuit at resonance.

Voltage across Resistor

The voltage across resistor is

$$V_R = IR$$

Substitute the value of I in the above equation.

$$V_R = \lgroup \frac{V}{R} \rgroup R$$

$$\Rightarrow V_R = V$$

Therefore, the voltage across resistor at resonance is V R = V .

Voltage across Inductor

The voltage across inductor is

$$V_L = I(jX_L)$$

$$V_L = \lgroup \frac{V}{R} \rgroup (jX_L)$$

$$\Rightarrow V_L = j \lgroup \frac{X_L}{R} \rgroup V$$

$$\Rightarrow V_L = j QV$$

Therefore, the voltage across inductor at resonance is $V_L = j QV$.

So, the magnitude of voltage across inductor at resonance will be

$$|V_L| = QV$$

Where Q is the Quality factor and its value is equal to $\frac{X_L}{R}$

Voltage across Capacitor

The voltage across capacitor is

$$V_C = I(-j X_C)$$

$$V_C = \lgroup \frac{V}{R} \rgroup (-j X_C)$$

$$\Rightarrow V_C = -j \lgroup \frac{X_C}{R} \rgroup V$$

$$\Rightarrow V_C = -jQV$$

Therefore, the voltage across capacitor at resonance is $\mathbf{\mathit{V_C = -jQV}}$.

So, the magnitude of voltage across capacitor at resonance will be

$$|V_C| = QV$$

Where Q is the Quality factor and its value is equal to $\frac{X_{C}}{R}$

Note − Series resonance RLC circuit is called as voltage magnification circuit, because the magnitude of voltage across the inductor and the capacitor is equal to Q times the input sinusoidal voltage V .

Network Theory - Parallel Resonance

In the previous chapter, we discussed the importance of series resonance. Now, let us discuss parallel resonance in RLC circuits.

Parallel Resonance Circuit Diagram

If the resonance occurs in parallel RLC circuit, then it is called as Parallel Resonance . Consider the following parallel RLC circuit , which is represented in phasor domain.

Here, the passive elements such as resistor, inductor and capacitor are connected in parallel. This entire combination is in parallel with the input sinusoidal current source.

Write nodal equation at node P.

$$- I + I_R + I_L + I_C = 0$$

$$\Rightarrow - I + \frac{V}{R} + \frac{V}{j X_L} + \frac{V}{-j X_C} = 0$$

$$\Rightarrow I = \frac{V}{R} - \frac{jV}{X_L} + \frac{jV}{X_C}$$

$\Rightarrow I = V[\frac{1}{R} + j \lgroup \frac{1}{X_C} - \frac{1}{X_L} \rgroup]$ Equation 1

The above equation is in the form of I = VY .

Therefore, the admittance Y of parallel RLC circuit will be

$$Y = \frac{1}{R} + j \lgroup \frac{1}{X_C} - \frac{1}{X_L} \rgroup$$

Now, let us derive the values of parameters and electrical quantities at resonance of parallel RLC circuit one by one.

We know that the resonant frequency, f r is the frequency at which, resonance occurs. In parallel RLC circuit resonance occurs, when the imaginary term of admittance, Y is zero. i.e., the value of $\frac{1}{X_C} - \frac{1}{X_L}$ should be equal to zero

$$\Rightarrow \frac{1}{X_C} = \frac{1}{X_L}$$

The above resonance condition is same as that of series RLC circuit. So, the resonant frequency, f r will be same in both series RLC circuit and parallel RLC circuit.

Therefore, the resonant frequency, f r of parallel RLC circuit is

$$f_r = \frac{1}{2 \pi \sqrt{LC}}$$

• L is the inductance of an inductor.

The resonant frequency, f r of parallel RLC circuit depends only on the inductance L and capacitance C . But, it is independent of resistance R .

We got the admittance Y of parallel RLC circuit as

Substitute, $X_L = X_C$ in the above equation.

$$Y = \frac{1}{R} + j \lgroup \frac{1}{X_C} - \frac{1}{X_C} \rgroup$$

$$\Rightarrow Y = \frac{1}{R} + j(0)$$

$$\Rightarrow Y = \frac{1}{R}$$

At resonance, the admittance , Y of parallel RLC circuit is equal to the reciprocal of the resistance, R. i.e., $\mathbf{\mathit{Y = \frac{1}{R}}}$

Voltage across each Element

Substitute, $\frac{1}{X_C} - \frac{1}{X_L} = 0$ in Equation 1

$$I = V [\frac{1}{R} + j(0)]$$

Therefore, the voltage across all the elements of parallel RLC circuit at resonance is V = IR .

At resonance, the admittance of parallel RLC circuit reaches to minimum value. Hence, maximum voltage is present across each element of this circuit at resonance.

Current flowing through Resistor

The current flowing through resistor is

$$I_R = \frac{V}{R}$$

Substitute the value of V in the above equation.

$$I_R = \frac{IR}{R}$$

$$\Rightarrow I_R = I$$

Therefore, the current flowing through resistor at resonance is $\mathbf{\mathit{I_R = I}}$.

Current flowing through Inductor

The current flowing through inductor is

$$I_L = \frac{V}{j X_L}$$

$$I_L = \frac{IR}{j X_L}$$

$$\Rightarrow I_L = -j \lgroup \frac{R}{X_L} \rgroup I$$

$$\Rightarrow I_L = -jQI$$

Therefore, the current flowing through inductor at resonance is $I_L = -jQI$.

So, the magnitude of current flowing through inductor at resonance will be

$$|I_L| = QI$$

Where, Q is the Quality factor and its value is equal to $\frac{R}{X_L}$

Current flowing through Capacitor

The current flowing through capacitor is

$$I_C = \frac{V}{-j X_C}$$

$$I_C = \frac{IR}{-j X_C}$$

$$\Rightarrow I_C = j \lgroup \frac{R}{X_C} \rgroup I$$

$$\Rightarrow I_C = jQI$$

Therefore, the current flowing through capacitor at resonance is $I_C = jQI$

So, the magnitude of current flowing through capacitor at resonance will be

$$|I_C| = QI$$

Where, Q is the Quality factor and its value is equal to $\frac{R}{X_C}$

Note − Parallel resonance RLC circuit is called as current magnification circuit. Because, the magnitude of current flowing through inductor and capacitor is equal to Q times the input sinusoidal current I .

An electric circuit is said to be a coupled circuit , when there exists a mutual inductance between the coils (or inductors) present in that circuit. Coil is nothing but the series combination of resistor and inductor. In the absence of resistor, coil becomes inductor. Sometimes, the terms coil and inductor are interchangeably used.

In this chapter, first let us discuss about the dot convention and then will discuss about classification of coupling.

Dot Convention

Dot convention is a technique, which gives the details about voltage polarity at the dotted terminal. This information is useful, while writing KVL equations.

If the current enters at the dotted terminal of one coil (or inductor), then it induces a voltage at another coil (or inductor), which is having positive polarity at the dotted terminal.

If the current leaves from the dotted terminal of one coil (or inductor), then it induces a voltage at another coil (or inductor), which is having negative polarity at the dotted terminal.

Classification of Coupling

We can classify coupling into the following two categories.

Electrical Coupling

Magnetic coupling.

Now, let us discuss about each type of coupling one by one.

Electrical coupling occurs, when there exists a physical connection between two coils (or inductors). This coupling can be of either aiding type or opposing type. It is based on whether the current enters at the dotted terminal or leaves from the dotted terminal.

Coupling of Aiding type

Consider the following electric circuit, which is having two inductors that are connected in series .

Since the two inductors are connected in series, the same current I flow through both inductors having self-inductances L 1 and L 2 .

In this case, the current, I enter at the dotted terminal of each inductor. Hence, the induced voltage in each inductor will be having positive polarity at the dotted terminal due to the current flowing in another coil.

Apply KVL around the loop of the above electric circuit or network.

$$V - L_1 \frac{dI}{dt} - M \frac{dI}{dt} - L_2 \frac{dI}{dt} - M \frac{dI}{dt} = 0$$

$$V = L_1 \frac{dI}{dt} + L_2 \frac{dI}{dt} + 2M \frac{dI}{dt}$$

$$V = (L_1 + L_2 + 2M)\frac{dI}{dt}$$

The above equation is in the form of $\mathbf{\mathit{V = L_{Eq} \frac{dI}{dt}}}$

Therefore, the equivalent inductance of series combination of inductors shown in the above figure is

$$L_{Eq} = L_1 + L_2 + 2M$$

In this case, the equivalent inductance has been increased by 2M. Hence, the above electrical circuit is an example of electrical coupling which is of aiding type.

Coupling of Opposing type

In the above circuit, the current I enters at the dotted terminal of the inductor having an inductance of L 1 . Hence, it induces a voltage in the other inductor having an inductance of L 2 . So, positive polarity of the induced voltage is present at the dotted terminal of this inductor.

In the above circuit, the current I leaves from the dotted terminal of the inductor having an inductance of L 2 . Hence, it induces a voltage in the other inductor having an inductance of L 1 . So, negative polarity of the induced voltage is present at the dotted terminal of this inductor.

$$V - L_1 \frac{dI}{dt} + M \frac{dI}{dt} - L_2 \frac{dI}{dt} + M \frac{dI}{dt} = 0$$

$$\Rightarrow V = L_1 \frac{dI}{dt} + L_2 \frac{dI}{dt} - 2M \frac{dI}{dt}$$

$$\Rightarrow V = (L_1 + L_2 - 2M)\frac{dI}{dt}$$

$$L_{Eq} = L_1 + L_2 - 2M$$

In this case, the equivalent inductance has been decreased by 2M. Hence, the above electrical circuit is an example of electrical coupling which is of opposing type.

Magnetic coupling occurs, when there is no physical connection between two coils (or inductors). This coupling can be of either aiding type or opposing type. It is based on whether the current enters at the dotted terminal or leaves from the dotted terminal.

Consider the following electrical equivalent circuit of transformer . It is having two coils and these are called as primary and secondary coils.

The currents flowing through primary and secondary coils are i 1 and i 2 respectively. In this case, these currents enter at the dotted terminal of respective coil. Hence, the induced voltage in each coil will be having positive polarity at the dotted terminal due to the current flowing in another coil.

Apply KVL around primary coil.

$$v_1 - L_1 \frac{d i_1}{dt} - M \frac{d i_2}{dt} = 0$$

$\Rightarrow v_1 = L_1 \frac{d i_1}{dt} + M \frac{d i_2}{dt}$ Equation 1

Apply KVL around secondary coil.

$$v_2 - L_2 \frac{d i_2}{dt} - M \frac{d i_1}{dt} = 0$$

$\Rightarrow v_2 = L_2 \frac{d i_2}{dt} + M \frac{d i_1}{dt}$ Equation 2

In Equation 1 and Equation 2, the self-induced voltage and mutually induced voltage have the same polarity. Hence, the above transformer circuit is an example of magnetic coupling , which is of aiding type.

Coupling of Opposing Type

Consider the following electrical equivalent circuit of transformer .

The currents flowing through primary and secondary coils are i 1 and i 2 respectively. In this case, the current, i 1 enters at the dotted terminal of primary coil. Hence, it induces a voltage in secondary coil. So, positive polarity of the induced voltage is present at the dotted terminal of this secondary coil.

In the above circuit, the current, i 2 leaves from the dotted terminal of secondary coil. Hence, it induces a voltage in primary coil. So, negative polarity of the induced voltage is present at the dotted terminal of this primary coil.

$$v_1 - L_1 \frac{d i_1}{dt} + M \frac{d i_2}{dt} = 0$$

$\Rightarrow v_1 = L_1 \frac{d i_1}{dt} - M \frac{d i_2}{dt}$ Equation 3

$$v_2 - L_2 \frac{d i_2}{dt} + M \frac{d i_1}{dt} = 0$$

$\Rightarrow v_2 = L_2 \frac{d i_2}{dt} - M \frac{d i_1}{dt}$ Equation 4

In Equation 3 and Equation 4, self-induced voltage and mutually induced voltage are having opposite polarity. Hence, the above transformer circuit is an example of magnetic coupling , which is of opposing type.

Network Theory - Two-Port Networks

In general, it is easy to analyze any electrical network, if it is represented with an equivalent model, which gives the relation between input and output variables. For this, we can use two port network representations. As the name suggests, two port networks contain two ports. Among which, one port is used as an input port and the other port is used as an output port. The first and second ports are called as port1 and port2 respectively.

One port network is a two terminal electrical network in which, current enters through one terminal and leaves through another terminal. Resistors, inductors and capacitors are the examples of one port network because each one has two terminals. One port network representation is shown in the following figure.

Here, the pair of terminals, 1 & 1’ represents a port. In this case, we are having only one port since it is a one port network.

Similarly, two port network is a pair of two terminal electrical network in which, current enters through one terminal and leaves through another terminal of each port. Two port network representation is shown in the following figure.

Here, one pair of terminals, 1 & 1’ represents one port, which is called as port1 and the other pair of terminals, 2 & 2’ represents another port, which is called as port2 .

There are four variables V 1 , V 2 , I 1 and I 2 in a two port network as shown in the figure. Out of which, we can choose two variables as independent and another two variables as dependent. So, we will get six possible pairs of equations. These equations represent the dependent variables in terms of independent variables. The coefficients of independent variables are called as parameters . So, each pair of equations will give a set of four parameters.

Two Port Network Parameters

The parameters of a two port network are called as two port network parameters or simply, two port parameters. Following are the types of two port network parameters.

Z parameters

Y parameters, t parameters.

• T’ parameters

h-parameters

G-parameters.

Now, let us discuss about these two port network parameters one by one.

We will get the following set of two equations by considering the variables V 1 & V 2 as dependent and I 1 & I 2 as independent. The coefficients of independent variables, I 1 and I 2 are called as Z parameters .

$$V_1 = Z_{11} I_1 + Z_{12} I_2$$

$$V_2 = Z_{21} I_1 + Z_{22} I_2$$

The Z parameters are

$$Z_{11} = \frac{V_1}{I_1}, \: when \: I_2 = 0$$

$$Z_{12} = \frac{V_1}{I_2}, \: when \: I_1 = 0$$

$$Z_{21} = \frac{V_2}{I_1}, \: when \: I_2 = 0$$

$$Z_{22} = \frac{V_2}{I_2}, \: when \: I_1 = 0$$

Z parameters are called as impedance parameters because these are simply the ratios of voltages and currents. Units of Z parameters are Ohm (Ω).

We can calculate two Z parameters, Z 11 and Z 21 , by doing open circuit of port2. Similarly, we can calculate the other two Z parameters, Z 12 and Z 22 by doing open circuit of port1. Hence, the Z parameters are also called as open-circuit impedance parameters .

We will get the following set of two equations by considering the variables I 1 & I 2 as dependent and V 1 & V 2 as independent. The coefficients of independent variables, V 1 and V 2 are called as Y parameters .

$$I_1 = Y_{11} V_1 + Y_{12} V_2$$

$$I_2 = Y_{21} V_1 + Y_{22} V_2$$

The Y parameters are

$$Y_{11} = \frac{I_1}{V_1}, \: when \: V_2 = 0$$

$$Y_{12} = \frac{I_1}{V_2}, \: when \: V_1 = 0$$

$$Y_{21} = \frac{I_2}{V_1}, \: when \: V_2 = 0$$

$$Y_{22} = \frac{I_2}{V_2}, \: when \: V_1 = 0$$

Y parameters are called as admittance parameters because these are simply, the ratios of currents and voltages. Units of Y parameters are mho.

We can calculate two Y parameters, Y 11 and Y 21 by doing short circuit of port2. Similarly, we can calculate the other two Y parameters, Y 12 and Y 22 by doing short circuit of port1. Hence, the Y parameters are also called as short-circuit admittance parameters .

We will get the following set of two equations by considering the variables V 1 & I 1 as dependent and V 2 & I 2 as independent. The coefficients of V 2 and -I 2 are called as T parameters .

$$V_1 = A V_2 - B I_2$$

$$I_1 = C V_2 - D I_2$$

The T parameters are

$$A = \frac{V_1}{V_2}, \: when \: I_2 = 0$$

$$B = -\frac{V_1}{I_2}, \: when \: V_2 = 0$$

$$C = \frac{I_1}{V_2}, \: when \: I_2 = 0$$

$$D = -\frac{I_1}{I_2}, \: when \: V_2 = 0$$

T parameters are called as transmission parameters or ABCD parameters . The parameters, A and D do not have any units, since those are dimension less. The units of parameters, B and C are ohm and mho respectively.

We can calculate two parameters, A and C by doing open circuit of port2. Similarly, we can calculate the other two parameters, B and D by doing short circuit of port2.

T ’ parameters

We will get the following set of two equations by considering the variables V 2 & I 2 as dependent and V 1 & I 1 as independent. The coefficients of V 1 and -I 1 are called as T’ parameters .

$$V_2 = A' V_1 - B' I_1$$

$$I_2 = C' V_1 - D' I_1$$

The T’ parameters are

$$A' = \frac{V_2}{V_1}, \: when\: I_1 = 0$$

$$B' = -\frac{V_2}{I_1}, \: when\: V_1 = 0$$

$$C' = \frac{I_2}{V_1}, \: when\: I_1 = 0$$

$$D' = -\frac{I_2}{I_1}, \: when \: V_1 = 0$$

T’ parameters are called as inverse transmission parameters or A’B’C’D’ parameters . The parameters A’ and D’ do not have any units, since those are dimension less. The units of parameters, B’ and C’, are Ohm and Mho respectively.

We can calculate two parameters, A’ and C’, by doing an open circuit of port1. Similarly, we can calculate the other two parameters, B’ and D’, by doing a short circuit of port1.

We will get the following set of two equations by considering the variables V 1 & I 2 as dependent and I 1 & V 2 as independent. The coefficients of independent variables, I 1 and V 2 , are called as h-parameters .

$$V_1 = h_{11} I_1 + h_{12} V_2$$

$$I_2 = h_{21} I_1 + h_{22} V_2$$

The h-parameters are

$$h_{11} = \frac{V_1}{I_1},\: when\: V_2 = 0$$

$$h_{12} = \frac{V_1}{V_2},\: when\: I_1 = 0$$

$$h_{21} = \frac{I_2}{I_1},\: when\: V_2 = 0$$

$$h_{22} = \frac{I_2}{V_2},\: when\: I_1 = 0$$

h-parameters are called as hybrid parameters . The parameters, h 12 and h 21 , do not have any units, since those are dimension-less. The units of parameters, h 11 and h 22 , are Ohm and Mho respectively.

We can calculate two parameters, h 11 and h 21 by doing short circuit of port2. Similarly, we can calculate the other two parameters, h 12 and h 22 by doing open circuit of port1.

The h-parameters or hybrid parameters are useful in transistor modelling circuits (networks).

We will get the following set of two equations by considering the variables I 1 & V 2 as dependent and V 1 & I 2 as independent. The coefficients of independent variables, V 1 and I 2 are called as g-parameters .

$$I_1 = g_{11} V_1 + g_{12} I_2$$

$$V_2 = g_{21} V_1 + g_{22} I_2$$

The g-parameters are

$$g_{11} = \frac{I_1}{V_1},\: when\: I_2 = 0$$

$$g_{12} = \frac{I_1}{I_2},\: when\: V_1 = 0$$

$$g_{21} = \frac{V_2}{V_1},\: when\: I_2 = 0$$

$$g_{22} = \frac{V_2}{I_2},\: when \: V_1 = 0$$

g-parameters are called as inverse hybrid parameters . The parameters, g 12 and g 21 do not have any units, since those are dimension less. The units of parameters, g 11 and g 22 are mho and ohm respectively.

We can calculate two parameters, g 11 and g 21 by doing open circuit of port2. Similarly, we can calculate the other two parameters, g 12 and g 22 by doing short circuit of port1.

In the previous chapter, we discussed about six types of two-port network parameters. Now, let us convert one set of two-port network parameters into other set of two port network parameters. This conversion is known as two port network parameters conversion or simply, two-port parameters conversion .

Sometimes, it is easy to find one set of parameters of a given electrical network easily. In those situations, we can convert these parameters into the required set of parameters instead of calculating these parameters directly with more difficulty.

Now, let us discuss about some of the two port parameter conversions.

Procedure of two port parameter conversions

Follow these steps, while converting one set of two port network parameters into the other set of two port network parameters.

Step 1 − Write the equations of a two port network in terms of desired parameters.

Step 2 − Write the equations of a two port network in terms of given parameters.

Step 3 − Re-arrange the equations of Step2 in such a way that they should be similar to the equations of Step1.

Step 4 − By equating the similar equations of Step1 and Step3, we will get the desired parameters in terms of given parameters. We can represent these parameters in matrix form.

Z parameters to Y parameters

Here, we have to represent Y parameters in terms of Z parameters. So, in this case Y parameters are the desired parameters and Z parameters are the given parameters.

Step 1 − We know that the following set of two equations, which represents a two port network in terms of Y parameters .

We can represent the above two equations in matrix form as

$\begin{bmatrix}I_1 \\I_2 \end{bmatrix} = \begin{bmatrix}Y_{11} & Y_{12} \\Y_{21} & Y_{22} \end{bmatrix} \begin{bmatrix}V_1 \\V_2 \end{bmatrix}$ Equation 1

Step 2 − We know that the following set of two equations, which represents a two port network in terms of Z parameters .

$$\begin{bmatrix}V_1 \\V_2 \end{bmatrix} = \begin{bmatrix}Z_{11} & Z_{12} \\Z_{21} & Z_{22} \end{bmatrix} \begin{bmatrix}I_1 \\I_2 \end{bmatrix}$$

Step 3 − We can modify it as

$\begin{bmatrix}I_1 \\I_2 \end{bmatrix} = \begin{bmatrix}Z_{11} & Z_{12} \\Z_{21} & Z_{22} \end{bmatrix}^{-1} \begin{bmatrix}V_1 \\V_2 \end{bmatrix}$ Equation 2

Step 4 − By equating Equation 1 and Equation 2, we will get

$$\begin{bmatrix}Y_{11} & Y_{12} \\Y_{21} & Y_{22} \end{bmatrix} = \begin{bmatrix}Z_{11} & Z_{12} \\Z_{21} & Z_{22} \end{bmatrix}^{-1} $$

$$\Rightarrow \begin{bmatrix}Y_{11} & Y_{12} \\Y_{21} & Y_{22} \end{bmatrix} = \frac{\begin{bmatrix}Z_{22} & -Z_{12} \\-Z_{21} & Z_{11} \end{bmatrix}}{\Delta Z}$$

$$\Delta Z = Z_{11} Z_{22} - Z_{12} Z_{21}$$

So, just by doing the inverse of Z parameters matrix , we will get Y parameters matrix.

Z parameters to T parameters

Here, we have to represent T parameters in terms of Z parameters. So, in this case T parameters are the desired parameters and Z parameters are the given parameters.

Step 1 − We know that, the following set of two equations, which represents a two port network in terms of T parameters .

Step 3 − We can modify the above equation as

$$\Rightarrow V_2 - Z_{22} I_2 = Z_{21} I_1$$

$$\Rightarrow I_1 = \lgroup \frac{1}{Z_{21}} \rgroup V_2 - \lgroup \frac{Z_{22}}{Z_{21}} \rgroup I_2$$

Step 4 − The above equation is in the form of $I_1 = CV_2 − DI_2$. Here,

$$C = \frac{1}{Z_{21}}$$

$$D = \frac{Z_{22}}{Z_{21}}$$

Step 5 − Substitute $I_1$ value of Step 3 in $V_1$ equation of Step 2.

$$V_1 = Z_{11} \lbrace \lgroup \frac {1}{Z_{12}} \rgroup V_2 - \lgroup \frac {Z_{22}}{Z_{21}} \rgroup I_2 \rbrace + Z_{12} I_2$$

$$\Rightarrow V_1 = \lgroup \frac {Z_{11}}{Z_{21}} \rgroup V_2 - \lgroup \frac{Z_{11} Z_{22} - Z_{12} Z_{21}}{Z_{21}} \rgroup I_2$$

Step 6 − The above equation is in the form of $V_1 = AV_2 − BI_2$. Here,

$$A = \frac{Z_{11}}{Z_{21}}$$

$$B = \frac{Z_{11} Z_{22} - Z_{12} Z_{21}}{Z_{21}}$$

Step 7 − Therefore, the T parameters matrix is

$$\begin{bmatrix}A & B \\C & D \end{bmatrix} = \begin{bmatrix}\frac{Z_{11}}{Z_{21}} & \frac{Z_{11}Z_{22} - Z_{12}Z_{21}}{Z_{21}} \\\frac{1}{Z_{21}} & \frac{Z_{22}}{Z_{21}} \end{bmatrix}$$

Y parameters to Z parameters

Here, we have to represent Z parameters in terms of Y parameters. So, in this case Z parameters are the desired parameters and Y parameters are the given parameters.

Step 1 − We know that, the following matrix equation of two port network regarding Z parameters as

$\begin{bmatrix}V_1 \\V_2 \end{bmatrix} = \begin{bmatrix}Z_{11} & Z_{12} \\Z_{21} & Z_{22} \end{bmatrix} \begin{bmatrix}I_1 \\I_2 \end{bmatrix}$ Equation 3

Step 2 − We know that, the following matrix equation of two port network regarding Y parameters as

$$\begin{bmatrix}I_1 \\I_2 \end{bmatrix} = \begin{bmatrix}Y_{11} & Y_{12} \\Y_{21} & Y_{22} \end{bmatrix} \begin{bmatrix}V_1 \\V_2 \end{bmatrix}$$

$\begin{bmatrix}V_1 \\V_2 \end{bmatrix} = \begin{bmatrix}Y_{11} & Y_{12} \\Y_{21} & Y_{22} \end{bmatrix}^{-1} \begin{bmatrix}I_1 \\I_2 \end{bmatrix}$ Equation 4

Step 4 − By equating Equation 3 and Equation 4, we will get

$$\begin{bmatrix}Z_{11} & Z_{12} \\Z_{21} & Z_{22} \end{bmatrix} = \begin{bmatrix}Y_{11} & Y_{12} \\Y_{21} & Y_{22} \end{bmatrix}^{-1}$$

$$\Rightarrow \begin{bmatrix}Z_{11} & Z_{12} \\Z_{21} & Z_{22} \end{bmatrix} = \frac{\begin{bmatrix}Y_{22} & - Y_{12} \\- Y_{21} & Y_{11} \end{bmatrix}}{\Delta Y}$$

$$\Delta Y = Y_{11} Y_{22} - Y_{12} Y_{21}$$

So, just by doing the inverse of Y parameters matrix , we will get the Z parameters matrix.

Y parameters to T parameters

Here, we have to represent T parameters in terms of Y parameters. So, in this case, T parameters are the desired parameters and Y parameters are the given parameters.

Step 2 − We know that the following set of two equations of two port network regarding Y parameters.

$$\Rightarrow I_2 - Y_{22} V_2 = Y_{21} V_1$$

$$\Rightarrow V_1 = \lgroup \frac{- Y_{22}}{Y_{21}} \rgroup V_2 - \lgroup \frac{-1}{Y_{21}} \rgroup I_2$$

Step 4 − The above equation is in the form of $V_1 = AV_2 − BI_2$. Here,

$$A = \frac{- Y_{22}}{Y_{21}}$$

$$B = \frac{-1}{Y_{21}}$$

Step 5 − Substitute $V_1$ value of Step 3 in $I_1$ equation of Step 2.

$$I_1 = Y_{11} \lbrace \lgroup \frac{- Y_{22}}{Y_{21}} \rgroup V_2 - \lgroup \frac{-1}{Y_{21}} \rgroup I_2 \rbrace + Y_{12} V_2$$

$$\Rightarrow I_1 = \lgroup \frac {Y_{12} Y_{21} - Y_{11} Y_{22}}{Y_{21}} \rgroup V_2 - \lgroup \frac{- Y_{11}} {Y_{21}} \rgroup I_2$$

Step 6 − The above equation is in the form of $I_1 = CV_2 − DI_2$. Here,

$$C = \frac {Y_{12} Y_{21} - Y_{11} Y_{22}}{Y_{21}}$$

$$D = \frac{- Y_{11}} {Y_{21}}$$

$$\begin{bmatrix}A & B \\C & D \end{bmatrix} = \begin{bmatrix}\frac{-Y_{22}}{Y_{21}} & \frac{-1}{Y_{21}} \\\frac{Y_{12}Y_{21} - Y_{11}Y_{22}}{Y_{21}} & \frac{-Y_{11}}{Y_{21}} \end{bmatrix}$$

T parameters to h-parameters

Here, we have to represent h-parameters in terms of T parameters. So, in this case hparameters are the desired parameters and T parameters are the given parameters.

Step 1 − We know that, the following h-parameters of a two port network.

$$h_{11} = \frac{V_1}{I_1}, \: when \: V_2 = 0$$

$$h_{12} = \frac{V_1}{V_2}, \: when \: I_1 = 0$$

$$h_{21} = \frac{I_2}{I_1}, \: when \: V_2 = 0$$

$$h_{22} = \frac{I_2}{V_2}, \: when \: I_1 = 0$$

Step 2 − We know that the following set of two equations of two port network regarding T parameters .

$V_1 = A V_2 - B I_2$ Equation 5

$I_1 = C V_2 - D I_2$ Equation 6

Step 3 − Substitute $V_2 = 0$ in the above equations in order to find the two h-parameters, $h_{11}$ and $h_{21}$.

$$\Rightarrow V_1 = -B I_2$$

$$\Rightarrow I_1 = -D I_2$$

Substitute, $V_1$ and $I_1$ values in h-parameter, $h_{11}$.

$$h_{11} = \frac{-B I_2}{-D I_2}$$

$$\Rightarrow h_{11} = \frac{B}{D}$$

Substitute $I_1$ value in h-parameter $h_{21}$.

$$h_{21} = \frac{I_2}{- D I_2}$$

$$\Rightarrow h_{21} = - \frac{1}{D}$$

Step 4 − Substitute $I_1 = 0$ in the second equation of step 2 in order to find the h-parameter $h_{22}$.

$$0 = C V_2 - D I_2$$

$$\Rightarrow C V_2 = D I_2$$

$$\Rightarrow \frac{I_2}{V_2} = \frac{C}{D}$$

$$\Rightarrow h_{22} = \frac{C}{D}$$

Step 5 − Substitute $I_2 = \lgroup \frac{C}{D} \rgroup V_2$ in the first equation of step 2 in order to find the h-parameter, $h_{12}$.

$$V_1 = A V_2 - B \lgroup \frac{C}{D} \rgroup V_2$$

$$\Rightarrow V_1 = \lgroup \frac{AD - BC}{D} \rgroup V_2$$

$$\Rightarrow \frac{V_1}{V_2} = \frac{AD - BC}{D}$$

$$\Rightarrow h_{12} = \frac{AD - BC}{D}$$

Step 6 − Therefore, the h-parameters matrix is

$$\begin{bmatrix}h_{11} & h_{12} \\h_{21} & h_{22} \end{bmatrix} = \begin{bmatrix}\frac{B}{D} & \frac{AD - BC}{D} \\-\frac{1}{D} & \frac{C}{D} \end{bmatrix}$$

h-parameters to Z parameters

Here, we have to represent Z parameters in terms of h-parameters. So, in this case Z parameters are the desired parameters and h-parameters are the given parameters.

Step 1 − We know that, the following set of two equations of two port network regarding Z parameters .

Step 2 − We know that, the following set of two equations of two-port network regarding h-parameters .

$$\Rightarrow I_2 - h_{21} I_1 = h_{22} V_2$$

$$\Rightarrow V_2 = \frac{I_2 - h_{21} I_1}{h_{22}}$$

$$\Rightarrow V_2 = \lgroup \frac{-h_{21}}{h_{22}} \rgroup I_1 + \lgroup \frac{1}{h_{22}} \rgroup I_2$$

The above equation is in the form of $V_2 = Z_{21} I_1 + Z_{22} I_2. Here,$

$$Z_{21} = \frac{-h_{21}}{h_{22}}$$

$$Z_{22} = \frac{1}{h_{22}}$$

Step 4 − Substitute V 2 value in first equation of step 2.

$$V_1 = h_{11} I_1 + h_{21} \lbrace \lgroup \frac{-h_{21}}{h_{22}} \rgroup I_1 + \lgroup \frac{1}{h_{22}} \rgroup I_2 \rbrace$$

$$\Rightarrow V_1 = \lgroup \frac{h_{11}h_{22} - h_{12}h_{21}}{h_{22}} \rgroup I_1 + \lgroup \frac{h_{12}}{h_{22}} \rgroup I_2$$

The above equation is in the form of $V_1 = Z_{11}I_1 + Z_{12}I_2$. Here,

$$Z_{11} = \frac{h_{11}h_{22} - h_{12}h_{21}}{h_{22}}$$

$$Z_{12} = \frac{h_{12}}{h_{22}}$$

Step 5 − Therefore, the Z parameters matrix is

$$\begin{bmatrix}Z_{11} & Z_{12} \\Z_{21} & Z_{22} \end{bmatrix} = \begin{bmatrix}\frac{h_{11}h_{22} - h_{12}h_{21}}{h_{22}} & \frac{h_{12}}{h_{22}} \\\frac{-h_{21}}{h_{22}} & \frac{1}{h_{22}} \end{bmatrix}$$

In this way, we can convert one set of parameters into other set of parameters.

Filters as the name suggests, they filter the frequency components. That means, they allow certain frequency components and / or reject some other frequency components.

In this chapter, let us discuss about the passive filters . Those are the electric circuits or networks having passive elements like resistor, inductor and capacitor.

Types of Filters

Filters are mainly classified into four types based on the band of frequencies that are allowing and / or the band of frequencies that are rejecting. Following are the types of filters.

Low Pass Filter

High pass filter, band pass filter, band stop filter.

Low pass filter as the name suggests, it allows (passes) only low frequency components. That means, it rejects (blocks) all other high frequency components.

The s-domain circuit diagram (network) of Low Pass Filter is shown in the following figure.

It consists of two passive elements resistor and capacitor, which are connected in series . Input voltage is applied across this entire combination and the output is considered as the voltage across capacitor.

Here, $V_i(s)$ and $V_o(s)$ are the Laplace transforms of input voltage, $v_i(t)$ and output voltage, $v_o(t)$ respectively.

The transfer function of the above network is

$$H(s) = \frac{V_o(s)}{V_i(s)} = \frac{\frac{1}{sC}}{R + \frac{1}{sC}}$$

$$\Rightarrow H(s) = \frac{1}{1 + sCR}$$

Substitute, $s = j \omega$ in the above equation.

$$H(j \omega) = \frac{1}{1 + j \omega CR}$$

Magnitude of transfer function is

$$|H(j \omega)| = \frac{1}{\sqrt{(1 + (\omega CR)^2}}$$

At ω = 0, the magnitude of transfer function is equal to 1.

At $\omega = \frac{1}{CR}$, the magnitude of transfer function is equal to 0.707.

At ω = ∞, the magnitude of transfer function is equal to 0.

Therefore, the magnitude of transfer function of Low pass filter will vary from 1 to 0 as ω varies from 0 to ∞.

High pass filter as the name suggests, it allows (passes) only high frequency components. That means, it rejects (blocks) all low frequency components.

The s-domain circuit diagram (network) of High pass filter is shown in the following figure.

It consists of two passive elements capacitor and resistor, which are connected in series . Input voltage is applied across this entire combination and the output is considered as the voltage across resistor.

$$H(s) = \frac{V_o(s)}{V_i(s)} = \frac{R}{R + \frac{1}{sC}}$$

$$\Rightarrow H(s) = \frac{sCR}{1 + sCR}$$

$$H(j \omega) = \frac{j \omega CR}{1 + j \omega CR}$$

$$|H(j \omega)| = \frac{\omega CR}{\sqrt{(1 + (\omega CR)^2}}$$

At ω = 0, the magnitude of transfer function is equal to 0.

At ω = ∞, the magnitude of transfer function is equal to 1.

Therefore, the magnitude of transfer function of High pass filter will vary from 0 to 1 as ω varies from 0 to ∞.

Band pass filter as the name suggests, it allows (passes) only one band of frequencies. In general, this frequency band lies in between low frequency range and high frequency range. That means, this filter rejects (blocks) both low and high frequency components.

The s-domain circuit diagram (network) of Band pass filter is shown in the following figure.

It consists of three passive elements inductor, capacitor and resistor, which are connected in series . Input voltage is applied across this entire combination and the output is considered as the voltage across resistor.

$$H(s) = \frac{V_o(s)}{V_i(s)} = \frac{R}{R + \frac{1}{sC} + sL}$$

$$\Rightarrow H(s) = \frac{s CR}{s^2 LC + sCR + 1}$$

$$H(j \omega) = \frac{j \omega CR}{1 - \omega^2 LC + j \omega CR}$$

$$|H(j \omega)| = \frac{\omega CR}{\sqrt{(1 - \omega^2 LC)^2 + (\omega CR)^2}}$$

At $\omega = \frac{1}{\sqrt{LC}}$, the magnitude of transfer function is equal to 1.

Therefore, the magnitude of transfer function of Band pass filter will vary from 0 to 1 & 1 to 0 as ω varies from 0 to ∞.

Band stop filter as the name suggests, it rejects (blocks) only one band of frequencies. In general, this frequency band lies in between low frequency range and high frequency range. That means, this filter allows (passes) both low and high frequency components.

The s-domain (network) of circuit diagram and stop filter is shown in the following figure.

It consists of three passive elements resistor, inductor and capacitor, which are connected in series . Input voltage is applied across this entire combination and the output is considered as the voltage across the combination of inductor and capacitor.

$$H(s) = \frac{V_o(s)}{V_i(s)} = \frac{sL + \frac{1}{sC}}{R + sL + \frac{1}{sC}}$$

$$\Rightarrow H(s) = \frac{s^2 LC + 1}{s^2 LC + sCR + 1}$$

$$H(j \omega) = \frac{1 - \omega^2 LC}{1 - \omega^2 LC + j \omega CR}$$

$$|H(j \omega)| = \frac{1 - \omega^2 LC}{\sqrt{(1 - \omega^2 LC)^2 + (\omega CR)^2}}$$

At $\omega = \frac{1}{\sqrt{LC}}$, the magnitude of transfer function is equal to 0.

Therefore, the magnitude of transfer function of Band stop filter will vary from 1 to 0 & 0 to 1 as ω varies from 0 to ∞.

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The Case for College in the Era of Online Learning

• Robert Walker

In-person education provides valuable experiences, opportunities, and skills that can’t be replicated online.

Does pursuing a college education still make sense in the age of online learning and AI — when we have access to information for free via the internet? The problem with this question is that it frames college as an information gatekeeper, misunderstanding much of its value. For many, higher education institutions offer more than that: a transformative journey where students can network and develop transferable soft skills that require teamwork and repetition. You can maximize your college experience by leaning into these opportunities while simultaneously staying up to date with the latest technological trends. By being agile, networking vigorously, cultivating problem-solving skills, and seeking learning opportunities in the real world while in school, you can prepare yourself for a successful career.

Today, we have access to more information than ever before. YouTube and TikTok can provide us with in-depth learning opportunities for free — from professional development tips to AI tutorials . In more recent years, large language models like ChatGPT and Gemini have shown they can answer almost any question that comes to mind with an increasing level of accuracy .

• RW Robert Walker is the director of high school admissions at University of Advancing Technology. Walker has over 12 years of in-depth experience in recruitment and technology, has a genuine passion helping others achieve their educations dream,s and holds advanced degrees in technology leadership and cyber security.  

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