This tutorial is intended to provide detailed information about the circuit or network analysis, methods of analysis and network theorems. It is just an introductory article, in which I gather all the laws, methods and theorems. This topic is usually a part of the ECE basic course on circuits. The term solving a circuit means determining all the voltage across each element and currents through each element present in a circuit.
Key Concepts:
- What are fundamental laws for solving circuits?
- Methods used for network/circuit analysis
- Network theorems
- What is the purpose of network theorems or why do we study network theorems
Fundamental Circuit Laws:
To determine current and voltage in an electric circuit, we need to gain knowledge of fundamental laws that govern electronic circuits.
- Kirchhoff's Voltage Law (KVL)
- Kirchhoff's Current Law (KCL)
Ohm's Law defines a linear relationship between voltage and current in an ideal conductor. This is one of the most important and fundamental laws of electric circuits.
Kirchhoff’s Current Law is used when analysing a parallel circuit. It is based on the idea of conservation of charge. According to KCL 'current entering the node is equal to current leaving the node’.
Kirchhoff's Voltage Law is used when analysing a series circuit. It is based on the idea of conservation of potential. According to KVL 'the sum of voltage drop or potential difference across a closed loop is zero’.
Methods of Analysis:
Analysis of a circuit is the determination of output response. These methods of analysis are based on basic circuit laws. These methods are restricted to linear circuits only. The two most common methods are
- Mesh analysis
- Nodal analysis
Nodal analysis is nothing but an application of KCL. In the nodal analysis, we apply KCL to each node. If we have 'n’ number of nodes, then there are (n-1) linearly independent node equations. These equations are in terms of node potential.
Mesh | loop analysis is nothing but an application of KVL. In mesh analysis, we apply KVL around each loop in a circuit. If we have 'b’ branches and 'n’ nodes in a circuit then we have b-(n-1) linearly independent equations. These equations are in terms of mesh currents.
Why do we study network theorems?
I suppose you are familiar with basic network analysis methods. Like node analysis and mesh analysis. When dealing with KCL and KVL we will have a fairly large number of independent equations. As I discussed in methods of analysis, we get (n-1) node equations and b-(n-1) mesh current equations, so total ‘b’ number of equations. Did you find them time-consuming, you have to deal with so many equations (the number of node and mesh equations are equal to the number of elements/branches present in a network). For example, you have a network/circuit having 4 passive elements, then there are 4 current or voltage equations. And if there are 5 passive elements you have to solve 5 equations and so on. Analysing more complex circuits by using these methods seem to be ridiculous. What do you think?? So instead of applying tedious mesh and nodal analysis to complex networks, we develop network theorems.
Network theorems
- Superposition theorem
- Reciprocating theorem
- Thevenin’s theorem
- Norton's theorem
- Compensation theorem
- Millman's theorem
- Substitution theorem
- Maximum power transfer theorem
- Tellegen's theorem
Applications
- Some of these apply to linear as well as non-linear circuits
- With the help of these theorems, we can solve DC as well as AC Circuits
- Easy comprehension of complex circuits
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