##### From Circuit Analysis I with MATLAB Applications

This chapter begins with nodal, loop and mesh equations and how they are applied to the solution of circuits containing two or more node-pairs and two or more loops or meshes. Other topics included in this chapter are the voltage-to-current source transformations and vice versa, Thevenin's and Norton's theorems, the maximum power transfer theorem, linearity, superposition, efficiency, and regulation.

## 3.1 Nodal, Mesh, and Loop Equations

*Network Topology* is a branch of network theory concerned with the equations required to completely describe an electric circuit. In this text, we will only be concerned with the following two theorems.

**Theorem 3.1**

Let *N* = *number of nodes in a circuit*; then *N* ? *1* independent nodal equations are required to completely describe that circuit. These equations are obtained by setting the algebraic sum of the currents leaving each of the *N* ? *1* nodes equal to zero.

**Theorem 3.2**

Let *L* = *M* = *number of loops or meshes*, *B* = *number of branches*, *N* = *number of nodes*, in a circuit; then *L* = *M* = *B* ? *N* + *1* independent loop or mesh equations are required to completely describe that circuit. These equations are obtained by setting the algebraic sum of the voltage drops around each of the *L* = *M* = *B* ? *N* + *1* loops or meshes equal to zero.

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3.2 Analysis with Nodal Equations In writing nodal equations, we perform the following steps: For a circuit containing N nodes, we choose one of these as a reference node assumed to be zero volts or...

This chapter begins with nodal, loop and mesh equations and how they are applied to the solution of circuits containing two or more node-pairs and two or more loops or meshes. Other topics included in...

3.3 Analysis with Mesh or Loop Equations In writing mesh or loop equations, we follow these steps: For a circuit containing M = L = B ? N + 1 meshes (or loops), we assign a mesh or loop current i 1,...

3.3 Analysis with Mesh or Loop Equations In writing mesh or loop equations, we follow these steps: For a circuit containing M = L = B ? N + 1 meshes (or loops), we assign a mesh or loop current i 1,...

LECTURE 31: REVIEW OF NODAL ANALYSIS AND MESH ANALYSIS OF CIRCUITS The Laplace transform is a very useful tool for analyzing linear time-invariant (LTI) electric circuits. It can be used to solve the...