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Chapter 3: Nodal and Mesh Equations Circuit Theorems
By Steven T. Karris
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From Circuit Analysis I with MATLAB Computing and Simulink/SimPowerSystems Modeling
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 heorems, the maximum power transfer theorem, linearity, superposition, efficiency, and regulation. 3.1 Nodal, Mesh, and Loop EquationsNetwork 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.
Copyright Orchard Publications 2009 under license agreement with Books24x7
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Topics of Interest
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...
(Read More)
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...
(Read More)
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...
(Read More)
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...
(Read More)
This chapter begins with the application of nodal analysis, mesh analysis, superposition, and Thevenin's and Norton's theorems in phasor circuits. Then, phasor diagrams are introduced, and the...
(Read More)
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