Like nodal and supernode for ac circuit that have the same procedure as in the dc circuit, mesh and supermesh for ac circuit will do the same.
Learning Kichhoff’s laws for AC circuit will lead us to:
- Node and supernode for ac circuit
- Mesh and supermesh for ac circuit
- Superposition for ac circuit
- Source transformation for ac circuit
- Thevenin and Norton for ac circuit
Mesh and Supermesh for AC Circuit
Kirchhoff’s voltage law (KVL) forms the basis of mesh analysis. The validity of KVL for ac circuit can be seen in Mesh Analysis for dc circuit here.
Keep in mind that the very nature of using mesh analysis is that it is to be applied to the planar circuit.
Make sure to read what is ac circuit first.
Mesh Analysis of AC Circuit
Like the nodal analysis of ac circuit, we will not cover the basic explanation of its principle. You have to read the link above in order to understand ‘how to use it’ properly.
Let us review the examples below to be able to analyze the ac circuit using mesh analysis.
Determine current Io in the circuit of Figure.(1) using mesh analysis.
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| Figure 1. Example of mesh analysis for ac circuit |
Applying KVL to mesh 1, we obtain
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| (1.1) |
For mesh 2,
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| (1.2) |
For mesh 3, I3 = 5. Substituting this to Equations.(1.1) and (1.2), we obtain
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| (1.3) |
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| (1.4) |
Equations.(1.3) and (1.4) can be rewritten in matrix form as
and its determinants are
The desired current is
Read also : energy in a coupled circuit
Supermesh Analysis of AC Circuit
Next, we will analyze an ac circuit with supermesh within it.
Before doing that, make sure you have understood the principle of supermesh analysis first.
Solve for Vo in the circuit of Figure.(2) with mesh analysis.
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| Figure 2. Example of supermesh analysis for ac circuit |
As shown above, meshes 3 and 4 form a supermesh due to the current source between the meshes. For mesh 1, KVL results
or
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| (2.1) |
For mesh 2,
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| (2.2) |
For the supermesh,
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| (2.3) |
Due to the current source between meshes 3 and 4, at node A,
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| (2.4) |
We reduce the above four equations to two by elimination, instead of solving them directly.
Combining Equations.(2.1) and (2.2),
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| (2.5) |
Combining Equations.(2.2) to (2.4),
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| (2.6) |
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| Figure 3. Analysis circuit in Figure.(2) |
From Equations.(2.5) and (2.6), we obtain the matrix equation
We obtain the determinants
Current I1 is obtained as
The required voltage Vo is
