Mesh Analysis
-One easier method of solving the above circuit is by using Mesh Current Analysis or Loop Analysis which is also sometimes called Maxwell´s Circulating Currents method. Instead of labelling the branch currents we need to label each “closed loop” with a circulating current.
What is Mesh?
- is a loop that does not enclose other loops.
What is a Supermesh?
- when two meshes have a(dependent or independent) current source in common.
What is a Supermesh?
- when two meshes have a(dependent or independent) current source in common.
Cases to be considered for Mesh Analysis:
Case 1:
- A current source exists only in a one mesh
Case 2:
- A current source exists between two meshes
Steps in Using Mesh Analysis:
1. Check if circuit is planar.
2. Identify meshes, mesh currents, and supermeshes.
a) Rearrange the circuit if possible to position current source on a single mesh.
b) Use i-v characteristic equations of ICS to find mesh currents and reduce the number of unknowns.
3. Write KVL at each mesh and supermesh.
4. Solve for mesh currents.
5. Calculate problem unknowns from mesh currents. If you need to calculate the voltage across a current source you may have to write KVL around a mesh containing the current source.
6. For consistency and elimination of errors, always markall mesh currents in clockwise direction and write down KVLs in the same direction.
- Examination of the circuit can also tell us which of the two methods are best suited for the circuit in hand. We always want to reduce the circuit equations into the smallest number of equations in the smallest number of unknowns. The number of equations from nodal analysis and mesh analysis are given:
NNV = Nnode − 1 − NVS
NMC = Nmesh − NCS
NMC = Nmesh − NCS
where NV S and NCS are numbers of voltage and current sources, respectively. Thus, always inspect the circuit, find NVS and NCS, and proceed with the method that results in the smallest number of equations to solve.
Note: You need to check to ensure that the circuit is a planar circuit. If it is not one cannot use mesh analysis and should use nodal analysis.
Watch a Video Using Mesh Analysis!
Reflection:
We have now finished discussing the two types of techniques in analyzing a circuit. For me, mesh analysis is more easier than nodal analysis. It may also depend on the person which method is convenient for him/her to use.
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