2.3 : Mesh Analysis

Mesh analysis is a valuable method for simplifying circuit analysis using mesh currents as key circuit variables. Unlike nodal analysis, which focuses on determining unknown voltages, mesh analysis applies Kirchhoff's voltage law (KVL) to find unknown currents within a circuit. This method is particularly convenient in reducing the number of simultaneous equations that need to be solved.

A fundamental concept in mesh analysis is the definition of meshes and mesh currents. A mesh is a closed loop within a circuit that does not contain any other loops within it. Each mesh is assigned a mesh current, typically assumed to flow in a clockwise direction within its respective loop.

For mesh analysis to be applicable, the circuit must be planar, meaning it can be drawn on a flat surface without branches crossing one another. Planar circuits are ideal for mesh analysis, as it simplifies the process. The steps involved in mesh analysis are as follows:

• Assign mesh currents to each of the "n" independent meshes in the circuit.
• Apply KVL to each of the "n" meshes, expressing element voltages in terms of mesh currents using Ohm's law.
• Solve the resulting "n" simultaneous equations to obtain the values of the mesh currents.

These mesh currents can then determine various branch currents within the circuit. It is important to note that mesh currents are distinct from branch currents unless a mesh is isolated.