56-mesh-analysis

Mesh analysis (or the mesh current method) is a method that is used to solve planar circuits for the currents (and indirectly the voltages). Planar circuits are circuits that can be drawn on a plane surface with no wires crossing each other. The mesh method is a well organized technique which relies on KVL. All equations are written according KVL, so it is important to have small number of loops.

Steps of the analysis:

  1. Find NB-(NN-1) independent loops in electric circuit. NB is number of branches, and NN is the number of nodes.
  2. In every chosen loop, draw loop current to be independent variable.
  3. Write set of equations based on KVL, where each of individual currents is taken into account by multiplying it with impedance on it’s path.
  4. Solve formed system of equations.
  5. Find branch currents as sum or difference of loop currents depending on current direction.

In the following example, the same scheme analyzed with nodal analysis, will be analyzed with mesh analysis.

nodal_a

In given scheme, there are two loops, so two equations should be written. However loop (mesh) equation can’t be written if current source is on the mesh. In this example, current source is contained between two essential meshes. In order to overcome problem, for writing first equation according to KVL, one loop that bypasses current source should be chosen.mesh01

For chosen mesh, equation is:

mesh_eq01

Another equation must be written according to KCL.

mesh02

Equation is:

mesh_eq02

Now, we have system of two linear equations with two variables (I2, I3) to be solved.

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