Mesh Analysis

 Mesh Analysis

For steady-state AC circuits we can use the same method of writing mesh equations by inspection if we replace resistances with impedances and conductances with admittances.

      Let's look at an example.

The matrix R is symmetric,  rkj = rjk and all of the off-diagonal terms are negative or zero.

The rkk  terms are the sum of all resistances in mesh k.

The rkj terms are the negative sum of the resistances common to BOTH mesh k and mesh j.

The vk (the kth component of the vector v) = the algebraic sum of the independent voltages in mesh k, with voltage rises taken as positive.

What happens if we have independent current sources in the circuit?

1. Assume temporarily that the voltage across each current source is known and write the mesh equations in the same way we did for circuits with only independent voltage sources.
2. Express the current of each independent current source in terms of the mesh currents and replace one of the mesh currents in the equations.
3. Rewrite the equations with all unknown mesh currents and voltages on the left hand side of the equality and all known voltages on the r.h.s of the equality.