AC Nodal and Mesh Analysis Discussion D11.1 Chapter 4

AC Nodal Analysis

How did you write nodal equations by inspection?

Writing the Nodal Equations by Inspection The matrix G is symmetric, gkj = gjk and all of the off-diagonal terms are negative or zero. The gkk terms are the sum of all conductances connected to node k. The gkj terms are the negative sum of the conductances connected to BOTH node k and node j. The ik (the kth component of the vector i) = the algebraic sum of the independent currents connected to node k, with currents entering the node taken as positive.

Example with resistors v1 v2 v3

For steady-state AC circuits we can use the same method of writing nodal equations by inspection if we replace resistances with impedances and conductances with admittances. Let's look at an example.

Problem 4.31 in text Change impedances to admittances

Matlab Solution

Nodal Analysis for Circuits Containing Voltage Sources That Can’t be Transformed to Current Sources If a voltage source is connected between two nodes, assume temporarily that the current through the voltage source is known and write the equations by inspection.

Problem 4.33 in text Note: V2 = 10 assume I2

Problem 4.33 in text Note: V2 = 10 assume I2

Matlab Solution

AC Mesh Analysis

How did you write mesh equations by inspection?

Writing the Mesh Equations by Inspection 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.

Example with resistors

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.

Problem 4.38 in text: Find I1 and I2

Matlab Solution

What happens if we have independent current sources in the circuit? 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. Express the current of each independent current source in terms of the mesh currents and replace one of the mesh currents in the equations. 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.

Problem 4.40 in text: Find I0 Assume you know V2 Note I2 = -2

Matlab Solution

Problem 4.40 in text: Find I0 Assume you know V2 Note I2 = -2