WEEK 7: AC Circuit Analysis using Nodal Analysis Techniques

Nodal analysis is generally best in the case of several voltage sources. In nodal analysis, the variables (unknowns) are the "node voltages."

Nodal Analysis Procedure:

1. Label the N node voltages. The node voltages are defined positive with respect to a common point (i.e., the reference node) in the circuit generally designated as the ground (V = 0).
2. Apply KCL at each node in terms of node voltages.
   1. Use KCL to write a current balance at N-1 of the N nodes of the circuit using assumed current directions, as necessary. This will create N-1 linearly independent equations.
   2. Take advantage of supernodes, which create constraint equations. For circuits containing independent voltage sources, a supernode is generally used when two nodes of interest are separated by a voltage source instead of a resistor or current source. Since the current (i) is unknown through the voltage source, this extra constraint equation is needed.
   3. Compute the currents based on voltage differences between nodes. Each resistive element in the circuit is connected between two nodes; the current in this branch is obtained via Ohm's Lawwhere V_m is the positive side and current flows from node m to n (that is, I is m --> n).

   

3. Determine the unknown node voltages; that is, solve the N-1 simultaneous equations for the unknowns, for example using Gaussian elimination or matrix solution methods.

Nodal Analysis Example

Label the nodal voltages. Apply KCL. KCL at top node gives IS = IL + IC Supernode constraint eq. of VL = VS Solve for VT for instance.