AC Network Analysis

Superposition Theorem

The superposition theorem for AC circuits is:
The current in any part of a network containing two or more sources can be calculated by analyzing the network one source at a time. The current due to each source is calculated for each branch of the network. The net current in each branch of the network is then the phasor sum of the respective branch currents due to each source.

The next example demonstrates application of the superposition theorem to AC circuits.

Example 1:
Solve the circuit of figure below with the superposition theorem.

Circuit for Example 1.

Solution:

1. The impedance network with V_b deleted, as shown in the figure below, can be solved for the branch currents due to V_a only.

Example circuit with voltage V_b replaced by a short circuit (solution for currents due to V_a)

2. The impedance network with V_a short-circuited, as shown in the figure below, can be solved for the branch currents due to V_b only.

Example circuit with voltage V_a replaced by a short circuit (solution for currents due to V_b)

3. The net branch currents are the phasor sums of the branch currents due to V_a and V_b.