Superposition

Superposition is a theorem that can be applied to any linear circuit. Essentially, when there are independent sources, the voltages and currents resulting from each source can be calculated separately, and the results are added algebraically. This simplifies the calculations because it eliminates the need to write a series of loop or node equations. An example is shown in Figure 2–11.

Figure 2–11.Superposition Example

When V1 is grounded, V2 forms a voltage divider with R3 and the parallel combination of R2 and R1. The output voltage for this circuit (VOUT2) is calculated with the aid of the voltage divider equation (2–23). The circuit is shown in Figure 2–12. The voltage divider rule yields the answer quickly.

Figure 2–12. When V1 is Grounded

Likewise, when V2 is grounded (Figure 2–13), V1 forms a voltage divider with R1 and the parallel combination of R3 and R2, and the voltage divider theorem is applied again to calculate VOUT (Equation 2–24).

Figure 2–13. When V2 is Grounded

After the calculations for each source are made the components are added to obtain the final solution (Equation 2–25).

The reader should analyze this circuit with loop or node equations to gain an appreciation for superposition. Again, the superposition results come out as a simple arrangement that is easy to understand. One looks at the final equation and it is obvious that if the sources are equal and opposite polarity, and when R1 = R3, then the output voltage is zero. Conclusions such as this are hard to make after the results of a loop or node analysis unless considerable effort is made to manipulate the final equation into symmetrical form.