"Chapter 1 - The Op Amp's Place in the World" - HTL Wien 10

Superposition
2.6 Superposition
2-8
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.
V1
Figure 2–11.Superposition Example
R1
R3
V2
R2
VOUT
When V 1 is grounded, V 2 forms a voltage divider with R 3 and the parallel combination of
R 2 and R 1. The output voltage for this circuit (V OUT2) 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 V 1 is Grounded
V OUT2 V 2
R3
V2 R1 R2 VOUT2
R 1 R 2
R 3 R 1 R 2
(2–23)
Likewise, when V 2 is grounded (Figure 2–13), V 1 forms a voltage divider with R 1 and the
parallel combination of R 3 and R 2, and the voltage divider theorem is applied again to calculate
V OUT (Equation 2–24).
Figure 2–13. When V 2 is Grounded
R1
V1 R3 R2 VOUT1