Electrical Engineering ⇒ Topic : Superposition Theorem with sinusoidal excitation

Superposition Theorem 

The superposition theorem can be used to analyse ac circuits containing more than one source. The superposition theorem states that the response in any element in a circuit is the vector sum of the responses that can be expected to flow if each source acts independently of other sources. As each source is considered, all of the other sources are replaced by their internal impedances, which are mostly short circuits in the case of a voltage source, and open circuits in the case of a current source. This theorem is valid only for linear systems. In a network containing complex impedance, all quantities must be treated as complex numbers

                                                        figure (a)

Consider a circuit which contains two sources as shown in Fig. (a)

Now let us find the current /passing through the impedance Z₂ in the circuit.According to the superposition theorem, the current due to voltage source V ∠O° V is I₁ with current source I_a ∠O° A open circuited.

                              figure (b)                                                                             figure (c)

The current due to I_a ∠ 0° A is I₂ with voltage source V∠ 0° short circuited

The total current passing through the impedance Z₂ is

                                     I = I₁ + I₂

The superposition theorem finds use in the study of AC circuits, amplifier circuits, where sometimes AC is often superimposed with DC. This theorem defines the behaviour of a linear circuit. Within the context of linear circuit analysis, this theorem provides the basis for all other theorems. Given a linear circuit, it is easy to see how mesh analysis and nodal analysis make use of the principle of superposition. It is not possible to apply superposition theorem directly to determine power associated with an element. In addition, application of superposition theorem does not normally lead to simplification of analysis. It is not best technique to determine all currents and voltages in a circuit, driven by multiple sources.

Superposition theorem works only for circuits that are reducible to series/parallel combinations for each of the sources at a time. This theorem is useless for analyzing an unbalanced bridge circuit. Networks containing components like lamps or varistors could not be analyzed.