Superposition Theorem

Superposition Theorem

The superposition theorem eliminates the need for solving simultaneous linear equations by considering the

effect on each source independently.

To consider the effects of each source we remove the remaining sources; by setting the voltage sources to

zero (short-circuit representation) and current sources to zero (open-circuit representation).

The current through, or voltage across, a portion of the network produced by each source is then added 

algebraically to find the total solution for current or voltage.

The only variation in applying the superposition theorem to AC networks with independent sources is that we

will be working with impedances and phasorsinstead of just resistors and real numbers.

The superposition theorem is not applicable to power effects in AC networks since we are still dealing with a 

nonlinear relationship.

It can be applied to  networks with sources of different frequencies only if the total response for each

frequency is found independently and the results are expanded in a nonsinusoidal expression .

One of the most frequent applications of the superposition theorem is to electronic systems in which the DC and AC analyses are treated separately and the total solution is the sum of the two.

When a circuit has sources operating at different frequencies,

•The separate phasor circuit for each frequency must be solved independently, and

•The total response is the sum of time-domain responses of all the individual phasor circuits.  

Sample Problem using Superposition.

I learned that superposition Theorem  to AC Networks with independent sources is that we are dealing with

impedances  and phasors instead of having real numbers.