Proof of superposition theorem for linear circuits

In summary, the conversation revolves around the proof of the superposition theorem in a circuit with only resistors, capacitors, inductors, and independent/dependent voltage/current sources. The suggestion is to start by demonstrating superposition for the individual components based on their transfer functions.
  • #1
Bipolarity
776
2
Can someone link me/explain to me the proof of this theorem? I can't seem to find it online. Thanks!

BiP
 
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  • #3
This is just part of the definition of a linear circuit: any circuit for which superposoption does NOT apply is nonlinear
 
  • #4
f95toli said:
This is just part of the definition of a linear circuit: any circuit for which superposoption does NOT apply is nonlinear

So how does one prove that the superposition theorem applies in a circuit containing only resistors, capacitors, inductors, and independent/dependent voltage/current sources?

BiP
 
  • #5
Perhaps start by demonstrating superposition for the individual components based on their transfer functions?

[tex] I_{total} = C\frac{d(v1+v2)}{dt} = C\frac{dv1}{dt} + C\frac{dv2}{dt} [/tex]
 

1) What is the superposition theorem for linear circuits?

The superposition theorem states that the response in any branch of a linear circuit is equal to the algebraic sum of the responses caused by individual sources acting alone, while all other sources are turned off. This allows for a simpler analysis of complex circuits with multiple sources.

2) How is the superposition theorem used in circuit analysis?

The superposition theorem is used in circuit analysis to break down a complex circuit into smaller, simpler circuits with only one source at a time. By analyzing each individual circuit, the total response of the complex circuit can be determined by taking the sum of the individual responses.

3) Can the superposition theorem be applied to non-linear circuits?

No, the superposition theorem is only applicable to linear circuits. Non-linear elements, such as diodes and transistors, do not follow the principle of superposition and therefore cannot be analyzed using this theorem.

4) What are the limitations of the superposition theorem?

The superposition theorem can only be applied to circuits that contain linear elements, such as resistors, capacitors, and inductors. It also assumes that the circuit is in a steady state and that all sources are independent.

5) Can the superposition theorem be used to calculate power in a circuit?

Yes, the superposition theorem can be used to calculate power in a circuit. The power dissipated by each source can be calculated separately, and then added together to find the total power in the circuit. However, care must be taken when dealing with non-linear elements, as their power dissipation may not follow the principle of superposition.

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