Superposition Theorem Analysis

This hardware involves capacitors and isolators.

The superposition theorem is that the linear responses in a circuit can be derived by summing the responses of the independent sources algebraically.

Homogeneity

Transistors are non-linear. The superposition theorem does not apply.

The superposition theorem rests upon two properties of linear circuits--homogeneity and additivity. Homogeneity means that the input and the output are related in a linear way--that is, when the input is multiplied by a constant (k), then the output will also be multiplied by k.

Linear circuits include circuits composed of resistors, capacitors, inductors and coupled inductors.

Additivity

Additivity means that separate outputs, created when a circuit is evaluated source by source, can be added together. The sum of the addition will equal the output when the sources are all on at once. In algebraic form: F(a) + F(b) = F(a+b).

Significance

The sigificance of superposition is that it allows otherwise complex matters to be treated simply.

It is crucial, though, to remember the limitation of the theorem. It only applies to linear circuits. Non-linear circuits such as transistors require different analyses.

As Omar Wing explained in a recent book, "Classical Circuit Theory," "[It] is the nonlinearity of the electronic devices that makes it possible to design such circuits as logic gates, amplifiers, multipliers and oscillators."

References

• Net Lecturer: Superposition Theorem
• University of Michigan, Dearborn: Superposition
• "Classical Circuit Theory"; Omar Wing; 2008.