Superposition principle

The superposition principle states that, in a linear system, the combined response to several inputs equals the sum of the responses to each input separately.

Linearity: A property of a system or map in which sums and scalar multiples are preserved. Superposition holds when the system’s response is linear in its inputs.
Wave interference: The combination of waves that produces a resultant displacement or field through addition. The resulting wave is the sum of the waves present at each point.
Linear differential equation: A differential equation in which the unknown function and its derivatives appear linearly. Its solution set is closed under addition when the equation is homogeneous.
Nonlinear optics: The study of how intense light changes a material’s optical response and interacts nonlinearly. At high intensities, optical responses can mix frequencies and cease to add independently.
Homogeneity (mathematics): A scaling property in which scaling an input scales its output by the same factor. Together with additivity, homogeneity characterizes linear response.
Linear circuit: An electrical circuit whose voltage and current responses obey linear relations. Its response to multiple sources can be found by adding separate source responses.
Boundary value problem: A differential equation problem specified by conditions imposed at the domain’s boundary. Superposition can combine solutions only when the governing equation and boundary conditions preserve linearity.
Saturation (electronics): A nonlinear operating regime in which an electronic device’s output stops increasing proportionally with input. Saturation prevents the output for combined signals from equaling the sum of separate outputs.
Additivity: A property in which a function maps a sum of inputs to the sum of their outputs. It is the part of linearity that lets individual source effects be summed.
Superposition theorem: A circuit-analysis method that computes each independent source’s effect separately and sums the results. It applies the principle directly to voltage and current in linear circuits.

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