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Nonlinear distortion is a term used to describe the phenomenon that the relation between the "input" and "output" signals of, for example, a device is not exactly linear. The term is used in fields such as electronics, audio and telecommunications.
Model
For many devices, a linear model is accurate only for small signal levels. For example, at 2 Volts input, a typical audio amplifier might put out 20 V, meaning the linear gain is 10 V/V. For 3 V input, it might then output 30 V. However, the model implies that at 50 V input it would produce 500 V, which is not possible with most amplifiers.
Mathematically, the input-output relationship of many devices should be described by a polynomial or Taylor series, as shown below.
<math>v = \sum_{k=1}^\infty a_ku^k<math>
For larger values of u, the higher order coefficients such as <math>a_2<math> and <math>a_3<math> come into play.
Effects of nonlinearity
Nonlinearity can have several effects, which are unwanted in typical situations. The <math>a_3<math> term for example would, when the input is a sine wave with frequency <math>\omega<math>, result in an extra sine wave at <math>3\omega<math>, as shown below.
<math>v = (a_1 + \frac{3}{4}a_3) sin(\omega t) - \frac{1}{4}a_3 sin(3\omega t)<math>
In certain situations, this spurious signal can be filtered away because the "harmonic" <math>3\omega<math> lies far outside the frequency range used, but in cable television, for example, third order distortion could cause a 200 MHz signal to interfere with the regular channel at 600 MHz. Similarly, "mixing" of two or more frequencies could occur.
Causes of nonlinearity
In electronic devices, the non-linearity of components such as resistors and transistors is one of the possible causes of signal distortion.
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