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Nonlinear distortion

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Signals phenomenon
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Nonlinear distortion is a term used (in fields such as electronics, audio and telecommunications) to describe the phenomenon of a non-linear relationship between the "input" and "output" signals of - for example - an electronic device.

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.

v = ∑ k = 1 ∞ a k u k {\displaystyle v=\sum _{k=1}^{\infty }a_{k}u^{k}}

For larger values of u, the higher order coefficients such as a 2 {\displaystyle a_{2}} and a 3 {\displaystyle a_{3}} come into play.

Effects of nonlinearity

Nonlinearity can have several effects, which are unwanted in typical situations. The a 3 {\displaystyle a_{3}} term for example would, when the input is a sine wave with frequency ω {\displaystyle \omega } , result in an extra sine wave at 3 ω {\displaystyle 3\omega } , as shown below.

v = ( a 1 + 3 4 a 3 ) s i n ( ω t ) − 1 4 a 3 s i n ( 3 ω t ) {\displaystyle v=(a_{1}+{\frac {3}{4}}a_{3})sin(\omega t)-{\frac {1}{4}}a_{3}sin(3\omega t)}

In certain situations, this spurious signal can be filtered away because the "harmonic" 3 ω {\displaystyle 3\omega } 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.

Nonlinear distortion applied to a superposition of two signals at different frequencies causes the circuit to act as a frequency mixer, creating intermodulation distortion.

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