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# Nonlinear distortion

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.

$v = \sum_{k=1}^\infty a_ku^k$

For larger values of u, the higher order coefficients such as a2 and a3 come into play.

## Effects of nonlinearity

Nonlinearity can have several effects, which are unwanted in typical situations. The a3 term for example would, when the input is a sine wave with frequency ω, result in an extra sine wave at , as shown below.

$v = (a_1 + \frac{3}{4}a_3) sin(\omega t) - \frac{1}{4}a_3 sin(3\omega t)$

In certain situations, this spurious signal can be filtered away because the "harmonic" 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.

Last updated: 05-24-2005 14:20:50
03-10-2013 05:06:04