Nonlinear distortion

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.

${\displaystyle v=\sum _{k=1}^{\infty }a_{k}u^{k}}$

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

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

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

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