Nonlinear distortion

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

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

Effects of nonlinearity

Nonlinearity can have several effects, which are unwanted in typical situations. The a 3 term for example would, when the input is a sine wave with frequency ω , result in an extra sine wave at 3 ω , 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 )

In certain situations, this spurious signal can be filtered away because the "harmonic" 3 ω 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.