Nonlinear distortion is a term used (in fields such as electronics

Electronics

Electronics is the branch of science, engineering and technology that deals with electrical circuits involving active electrical components such as vacuum tubes, transistors, diodes and integrated circuits, and associated passive interconnection technologies...

, 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 volt

Volt

The volt is the SI derived unit for electric potential, electric potential difference, and electromotive force. The volt is named in honor of the Italian physicist Alessandro Volta , who invented the voltaic pile, possibly the first chemical battery.- Definition :A single volt is defined as the...

s input, a typical audio amplifier

Amplifier

Generally, an amplifier or simply amp, is a device for increasing the power of a signal.In popular use, the term usually describes an electronic amplifier, in which the input "signal" is usually a voltage or a current. In audio applications, amplifiers drive the loudspeakers used in PA systems to...

 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

Polynomial

In mathematics, a polynomial is an expression of finite length constructed from variables and constants, using only the operations of addition, subtraction, multiplication, and non-negative integer exponents...

 or Taylor series

Taylor series

In mathematics, a Taylor series is a representation of a function as an infinite sum of terms that are calculated from the values of the function's derivatives at a single point....

, as shown below.



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

Effects of nonlinearity

Nonlinearity can have several effects, which are unwanted in typical situations. The term for example would, when the input is a sine

Sine

In mathematics, the sine function is a function of an angle. In a right triangle, sine gives the ratio of the length of the side opposite to an angle to the length of the hypotenuse.Sine is usually listed first amongst the trigonometric functions....

 wave with frequency , result in an extra sine wave at , as shown below.



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

Harmonic

A harmonic of a wave is a component frequency of the signal that is an integer multiple of the fundamental frequency, i.e. if the fundamental frequency is f, the harmonics have frequencies 2f, 3f, 4f, . . . etc. The harmonics have the property that they are all periodic at the fundamental...

" 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

Frequency mixer

In electronics a mixer or frequency mixer is a nonlinear electrical circuit that creates new frequencies from two signals applied to it. In its most common application, two signals at frequencies f1 and f2 are applied to a mixer, and it produces new signals at the sum f1 + f2 and difference f1 -...

, creating intermodulation distortion.