- Source: Nonlinear distortion
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.