When a signal x(t) of a particular frequency f1 passes through a nonlinear system, the output of the system consists of f1 and its harmonics. The following expression describes the relationship between f1 and its harmonics.
f1, f2 = 2f1, f3 = 3f1, f4 = 4f1, …, fn = nf1
The degree of nonlinearity of the system determines the number of harmonics and their corresponding amplitudes the system generates. In general, as the nonlinearity of a system increases, the harmonics become higher. As the nonlinearity of a system decreases, the harmonics become lower.
The following figure shows an example of a nonlinear system where the output y(t) is the cube of the input signal x(t).
The following equation defines the input for the system shown in the previous figure.
x(t) = cos(ωt)
The following equation defines the output of the system shown in the previous figure.
x3(t) = 0.5cos(ωt) + 0.25[cos(ωt) + cos(3ωt)]
In the previous equation, the output contains not only the input fundamental frequency ω but also the third harmonic 3ω.
A common cause of harmonic distortion is clipping. Clipping occurs when a system is driven beyond its capabilities. Symmetrical clipping results in odd harmonics. Asymmetrical clipping creates both even and odd harmonics.