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Harmonics due to clipping and non-linear PAbasics

Harmonics are unwanted higher frequencies which superimposed on the fundamental waveform creating a distorted wave pattern.

Harmonics are created by an electrical or electronic device or circuit that has a voltage-current characteristic which is not linear. I.e., the output voltage is not proportional to the input voltage.

Harmonics due to clipping

Denote the original unclipped signal as , the clipped signal is . While the original signal has only one frequency component f, the clipped signal will have higher order harmonics with frequency components of n·f.

  • Typically, clipping is symmetric in both positive and negative directions, i.e., . Symmetric clipping generates odd harmonics with n = {3, 5, 7, ...}.
  • An asymmetric clipping generates both even and odd harmonics with n = {0, 2, 3, 4, 5, ...}.
Toolbox: harmonics due to clipping
Time domainFrequency domain
original signal:
  • f [Hz] =
  • A =
Clipped signal:
  • Cmax =

Harmonics due to non-linear power amplifier (PA)

A power amplifier is linear if its output voltage is simply a constant times the input voltage:

But in reality they have non-linearities that make the output voltage a function of higher order terms of the input voltage. The output voltage for such non-linear amplfier can be expressed as a Taylor series: . In addition, power amplifier may also clip the input signal.

Below shows the impact of a non-linear power amplifier to the input signal.

Toolbox: harmonics due to non-linear power amplifier
Time domainFrequency domain
Input signal:
  • f [Hz] =
  • A =
Output signal:
  • Cmax =