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, ...}.
| Time domain | Frequency domain | |
|---|---|---|
original signal:
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Clipped signal:
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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 domain | Frequency domain | |
|---|---|---|
Input signal:
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Output signal:
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