Wednesday, October 8, 2014

Total Harmonic Distortion (THD)

Before I dive into discussing Total Harmonic Distortion (THD), let me take time to clarify a few terms related to it in the context of audio systems.
In Audio Systems, the behavior of linear and nonlinear audio signals can be adequately represented by a sinusoid. Nonlinear signals can always be decomposed to multiple sinusoids using an FFT technique (Fast Fourier Transform). When a sinusoidal signal is impressed upon a linear system, the output is also a sinusoidal signal, which in some cases might be phase or amplitude shifted. The scenario is quite different for a nonlinear system. In this case, the output signal is composed several sinusoids of smaller amplitudes or magnitudes superimposed on the original signal as can be seen in the next diagram. If you are outputting such a signal to a driver (speaker), it manifests elements of distorted percussion or noise which becomes significant with increase in the power of  the unwanted sinusoids. This phenomenon is known as harmonic distortion.

Higher order harmonic distortions

    Harmonic Distortion is thus a form of nonlinearity in which unwanted signals harmonically related to the the input signal are added to it. These unwanted harmonic signals always manifest at integral frequency multiples of the fundamental frequency (input signal), i.e at 2x the original signal, 3x, 4x, 5x, etc, and none at say, 1.5x the original, or any fractional multiplier. 

    If you  were to sum up the output power of all the resulting harmonic signals and express them as a ratio to the output power of the fundamental component, then you will have determined the Total Harmonic Distortion for that particular audio system. This is however never an easy feat to achieve for it is not practical and critical to measure all the harmonics for the entire audio signal range, 20Hz - 20kHz. Instead, manufacturers tend to ignore harmonic components at barely audible frequencies from 10kHz - 20kHz.  Very often, THD is specified at 1kHz. A low THD value implies a minimally distorted resulting output audio signal and consequently a good audio system or Amp.

     Some known facts about THD in audio systems


    Accurately measuring individual harmonics for the entire signal range is a very laborious task and is achieved by sweeping and plotting results on a spectrum analyzer to obtain the level of each harmonic. Manufacturers, do commonly avoid this THD test and instead opt for the simpler THD + Noise (THD+N), though in gadget sheets you  see plain THD. In the THD+N test, a specified number of harmonic amplitudes are measured under a specific test signal frequency, level and gain settings on the tested unit.


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