# Harmonic distortion in power amplifiers

jojo January 14, 2014 6 Comments

### Harmonic distortion in power amplifiers.

Distortion is a serious problem faced in power amplifier design. In faithful amplification the output signal must be a scaled replica of the input signal and if there is any dissimilarity between the input and output waveform, then the output is said to be distorted. Unpleasant sound output coming from an audio system, which is no more the faithful reproduction of the original audio is mainly due to distortion. Other reasons for bad sound output are noise, clipping etc and they are not discussed here. The figure given below shows faithful amplification and distorted amplification. In the above figure you can see that every point in the input waveform (waveform1) is exactly reproduced in the non distorted output (waveform2) and the falling edges of the input waveform are unfaithfully reproduced in the distorted output (waveform 3).

#### Harmonic distortion.

Harmonic distortion can be explained as any distortion or corruption in the output waveform due to the generation of harmonics. The integer multiples of a fundamental frequency are called harmonics. In audio amplifier domain, the frequency of the input signal is taken as the fundamental frequency. For example, if  “x” is the fundamental frequency then 1x,2x, 3x, 4x………nx are the harmonics.

Harmonic distortion in power amplifiers are mainly caused by the non linearities of the active elements (transistors). The active element used for amplification whether BJT, FET, MOSFET or anything like that  may not equally amplify every points in the input waveform and this is the reason behind the non-linearity. In different amplifier configurations Class A has the highest linearity, then class AB, then Class B and finally Class C has the worst linearity.

How well designed the audio amplifier may be , its output might  contain some distortion mainly in the form of even harmonics. Out of the even harmonics 2nd order harmonics will be generally the prominent one. Second order harmonic distortion is the amount of 2nd order harmonic content present in the output signal with respect to the fundamental frequency.

#### Total Harmonic Distortion or THD.

Total harmonic distortion or THD is a very important parameter in the audio amplifier domain. THD is a measure of the amount of harmonic components present in a signal. It can be defined as the ratio of the sum of the powers of all the harmonic components to the power of the fundamental frequency. In audio amplifier applications the signals must be commonly of sine wave type and in this case the THD is defined as the  ratio of the RMS amplitude of the higher order harmonic frequencies  to the RMS amplitude of the fundamental frequency. THD is usually expressed in percentage .

If V1 is the amplitude of the fundamental frequency and V2, V3, V4……..Vn are the amplitudes of the higher order harmonic frequencies, then THD can be expressed as

THD = √(V2²+V3²+V4²………+Vn²) / √(V1²)

ie;        THD = {√(V2²+V3²+V4²………+Vn²)} / V1

#### THD+N ratio.

THD+N is another scale used for expressing the sound quality of an audio power amplifier. It means total harmonic distortion plus noise. THD+N is very commonly used now a days and it covers almost every type of corruption present in the signal. THD+N can be defined as the ratio of the summation of all higher order harmonics plus  summation of all noise components to the fundamental frequency. Since noise is also accounted in this scale it is better than the THD scale. The reason for the noise present in the amplifier output includes, the power supply interference, RF interference, switching noises, thermal noise of the active elements etc.

THD+N is usually measured using a distortion analyzer. This is done by separating the fundamental frequency using a notch filter  and then measuring what is left over. The left over usually consists of the harmonics plus all noise components. THD+N is also represented in percentage and the lower it is, better the sound quality of the amplifier.

##### Intermodulation distortion.

Intermodulation distortion is another type of distortion seen in audio amplifiers. Even though intermodulation distortion is not directly related to harmonic distortion, I think it is worthy to have a brief explanation here. An ideal power amplifier will be purely linear and it will not produce any intermodulation. A practical audio amplifier will have some non-linearity and when such a system if fed with two or more input frequencies, amplitude modulation occurs between the frequencies and the output may contain sum frequencies, difference frequencies, integer multiples of sum frequencies and integer multiples of difference frequencies.

If F1 and F2 are the two frequencies given to a  non-linear system then the result of intermodulation distortion will be F1+F2, F1-F2, n(F1+F2), and n(F1-F2) where “n” is an integer. The integer multiples of the base frequencies F1 and F2 are not produced by intermodulation distortion. In simple words, intermodulation distortion induces additional frequency components in the output signal which are not harmonically related to the fundamental frequencies (input). Intermodulation distortion is usually expressed as the ratio of the RMS value of the additional frequency components in the output  to the RMS value of the original output.

##### Signal to noise ratio  S/N or SNR.

Signal to noise ratio or SNR or S/N is another important audio amplifier parameter. The SNR also has nothing to do with the harmonic distortion, but it deserves a short discussion here. Signal to noise ratio can be defined as the ratio of the useful signal power to the unwanted (noise) signal power. The SNR actually gives an estimate of the false-information present in a signal. A signal to noise ratio (SNR) more than one means the useful signal component will be larger than the noise components. SNR is usually expressed in decibel (dB).

Signal to noise ratio  (SNR) is measured in two steps. Firstly the output signal level of the amplifier with input (usually sine wave) is measured. Then the input signal is removed and the output level is measured. No input signal doesn’t mean that the input terminals of the amplifier are left open. The common approach is to connect it to a signal generator and voltage output of the signal generator is reduced to zero.That way the input of the amplifier gets connected to a low-impedance source with zero amplitude. Then both values are divided to get the SNR.

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