Distortion factor

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A main cause for bad sound quality in a hifi amplifier are nonlinear distortions. A measure for nonlinear distortions is the distortion factor.


The distortion factor is the result from a mathematical equation. The equation is resembles the geometrical means. It is a measure for the intensity of the nonlinear distortions. The distortion factor computes itself from the primary wave and their harmonics. All other disturbances do not have to do anything with the distortion factor.With a Hifi amplifier is the indication of the distortion factor an important characteristic. An indication alone is however not sufficiently, in particular in interaction with the human hearing.

An example of distortion factor calculation:

Equations for distortion factor computation

Fig. 1  shows the definition of the variables in the distortion factor model. To see are the primary wave with 1 kHz and additional harmonious Frequenzen.  

An integral multiple of the primary wave means harmoniously. In our case the fundamental wave has a frequency of 1 kHz. That means the harmonious frequencies amount to 2 kHz, 3 kHz, 4 kHz etc..

The simulated time intervall covers 0 to 2 milliseconds. U1(t) is the undistorted sine wave. Udis(t) is the distorted sine wave, whose distortion factor is computed.

Fundamentally sine wave and harmonics

Fig. 2 shows the individual sine waves. The harmonious frequencies have consciously a high amplitude, in order to be well recognizable in the diagram. The red curve U1(t) is the undistorted ideal sine.

More distorted and not distorted sine in the 

Fig. 3  shows ideal sine wave U1(t) in red and a distorted sine wave Udis(t) in blue. Now we want to compute the distortion factor of the blue signal.

Distortion factor computation for the example

Fig. 4 points the equation to the computation of the distortion factor. This equation is appropriate for four harmonics here. If more or less harmonious one is to be considered, then it is to be extended or reduced. The distortion factor is always positive and can reach values minimum between 0 and maximally 1. The distortion factor is normally indicated in per cent. In our example Udis(t) has a distortion factor of 11.2 %.

Measurement distortion factor

A measuring instrument which can divide the distorted voltages into their spectral portions, is necessary for. A spectrum analyzer or FFT analyzer is very well suitable. They measure the amplitudes of the harmonious frequencies. The measured values must be processed thereafter with the distortion factor equation.

Example of a measurement with the spectrum analyzer

K2_Spektrum.jpg (28091 byte)

The picture shows the spectrum of an amplifier, measured with a Hewlett Packard  HP 3580A spectrum analyzer. It shows a fundamental wave of 10 kHz, a second harmonic with 20 kHz and the third harmonic with 30 kHz. The amplitudes amount to: xa=(0dB) 1 V, xb=(-34dB) 20 mVolt, xc=(-78dB) 126 µVolt

Calculation with the distortion factor equation:

Distortion factor computation for an amplifier

The distortion factor amounts to nevertheless 2 %. The principal part by the distortion factor is the second harmonic. Odd-numbered third harmonic is very small. The measurement originates from the attempt Hifi amplifier with tubes sound

Another method the distortion factor to measure are special measuring instruments, e.g. a HEWLETT PACKARD HP8903A or HP8903B. This distortion factor of these instruments work according to another principle. They use an adjustable filter, which can reject the fundamental from the total signal. They do not use the computation with distortion factor equation. The indicated result is the total harmonic distortion plus noise THD+N. THD+N is ever larger in practice than the purely harmonious distortion factor THD.

Distortion factor and Hifi amplifier

Again, the equation for the distortion factor gives only a number. This number says something about the size of the distortion factor, however nothing about the spectral composition. The spectral composition is very important for a Hifi amplifier. The question is: the weighting of the even-numbered or do the odd-number cause the harmonious distortion factor? If the distortion factor consists predominantly of even-numbered harmonious ones, then these distortions are clearly less audible. If the principal parts are however odd-number, the distortions are clearly more audible. Therefore e.g. the specification of the distortion factor in the folder of a Hifi amplifier is to be always regarded with caution. A distortion factor of e.g.. 1 %, are not a world fall, if it concerns only even-numbered harmonious. Consist this 1 % however of odd-number harmonious ones, they are surely clearly more audible. Besides, the most important at the indication of the distortion factor is not the exact amount or the number of zeros. Surely, the order of magnitude is of importance, very importantly however is the spectral composition of the distortion factor. Also the boundary conditions of the measurement are to be considered. At the edge noticed, the most important at the indication of the distortion factor is not the accurate number or the amount of the zeros. The order of magnitude is safe, importantly is already, very importantly naturally the spectral composition of the distortion factor. Important are also the boundary conditions of the measurement. The boundary conditions are e.g. the indication of: load impedance at the amplifiers output, output voltage, signal frequency and temperature of the output stage. The boundary conditions have much influence on the distortion factor. Often in an amplifier folder is indicated only rarely the spectral composition of the signal, still more rarely the boundary conditions of the measurement. From electrotechnical view that is incomplete results of measurement. The economical aspect is another.

Distortion factor and mathematician

this person's group does not have problems with the distortion factor. From mathematical view this equation is simplest toy.

Distortion factor and theoretician

have it already more heavily. It must think over the causes its and develop models for it.

Distortion factor and practical man

the poor boy has it most heavily. He gets an equation from the mathematician and from the theoretician a theory. Both say to him like distortion factor develop and as he to be computed are. The theoretician says also which against it to be done is. The practical man tries it out and announces: it did not always function. He builds already for a long time at his circuit and gets ever more the opinion: the topic is extremely complicated and in the refinement hardly still theoretically controllable. In particular with the task to increase the zeros behind the comma still further. In practice inserting of zeros is far behind the comma a lengthy task, which can degenerate into a life's work.

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