chapter  32

## Distortion Measurement

WithMichael F. Toner, Gordon W. Roberts

A sine-wave signal will have only a single-frequency component in its spectrum, that is, the frequency of the tone. However, if the sine wave is transmitted through a system (such as an amplifier) having some nonlinearity, then the signal emerging from the output of the system will no longer be a pure sine wave. That is, the output signal will be a distorted representation of the input signal. Since only a pure sine wave can have a single component in its frequency spectrum, this situation implies that the output must have other frequencies in its spectral composition. In the case of harmonic distortion, the frequency spectrum of the distorted signal will consist of the fundamental (which is the same frequency as the input sine wave) plus harmonic frequency components that are at integer multiples of the fundamental frequency. Taken together, these will form a Fourier representation of the distorted output signal. This phenomenon can be described mathematically. Refer to Figure 32.1, which depicts a sine-wave input signal x(t) at frequency f 1, applied to the input of a system A(x), which has an output y(t). Assume that system A(x) has some nonlinearity. If the nonlinearity is severe enough, then the output y(t) might have excessive harmonic distortion such that its shape no longer resembles the input sine wave. Consider the example where the system A(x) is an audio amplifier and x(t) is a voice signal. Severe distortion can result in a situation where the output signal y(t) does not represent intelligible speech. The total harmonic distortion (THD) is a figure of merit that is indicative of the quality with which the system A(x) can reproduce an input signal x(t). The output signal y(t) can be expressed as