# Defining Distortion

Applying a pure single-frequency sine wave to a perfectly linear system produces an output signal having the same frequency as that of the input sine wave. However, the output signal might have a different amplitude and/or phase than the input sine wave. Also, when you apply a composite signal consisting of several sine waves at the input, the output signal consists of the same frequencies but different amplitudes and/or phases.

Many real-world systems act as nonlinear systems when their input limits are exceeded, resulting in distorted output signals. If the input limits of a system are exceeded, the output consists of one or more frequencies that did not originally exist at the input. For example, if the input to a nonlinear system consists of two frequencies f1 and f2, the frequencies at the output might have the following components:

- f1 and harmonics, or integer multiples, of f1
- f2 and harmonics of f2
- Sums and differences of f1, f2
- Harmonics of f1 and f2

The number of new frequencies at the output, their corresponding amplitudes, and their relationships with respect to the original frequencies vary depending on the transfer function. Distortion measurements quantify the degree of nonlinearity of a system. Common distortion measurements include the following measurements:

- Total harmonic distortion (THD)
- Total harmonic distortion + noise (THD + N)
- Intermodulation distortion

## Application Areas

You can make distortion measurements for many devices, such as A/D and D/A converters, audio processing devices, analog tape recorders, cellular phones, radios, televisions, stereos, and loudspeakers.

Measurements of harmonics often provide a good indication of the cause of the nonlinearity of a system. For example, nonlinearities that are asymmetrical around zero produce mainly even harmonics. Nonlinearities symmetrical around zero produce mainly odd harmonics. You can use distortion measurements to diagnose faults such as bad solder joints, torn speaker cones, and incorrectly installed components.

However, in some cases you might want to use nonlinearities. For example, many musical sounds are produced specifically by driving a device into its nonlinear region.