Sonic Mayhem

Simply put, distortion is any change to a signal other than a simple gain change or delay. Given that definition, one could reasonably look at compression and equalization as forms of distortion, but it''s probably more useful to take them at face value and look for any unintended consequences as distortion. For example, many EQ circuits change the phase of filtered frequencies relative to unfiltered frequencies—linear phase equalizers are designed to avoid this phase distortion.
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Isn't it ironic that a perfectly accurate account can completely miss the essential truth of an event, while fiction often reveals the most profound truths? As electronic musicians, many of us dance freely between these two realities, sometimes documenting a performance literally and sometimes fabricating a performance out of whole cloth. Often we find ourselves capturing an event as carefully as possible, just to transmogrify it thereafter for our own nefarious purposes.

The concept of distortion, then, is near and dear to our yin and anathema to our yang. In a guitar amp, distortion is treasured, whereas in a mic preamp it is most often reviled. In this article we'll take a close look at distortion. What is it, and what types exist? How is distortion described, and how is it measured?

Deviant Behavior

Simply put, distortion is any change to a signal other than a simple gain change or delay. Given that definition, one could reasonably look at compression and equalization as forms of distortion, but it's probably more useful to take them at face value and consider any unintended consequences to be distortion. For example, many EQ circuits change the phase of filtered frequencies relative to unfiltered frequencies — linear phase equalizers are designed to avoid this phase distortion.

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FIG. 1: In an ideal device, output would change in direct proportion to input, but in real-world devices, the relationship between input and output is not linear, resulting in distortion.

Distortion ordinarily arises when any processor exhibits nonlinear behavior (see Fig. 1). In a hypothetical distortion-free device, for every change in the input signal, there would be a corresponding and proportional change in the output signal. In a guitar amplifier, for instance, playing twice as loud would result in twice the volume from the amp. Although this may in fact be more or less what happens most of the time, real-world devices always deviate from this behavior at least to some small degree.

All devices have their limitations, and distortion most often occurs as you approach these limitations. At more moderate levels there may be negligible distortion, but at the device's operational limits it misbehaves. If you push too much signal through a device, it will overload and distort. Crank up the volume on an amplifier too much, and it will overdrive and distort. These are amplitude distortions, wherein the output-to-input relationship changes at different volumes.

Usually, if a piece of gear's performance varies according to input frequency, we describe that behavior with a frequency-response curve. However, if that gear's frequency response varies with input level, that's frequency distortion.

Harmonic Convergence

The best-known form of distortion is harmonic distortion. This is a distortion in which the output contains additional components occurring at harmonics of the input signal. Harmonics, or overtones, are whole-number multiples of a fundamental frequency. If a 100 Hz sine wave were fed to the input of a device, harmonic distortion would exhibit itself as one or more additional tones at the output, at frequencies of 200, 300, 400, or 500 Hz and possibly other such harmonic frequencies.

If you think this sounds like terrific fodder for synthesis, you're right. Distortion techniques such as waveshaping allow the creation of complex waveforms from relatively simple oscillators. However, excessive distortion in a mic preamp is usually unwelcome.

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FIG. 2: When a device reaches its operational limits, it starts to flatten the waveform, and in extreme cases it clips the top right off.

When a device clips, the waveform is flattened (see Fig. 2). Analog tape tends to flatten the top of the waveform gently and progressively — in moderate amounts, this distortion is known by the pleasant name saturation — whereas digital converters and processors chop the top off abruptly, sharply, and unceremoniously. If this flattening happens symmetrically, the distortion produces odd-numbered harmonics. In the extreme case, the result is a square wave, which by definition comprises a fundamental plus its odd-numbered harmonics in appropriate proportion. This is known as odd-order harmonic distortion.

Even-order harmonic distortion arises from asymmetric nonlinearity, such as that found in single-ended amplification stages. Although this type of distortion is often correlated with tube designs, there are in fact symmetric (“push-pull”) tube designs and single-ended solid-state designs.

It is generally held that even-order distortion is more pleasant sounding than odd-order distortion. The reason for this is found in the musical relationships of the first odd and even harmonics to the fundamental. The first two even harmonics are one and two octaves above the fundamental, so even-order distortion results in tones that blend with the original signal under any conditions (see Fig. 3). The first two odd harmonics, however, are an octave plus a fifth and two octaves plus a major third above the fundamental, forming a major chord that imposes its own tonality on the music.

Totally Heinous, Dude

We can assess the impact of harmonic distortion with a measurement known as total harmonic distortion (THD). THD is measured by sending a sine wave through a device and measuring the strength of the harmonics that result. These measurements are then added together and divided by the strength of the fundamental.

More commonly, harmonic distortion is expressed in terms of total harmonic distortion + noise (THD + N). THD + N is measured by sending a sine wave through a device, filtering the sine wave from the device's output, and measuring what remains. This measurement is then divided by the strength of the fundamental. THD + N is not only more practical to measure than THD, it is also generally considered more useful in evaluating a device's performance.

However, both measurements are fraught with hazards. Because THD + N will always be a higher number than THD, some manufacturers cite only THD, making direct comparison between devices difficult. It is also common for them to leave out important details about the measurements, such as the frequency range and level of the test signals and how many harmonics were measured.

I M Different

A more severe form of distortion results from the interaction of multiple signals within a device. Intermodulation distortion (IMD) creates output frequencies that are equal to the sum and difference of the input frequencies and, to a lesser extent, the sums and differences of their multiples. This is directly analogous to the sum and difference tones we experience in the acoustic interaction of musical tones, but it is ordinarily considered an undesirable behavior within a circuit.

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FIG. 3: Even-order harmonic distortion is considered more pleasing than odd-order distortion because its primary components are octaves of the fundamental, whereas the major triad formed by the first two odd harmonics forces its own modality on the sound.

Because IMD results in by-products that are not musically related to the input signal, it is rarely considered useful. Therefore, some think it is a more useful measure of a device's distortion characteristics than either THD or THD + N. Judging IMD specs carries its own pitfalls, however, as there are different standards for measuring it. Each uses a different pair of input frequencies, and different relative strengths as well, so the expected results are much different. If the particular standard isn't cited with the measurement, no valid comparison with another device can be made.

Distortion is only one of many misbehaviors inherent in audio circuit design that we must understand to judge and use our gear appropriately. (Others include noise, crosstalk, wow and flutter for analog recorders, and jitter for digital recorders.) Somehow it holds a special place, though, as the one that is most obvious as a flaw and most interesting as a creative tool. When you find yourself trying to get a really accurate recording of a distorted guitar, you realize that “truth,” in a creative context at least, is relative.

Brian Smithers is course director of advanced audio workstations at Full Sail Real World Education in Winter Park, Florida. He also teaches music technology at Stetson University in DeLand, Florida.