# Distortion Measurement

### Introduction

Distortion, in audio systems, is usually understood as meaning ‘non-linear distortion’, which is heard as a roughness and confusion of the sound. Non-linearity often refers to a lack of proper correspondence between instantaneous input signal voltage and instantaneous output signal voltage. In a linear system, one with a linear transfer function that is, twice the input voltage produces twice the output voltage, but in practical systems this may not be the case.

### THD (total harmonic distortion)

Plotting output versus input to determine the transfer function is not a useful method for determining distortion in audio systems though, for two reasons. Firstly, they usually respond only to changing signals (not DC), in the audio frequency range. Secondly they may suffer varying time delays (phase shift) at different frequencies. Both of these effects would produce a non-linear response to, say, a voltage ramp, even in a system free from non-linear distortion. Testing with a sine-wave input conveniently avoids these problems, while allowing the distortion to be quantified in terms of ‘harmonics’ (new components appearing at the output with frequencies that are multiples of the input sine wave frequency). The term ‘Total Harmonic Distortion’ refers to the sum of all these components, measured rms (root mean square) as a percentage of the total (rms) output.

THD is commonly measured by using a notch filter to remove the input frequency from the output, allowing what is left to be measured, and in this case the measurement should strictly be referred to as THD+N (noise), since it includes any random noise on the output.

### Crossover Distortion and how THD Fails as a Measure of Audibility

In the early days of audio, one form of non-linearity dominated in all systems. Valves (tubes), tape recordings and transformers all tended to produce less output at high levels of input, in a symmetrical manner (affecting positive and negative sides of the signal equally). This ‘soft limiting’ squashes the peaks of the sine-wave, producing a form of distortion known as ‘odd-order’ which contains only odd harmonics of the input (3rd, 5th etc). Processes that cause asymmetric distortion generate only even harmonics (2nd, 4th etc) and are rarer. Odd order distortion products are sometimes considered more objectionable than even order, since they are not musically related in the way that even order products are (by octave intervals).

With the introduction of transistor amplifier though, a new form of distortion arose, known as ‘crossover distortion’ and caused by a kink in the transfer characteristic as the sine-wave crosses zero. This is a form of ‘high order’ distortion, and produces odd harmonics (3rd, 5th, 7th, 9th etc) which extend right up the frequency range, with little reduction in amplitude, and because the ear analyses sounds in terms of frequency components, and is most sensitive to frequencies in the 2kHz-8kHz region, it turns out that we are particularly sensitive to even small amounts of crossover distortion, when compared to the ‘low-order’ distortion of valves and tape, which generate mostly 3rd harmonic.

While early experiments had determined that 0.1% THD (-40dB) was the very minimum that could be heard, it soon became apparent that this was not the case for transistor power amplifiers, where 0.01% or less could be heard as harshness on the sound. Nevertheless, THD measurements continued to be quoted, and audio measurement itself got a bad reputation among the ‘hi-fi’ fraternity, who turned to listening tests as the only way to assess audio equipment.

### Attempts at Weighted Distortion measurement

What was really need was a subjectively valid method of measurement. To simply assume that measurements of noise, distortion or anything else are meaningful in themselves is to miss the point. Audio measurement, if it is to give useful results, should never be about quantifying a system in purely engineering terms. It must be about using methods that have already been shown to correspond to subjective effect, and such methods must rely in the first instance on listening tests. So why not just listen? There are many good reasons for measuring, rather than listening. Our ears vary greatly, between individuals and from day to day (depending on what levels of sound we have been exposed to) so they are not reliable tools. They also have dificulty distinguishing one form of corruption (such as distortion) in the presence of another (such as noise, or flutter, or the reverberation of the listening room). Then there is the problem of the long signal chain, in which recordings pass through numerous items, for example from microphone to mixer to tape recorder to transmitter to broadcast receiver to loudspeaker. If we are to guarantee that what we hear will be indistinguishable from the original, then each part of the chain must contribute a lower level of distortion or noise than our ears could possibly detect, if their sum total is to be inaudible.

### Distortion Residue Measurement

There is a relatively simple way to weight distortion, which works remarkably well across all devices from tape to power amps and digital systems, and has been incorporated into an IEC standard. Lindos Electronics recommends this, and has chosen to call the result ‘Distortion Residue’ for easy identification as distinct from THD. It involves nulling out the fundamental of a 1kHz test tone, and then measuring what remains just as if it were noise, using the ITU-R 468 weighted measurement method (which Lindos Electronics refer to as simply 468-weighted). This emphasises high-order harmonics around 6kHz by 12dB but attenuates those above 10Khz, and ignores those above 20kHz. Because it uses a Quasi-Peak rectifier, the method also gives proper temporal weighting to brief bursts that would be largely ignored by the averaging inherent in rms measurement.

### Why the Distortion Residue Method Works

When we listen to speech and music, the content is mostly in the 300Hz to 3kHz region. Because real sounds are complex and constantly changing, any low order distortion products from this region will appear more as random noise than as individual harmonics tones, but predominantly in the 900Hz to 9kHz part of the spectrum (3rd harmonic predominantly). If they were tones, we could fairly assess them using the A-weighting curve, derived from equal-loudness contours for our hearing process, but for noise such weighting is not valid. Rather than being most sensitive in the 2kHz region, as the A-weighting curve would suggest, our ears are much more sensitive in the 6kHz region, for reasons to do with spectral density that are explained elsewhere. This is why the 468-weighting curve, which was designed to reflect our sensitivity to noise rather than tones, should be used, with its 12.2dB of emphasis at 6.3kHz.

If we now consider speech or music subject to crossover distortion in a power amplifier, another very important consideration arises. Typical speech and music waveforms do not cross zero very often. There may be violins or cymbals contributing significant high frequencies to the waveform, but most of the time these will be riding on top of bass notes such that zero-crossings are much less frequent than they would be for a pure tone. Where a relatively pure tone does arise from a violin note, it will not have many audible harmonics, whatever the distortion mechanism, because the 3rd harmonic of a 3kHz tone is at 9kHz, and the 5th is at 15kHz which will not be heard by most listeners. Most people are surprised to find that they can tell absolutely no difference between a 6kHz square wave and a 6kHz sine wave, but of course the 3rd harmonic is at 18kHz, and even listeners who can hear to 18kHz will usually have greatly reduced sensitivity at this frequency.

The distortion residue from a typical speech or music signal passed through a power amplifier is therefore better imagined as a series of ‘clicks’ occurring every time the waveform passes through zero. Their total contribution to a Fourier Analysis over a period of seconds, as shown on a spectrum analyser, is very low, hence the low THD figures traditionally obtained from ‘bad’ amplifiers, but our ears do not analyse over seconds. Each hair-cell in the cochlea responds as a narrow band filter over a period of milliseconds (the higher the frequency the shorter the response time) and so it can give a brief comparatively high level response, heard as a click, to each crossover event. Whether we hear a given even depends on this short-term response, not some average over a relatively long period, as is implicit in any rms (root mean square) measurement.

The Quasi-Peak rectifier used for 468-weighted measurement, was based on listening tests in which subjects were asked to rate the loudness of various clicks, tone bursts, and other sounds of various duration, and with various repetition rates, against a reference tone. It therefore reflects pretty well the temporal aspects of hearing, and does not diminish the effect of each click by averaging, though it gives less weight to very short bursts, which our ears do not have time to respond to fully, or to bursts with a low repetition rate which our brains give less importance to.

### Distortion Residue Measurement in Practice

Distortion Residue measurement works, and its use is to be encouraged (hence its adoption as the sole method of distortion measurement in the Lindos MiniSonic MS20). It will always give a result higher than the corresponding THD measurement, but this is an advantage, making for easier measurement. On tape machines for example, where distortion is mostly 3rd-harmonic it will give a result some 8dB worse than a corresponding THD measurement, and if significant modulation noise is present, as on compact cassette, then this too will be properly emphasised leading to an even higher figure. On power amplifiers, the result may be 10 or 20dB worse than a corresponding THD measurement, depending on the harshness (order) of the crossover characteristic, giving quite a reliable indication of audible performance. Where once it used to be said that 0.1% THD (-60dB) represented the threshold of audibility for distortion, except for power amplifiers, it is probably now fair to say that 0.3% Distortion Residue (-50dB) represents the threshold of audibility regardless of what equipment is being measured. Digital systems normally produce distortion that is more like noise than harmonics, and faulty digital convertors are likely to produce repeating ‘clicks’ rather than tones, in much the same way as crossover distortion does, so the method is very well suited to digital measurements.

It should be noted that attempting to measure distortion residue at frequencies other than 1kHz would not be useful. At low frequencies (100Hz) the effect of the weighting filter would be to severely attenuate all the low order harmonics. Whilst weighted measurement of low frequency distortion might be a useful concept, emphasising the enhanced audibility of harmonics over their fundamental, the weighting curve would have to be normalised to a low frequency (such as 100Hz) rather than 1kHz, and should probably be closer to A-weighting, since low frequency distortion is commonly noticed on sustained bass notes.

### Other Types of Distortion Measurement

Intermodulation distortion measurement is a valid way of measuring the interaction between components of different frequencies, and three main methods have been used, as explained elsewhere. The quoting of figures for intermodulation distortion never seems to have caught on though, possibly because the results from tape machines for example are atrociously high. This, coupled with the fact that tape recordings can sound very good, lends weight to the assertion that intermodulation distortion is not in itself as significant as some would have us believe.

The same is true of ‘Transient distortion measurement’, a topic that gained popularity for a while in audiophile circles. Provided that recordings are limited to 20kHz, as they should be, all that is needed is for every part of the signal path to be able to handle 20kHz at maximum level, a statement that again gains support from the fact that some of the best recordings were made on analog tape recorders, which struggle to manage this, and certainly cannot record square waves!

This is a complex topic, but Lindos recommends that distortion residue measurement is probably all that is generally required to indicate whether a signal path is likely to give audible distortion on programme material.