Total harmonic distortion tutorial (THD)

What is distortion ?

In this total harmonic distortion tutorial, we’re gonna explain the different types of distortion and how they go about their business. Distortion happens when an audio signal is “distorted” from its original state. We call distortion, any form of alteration that you bring to an audio signal, regardless of the type or source. Distortion can affect several aspects of the sound signal, but the main ones include :

• The amplitude.
• The phase.
• The creation of spurious frequencies that did not exist in the input signal.

These spurious frequencies that appear (and should not), are called harmonics and we will explain them in this total harmonic distortion tutorial. The harmonic distortion can occur on any level of the sound chain (signal processor, amplifier, loudspeaker etc). When it occurs on the source or amplifier circuitry, it gives the impression that the loudspeakers are breaking up. This is because they produce the same sound like when the loudspeakers are over-driven. It can also lead to premature loudspeaker failure.

Sometimes distortion is created with a certain purpose and its presence is desirable. This is the case with guitar amplifiers and speaker systems where the coloration, as a result of distortion, is intentional. Many musical instruments take advantage of distortion to produce a sound that we are now very familiar with. However, most of the time, distortion is a bad thing, and people try to minimize it.

Total harmonic distortion tutorial

Like we said earlier, harmonics are spurious frequencies that appear in the audio signal, but weren’t present in the original signal. Harmonic distortion is composed of one or more signal components that are whole number multiples of the input frequency.

For example :

If a pure 100 Hz sine wave serves as an input signal, and the output signal contains, not only the 100 Hz tone, but also 200 Hz, 300 Hz, 400 Hz and 500 Hz tones (whole number multipliers of 100 Hz), this means that the signal exhibits harmonic distortion.

• 100 Hz = The fundamental.
• 200 Hz = 2nd harmonic.
• 300 Hz = 3rd harmonic.
• 400 Hz = 4th harmonic.
• 500 Hz = 5th harmonic.
• etc.

What is interesting with harmonics is that our ears tend to pick them up in different ways depending on their order :

• Odd-order harmonics are more noticeable than even-order harmonic (ex : 3rd, 5th , 7th).
• Higher order harmonics are more noticeable  than lower order harmonics (ex : 6th,  7th).

As you can see from the graph above, we have the fundamental, which is the 100 Hz test tone, and its respective harmonics on multipliers of 100 Hz. In an ideal world, we will have just the 100 Hz tone and nothing else, but since harmonics are present, the tone will present a certain amount of distortion. The values of each harmonic is expressed by either a negative decibel rating, which states how many decibels the harmonic is below the test signal, or by percentage, which states the percentage of the main signal.

If you add up the values of all the harmonics, you will get the value of the Total Harmonic Distortion (THD). Sometimes,  the manufacturer specifies the value for each harmonic, but most common is the total harmonic distortion value.

Causes for harmonic distortion

For amplifiers : Harmonic distortion occurs in amplifiers when the waveform is clipped. This happens when you push the amplifier beyond its comfort zone, to the point where the output cannot produce adequate voltage to trace the input waveform. Other causes may include circuit faults or design errors.

For loudspeakers : Loudspeakers induce harmonic distortion when the voice coil is rubbing or striking against the magnetic assembly. Resonances can also induce harmonic distortion, diaphragm break-up also.

How to measure harmonic distortion ?

In this total harmonic distortion tutorial, we will try to enumerate a few methods on how to measure the THD. One method is to use a notch filter. You feed a test tone into the input of the device we are testing, and then we use a deep, very narrow band rejection filter on the same signal. In a perfect world, there will be no signal at the output. In reality, anything that is picked up at the output is distortion. Because it measures evrything besides the test tone (which is not there anymore, because of the notch filter), it actually measures the total harmonic distortion. The problem with this measurement is that it also measures any noise present at the output

Quoted THD

You will sometimes see manufactures use specifications like these :

THD+N < 1% @ +4 dBm. Which is the equivalent of :

Total Harmonic distortion & Noise is less than 1% at +4 dBm.

If you look at the other specs of the equipment and see that the noise specification is low, you can tell that the 1% rating is mostly distortion. If the noise is high, then maybe a large part of the distortion is noise voltage. To reduce this noise problem, we forget the notch filter and use a wave analyzer instead. The analyzer will present the signals bands in 1/10 octave accuracy. You will have a detailed graphic view of the entire output waveform, which includes frequency and amplitude. With this information at hand, we can easily identify each harmonic and measure them. When using this type of measuring for total harmonic distortion, you will find specifications that will look like this :

2nd Harmonic – 50 dB.

3rd Harmonic -75 dB at 200 W of output at 1 kHz.

When you see this type of specification, you will know that an analyzer took part in the measurement, and noise is not a factor, unless there is a very high noise level.

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dB vs percentage

If you want to convert the harmonic levels into percentages, you can use the following formula (if the ratings are in relation to watts, not volts) :

Distortion (%) = 100 * 10^_db/10

So for the above example, we have the 2nd harmonic percentage equal to 100 * 10^-50/10 = 100 * 0.00001 = 0.001 %. You must understand that if you have the values of each individual harmonic in decibels, you cannot just add them together, you will have to you the following formula :

Distortion (Total dB) = 10 log (10^dB1/10 + 10^dB2/10 + 10^db3/10 + … + 10^dBn/10).

Example for calculating THD

We have a sound card with the following harmonic distortion :

• 2nd Harmonic -40 dB.
• 3rd Harmonic -65 dB.
• 4th Harmonic -50 dB.
• 5th Harmonic -70 dB.
• All other harmonics are negligible (below -80 dB).
• Values are relative to 252 mW.

Total dB = 10 log ( 10^-40/10 + 10^-65/10 + 10^-50/10 + 10^-70/10) = 10 log (10^-4 + 10^-6.5 + 10^-5 + 10^-7) = 10 log ( 0.0001 + 0.0000003162 + 0.00001 + 0.0000001) = 10 log (0.0001104162) = 10 * (-3.956967203) = -39.6 dB

If you want to convert this value into percentage, you will have :

THD (%) = 100 * 10 ^-39.6/10 = 100 * 10^-3.96 = 100 * 0.0001096 = 0.001 %

THD = 0.001%

How to accurately interpret manufacturer specifications ?

Let’s continue our total harmonic distortion tutorial with a few tips on how to interpret numbers. We all know that, in these days, we should take the manufacturer specifications with a grain of salt. Not necessarily because the specs have measurement errors, but because they might use a measuring procedure that inflates the numbers. This might deceive an inexperienced person. We all know about amplifier power ratings, some quoted as RMS, some as peak power, musical power etc. While all of them represent some kind of measurement, not all of them will translate into real world performance. In this total harmonic distortion tutorial, we will explain what to look after when reading THD specs.

To get the most accurate total harmonic distortion specifications, you should ask the following questions :

• At what operating level / levels was the measurement made?
• At what frequency, or frequency range, was the measurement made?
• What input termination and output load was used ?
• Was noise part of the measurement, or was it a pure distortion test?

Distortion is dependent on the output voltage, and the frequency of the test tone. When you reach the maximum voltage or power output, distortion will rise dramatically and suddenly. This is because of the clipping we talked earlier. For this reason, manufacturers will quote distortion figures somewhere below this rise.

Distortion will sometimes be higher at low frequencies in transformer coupled equipment, particularly at higher levels, due to transformer core saturation. In most audio circuits, distortion will rise with higher frequencies. This is the reason, manufacturers measure total harmonic distortion at 1 kHz, as it will give the most favorable number.

Conclusion

As we wrap this total harmonic distortion tutorial, we can definitely say that distortion is always something to avoid, with a select few exceptions. Reducing THD as much as possible, is always a good idea, and it ensures a pleasurable listening experience. While total harmonic distortion specs are most common in electronic devices (amplifiers, sound processors etc), don’t forget about the last piece in your audio chain. People usually neglect the harmonic distortion of speakers and only focus on their frequency response. Speakers with bad harmonic distortion will almost certainly yield a bad experience.

References

1. The Sound Reinforcement Handbook 2nd Edition by Gary Davis and Ralph Jones (Yamaha, 1988). (Amazon affiliate paid link)
2. Image source : link.