Love it or hate it, distortion is something we should always be listening for in our microphones, audio chain, and playback. Measuring distortion quantitatively is difficult but total harmonic distortion provides a decent method of calculating distortion in an audio signal.
What is total harmonic distortion in audio and microphones? Total harmonic distortion (THD) is a measurement of the harmonic distortion in an audio signal as a percentage of cumulative overtones added to a fundamental frequency. It is most easily measured with a sine wave. 1% THD is the typical threshold when measuring a mic’s maximum sound pressure level.
Let’s dive deeper into the definition of total harmonic distortion and discuss its use in microphones and audio.
What Is Audio Distortion?
Before we get into total harmonic distortion, let’s first look at microphone and audio distortion in general.
Audio distortion is described as any deformation of an audio signal at an output compared to an input.
Typically this comes from limitations in electronic components (analog or digital).
Note that gain, in and of itself, boosts the amplitude of audio signals without causing any deformation of the signal. Therefore gain does not mean distortion. However, too much gain will certainly push the aforementioned electronic components above their limitations and cause signal distortion. This is often unwanted (like in microphone signals and audio mixes) and sometimes intentional (guitar amplifiers and effects).
Audio can be either analog or digital and each type has its own distortion.
Digital Audio Distortion
Digital distortion (also referred to as clipping) often sounds harsh, over-compressed, and may severely deform the original audio signal. Digital clipping is generally avoided at all costs unless it is for special effect.
In digital audio, we use a decibels full scale (dBFS) to denote signal amplitude. 0 dBFS is the digital ceiling where all bits are 1s. This is referred to as the ceiling. It’s the absolute maximum amplitude a digital audio signal can have.
Any signal peak (or trough) that is boosted above 0 dBFS is effectively flattened or “clipped.”
The result is a harsh and over-compressed output signal.
Analog Audio Distortion
Although analog distortion, at its extremes, will also sound harsh and over-compressed, it is much more forgiving than digital distortion.
Analog distortion happens when the electronic components that pass audio signals (AC voltages) are overloaded. When the signal is too strong for these components, it will become distorted.
Analog distortion comes on much more gradually than digital and sounds much warmer, rather than so harsh.
In fact, analog distortion is often strived for due to saturation. Signal saturation is the effect that analog distortion has on creating or boosting the harmonics of an analog signal. Saturation adds character to audio signals and is a big reason why many listeners prefer analog over digital audio recordings.
Microphone transducers are inherently analog. Overloading any of the microphone’s electrical components will results in audio distortion.
Very rarely are microphone diaphragms overloaded (though ribbon diaphragms may be susceptible to this at very high sound pressure levels). Rather, it’s particularly the active electronics in microphones that have the greatest of being overloaded.
More distortion may happen at the mic preamplifier level once gain is applied to the signal. We must ensure that we aren’t applying too much gain in order to avoid distortion.
Digital distortion of mic signals can happen once the signal is converted to digital audio via an analog-to-digital converter ADCs. These ADCs are typically designed into audio interfaces but can also be designed into digital microphones (like USB mics).
To learn more about analog and digital microphones, check out my article Are Microphones Analog Or Digital Devices? (Mic Output Designs).
Sine Wave Distortion
The first thing to note about total harmonic distortion (THD) is that it is measured in percentage rather than in absolute value.
THD is measured against a single frequency audio signal (a sine wave).
When a sine wave becomes distorted, its waveform typically becomes more and more square-like:
A sine wave with the maximum amount of distortion possible takes on the form of a square wave. This is not actually physical possible in reality, but represents the idea of an incredibly distorted sine wave quite well.
The sine wave has a single frequency and no harmonics.
The ideal square wave, however, contains an infinite series of odd integer harmonics. Amplitudes of even integer harmonics are zero while odd integer harmonics are calculated with the following formula:
An = 2A0 [2 / (π·n)]
An is the amplitude of the nth harmonic
A0 is the amplitude of the fundamental frequency
n is the number of the harmonic
Note that with square waves, the amplitude of the “zeroth harmonic” or fundamental frequency (A0) is half the value from peak to trough. For example, a square wave with a peak at 1 V and a trough a 0 V would have:
A0 = 0.5 V
A1 = 0.63 V
A2 = 0 V (even integer harmonic)
A3 = 0.21 V
and so on…
The point of the above equation is to show that as a sine wave becomes distorted, harmonics are created!
With this in mind, let’s look at total harmonic distortion.
What Is Total Harmonic Distortion?
Total harmonic distortion is defined as the ratio of the sum of the power of all harmonics to the power of their fundamental frequency.
In an equation, this looks like:
THD = (√V12+V22+V32+···) / V0
V0 is the rms voltage of the fundamental frequency
Vn is the rms voltage of the harmonics
The particularity of THD distortion is that it can applies to signals that cover full frequency ranges. However, it becomes overly complicated unless measured from a single frequency sine wave.
It’s important to note that the audible range of human hearing is from 20 Hz – 20,000 Hz. Therefore, any harmonics above 20 kHz do not affect our perception of signal distortion and are generally left out of the equation.
For example, if we had a fundamental frequency of 400 Hz, our audible harmonics would be:
- F0 = 400 Hz
- F1 = 800 Hz
- F2 = 1600 Hz
- F3 = 3200 Hz
- F4 = 6400 Hz
- F5 = 12,800 Hz
- F6 = 25,600 Hz but we would never hear it, so it’s power is typically omitted from the calculation.
So, from what we’ve gathered above, a pure sine wave would only have a fundamental frequency and would, therefore, have a THD of 0%.
However, as this sine waves distorts, harmonics are produced and THD becomes a factor.
As the extreme distortion of an [ideal] square wave, the THD would be equal to a whopping 48.3%. With this amount of distortion, it makes sense that the square wave sounds so obviously different than the sine wave.
Usually a 1% THD value is enough to notice and say the signal is distorted. However, as we’ve discussed, we’re really only capable of calculating THD in sine waves. Real world sounds are complex and THD is very difficult to figure out, even though real world sounds can be broken down into a series of sine waves.
THD And Maximum Sound Pressure Level
So why is THD so important to us as audio and microphone enthusiasts?
Total harmonic distortion is used to calculate the maximum sound pressure levels of microphones.
Typically microphone manufacturers use 1% THD as a limit to measure max SPL though some go lower to 0.5%.
Essentially, the microphone is subjected to a 1 kHz tone (a sine wave).
This can be done through a calibrated zero-distortion loudspeaker at the mic’s diaphragm. Alternatively, a 1 kHz AC signal can be injected directly into the microphone’s circuitry at the capsule output. Remember that the diaphragm is rarely, if ever, overloaded and so it can be bypassed.
The 1 kHz sine wave is then increased in amplitude (either in sound pressure level via a speaker or by volts rms vis direct injection). The clean sine wave’s amplitude is increased until the mic’s output suggests a set total harmonic distortion percentage.
At this point, manufacturers know that the microphone will begin to distort at 1 kHz at a certain SPL or AC voltage. Manufacturers take this SPL, or the voltage to calculate a theoretical SPL, as the microphone’s maximum sound pressure level.
For more information on max SPL, check out my article What Does A Microphone’s Maximum Sound Pressure Level Actually Mean?
What is mic level? Mic level is the typical and expected analog audio signal level of professional microphone outputs and mic preamplifier inputs. Nominal mic level is generally between 1 to 100 millivolts AC (-60 to -20 dBV). Mic level signals need amplification to reach line level for use in mixing consoles and DAWs.
To learn more about microphone signals and mic level, check out the following My New Microphone articles:
What Is A Microphone Audio Signal, Electrically Speaking?
Do Microphones Output Mic, Line, Or Instrument Level Signals?
What is microphone gain? Microphone gain increases the amplitude of a microphone signal. Gain boosts signal strength from mic level to line level so the microphone signal is compatible with professional audio equipment. Mic preamps control gain and are the first circuits a signal passes through after the microphone output.
For a deep read about microphone gain, check out my article What Is Microphone Gain And How Does It Affect Mic Signals?