Distortion figures and the decibel

Distortion adds frequencies that were not in the original signal. Datasheets quote it as a percentage, which looks tiny and is hard to compare with other specifications given in decibels. A conversion makes the comparison easy.

What THD measures

Total harmonic distortion (THD) is the combined level of the harmonics generated by a device, relative to the level of the fundamental at the output. A pure sine wave in, a sine plus harmonics out; all the values in the formula are measured on the output signal, never the input (with 20 dB of gain, using the input tone would make the figure ten times too high). The percentage is an amplitude ratio:

THD = √(V₂² + V₃² + V₄² + …) / V₁ · 100 %

where V₁ is the output fundamental and V₂, V₃, … are the output harmonics. THD+N includes the noise as well.

Percent and decibels

Because the percentage is an amplitude ratio, the conversion uses 20 · log:

So an amplifier with 0.003 % THD+N has distortion and noise about 90 dB below the signal. Convert any value with the distortion tool.

What can be heard

• Distortion below 0.1 % is rarely audible for music in normal conditions.
• The type matters: low-order harmonics (second, third) are masked by the signal and sound like a change in tone. High-order harmonics and distortion that does not follow the signal (crossover distortion in an amplifier) are far more audible.
• Loudspeakers have far more distortion than electronics, from 1 % to 10 % at high levels, and mostly at low frequencies.

Intermodulation

When two or more tones go through a non-linear device, the output contains their sum and difference frequencies as well as harmonics. Intermodulation distortion (IMD) sounds harsher than harmonic distortion because it is not related harmonically to the music. It is therefore measured separately.

Where distortion comes from

• Clipping: the extreme case, which produces strong odd harmonics.
• Saturation of transformers and tape, which is gentler and sometimes used on purpose.
• Non-linear amplification, such as an output stage working near its limits.

Signal-to-noise ratio and dynamic range

The same dB arithmetic applies to noise: a signal-to-noise ratio of 90 dB means that the noise is 0.003 % of the signal. See Decibels explained.

Reading specifications

1. Check at what level and frequency the THD was measured. Many devices are measured at 1 kHz and well below clipping.
2. Check the bandwidth of the measurement, since wider bandwidth includes more noise.
3. Prefer figures that include both distortion and noise.

Draft: written by an AI assistant, awaiting technical review.