What is Distortion and How Do We Perceive it?

In the chain of modern audio equipment, the speakers will almost always be the weakest link in terms of accurate reproduction, and a major contribution to that weakness is the errant reproduction of bass. This article discusses some of the ways speakers and subwoofers distort accurate playback of low frequency content, and we will concern ourselves mainly at which point that it becomes audibly noticeable. We should emphasize that your speakers and subwoofers do distort bass sound, and this distortion is unavoidable and constant when in use, and it can be extensive at high amplitudes or very low frequencies. The amount of distortion produced by the low frequency driver would be considered atrocious in the signal chain up to the driver (excepting LP record playback), but the driver is nowhere near as linear of a device as the electronic signal processing. The nonlinearity of the driver may still be well below human perception, and since human perception is the end toward which all our audio equipment is merely a means, it is essential that we make this the aim of our discussion. This is just as well, since it would be hugely impractical to attempt to make a speaker or subwoofer playback bass with the accuracy of modern digital electronics signal processing.

When one considers the task of reproducing low frequencies from the perspective of physics, it is no wonder the most distortion is incurred in this band of the sound spectrum. Consider how much more air displacement in cubic inches is needed for a sealed 12” woofer to retain the same output level at 1 meter as frequency decreases. See Table 1:

Air Displacement vs Frequency and SPL



10 Hz 20 Hz 50 Hz 100 Hz 1000 Hz 80 dB 34.06 8.52 1.36 0.34 0.0034 100 dB 340.64 85.16 13.63 3.41 0.034 110 dB 1077.20 269.30 43.09 10.77 0.11

Table 1. Air displacement in cubic inches needed for a sealed 12” woofer to produce SPL/ frequency at 1m.

From this you can see that the challenge of linear bass playback rises exponentially as the frequencies fall. While our 12” woofer only needs to move .000952 inches to reproduce 110 dB at 1,000 Hz (a much smaller distance than the thickness of the average human hair), it must move 9.52 inches to achieve the same loudness level at 10 Hz!

Needless to say, the precise displacement of such large volumes of air is a formidable task, and at extremely deep frequencies producing even modest levels of output can overtax an ordinary low frequency driver . The stress of the high excursion levels needed to displace that much air manifests itself as various forms of distortion. At these limits of the transducer’s performance, stresses occur in a number of different system points, and these points contribute their individual distortions to the overall system distortion. We will briefly describe a few of these system points, but those unfamiliar with driver design and individual driver components may first want to read the beginning section of this loudspeaker driver design article to acquaint themselves with the basics before continuing. It should be said here that for this article we will focus on the more gradual and commonly heard forms of distortion which plague low frequency drivers rather than the sudden and glaring disruptions such as ‘bottoming out’ noises or ‘chuffing’ from port turbulence.

Some Causes of Distortion

Fig. 1. Driver in motion (GIF image courtesy of Kyle Dell’aquilas)

One of the chief sources of distortion, if not the dominant source of distortion in a bass driver, is variation in the magnetic field due to the travel of the voice coil with respect to the permanent magnet. Ideally, the force of the magnetic field between the voice coil and permanent magnet would remain the same at all times during excursion, but as the voice coil moves away from the center of its rest position, the force of the magnetic field exerted on the voice coil changes. At small excursions, the change of this magnetic force is slight, but at high excursions a larger section of the voice coil leaves the central magnetic field of the permanent magnet (called ‘the gap’), and, as a consequence, the magnetic force between the voice coil and permanent magnet is substantially weakened. Since the magnetic field has a weaker grip over the voice coil, control over the entire moving assembly has diminished. The loss of cone control manifests itself in distortion.

Another major contributor of distortion is the driver’s suspension, which consists of the spider and surround. The spider has a tough job; it has to keep the voice coil and former tightly centered in the gap yet allow the voice coil and former consistent, predictable travel perpendicular to their axis. The compliance of the spider becomes a big deal here; if the spider is too stiff, it makes the moving assembly (voice coil, former, and cone) too tough to move, but if it is too loose, it will not be able to keep the voice coil properly centered in the gap. The spider and surround must have a specific amount of compliance for the linear travel of the moving assembly, however both do exhibit nonlinear restoring forces. At small amplitudes the resulting distortions are inaudible, but they increase with sound level. At the extremes of excursion, the spider gains a severely inordinate amount of tension, and linear travel of the moving assembly is greatly diminished. At that point the cone cannot track the signal, and distortion sets in.

A third major cause of distortion is due to the inductance generated by the motion of the voice coil. To put it very simply, the motion of the charged voice coil within the magnetic field of the gap induces a counter voltage with its own corresponding magnetic field, and this counter magnetic field interferes with the initially desired electrodynamic relationship between the voice coil and permanent magnet. This phenomenon is a consequence of Lenz’s Law. There are ways of lessening adverse inductance effects, such as shorting rings, but it cannot be eradicated entirely.

One more cause of distortion is the effects of heat on the driver. A steady flow of electricity through the thin wire of the voice coil will inevitably cause it to heat up, and this heat raises the electrical resistance of the voice coil, which thereby reduces the current. Heat also causes a reduction in the magnetic force of the permanent magnet. Together these lead to a loss in sensitivity, a warping of frequency response, and a lowering of output capability. These effects are collectively known as thermal compression (or perhaps more commonly known as ‘power compression’), which can be seen in Figure 2.

Fig. 2. Thermal compression chart - courtesy of Klippel GmbH

Something to keep in mind is that the above discussed loudspeaker driver failings occur in every conventional driver. In well-engineered drivers, they only become a problem at the upper limits of their performance. However, for a poorly engineered driver, these can become problematic even at modest levels, so these issues may not only be relegated to loud output levels.

Types of Distortion: Linear vs. Nonlinear

We have discussed a few of the causes of distortion, but before we proceed to talk about the levels of audibility of distortion, we need to cover distortion types. Distortion can be divided into two groups: linear and nonlinear.

Linear distortion in speakers is considered to be mainly changes in amplitude and phase with respect to frequency response. Examples of those are effects are similar to what happens when using a filter or equalizer. In linear distortion, individual frequency bands may have altered amplitudes and thus a distorted balance of loudness in output, but the level of distortion remains proportionate to itself in that it does not depend on the input signal level; in a sense, linear distortion is ‘blind’ to the content it is distorting.

Nonlinear distortion, on the other hand, is dependent on the level and frequency of the input signal and can often create many output frequencies based on a single input frequency. Nonlinear distortion is much more difficult to predict and assess, because you have to know what the input signal is like in order to understand its relation to the output, whereas in linear distortion, the distorting mechanism will treat every incoming signal the same way.

The Audibility of Linear Distortion in Low Frequencies

Linear distortion makes itself known by changes in amplitude and phase. Since the audibility of phase distortion was previously covered quite well in this phase distortion article, we will simply encourage you to read that to address that topic. The audibility of amplitude changes was covered in this article on human amplitude sensitivity (which we recommend you read if you don’t yet have a good understanding of that subject), however, what wasn’t emphasized in that article, but what is important to our discussion, is the extra sensitivity to changes in loudness in low frequencies. To explain, let’s direct our attention to the behavior of frequencies below 150 Hz on the equal loudness chart on Figure 3. For those unfamiliar with the equal loudness curve, here is an explanation, but to briefly explain, it is a graph of the perceived loudness of sound at frequencies for an absolute loudness level. For those familiar with the Fletcher-Munson Curves, it is an updated version of that research.



Fig. 3. Equal Loudness Contour -used by permission of sengpielaudio.com

Notice how in the bass region, the perceptual constant loudness lines are more tightly bunched up above the minimum audible threshold. This is significant to us, because what it means is that we hear changes of loudness in bass more easily than in any other frequencies. When we consider that, with normal hearing, we can discern about a 1 dB difference over a broad range of frequencies and loudness levels, it gives us a perspective on how particularly acute our sensitivity to bass loudness is above the minimum audible threshold. Studies have shown it takes a 10 dB increase in SPL for a perceived doubling of loudness in mid and high frequencies but only a 6 dB increase for a perceived doubling of loudness at bass frequencies. Keeping that in mind, consider the how a drop of 5 dB below 30 Hz can change the character of a movie scene, or how a 5 dB spike around 60 Hz can alter the reproduction of a full orchestra.

The most grievous cause of linear distortion in bass is undoubtedly the effects of room acoustics where 20 dB peaks and dips are not uncommon. Since that subject has been addressed by Audioholics in past articles such as this room acoustics article, we won’t repeat what has already been said and instead encourage you to read it if you don’t already know how enormously destructive room acoustics can be on the linear reproduction of bass.

Another serious contributor of linear distortion in amplitude is the previously discussed thermal compression, where drops in output can be much less than half the original loudness. One might guess that it takes a while for heat buildup to take its toll on the output capability of a driver, but one highly-regarded pro-audio bass driver was demonstrated to lose 4 dB of output capacity in 2 seconds under a heavy load. At large signal amplitudes (i.e. head-banging levels of loudness), the effects of thermal compression can be formidable. We should mention that thermal effects can produce another potential distortion from thermal behavior from the driver: if too much current is continuously supplied, the voice coil can burn off its insulation and potentially start a fire; however, the sound of your speaker burning is almost certainly a nonlinear distortion.

One more linear distortion in bass we will discuss is called group delay. Group delay is the measurement of how much time it takes for individual frequency bands of an input signal to be produced by the speaker. It can indicate that some frequency components are developing slower than others or are taking longer to decay. Its effects are temporal but can sometimes be seen in a frequency response measurement as peaks from stored energy or ringing. The audibility of group delay depends on the length of the time lag between different frequencies and can be measured in either cycles or milliseconds. The absolute playback level has also been found to be a factor in the audibility of group delay. The minimum audible thresholds of group delay for low frequencies has not been studied as extensively as higher frequencies where it was found humans begin to perceive group delay at around 1.5 to 2 milliseconds at 1 kHz and above. However, bass frequency cycles last substantially longer than 2 milliseconds: a 100 Hz cycle has a duration of 10 milliseconds, a 50 Hz cycle has a duration of 20 milliseconds, and a 20 Hz cycle has a duration of 50 milliseconds, to name a few examples. It can be seen from these cycle lengths that group delay has more potential to be heard from sharp transient sounds such as kick drums or bass guitar plucks, where the attacks and releases of the sound envelope are sudden. It may be worth mentioning at this point that human perception may have a sort of built-in group delay, as it was found that the hearing system requires a much lower time interval to assess the spectral content of a mid-frequency tone as opposed to a low frequency sound. Although the audibility of group delay in bass frequencies hasn’t been found to be the subject of extensive research, an informal guideline in the audio business is that group delay under 1.5 cycles in bass frequencies isn’t likely to be audible, and in very deep frequency playback at around 30 Hz and under, human hearing will tolerate even higher levels of group delay before noticing it. According to the respected audio researcher Peter Mitchell, group delay in excess of 20 milliseconds can alter the subjective character of bass in more commonly heard bass frequencies, so for 50 Hz and above group delay should be kept to less than a single cycle for total inaudibility.

Fig. 4. Group delay graph - output above red line may be audible. Measurement taken by Josh Ricci.