We all know what distortion sounds like. We’ve heard it in heavy metal tunes, cheap iPod docks and the crummy speakers at drive-thrus. And we’ve all read distortion specs on things like receivers and subwoofers. But other than a general understanding that distortion isn’t something we want in home audio gear, most people really don’t know what it is.
It dawned me the other day that not only do I hear a lot more distortion than most people (’cause as an audio reviewer I gotta crank stuff up to find its limits), I also see distortion. The recently developed CEA-2010 subwoofer measurement technique shows the effects of distortion on your computer screen as you’re measuring it. I thought it might be interesting to put together some graphics and tones that demonstrate some of the distortion characteristics I deal with so often. Because once you see distortion, it’s much easier to understand what you’re hearing. (Which means distortion has a lot in common with Lady Gaga.)
Defining distortion
Although distortion can be defined as any alteration in the waveform of an audio signal, the kind of distortion we’re usually talking about in audio is harmonic distortion, which you see cited in amplifier specs as THD, or total harmonic distortion. Harmonic distortion in amplifiers is usually caused by the amplifier needing more voltage than its power supply can provide. It can also be caused by some part of the internal circuit (usually the output transistors) exceeding its output capacity. Thus, instead of reproducing the peaks of an audio waveform, the amplifier clips them off, hence the term “clipping”.
You can see an extreme example of clipping in the oscilloscope chart (Figure 1) shown here. It shows a sine wave at top and a heavily clipped version of the same wave at bottom. The peak of the audio wave is clipped off at the point where the amplifier’s power hits its maximum output. Thus the original sine wave becomes something closer to a square wave. This creates extra harmonics at multiples to the original tone. If you have a 1,000 Hz tone, you’ll get distortion harmonics at 2000Hz (the second-order harmonic), 3000Hz (the third-order harmonic) and so on.
Of course, speakers also produce harmonic distortion and other types of distortion. Speaker distortion can arise from a diaphragm (like a woofer cone) reaching the limits of its excursion; from high-frequency resonances (commonly referred to as “breakup modes”) in the diaphragm; and also from things like port turbulence and insufficiently robust crossover parts. Although the physics are different, the end result is often similar, but speaker distortion tends to be much higher than amplifier distortion, especially in subwoofers.
What’s your percentage?
Distortion is commonly expressed in percentages. Calculating it is a complex mathematical operation (explained in depth here), but to put it very simply, 1 per cent THD is -40dB below the original signal, 3 per cent THD is about -30dB below, 10 per cent THD is -20dB below, and so on.
This tone demonstrates how different levels of distortion sound. (Better put on your headphones for this; lower-level distortion will probably be hard to hear on your computer speakers.) The first three seconds is an undistorted 400Hz tone. The next three seconds is the same tone at 0.5 per cent THD, which some people can hear and some can’t. The next three seconds is at 1 per cent THD, which most people can hear. The next is at 5 per cent, which anybody but Ted Nugent can hear. The final three seconds is at 10 per cent, which sounds so grating because it’s your amplifier’s last desperate plea for mercy. Now when you see an amplifier’s power specified at 0.5 per cent or 1 per cent THD, you’ll have some idea of the real-world implications.
While I was making the tone, I also monitored the result through my computer running TrueRTA spectrum analyser software. This let me grab some screen shots so you can see how different levels of distortion appear on an analyser.
As we’ll discuss later in this article, distortion of a certain percentage doesn’t always sound the same. It varies depending on the level of the different harmonics. I made the tone and graphs here by cutting the supply voltage on my Bottlehead Quickie preamp from 36 volts to 12 volts so it would distort easily. Because the Quickie is a single-ended tube preamp, it has more second-order harmonic distortion than a typical transistor preamp, thus the 5 per cent THD you hear in this tone may sound different from the 5 per cent THD you’d get from a transistor preamp.
Figure 2 gives you an idea of what 0.2 per cent THD looks like. You can see the second-order distortion harmonic appearing at 800Hz to the right of the fundamental tone at 400Hz. Again, with a solid-state preamp, you’d probably see more third-order harmonic (1200Hz).
Figure 3 shows the Quickie preamp at 1 per cent THD. The 2nd-order distortion harmonic at 800Hz is a little higher in level, and now it’s joined by the third harmonic at 1200 Hz and the fourth harmonic at 1800Hz.
Figure 4 shows 5 per cent THD. At this amount of distortion, all hell breaks loose. Even the eighth- and ninth-order distortion harmonics (at 3520Hz and 3960Hz, respectively) are clearly visible, and the lower-order harmonics are getting closer to the level of the fundamental tone.
Following orders
Sometimes added harmonics don’t sound so bad. That’s why many guitar players intentionally add distortion to their sound. But sometimes these harmonics sound really awful. It depends on the order of the harmonic.
A second-order harmonic is double the original frequency, so for a 440Hz tone it’s 880Hz. That doesn’t necessarily sound all that bad, because it’s exactly one octave up and it thickens the sound in a way that can be pleasing. In fact, guitar players such as Wes Montgomery, Pat Metheny and Steve Howe often play in octaves, picking both the fundamental note and the same note one octave up. And if you got a problem with Wes Montgomery’s sound, we need to step outside.
While second-order harmonics can be unobjectionable or even kinda nice, third-order harmonics are as unwelcome as bagpipes in a blues band. That’s because the extra harmonic isn’t in tune with the fundamental tone. Take that same 440Hz tone, which is an A note. Second-order distortion just adds another A note an octave higher at 880Hz. But third-order distortion adds a slightly out-of-tune E note at 1318Hz, which is a musical interval roughly an octave and a fifth above the fundamental. A fifth is the interval guitar players add to the root note to form a power chord. Thus, too much 3rd-order harmonic distortion suddenly makes Beethoven’s “Ode to Joy” sound more like “Smoke on the Water”, which I’m confident wasn’t what Beethoven intended. (I just said that in the hope it will inspire a nasty email from Ritchie Blackmore. Then I can say I got an email from Ritchie Blackmore.)
This tone I made demonstrates the difference between second- and third-order harmonic distortion. A 400Hz tone plays for three seconds, then it’s joined by an 800Hz tone at -20dB, simulating 10 per cent second-order distortion. Three seconds later the 800Hz tone is replaced by a 1200Hz tone at -20dB, simulating 10 per cent third-order distortion. Then you hear three more seconds of the original 400Hz tone.
The second-order harmonic is actually rather pleasant, like a violin playing in unison with a cello. But the third-order harmonic is quite jarring, it’s it? Same rules go for higher harmonics, too. The fourth-order harmonic is two octaves above the fundamental, so it sounds not so bad. The fifth-order harmonic is two octaves and an out-of-tune third above the fundamental, so it sounds awful. This is why you often hear that odd-order harmonic distortion is more objectionable than even-order harmonic distortion.
While audio experts often disagree about how important harmonic distortion is, how audible it is and how best to measure it, there’s no question that it can greatly affect the sound you hear. And as we move to smaller, more portable sound systems with tiny speaker drivers and low-powered internal amplifiers, we’re likely to hear a lot more distortion in the future.
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