The Numbers Game

In most of the electronics field, the characterization of performance is pretty straight forward. If a video amplifier has inadequate bandwidth that causes the loss of fine detail, and excessive phase nonlinearity that smears images across the screen, or puts out all the wrong colours, no one who isn't blind as a bat will disagree that it is a very poor design. If a servo doesn't track accurately, no one will argue about the finer points of that kind of distortion.

The audio field is something else entirely. Eyes don't lie, but ears deceive. Characterizing the performance of audio electronics is complicated by the very fickleness of the end user. What sounds just great to one will be judged inferior by another. Different people hear different things, and there may very well be those (the "golden ears") who hear things that the rest of us can not hear at all. Throw in musical preferences, and it gets even more complex. It's highly doubtful that the head-banger and the Classical aficionado will agree that the same amp is superior to other offerings.

The marketing department needs a selling point, and that has long been THD. The Williamson of 1948 made THD fashionable, and started the fallacy that gNFB was the cure for all ills. Between 1948 and 1956, the Williamson design was all but universal. The commercial "Big Box" manufacturers went for more power and ever greater feedback factors to drive those THD numbers ever lower. By 1960, Big Box products had excessive bandwidth (necessary for stability) and enormous feedback factors. UL EL34s in Class AB had become quite fashionable. The demand for more feedback led designers to abandon the lower distortion, lower gain types (6C5, 6J5, 6SN7, 6CG7) for high-u triodes and small signal pentodes. These high gain devices are less linear, adding more open loop distortion that was then corrected by high gNFB. Solid state was a natural progression since transistors have almost unlimited gain available, getting rid of the OPT removed an obstacle to driving up gNFB, and, of course, the gross nonlinearity of transistors demanded even more correction. This naturally led to a certain sloppiness in the open loop design. Why worry about poor open loop performance, add enough gNFB and you can sweep your mistakes under the carpet where no one will ever find them. Unfortunately, you also sweep away much of the musical detail.

The end result: sound-alike amps, with that lifeless "Big Box" sound.

The supreme irony of this is that there is almost no correlation between the THD figure and listener satisfaction. Unless something measures really badly can it be said that it will sound really bad. If THD had everything to do with it, we would have attained audio perfection a long time ago. Solid state amps have THD figures of 0.001% or even better, yet when was the last time you ever heard a manufacturer of VT equipment brag that their amps had that great transistor sound?

There are further complications that you just don't see in other areas of electronic design. An RF amp works on a very narrow band of frequencies into a well characterized load that's almost pure resistance: either a transmission line or antenna. If there are any reactive components, you can tune them out. Whatever device distortion is produced is of no consequence since one or more tuned LC circuits and/or bandpass filters will reject any harmonic distortion. This does not apply to audio. Even though we draw nice, straight loadlines representing a resistive load impedance, speakers are anything but. A spec that says a speaker is an "8 ohm speaker" refers to the DC resistance of the voice coil winding. In operation, the device is an AC synchronous motor. The only difference is that the voice coil moves back and forth instead of going around. Any time you have coils moving in a magnetic field, you have a voltage induced in the coil. That induced "back EMF" adds to the incident voltage to produce an impedance that varies in both magnitude and phase. In practice, your loadline opens up into an ellipse (for one frequency only). This is bad news for your output devices, which like to see a constant load. Then there's the question of OPTs. A transformer designed to operate at a frequency of 20Hz is going to be very different from one that's designed to operate at 20KHz. And yet, OPTs are expected to do both, everything in between, all at once. By all rights, it shouldn't work at all, let alone as well as it does.

Distortion is not created equal, nor is distortion necessarily undesirable. If that were the case, then no one would ever use a tone control or graphic equalizer. Since these suppress or enhance various frequency components, what comes out is no longer the same as what went in. In other words, the output is distorted. The undesirable, but inevitable, distortions are not created equal either. You can see this with an oscilloscope. If you add 10% of second harmonic to a pure sine wave, the difference is hardly noticeable at all. Even if you know what to look for, you'll probably miss it. It's not until you get to about 20% h2 that the disturbance becomes obvious (flattening of the peaks on one side only, all even harmonics produce asymmetric waveforms). Just 10% of the third harmonic will make for clearly distorted waveforms (nearly triangular waves). Smaller amounts of higher order harmonics make for even more severely distorted sine waves. This means that you can tolerate more lower order harmonics than high order. If the THD is several percent, but it is all h2, you probably won't notice it at all. It is this type of distortion that low-u triodes tend to produce. On the other hand, even very small amounts of high order harmonics can be all but unlistenable. The cross over distortion produced by underbiased transistor amps -- or Class B VT amps -- is a good example of this, and it does sound quite nasty, even in small quantities. It is for this reason that Class B is relegated to RF amplification, or audio amplification where power and efficiency are more critical than fidelity.

As for what the various distortions sound like, well, that depends. Unless the distortion is extremely bad, it isn't really all that obvious. Some harmonic distortion doesn't sound any different than background static, or hissy "esses", or background crackles. Often, there really isn't any one thing one can identify, other than listening becomes fatiguing after awhile. The least harmful is h2. Since the second harmonic is musically correlated, being one octave higher, it tends to make for a "richer" sound. Excessive amounts tend towards a "darker" sound, as has been the complaint against the very nonlinear 12AV7. From a design point of view, this would not look like too much of a problem, since even order harmonics are nulled with balanced circuitry. As for h3, this, too, is musically correlated, being nearly an octave-and-a-half. The effect of h3 is to lend a sense of "detail". More h3 lends "edge" or "brightness" to the sound. For some types of music, this can be desirable. As for higher order harmonics, these aren't musically correlated, and sound very dissonant and unpleasant. The higher order the harmonic, the less of it you can tolerate.

THD numbers really tell you very little. The spec sheet for the 6L6, for example, gives a THD figure of just 1.8%, before any NFB is ever applied. That is really quite outstanding. The lowest THD figure for the 6V6 -- another audio type -- is 3.5%. However, operating open loop without any NFB, 6L6s definitely sound worse, with lots of "pentode nastiness" that quickly wears the listener out. With some program material, the effect is as annoying as fingernails on a blackboard. O. Schade, the developer of the 6L6, recognized this problem back in 1936. O. Schade recommended that local NFB be applied to correct for the problem of higher order harmonics. Even though the 6V6 measures worse by a significant margin, it produces mainly h3. This doesn't mean that you won't need NFB, however, running open loop, produces mainly an overly "aggressive", "edgy", or "bright" sound. The type doesn't need the added assistance of local NFB in order to sound right. Fifty or so years ago, Norman Crowhurst proposed a weighting system of distortion measurement that would account for this: undervaluing the less destructive low order harmonics, and emphasizing the higher order harmonics. Simple THD measurements don't do this. Of course, the industry wanted nothing to do with it.

There is another type of distortion that's much worse than harmonic distortion, and that's IMD. IMD arises from the same source as harmonic distortion: active device nonlinearity. IMD occurs whenever a lower frequency mixes and modulates a higher frequency. It's really the same as AM with a very small modulation index. All IMD is quite bad since its frequency components are rarely, if ever, musically correlated. This is the reason to stay away from nonlinear devices and nonlinear operating points. IMD is also the reason why poorly filtered DC sounds worse than AC for filament heating. With AC, you have just the one frequency to deal with. DC, unless well filtered, adds quite a few harmonics of the line frequency. Even if the level doesn't seem all that high, there is sufficient to mix with signal frequencies via intermodulation to degrade sonic performance.

The simplistic answer is to add as much NFB as you can manage while maintaining a reasonable level of stability. Unfortunately, it's not that easy. Over fifty years ago, Norman Crowhurst looked into the problem, and discovered that the main effect of NFB is the reduction of h2 and h3. It doesn't do much, if anything, for removing low levels of higher order harmonics. NFB can make the situation even worse by filling the noise floor with lots of low level, high order harmonics. This can, and does, ruin any pretense to sound stage. In much the same way as NFB, the unavoidable quantizing noise that accompanies analog to digital conversion also adds lots of uncorrelated harmonic noise to the noise floor. It has been proposed that this quantizing noise is the reason that some find the CD sound to be inferior to vinyl and tape. This is also a problem with certain audio file compressions, such as mp3. This is a "lossy" compression, in that some of the bits are thrown away. The first consideration in which bits those should be were the ones encoding near noise floor audio. These mp3 audio files just don't sound quite right because of that missing detail (And to think some people actually expect you to pay for mp3's!) What's going on at the nearly subaudible level seems to be a good deal more important than once suspected.

The main lesson is to design for the best open loop performance, and add just as much NFB as needed to improve the overall sonics. Of course, it is a trade-off: sound stage for better bass and less of the excessive harshness that often comes with open loop operation.


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