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Grasp negative feedback in audio amps (Part 2)

06 Jan 2016  | Bruno Putzeys

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A second step in the experiment consisted of placing a resistor across compensation capacitor C that reduced DC gain to the same value as that at 20kHz (figure 12, trace 4). The test amplifier was of the folded-cascode persuasion, which allowed this. At this stage, loop gain has indeed been reduced across the full audio range. I surmise that since the amplifier's distortion was never negligible, making it constant across the audio band makes it fly under the psychoacoustic radar more easily. My own subjective experience would support this.

To my ears, amplifiers with the normal 20dB/decade behaviour but whose distortion is not negligible at the end of the audio range have glassy mid-highs, a "superglue stereo image" as KK once put it, and the illusion of spectacularly, unnaturally tight and impossibly controlled bass. Some love this, and seceded into a subculture of ultra-beefy amplifiers. I don't and when forced to make a choice I'll take higher but consistent distortion across the band.

The fourth step is a very important one to our story: to eliminate the feedback loop altogether and set the gain using only emitter degeneration and a resistor en lieu of C. Several commercially available class A amps are still made in this manner.

I heard that this last change was a bit of an epiphany. There is no discussion here: loop gain was reduced from about 26dB (at 20kHz) to none at all. Unlike the first step, this one does point at a valid relationship between loop gain and perceived sound quality. Something interesting is happening here.


Storyline 2: Re-entrant distortion
I said earlier that the error is signal dependent. In 1978, Baxandall noted that negative feedback around simple non-linearities creates distortion components that weren't there before (figure 14).


Figure 14: Spectral decomposition of the output of Figure 15 as a function of A (dB). Top to bottom: fundamental, 2nd harmonic, 3rd harmonic, etc.


Trying to solve analytically an integrating control loop that has a dependent error in it is impossible. Differential equations with non-linearities in them do not have algebraic solutions. Luckily we can get a qualitative understanding of the issue by looking only at very low frequencies where gain is constant.

Imagine a hefty but purely second-order non-linearity with a loop wrapped around it (figure 15).


Figure 15: Purely 2nd-order non-linearity within a feedback loop.


The non-linearity is parabolic. As soon as feedback is added, it will become something that is neither a straight line nor a parabola. In fact, the answer has a square root in it. That has an infinite series expansion which includes both even and odd terms. Plotting the harmonic distribution against loop gain, we get Baxandall's familiar picture of figure 14.

Forget the old pot-boiler that second-harmonic distortion is inaudible or uncritical, it's not. Even-order terms produce IMD products that clog up the whole bottom end. Nevertheless there is little doubt that higher harmonics are both increasingly detectable and increasingly annoying. This mathematically derived graph predicts exactly what experimenters found: if you start with a decently sounding zero-feedback amplifier and you add some feedback, it sounds somewhat opener in the bottom end but otherwise more unpleasant. The trend continues at least for the first 10dB to 20dB so one finds oneself compromising between musicality and something we'll call "accuracy" for want of a better term.

The trouble is that such listening experiments are by necessity done on amplifiers that are flat all the way to 20kHz, even in open loop, usually valve amplifiers. A valve amplifier that has a flat response from 20Hz-20kHz is very likely to have an uncontrolled outgrowth of poles just outside this range and will become unstable well before loop gain hits 15dB. You get worsening musicality right up to the point when the whole thing no longer works.

Of course this experiment gives the impression that more feedback is worse. You have to get past that bump. Hardly anybody who has ever tried it like this has actually heard the inevitable (and frankly magical) improvement that happens once you do get beyond, say 20 or 30dB. From there on you get an unambiguous net improvement that goes on forever.

In a flight of fancy I set a friendly audio company in the south of the Netherlands on this by suggesting a method of wrapping almost 60dB of loop gain over the full audio range around a valve amplifier using a third-order loop. Whenever it was stable it sounded immaculate. Measured rather well too.

The story of re-entrant distortion has an unambiguous conclusion: there simply is no such thing as "too much" feedback. There is only something as not enough feedback and it happens to be exactly what so-called moderate audio designers call "modest amounts" of feedback.

At this stage we understand how at a certain juncture enthusiastic, knowledgeable audiophiles were getting confused about feedback, and drew tentative, negative conclusions about it. Normally though, science and engineering works by making mistakes and rectifying them as work continues. Therefore, a third factor is needed to explain how a tentative conclusion suddenly got cemented into an immovable orthodoxy.


Storyline 3: Marketing hype, specmanship and "lots of zeros"
During my tender years, "Japanese Transistor Amps" were held up as prime examples of things that measured well and sounded terrible. Dare, even today, to extol the virtues of an amplifier as having really low distortion and some know-it-all will stand up and say "you know measurements don't say it all; remember the 80s when we were flooded with amps that had 0.00001% distortion and sounded all screechy," bystanders nodding vigorously. One of them will go on, inevitably, to make the same point in another audio meeting, adding an extra zero. Such figures were never claimed by anyone at the time.

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