Negative Feedback in Power Amplifiers
It is not the role of this book to step through elementary theory, which can be found easily in any number of textbooks. However, correspondence in audio and technical journals shows that considerable confusion exists regarding NFB as applied to power amplifiers; perhaps there is something inherently mysterious in a process that improves almost all performance parameters simply by feeding part of the output back to the input, but inflicts dire instability problems if used to excess. This chapter therefore deals with a few of the less obvious points here.
The main uses of NFB in amplifiers are the reduction of harmonic distortion, the reduction of output impedance, and the enhancement of supply-rail rejection. There are analogous improvements in frequency response and gain stability, and reductions in DC drift, but these are usually less important in audio applications.
By elementary feedback theory, the factor of improvement for all these quantities is
where A is the open-loop gain and β is the attenuation in the feedback network, that is, the reciprocal of the closed-loop gain. In most audio applications the improvement factor can be regarded as simply open-loop gain divided by closed-loop gain.
In simple circuits you just apply NFB and that is the end of the matter. In a typical power amplifier, which cannot be operated without NFB, if only because it would be saturated by its own DC offset voltages, several stages may accumulate phase shift, and simply closing the loop usually brings on severe Nyquist oscillation at HF. This is a serious matter, as it will not only burn out any tweeters that are unlucky enough to be connected, but can also destroy the output devices by overheating, as they may be unable to turn off fast enough at ultrasonic frequencies.
The standard cure for this instability is compensation. A capacitor is added, usually in Miller-integrator format, to roll off the open-loop gain at 6 dB per octave, so it reaches unity loop gain before enough phase shift can build up to allow oscillation. This means
that the NFB factor varies strongly with frequency, an inconvenient fact that many audio commentators seem to forget.
It is crucial to remember that a distortion harmonic, subjected to a frequency-dependent NFB factor as described earlier, will be reduced by the NFB factor corresponding to its own frequency, not that of its fundamental. If given a choice, generate low-order rather than high-order distortion harmonics, as the NFB deals with them much more effectively.
NFB can be applied either locally (i.e., to each stage, or each active device) or globally; in other words, right around the whole amplifier. Global NFB is more efficient at distortion reduction than the same amount distributed as local NFB, but places much stricter limits on the amount of phase shift that may be allowed to accumulate in the forward path.
Above the dominant pole frequency, the VAS acts as a Miller integrator and introduces a constant 90° phase lag into the forward path. In other words, the output from the input stage must be in quadrature if the final amplifier output is to be in phase with the input, which to a close approximation it is. This raises the question of how the 90° phase shift is accommodated by the NFB loop; the answer is that the input and feedback signals applied to the input stage are subtracted, and the small difference between two relatively large signals with a small phase shift between them has a much larger phase shift. This is the signal that drives the VAS input of the amplifier.
Solid-state power amplifiers, unlike many valve designs, are almost invariably designed to work at a fixed closed-loop gain. If the circuit is compensated by the usual dominant pole method, the HF open-loop gain is also fixed, and therefore so is the important NFB factor. This is in contrast to valve amplifiers, where the amount of NFB applied was regarded as a variable and often user-selectable parameter; it was presumably accepted that varying the NFB factor caused significant changes in input sensitivity. A further complication was serious peaking of the closed-loop frequency response at both LF and HF ends of the spectrum as NFB was increased due to the inevitable bandwidth limitations in a transformer-coupled forward path. Solid-state amplifier designers go cold at the thought of the customer tampering with something as vital as the NFB factor, and such an approach is only acceptable in cases such as valve amplification where global NFB plays a minor role.
10.6.1 Some Common Misconceptions About Negative Feedback
All of the comments quoted here have appeared many times in the hi-fi literature. All are wrong.
NFB is a bad thing. Some audio commentators hold that, without qualification, NFB is a bad thing. This is of course completely untrue and based on no objective reality. NFB is one of the fundamental concepts of electronics, and to avoid its use altogether is virtually impossible; apart from anything else, a small amount of local NFB exists in every common emitter transistor because of the internal emitter resistance. I detect here distrust of good fortune; the uneasy feeling that if something apparently works brilliantly then there must be something wrong with it.
A low NFB factor is desirable. Untrue; global NFB makes just about everything better, and the sole effect of too much is HF oscillation, or poor transient behavior on the brink of instability. These effects are painfully obvious on testing and not hard to avoid unless there is something badly wrong with the basic design.
In any case, just what does low mean? One indicator of imperfect knowledge of NFB is that the amount enjoyed by an amplifier is almost always baldly specified as so many dB on the very few occasions it is specified at all, despite the fact that most amplifiers have a feedback factor that varies considerably with frequency. A dB figure quoted alone is meaningless, as it cannot be assumed that this is the figure at 1 kHz or any other standard frequency.
My practice is to quote the NFB factor at 20 kHz, as this can normally be assumed to be above the dominant pole frequency and so in the region where open-loop gain is set by only two or three components. Normally the open-loop gain is falling at a constant 6-dB/ octave at this frequency on its way down to intersect the unity-loop-gain line and so its magnitude allows some judgment as to Nyquist stability. Open-loop gain at LF depends on many more variables, such as transistor beta, and consequently has wide tolerances and is a much less useful quantity to know.
NFB is a powerful technique and therefore dangerous when misused. This bland truism usually implies an audio Rakes’s progress that goes something like this: an amplifier has too much distortion and so the open-loop gain is increased to augment the NFB factor. This causes HF instability, which has to be cured by increasing the compensation capacitance. This is turn reduces the slew-rate capability, resulting in a sluggish, indolent, and generally bad amplifier.
The obvious flaw in this argument is that the amplifier so condemned no longer has a high NFB factor because the increased compensation capacitor has reduced the open-loop gain at HF; therefore feedback itself can hardly be blamed. The real problem in this situation is probably an unduly low standing current in the input stage; this is the other parameter determining slew rate.
NFB may reduce low-order harmonics but increases the energy in the discordant higher harmonics. A less common but recurring complaint is that the application of global NFB is a shady business because it transfers energy from low-order distortion harmonics—considered musically consonant—to higher order ones that are anything but. This objection contains a grain of truth, but appears to be based on a misunderstanding of one article in an important series by Peter Baxandall24 in which he showed that if you took an amplifier with only second-harmonic distortion and then introduced NFB around it, higher order harmonics were indeed generated as the second harmonic was fed back round the loop. For example, the fundamental and the second harmonic intermodulate to give a component at third-harmonic frequency. Likewise, the second and third intermodulate to give the fifth harmonic. If we accept that high-order harmonics should be numerically weighted to reflect their greater unpleasantness, there could conceivably be a rise rather than a fall in the weighted THD when NFB is applied.
All active devices, in Class-A or -B (including FETs, which are often erroneously thought to be purely square law), generate small amounts of high-order harmonics. Feedback could and would generate these from nothing, but in practice they are already there.
The vital point is that if enough NFB is applied, all the harmonics can be reduced to a lower level than without it. The extra harmonics generated, effectively by the distortion of a distortion, are at an extremely low level, providing a reasonable NFB factor is used. This is a powerful argument against low feedback factors such as 6 dB, which are most likely to increase the weighted THD. For a full understanding of this topic, a careful reading of the Baxandall series is absolutely indispensable.
A low open-loop bandwidth means a sluggish amplifier with a low slew rate. Great confusion exists in some quarters between open-loop bandwidth and slew rate. In truth,
open-loop bandwidth and slew rate have nothing to do with each other and may be altered independently. Open-loop bandwidth is determined by compensation Cdom, VAS �, and resistance at the VAS collector, whereas slew rate is set by the input stage standing current and Cdom • Cdom affects both, but all the other parameters are independent.
In an amplifier, there is a maximum amount of NFB you can safely apply at 20 kHz; this does not mean that you are restricted to applying the same amount at 1 kHz, or indeed 10 Hz.The obvious thing to do is to allow the NFB to continue increasing at 6 dB/octave—or faster if possible—as frequency falls so that the amount of NFB applied doubles with each octave as we move down in frequency, and we derive as much benefit as we can. This obviously cannot continue indefinitely, for eventually open-loop gain runs out, being limited by transistor beta and other factors. Hence the NFB factor levels out at a relatively low and ill-defined frequency; this frequency is the open-loop bandwidth and, for an amplifier that can never be used open loop, has very little importance.