Both articles mentioned in part 1 are less than ideal when making decisions about how much negative feedback to use in an audio amplifier design. The 'Cathode Ray' analysis is really about clipping, which need never happen if an amplifier of sufficient power rating is used, and the Baxandall analysis is of a fixed amplifier with varying feedback network, so in fact it is the closed-loop gain which is being varied while the open-loop gain is kept constant. In practice we usually have some required closed-loop gain, typically 30dB, and what we need to decide is how much open-loop gain to use. The effectiveness of the feedback in reducing distortion then depends on where it is being generated. Input stage distortion is reduced in two ways. If the gain of a later stage is increased, then for a given amplifier output the signal level in the input stage reduces, and so its distortion also reduces. The negative feedback loop gain also increases, giving a further reduction in distortion. Output stage distortion however is only reduced by the feedback for a given output signal level. Using very high overall feedback loop gain in my mosfet amplifier design the input stage distortion vanishes under the noise, and any remaining distortion is almost entirely from the output stage. (In a non-inverting amplifier common-mode input stage distortion may still be a problem.)
If feedback is avoided, for example in single-ended tube or mosfet amplifiers, to try to prevent the generation of high order harmonics, then there are other problems. The feedback mechanism in which low order output distortion feeds back to the input and intermodulates with the input signal to generate high order products is invariably analysed only for a single frequency input signal. Music is rarely if ever a pure sine-wave, and already any single note will include harmonics. If the amplifier is so non-linear that it generates significant intermodulation products then it will do so for the input frequency with its harmonics, without the need for these harmonics to be supplied by distortion feedback. A flute tone will already include the second harmonic, and intermodulation in the amplifier will therefore generate some third harmonic which will add to or subtract from the third harmonic component of the flute, giving an incorrect level. Problems similar to those claimed for feedback will still occur in an amplifier without feedback, maybe at a higher level because of poorer amplifier linearity. A violin may have significant harmonic levels up to the tenth and beyond, and passing this through even a perfect square-law mosfet stage would alter the relative levels of these harmonics because of intermodulation, even though for a single sine-wave only second harmonic would be added. (There are certain combinations of harmonics for which the square law response will not alter the relative amplitudes or phases, but these are unlikely to occur in music signals.)
An example was analysed to demonstrate the effect. An amplifier with a square-law response with input Vi has output:
Vo = 10Vi + Vi2.
With single frequency input Vi = sin(wt) there will be just 5% second harmonic output distortion.
Suppose however we use an input from a musical instrument which already includes the fundamental frequency plus second harmonic at 20% and third harmonic at 10%.
i.e. Vi = sin(wt) + 0.2 sin(2wt) + 0.1 sin(3wt)
Substituting this into the equation for Vo we find that the second and third harmonics are increased a little, but in addition there is now:
1.2% 4th harmonic
0.2% 5th harmonic
0.05% 6th harmonic
This ideal square-law amplifier even with no overall feedback at all is still adding harmonic distortion at higher harmonics not present in the original input signal. The 5th harmonic, for example, is generated by intermodulation between the 2nd and 3rd harmonics of the input signal. Any amplifier adding 0.2% 5th harmonic to a sine wave signal would be considered very poor by current standards, but if music signals are to be used the low order harmonic distortion needs to be low otherwise these higher harmonics will also be generated.There is therefore no great advantage in avoiding overall feedback if we want to prevent the generation of high order harmonics, unless we intend to listen only to single frequency sine-waves. Clearly the extent to which high order harmonics are added depends on the level of harmonics in the input signal, and different musical instruments have widely varying levels, so it is difficult to come to any general conclusions about the seriousness of the effect, or how low the amplifier distortion needs to be. Just ensuring that the sine-wave distortion is confined to low order harmonics may not be good enough however. It may be that the levels of harmonics generated are pleasant to listen to, or that our ears or brains can more easily compensate for the results of a square-law response, but reducing all harmonic distortion to low levels I suggest is a safer approach.
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