Negative Feedback:Maximizing Negative Feedback and Maximizing Linearity Before Feedback

Maximizing Negative Feedback

Having freed ourselves from fear of feedback, and appreciating the dangers of using only a little of it, the next step is to see how much can be used. It is my view that the amount of NFB applied should be maximized at all audio frequencies to maximize linearity, and the only limit is the requirement for reliable HF stability. In fact, global or Nyquist oscillation is not normally a difficult design problem in power amplifiers; the HF feedback factor can be calculated simply and accurately, and set to whatever figure is considered safe. (Local oscillations and parasitics are beyond the reach of design calculations and simulations and cause much more trouble in practice.)

In classical control theory, the stability of a servomechanism is specified by its phase margin, the amount of extra phase shift that would be required to induce sustained oscillation, and its gain margin, the amount by which the open-loop gain would need to be increased for the same result. These concepts are not very useful in amplifier work, where many of the significant time constants are known only vaguely. However, it is worth remembering that the phase margin will never be better than 90° because of the phase lag caused by the VAS Miller capacitor; fortunately, this is more than adequate.

In practice, the designer must use his judgment and experience to determine an NFB factor that will give reliable stability in production. My own experience leads me to believe that when the conventional three-stage architecture is used, 30 dB of global feedback at 20 kHz is safe, providing an output inductor is used to prevent capacitive loads from eroding the stability margins. I would say that 40 dB was distinctly risky, and I would not care to pin it down any more closely than that.

The 30-dB figure assumes simple dominant-pole compensation with a 6-dB/octave roll-off for the open-loop gain. The phase and gain margins are determined by the angle at which this slope cuts the horizontal unity loop-gain line. (I am deliberately terse here; almost all textbooks give a very full treatment of this stability criterion.) An intersection of 12 dB/ octave is definitely unstable. Working within this, there are two basic ways in which to maximize the NFB factor.

1. While a 12-dB/octave gain slope is unstable, intermediate slopes greater than 6 dB/octave can be made to work. The maximum usable slope is normally considered to be 10 dB/octave, which gives a phase margin of 30°.This may be acceptable in some cases, but I think it cuts it a little fine. The steeper

fall in gain means that more NFB is applied at lower frequencies and so less distortion is produced. Electronic circuitry only provides slopes in multiples of 6 dB/octave, so 10 dB/octave requires multiple overlapping time constants to approximate a straight line at an intermediate slope. This gets complicated, and this method of maximizing NFB is not popular.

2. The gain slope varies with frequency so that maximum open-loop gain and hence NFB factor is sustained as long as possible as frequency increases; the gain then drops quickly, at 12 dB/octave or more, but flattens out to 6 dB/octave before it reaches the critical unity loop-gain intersection. In this case the stability margins should be relatively unchanged compared with the conventional situation.

Maximizing Linearity Before Feedback

Make your amplifier as linear as possible before applying NFB has long been a cliché. It blithely ignores the difficulty of running a typical solid-state amplifier without any feedback to determine its basic linearity.

Virtually no dependable advice on how to perform this desirable linearization has been published. The two factors are the basic linearity of the forward path and the amount of NFB applied to further straighten it out. The latter cannot be increased beyond certain limits or else high-frequency stability is put in peril, whereas there seems no reason why open-loop linearity could not be improved without limit, leading us to what in some senses must be the ultimate goal—a distortionless amplifier. This book therefore takes as one of its main aims the understanding and improvement of open-loop linearity.

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