Negative Feedback 377In the fi nal case F, a sixth pole is added to see if this permitted sustained oscillation
is above 500 kHz. This seems not to be the case; the highest frequency that could be
obtained after a lot of pole twiddling was 475 kHz. This makes it clear that this model
is of limited accuracy (as indeed are all models—it is a matter of degree) at high
frequencies and that further refi nement is required to gain further insight.
12.2 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 diffi cult design problem in power amplifi ers; the HF feedback factor can
be calculated simply and accurately, and set to whatever fi gure 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 specifi ed 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 amplifi er
work, where many of the signifi cant 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 fi gure 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