368 Chapter 12
how high the feedback factor. The linearization of the VAS by local Miller feedback is a
good example. However, more complex circuitry, such as the generic three-stage power
amplifi er, has more than one time constant, and these extra poles will cause poor transient
response or instability if a high feedback factor is maintained up to the higher frequencies
where they start to take effect. It is therefore clear that if these higher poles can be
eliminated or moved upward in frequency, more feedback can be applied and distortion
will be less for the same stability margins. Before they can be altered—if indeed this is
practical at all—they must be found and their impact assessed.
The dominant pole frequency of an amplifi er is, in principle, easy to calculate; the
mathematics are very simple. In practice, two of the most important factors, the effective
beta of the VAS and the VAS collector impedance, are only known approximately, so
the dominant pole frequency is a rather uncertain thing. Fortunately, this parameter in
itself has no effect on amplifi er stability. What matters is the amount of feedback at high
frequencies.
Things are different with the higher poles. To begin with, where are they? They are
caused by internal transistor capacitances and so on, so there is no physical component
to show where the roll-off is. It is generally regarded as fact that the next poles occur
in the output stage, which use power devices that are slow compared with small-signal
transistors. Taking the Class-B design, the TO-92 MPSA06 devices have an Ft of
100 MHz, the MJE340 drivers about 15 MHz (for some reason this parameter is missing
from the data sheet), and the MJ802 output devices an Ft of 2.0 MHz. Clearly the output
stage is the prime suspect. The next question is at what frequencies these poles exist.
There is no reason to suspect that each transistor can be modeled by one simple pole.
There is a huge body of knowledge devoted to the art of keeping feedback loops stable
while optimizing their accuracy; this is called control theory, and any technical bookshop
will yield some intimidatingly fat volumes called things like “ control system design. ”
Inside, system stability is tackled by Laplace-domain analysis, eigenmatrix methods, and
joys such as the Lyapunov stability criterion. I think that makes it clear that you need to
be pretty good at mathematics to appreciate this kind of approach.
Even so, it is puzzling that there seems to have been so little application of control theory
to audio amplifi er design. The reason may be that so much control theory assumes that
you know fairly accurately the characteristics of what you are trying to control, especially
in terms of poles and zeros.