Audio Engineering

Negative Feedback 373

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v(3) v(7)

Figure 12.4: Adding a second pole P 2 causes overshoot with smaller values Cdom, but cannot

bring about sustained oscillation.

positive feedback, which means that a total phase shift of 180° must have accumulated in
the forward path and reversed the phase of the feedback connection. With only two poles
in a system the phase shift cannot reach 180°. The VAS integrator gives a dependable 90°
phase shift above P 1 , being an integrator, but P 2 is instead a simple lag and can only give
a 90° phase lag at infi nite frequency. So, even this very simple model gives some insight.
Real amplifi ers do oscillate if Cdom is too small, so we know that the frequency response
of the output stage cannot be modeled meaningfully with one simple lag.

A certain president of the United States is alleged to have said: “ Two wrongs don’t make
a right—so let’s see if three will do it. ” Adding in a third pole, P 3 , in the shape of another
simple lag gives the possibility of sustained oscillation.

Stepping the value of P 2 from 0.1 to 5 μ s with P 3  500 ns shows sustained oscillation
starting to occur atP 2  0.45 μ s. For values such as P 2  0.2 μ s, the system is stable