Audio Engineering

376 Chapter 12

1.0 kV

0.5 kV

0V

0.5 kV

0s 10 μs20μs30μs

Time

40 μs50μs

v(3) v(7)

Figure 12.7: Adding a third pole makes possible true instability with an exponentially

increasing amplitude of oscillation. Note the unrealistic voltage scale on this plot.

Table 12.1: Instability Onset: P 2 is Increased Until Sustained Oscillation Occurs

Case Cdom P 2 P 3 P 4 P 5 P 6

A 100p 0.45 0.5 – – 200 kHz

B 100p 0.5 0.2 0.2 – 345 kHz

C 100p 0.2 0.2 0.2 0.01 500 kHz

D 100p 0.3 0.2 0.1 0.05 400 kHz

E 100p 0.4 0.2 0.1 0.01 370 kHz

F 100p 0.2 0.2 0.1 0.05 0.02 475 kHz

Having P 2 , P 3 , and P 4 all at the same frequency does not seem very plausible in physical
terms, so case D shows what happens when the fi ve poles are staggered in frequency. P 2
needs to be increased to 0.3 μ s to start the oscillation, which is now at 400 kHz. Case E is
another version with fi ve poles, showing that if P 5 is reduced, P 2 needs to be doubled to
0 4 μ s for instability to begin.