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How many poles below the unity-gain frequency can a loop tolerate?

  • A.Any number, if the gain is high enough
  • B.One, comfortably
  • C.Two, comfortably
  • D.Three, provided they are spaced

Answer: B

One pole gives ninety degrees at most and so is unconditionally stable, while a second pole approaching its own break pushes the phase towards inversion and the margin disappears. Three is worse still, and a high gain makes matters worse rather than better by pushing the unity-gain frequency higher. The whole of dominant-pole compensation is an arrangement to make sure only one pole is encountered before the gain has gone. Most errors here come from carrying a result across from a neighbouring case where it does not hold.

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