Gain margin and phase margin

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Gain margin and phase margin

• Closed-loop gain of amplifiers with feedback is
• replacing sj2pf gives the closed loop gain
  as a function of frequency
• For a given frequency f1, if ßA(f1)-1, the close
  loop gain becomes infinite. This corresponds to a
  pole on the jw axis at s j2pf1. The transient
  response then contains a constant-amplitude
  sinusoid.
• In considering the stability of a feedback
  amplifier, we examine the bode plot for the loop
  gain ßA(f) to find the frequency fgm for which
  the phase shift is 180 degrees. If the magnitude
  of the loop gain is less than unity at fgm, the
  amplifier is stable. On the other hand, if the
  loop gain magnitude is greater than unity, the
  amplifier is unstable.
• For a stable amplifier, the amount that the loop
  gain magnitude is below 0db is called the gain
  margin. A gain margin of zero implies that a pole
  lies on jw axis. In general, a larger gain margin
  results in less ringing and faster decay of
  transient response.
• Another measue of stability from the loop gain
  bode plot is the phase margin, which is
  determined at the frequency fpm for which the
  loop gain is unity (0db). The phase difference
  between the actual phase and -180 degrees is the
  phase margin.

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Stability of amplifier

• Since we want to design feedback amplifiers to
  avoid transient response ringing and frequency
  response peaks, a generally accepted rule of
  thumb is to design for a minimum gain margin of
  10db and phase a minimum phase margin of 45
  degrees.
• Typical magnitude and phase plot for stability
  consideration

3
Pole compensation I

• Negative feedback is useful to reduce distortion,
  stabilize gain and increase bandwidth. But to
  achieve these benefits, the loop gain
• must be much larger than unity.
• On one hand, we can design an amplifier with a
  large open-loop gain. This calls for several
  stages of amplification, and multi-stage
  amplifiers invariably introduce multiple poles.
• On the other hand, a large value of feedback
  coefficient may lead to instability in a
  multiple-pole amplifier.
• Thus, we must deliberately modify the pole
  locations (or equivalently frequency and
  transient response) of the amplifier before
  feedback can be used effectively. The is called
  compensation.

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Pole compensation II

• Instability occurs if the magnitude of loop gain
  is greater than 0db at the frequency for
  which the phase is -180.
• Each pole potentially contributes a phase shift
  between 0 to -90 at any given frequency.
• For a single amplifier, instability is not a
  problem, since the extreme phase is -90.
• For a two pole amplifier, the extreme phase is
  -180, which occurs until frequency approaches
  infinity. However, it is possible for the phase
  to become very close to -180 at the frequency for
  which the loop gain is 0db, resulting in very
  small phase margin, hence long transient ringing
  and large frequency response peaking.
• For three or more poles amplifier, a phase shift
  of -180 is possible before the loop gain
  magnitude has dropped below 0db. Thus, an
  amplifier having three or more poles can become
  unstable.
• There are several approaches to compensate the
  pole location. One popular method, called
  dominant-pole compensation, is to add another
  pole at a very low frequency, such that the
  loop-gain drops to unity by the time the phase
  reaches X (e.g. -135 degrees). In this way, a
  phase margin of X180 (e.g. 45 degrees) could be
  achieved.

5
Pole compensation III

• Most of the amplifier design are OpAmp based
  design.
• A good example for pole compensation at the
  concept
• level is illustrated in the book Page 623,
  E.g. 9.11.

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Before compensation
After compensation
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Frequency response
Transient response
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Two examples of IC OpAmp I
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Two examples of IC OpAmp II
http//en.wikipedia.org/wiki/Operational_amplifier
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Two examples of IC OpAmp III
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Two examples of IC OpAmp IV