Answer: (a) and (b)
The primary objective of the control loop is to stabilize the power supply against variations in component values over production, as well as variations in line voltage and output load.

When an oscillating power supply is stabilized, there is also an added benefit of increased throughput efficiency. Thus the feedback loop also plays a role in improving the efficiency, although this is not its primary objective.

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(a) For a control loop to become unstable and oscillate two conditions must simultaneously exist:

1. The phase response from input to output will be -180° (assuming 0° phase shift at DC). 
2. The loop gain of the system will be 0dB (gain cross over).

Gain margin is the absolute value of the measured loop gain at phase crossover (where the phase has crossed -180°).

Phase margin is the measured phase above—180° at the gain crossover frequency.  The value represents the amount the phase would have to reduce by (that is, lag) to meet the criteria for instability.

A well-designed system should have at least 6 dB of gain margin and 45° to 60° of phase margin.

(b) 1 kHz cross over frequency, 33° Phase margin, and 30 dB gain margin.

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(a) The phase boost network adds a pole-zero pair to the controller transfer function. The component values are chosen in such a manner so that the zero is added at a frequency close to the crossover frequency, and the pole is placed a decade apart, thereby increasing the phase margin of the system.

The PI Expert design tool calculates values for feedback components, provides gain phase plots, and recommends when a phase boost network should be used.

(b) The resultant gain and phase response is shown below.  Cross over frequency is 1.1 kHz, the gain margin is 30 dB and phase margin 64°.

Figure 2

Should the phase margin reduce to zero (phase reaches or exceeds –180°) while the gain is greater than zero, then the loop is considered conditionally stable.

Although theoretically a system with a phase margin of 1° is considered stable, in practice the phase margin in a power supply can vary significantly due to component tolerances and line and load variations.

Conditional stability is therefore not desirable, as in this state these variations can cause the loop gain to reduce, shifting the gain cross over to a lower frequency, where phase margin is inadequate, and causing the power supply to become unstable and oscillate.

This often happens during start-up or other load transients, when the control loop commands maximum or minimum duty cycle.

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