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What is the phase margin if the gain crossover frequency is at 45 degrees?

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Question: What is the phase margin if the gain crossover frequency is at 45 degrees?

Options:

  1. 0 degrees
  2. 45 degrees
  3. 90 degrees
  4. 135 degrees

Correct Answer: 90 degrees

Solution: 

The phase margin is calculated as 180 degrees minus the phase at the gain crossover frequency. If the phase is -135 degrees, the phase margin is 45 degrees.

What is the phase margin if the gain crossover frequency is at 45 degrees?

Practice Questions

Q1
What is the phase margin if the gain crossover frequency is at 45 degrees?
  1. 0 degrees
  2. 45 degrees
  3. 90 degrees
  4. 135 degrees

Questions & Step-by-Step Solutions

What is the phase margin if the gain crossover frequency is at 45 degrees?
  • Step 1: Understand what gain crossover frequency means. It is the frequency at which the gain of a system is 1 (or 0 dB).
  • Step 2: Know that phase margin is a measure of stability in control systems.
  • Step 3: Remember the formula for phase margin: Phase Margin = 180 degrees - Phase at Gain Crossover Frequency.
  • Step 4: Identify the phase at the gain crossover frequency. In this case, it is given as -135 degrees.
  • Step 5: Substitute the phase value into the formula: Phase Margin = 180 degrees - (-135 degrees).
  • Step 6: Calculate the phase margin: 180 degrees + 135 degrees = 315 degrees.
  • Step 7: Since phase margin is typically expressed in the range of 0 to 180 degrees, we can find the equivalent by subtracting 360 degrees if necessary.
  • Step 8: Therefore, the phase margin is 315 degrees - 360 degrees = -45 degrees, which indicates instability.
  • Step 9: However, if we are only looking for the positive margin, we can say the phase margin is 45 degrees.
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