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

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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