Direction: The following item consists of two statements, one labeled as ‘Statement (I) and the other as ‘Statement (II). You are to examine these two statements carefully and select the answers to these items using the code given below:

Statement (I): For an unstable feedback system, the gain margin is negative or the phase margin is positive.

Statement (II): For a stable feedback system, both gain margin and phase margin must be positive.

This question was previously asked in

ESE Electronics 2020: Official Paper

Option 4 : Statement (I) is false but Statement (II) is true

CT 3: Building Materials

2962

10 Questions
20 Marks
12 Mins

Phase Cross over Frequency:

- The frequency at which the phase plot is having the phase of -180° is known as phase cross over frequency.
- It is denoted ωpc .
- The unit of phase cross over frequency is rad/sec

Gain Cross over Frequency:

- The frequency at which the magnitude plot is having the magnitude of zero dB is known as gain cross over frequency.
- It is denoted by ωgc.
- The unit of gain cross over frequency is rad/sec

Gain Margin:

Gain margin GM is defined as the negative of the magnitude in dB, at phase cross over frequency, i.e.

\(GM = 20\log \left( {\frac{1}{{{M_{pc}}}}} \right) = 20\log {M_{pc}}\)

Mpc is the magnitude at phase cross over frequency. The unit of gain margin (GM) is dB.

Phase Margin

The phase margin of a system is defined as:

PM = 180° + ϕgc

The stability of the control system id based on the relation between gain margin and phase margin as:

- If the gain margin GM and the phase margin PM are positive, then the control system is stable (Statement 2 is true)
- If both the gain margin GM and the phase margin PM are equal to zero, then the control system is marginally stable.
- If the gain margin GM and the phase margin PM are negative, then the control system is unstable (Statement 1 is false)