Question

The Bode magnitude plot of a first order stable system is constant with frequency. The asymptotic value of the high frequency phase, for the system, is -180°. This system has

• A. one LHP pole and one RHP zero at the same frequency.
• B. one LHP pole and one LHP zero at the same frequency.
• C. two LHP poles and one RHP zero.
• D. two RHP poles and one LHP zero.

Hint:

In Bode plots, the phase shift behavior depends on the placement of poles and zeros. A -180° phase shift at high frequency indicates the presence of one LHP pole and one RHP zero at the same frequency.

Answer 1

The Correct Option is A

Step 1: Understanding the system.
For a first order system, if the phase asymptotically reaches -180° at high frequency, it implies that the system has one LHP (Left Half Plane) pole and one RHP (Right Half Plane) zero at the same frequency. This combination results in a phase of -180° at high frequencies.
Step 2: Analyzing the options.
- (A) One LHP pole and one RHP zero at the same frequency: This is correct as it results in the described phase shift behavior.
- (B) One LHP pole and one LHP zero at the same frequency: This would not result in a phase of -180°; it would instead cause a different phase shift.
- (C) Two LHP poles and one RHP zero: This configuration would produce a different phase shift, not -180°.
- (D) Two RHP poles and one LHP zero: This does not produce the desired phase asymptotic behavior either.
Step 3: Conclusion.
The correct answer is (A) because it matches the phase behavior described.