Question

The asymptotic Bode magnitude plot of minimum phase transfer function G(s) is shown below.

Consider the following statements:
Statement-1: Transfer function G(s) has three poles and one zero.

Statement -2: At very high frequency $(\omega \to \infty )$, the phase angle $\angle G\left(j\omega \right)=-\frac{3\pi }{2}$
Which of the following option is correct ?

• A. Statement 2 is true and statement 1 is false.
• B. Both the statements are false.
• C. Both the statements are true.
• D. Statement 1 is true and statement 2 is false.

Answer 1

The correct option is A Statement 2 is true and statement 1 is false.

$G\left(s\right)=\frac{k}{s(1+\frac{s}{1})(1+\frac{s}{20})}$
Transfer function shows 2 poles and no zeros.
So statement 1 is wrong.
$\angle G\left(j\omega \right)=-90-ta{n}^{-1}\omega -ta{n}^{-1}\frac{\omega }{20}$
$\angle G\left(j\omega \right){|}_{\omega \to \infty }=-{270}^{\circ }=-\frac{3\pi }{2}rad$
So statement 2 is correct.