Question

The transfer function of a second order real system with a perfectly flat magnitude response of unity has a pole at $(2-j3)$. List all the poles and zeros.

• A. Poles at $(2\pm j3)$, no zeros.
• B. Poles at $(\pm 2-j3)$, one zero at orgin.
• C. Poles at $(2-j3),(-2+j3),$ zeros at $(-2-j3),(2+j3)$.
• D. Poles at $(2\pm j3)$, zeros at $(-2\pm j3).$

Answer 1

The correct option is D Poles at $(2\pm j3)$, zeros at $(-2\pm j3).$

Responce of transfer function is unit for all $\omega$.

$M=1;P_1=2-j3$

Second order system, hence number of poles = 2

Therefore, second pole $P_2=2+j3$

Now for M = 1, and due to x-axis symmetry of root locus of transfer function, position of zeroes must be

$Z_1=-2-j3and{Z}_2=-2+j3$