Question

Determine the number of poles and zeros of the transfer function \(\frac{{s + 1}}{{s({s^2} + 4)}}\)
1. Number of poles = 2, and number of zeros = 3
2. Number of poles = 3, and number of zeros = 1
3. Number of poles = 1, and number of zeros = 3
4. Number of poles = 3, and number of zeros = 2

Answer 1

Correct Answer - Option 2 : Number of poles = 3, and number of zeros = 1

Concept:

The standard form of the transfer function is described as:

\(T\left( s \right) = \frac{{K(s + z_1)(s+z_2)......}}{{\left( {s + P_1} \right)\left( {s + P_2} \right)}.......}\)

z1 and z2 are the zeros of the transfer function

P1 and P2 are the poles of the transfer function

Analysis:

Given transfer function \(\frac{{s + 1}}{{s({s^2} + 4)}}\)

Zero = -1

Pole = 0, ± j2

Number of zero = 1

Number of poles = 3