Question

Determine the location of poles and zeros of the following transfer function.

\(Y(s) = \frac{{(s + 2)(s + 4)}}{{s(s + 1)(s + 3)}}\)

1.

Poles: 0, -1, -3

Zeros: -2, -4

2.

Poles: -2, -4

Zeros: 0, -1, -3

3.

Poles: 2, 4

Zeros: 0, 1, 3

4.

Poles: 0, 1, 3

Zeros: 2, 4

Answer 1

Correct Answer - Option 1 :

Poles: 0, -1, -3

Zeros: -2, -4

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

Application:

The given transfer function is:

\(Y(s) = \frac{{(s + 2)(s + 4)}}{{s(s + 1)(s + 3)}}\)

For location of zeros, put numerator = 0

s = -2 and -4

For the location of poles, put denominator = 0

s = 0, -1 and -3

So, option A is correct.

• Zeros are the roots of the transfer function at which the transfer function becomes zero.
• In a transfer function, the frequencies for which the value of the numerator becomes zero are called Zeros.
• Poles are the roots of the transfer function at which transfer function becomes infinity.
• In a transfer function, the frequencies for which the value of the denominator becomes zero are called Poles.