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Identify the number of poles and zeros of the transfer function whose frequency response is given as:

Identify the number of poles and zeros of the transfer function whose frequency response is given as: Correct Answer P = 3 and Z = 1

Concept:

  • Initial slope gives the indication of type of the system.
  • For type-1 system, initial slope is -20dB/dec.
  • For type-2 system, initial slope is -40dB/dec.
  • For type-3 system, initial slope is -60dB/dec.
  • For induction of 1 pole, slope changes by -20dB/dec.
  • For induction of 1 zero, slope changes by +20dB/dec.

 

Analysis:

Here initial slope is -20dB/dec, Hence, it is type-1 system

Type-1 system indicates one pole at origin.

At ω1 we have change of slope by -20dB/dec. Hence, one pole is there.

At ω = 6 we have slope change by +20dB\dec. Hence, one zero is there.

At ω3 we have slope change by -20dB\dec. Hence, one pole is there.

So, For the system we have 3 poles and 1 zero.

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