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The driving-point impedance Z(s) of a network has a pole-zero location as shown in the given figure:

F3 Savita Engineering 20.05.2022 D15

If Z(0) = 3, then Z(s) is

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  1. \(Z(s) = \frac{{3(s + 3)}}{{{s^2} + 2s + 3}}\)
  2. \(Z(s) = \frac{{2(s + 3)}}{{{s^2} + 2s + 2}}\)
  3. \(Z(s) = \frac{{3(s - 3)}}{{{s^2} - 2s - 2}}\)
  4. \(Z(s) = \frac{{2(s - 3)}}{{{s^2} - 2s - 3}}\)

Answer (Detailed Solution Below)

Option 2 : \(Z(s) = \frac{{2(s + 3)}}{{{s^2} + 2s + 2}}\)
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Detailed Solution

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Calculation:

F3 Savita Engineering 20.05.2022 D15

From the pole-zero diagram:

  • One zero at -3
  • Complex conjugate poles at (-1± j)
  • Then, the driving-point impedance Z(s) of a network is given by:

\(Z(s) = {s+3 \over (s+1+j)(s+1-j)}\)

\(Z(s) = {s+3 \over s^2+2s+2}\)

Given, DC gain : Z(0) = 3

Hence, Z(s) has to be multiplied by 2 in order to get DC gain value equal to 3.

\(Z(s) = {2(s+3) \over s^2+2s+2}\)

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