Topic: Network Theory
The driving-point impedance of a network is given by: $Z(s)=\frac{s^{2}+3s+2}{s(s+2)}$
Which of the following statements is correct regarding the synthesis of this network?
- A. The function is not realizable using passive elements only
- B. The function can be realized using L and C elements only
- C. The function can be realized using passive elements only
- D. The function is not positive real and cannot be synthesized
Answer: C. The function can be realized using passive elements only
Explanation: Simplifying the given impedance function: $Z(s) = \frac{(s+1)(s+2)}{s(s+2)}$. Canceling the $(s+2)$ term gives $Z(s) = \frac{s+1}{s} = 1 + \frac{1}{s}$.
This corresponds precisely to a $1~\Omega$ resistor in series with a $1$ F capacitor. Since both are passive elements, the function is positive real and can be synthesized using passive elements only.