Topic: Network Theory
For the circuit shown, the impedance $Z_{1}$ looking into port 1 is $K_{1}\frac{s+2}{s+5}$. Find the impedance $Z_{2}$ looking into the output port, where $K_{1}$ and $K_{2}$ are constants.
- A. $K_{2}\frac{s}{s+5}$
- B. $\frac{s+5}{s K_{2}}$
- C. $K_{2}\frac{s}{s+6}$
- D. $\frac{s+6}{s K_{2}}$
Answer: A. $K_{2}\frac{s}{s+5}$
Explanation: $Z_{1}$ is the equivalent impedance from port 1, which equals $R_1 || (R_2 + Ls) = \frac{R_1(s + R_2/L)}{s + (R_1+R_2)/L}$. Matching with the given expression, $R_2/L = 2$ and $(R_1+R_2)/L = 5$. $Z_{2}$ from the other side is $(R_1+R_2) || Ls = \frac{s L(R_1+R_2)}{sL + R_1 + R_2} = \frac{s(R_1+R_2)}{s + 5}$. This takes the form $K_{2}\frac{s}{s+5}$.