Topic: Network Theory
The 2-port network of figure A has open circuit impedance parameters given by matrix
- A. $\begin{bmatrix}R&R\\ R&R\end{bmatrix}$
- B. $\begin{bmatrix}R&0\\ 0&R\end{bmatrix}$
- C. $\begin{bmatrix}\infty&R\\ R&\infty\end{bmatrix}$
- D. $\begin{bmatrix}R&\infty\\ \infty&R\end{bmatrix}$
Answer: A. $\begin{bmatrix}R&R\\ R&R\end{bmatrix}$
Explanation: $Z_{11}=Z_a+Z_c$\n$Z_{22}=Z_b+Z_c$\n$Z_{12}=Z_{21}=Z_c$\nCompare figure (a) and figure (b)\n$Z_{11}=0+R=R$\n$Z_{22}=0+R=R$\n$Z_{12}=Z_{21}=R$\nOpen circuit impedance $\begin{bmatrix}Z_{11}&Z_{12}\\ Z_{21}&Z_{22}\end{bmatrix}=\begin{bmatrix}R&R\\ R&R\end{bmatrix}$