Topic: Network Theory
Y-parameter for following network is given as
- A. $\begin{bmatrix}\frac{9(s+1)}{8}&\frac{-3(2s+2)}{8}\\ \frac{-3(2s+2)}{8}&\frac{9(s+1)}{8}\end{bmatrix}$
- B. $\begin{bmatrix}\frac{9(2s+1)}{8}&\frac{-3(2s+1)}{8}\\ \frac{9(2s+1)}{8}&\frac{9(2s+1)}{8}\end{bmatrix}$
- C. $\begin{bmatrix}\frac{9(2s+1)}{8}&\frac{-3(2s+1)}{16}\\ \frac{9(2s+1)}{16}&\frac{9(2s+1)}{8}\end{bmatrix}$
- D. $\begin{bmatrix}\frac{9(s+1)}{8}&\frac{-3(2s+1)}{8}\\ \frac{-3(2s+1)}{8}&\frac{9(s+1)}{8}\end{bmatrix}$
Answer: B. $\begin{bmatrix}\frac{9(2s+1)}{8}&\frac{-3(2s+1)}{8}\\ \frac{9(2s+1)}{8}&\frac{9(2s+1)}{8}\end{bmatrix}$
Explanation: Evaluating the network at DC (s=0), the capacitors become open circuits, leaving a resistive H-bridge. Calculating the Y-parameters for this purely resistive network yields $y_{11} = 9/8$ and $y_{12} = -3/8$. Matching these conditions at s=0 against the provided options points to option (b).