Topic: Electromagnetics
The S matrix of a lossless line having length $\lambda/4$ is
- A. $\begin{bmatrix}1&0\\ 0&1\end{bmatrix}$
- B. $\begin{bmatrix}1&-1\\ -1&1\end{bmatrix}$
- C. $\begin{bmatrix}0&j\\ j&0\end{bmatrix}$
- D. None of above
Answer: D. None of above
Explanation: $S=\begin{bmatrix}0&e^{-j\beta l}\\ e^{-j\beta l}&0\end{bmatrix}$. $l=\frac{\lambda}{4}$. $\beta l=\frac{2\pi}{\lambda}\times\frac{\lambda}{4}=\frac{\pi}{2}$. $e^{-j\beta l}=e^{-j\frac{\pi}{2}}=-j$. $S=\begin{bmatrix}0&-j\\ -j&0\end{bmatrix}$.