ISRO EC 2023 Q.36: solution and answer

Official answer: BSource: ISRO's revised and final answer key of 16 February 2024

1. A junction is matched at a port when, with every other port terminated in a matched load, a wave sent into that port is not reflected.

2. The reflection coefficient at port 1 is $S_{11}=\frac{b_1}{a_1}{|}_{a_2=0}$. Matching means the reflected wave is zero, $b_1=0$, for an incident wave $a_1$. Hence $S_{11}=0$, and in the same way every diagonal element $S_{ii}=0$.

3. Option (a), $S_{11}\ne 0$, describes a mismatched port, so it is wrong.

4. Option (c), $S_{21}=1$, would need lossless transmission with zero phase shift. Matching does not require this: a matched attenuator has $S_{11}=0$ but $|S_{21}|<1$, and a matched line section has $S_{21}=e^{-j\beta l}$, whose phase is not zero.

5. Option (d), $|S_{21}|=0$, would mean that no power is transmitted. Matching does not imply this: a matched through-line has $|S_{21}|=1$.

6. The only statement that always holds for a matched junction is $S_{11}=0$, which is option (b).