GATE EC 2010 Electromagnetics Solution Q 4

GATE EC 2010 Electromagnetics Solution Q 4

If the scattering matrix[S] of a two port network is

\lbrack s\rbrack=\begin{bmatrix}0.2\angle0^0&0.9\angle90^0\0.9\angle90^0&0.1\angle90^0\end{bmatrix}

then the network is_____.

a) lossless and reciprocal

b) lossless but not reciprocal

c) not lossless but reciprocal

d) neither lossless nor reciprocal

Ans-(c)

Explanation

We know that,

For reciprocal networks, S_{12}=S_{21}

For lossless reciprocal networks, columns have unit magnitude and are orthogonal. So,

\left|S_{11}\right|^2+\left|S_{12}\right|^2=1

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