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GATE ECE 2007 | Question-67

A load of $50 \Omega$ is connected in shunt in a $2$-wire transmission line of $Z_{0}=50 \Omega$ as shown in the figure. The $2$-port scattering parameter matrix (S-matrix) of the shunt element is
 

  1. $\left[\begin{array}{rr}-\frac{1}{2} & \frac{1}{2} \\ \frac{1}{2} & -\frac{1}{2}\end{array}\right]$
  2. $\left[\begin{array}{ll}0 & 1 \\ 1 & 0\end{array}\right]$
  3. $\left[\begin{array}{rr}-\frac{1}{3} & \frac{2}{3} \\ \frac{2}{3} & -\frac{1}{3}\end{array}\right]$
  4. $\left[\begin{array}{rr}\frac{1}{4} & -\frac{3}{4} \\ -\frac{3}{4} & \frac{1}{4}\end{array}\right]$
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