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GATE 2014 EC (EC1) – Question 34

Networks, Signals and Systems · Two-Port Networks and Wye-Delta Transformation · 1 mark · Multiple choice

A two-port has $S=\begin{pmatrix}s_{11}&s_{12}\\s_{21}&s_{22}\end{pmatrix}$. Port 2 is shorted. Find the resulting one-port $s_{11}$ parameter.

  1. $\frac{s_{11}-s_{11}s_{22}+s_{12}s_{21}}{1+s_{22}}$
  2. $\frac{s_{11}+s_{11}s_{22}-s_{12}s_{21}}{1+s_{22}}$
  3. $\frac{s_{11}+s_{11}s_{22}+s_{12}s_{21}}{1-s_{22}}$
  4. $\frac{s_{11}-s_{11}s_{22}+s_{12}s_{21}}{1-s_{22}}$

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Correct answer: (B) $\frac{s_{11}+s_{11}s_{22}-s_{12}s_{21}}{1+s_{22}}$

Explanation

The terminated two-port input reflection coefficient is Γin=S11+S12S21ΓL/(1−S22ΓL). A short has ΓL=−1. Substitution gives S11−S12S21/(1+S22)=(S11+S11S22−S12S21)/(1+S22), matching **B**.