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GATE 2014 EC (EC4) – Question 43

Networks, Signals and Systems · Two-Port Networks and Wye-Delta Transformation · 2 marks · Multiple choice

Find the impedance matrix Z (Ω) for the two-port network shown.

Diagram for GATE 2014 EC (EC4) question 43
  1. $\begin{pmatrix}6&24\\42&9\end{pmatrix}$
  2. $\begin{pmatrix}9&8\\8&24\end{pmatrix}$
  3. $\begin{pmatrix}9&6\\6&24\end{pmatrix}$
  4. $\begin{pmatrix}42&6\\6&60\end{pmatrix}$

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Correct answer: (C) $\begin{pmatrix}9&6\\6&24\end{pmatrix}$

Explanation

The admittance matrix is [[1/10+1/30,−1/30],[−1/30,1/60+1/30]]=[[2/15,−1/30],[−1/30,1/20]]. Its determinant is1/180. Invert it to obtain **Z=[[9,6],[6,24]]Ω,C**. The equal off-diagonal entries reflect network reciprocity.