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GATE 2016 EC (EC3) – Question 44

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

The z-parameter matrix of the shown two-port network is

Diagram for GATE 2016 EC (EC3) question 44
  1. $$\begin{bmatrix}2&-2\\-2&2\end{bmatrix}$$
  2. $$\begin{bmatrix}2&2\\2&2\end{bmatrix}$$
  3. $$\begin{bmatrix}9&-3\\6&9\end{bmatrix}$$
  4. $$\begin{bmatrix}9&3\\6&9\end{bmatrix}$$

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Correct answer: (A) $$\begin{bmatrix}2&-2\\-2&2\end{bmatrix}$$

Explanation

The crossed wires are not joined at their crossing. They connect input upper to output lower and input lower to output upper, reversing the two port voltage polarities.

The 3 Ω and 6 Ω resistors are in parallel between the same two nodes, giving 2 Ω. With currents defined entering each upper port, $V_1=2(I_1-I_2)$ and $V_2=-V_1$.

Thus $z_{11}=z_{22}=2$ Ω and $z_{12}=z_{21}=-2$ Ω, **A**.

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