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GATE 2020 EC – Question 25

Networks, Signals and Systems · Two-Port Networks and Wye-Delta Transformation · 1 mark · Numerical answer

In the given circuit, the two-port network has the impedance matrix $[Z]=\begin{bmatrix}40&60\\60&120\end{bmatrix}\Omega$. The value of $Z_L$ for which maximum power is transferred to the load is ________ $\Omega$.

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Correct answer: 48

Explanation

For maximum power, $Z_L$ equals the Thevenin impedance seen from port 2 with the source replaced by its $10\ \Omega$ internal resistance: $Z_{th}=Z_{22}-\frac{Z_{12}Z_{21}}{Z_{11}+10}=120-\frac{60\times60}{50}=48\ \Omega$.