The GATE Grind

GATE 2023 EC – Question 33

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

For the two port network shown below, the $[Y]$-parameters is given as

$$[Y]=\frac1{100}\begin{bmatrix}2&-1\\-1&\frac43\end{bmatrix}S.$$

The value of load impedance $Z_L$, in Ω, for maximum power transfer will be ________ (rounded off to the nearest integer).

Diagram for GATE 2023 EC question 33

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: 80

Explanation

Maximum power transfer needs $Z_L=Z_{out}$ of the network including the source resistance (10 Ω). $Y_{out}=y_{22}-\dfrac{y_{12}y_{21}}{y_{11}+Y_s}$ with $Y_s=1/10=0.1$ S. $y_{22}=0.013333$, $y_{12}y_{21}=10^{-4}$, $y_{11}+Y_s=0.02+0.1=0.12$. $Y_{out}=0.013333-0.000833=0.0125$ S, so $Z_L=1/0.0125=80\ \Omega$.