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GATE 2016 EC (EC2) – Question 19

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

The z-parameter matrix of the shown two-port network is
$$\begin{bmatrix}2j\omega&j\omega\\j\omega&3+2j\omega\end{bmatrix}\ \Omega.$$
If $Z_b(j\omega)=R_b+j\omega$, the value of $R_b$ in ohms is ________.

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Correct answer: 2.98 to 3.02

Explanation

For a T network, $z_{12}=z_{21}=Z_c$ and $z_{22}=Z_b+Z_c$. Hence $Z_c=j\omega$.

Subtracting gives $Z_b=z_{22}-z_{12}=3+j\omega$. Its real part is the resistance, so **$R_b=3\ \Omega$**. The first port similarly gives $Z_a=j\omega$, consistent with the network.

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