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GATE EE 2024 Set 1 — Question 48

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NAT+2 / -0HardParameter ConversionTwo-Port NetworksElectric CircuitsInterconnection of Two-Ports

Electric Circuits → Two-Port Networks → Interconnection of Two-Ports

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Question

Two passive two-port networks P and Q are connected as shown in the figure. The impedance matrix of network P is ZP=[40 Ω60 Ω80 Ω100 Ω]\mathbf{Z_P} = \begin{bmatrix} 40\ \Omega & 60\ \Omega \\ 80\ \Omega & 100\ \Omega \end{bmatrix}. The admittance matrix of network Q is YQ=[5 S−2.5 S−2.5 S1 S]\mathbf{Y_Q} = \begin{bmatrix} 5\ \text{S} & -2.5\ \text{S} \\ -2.5\ \text{S} & 1\ \text{S} \end{bmatrix}. Let the ABCD matrix of the two-port network R in the figure be [αβγδ]\begin{bmatrix} \alpha & \beta \\ \gamma & \delta \end{bmatrix}. The value of β\beta in Ω\Omega is _____________ (rounded off to 2 decimal places).
Block diagram showing two-port networks P and Q connected in cascade to form network R
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