The ABCD parameters of the following 2-port network are

[\begin{matrix} 3.5 + j 2 & 20.5 20.5 & 3.5 - j 2 \end{matrix}]

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[\begin{matrix} 3.5 + j 2 & 0.5 0.5 & 3.5 - j 2 \end{matrix}]

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[\begin{matrix} 10 & 2 + j 0 2 + j 0 & 10 \end{matrix}]

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[\begin{matrix} 7 + j 4 & 0.5 30.5 & 7 - j 4 \end{matrix}]

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Solution

The correct option is B $[\begin{matrix} 3.5 + j 2 & 0.5 0.5 & 3.5 - j 2 \end{matrix}]$

$[\begin{matrix} V_{1} I_{1} \end{matrix}] = [\begin{matrix} A & B C & D \end{matrix}] [\begin{matrix} V_{2} - I_{2} \end{matrix}]$

$W h e n I_{2} = 0$

$V_{1} = (5 + j 4 + 2) I_{1}$

$V_{2} = 2 I_{1}$

$A = {\begin{matrix} \frac{V_{1}}{V_{2}} \end{matrix} ∣ ∣ ∣}_{I_{2} = 0} = \frac{7 + j 4}{2} = 3.5 + j 2$

$C = {\begin{matrix} \frac{I_{1}}{V_{2}} \end{matrix} ∣ ∣ ∣}_{I_{2} = 0} = \frac{1}{2} = 0.5 ℧$

From here only option (b) matches.

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