Which one of the following is the transmission matrix equation for network N_s if two networks N_s and N_b are cascaded as shown in the figure?

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ESE Electronics Prelims 2021 Official Paper

\(\left[ {\begin{array}{*{20}{c}} {{V_1}}\\ {{I_1}} \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} {{A_a}}&{{B_a}}\\ {{C_a}}&{{D_a}} \end{array}} \right]\left[ {\begin{array}{*{20}{c}} { - {V_{2a}}}\\ {{I_{2a}}} \end{array}} \right]\)
\( \left[ {\begin{array}{*{20}{c}} {{V_1}}\\ {{I_1}} \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} {{A_a}}&{{B_a}}\\ {{C_a}}&{{D_a}} \end{array}} \right]\left[ {\begin{array}{*{20}{c}} {{V_{2a}}}\\ { - {I_{2a}}} \end{array}} \right]\)
\( \left[ {\begin{array}{*{20}{c}} {{V_1}}\\ {{I_1}} \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} {{A_a}}&{{B_a}}\\ {{C_a}}&{ - {D_a}} \end{array}} \right]\left[ {\begin{array}{*{20}{c}} { - {V_{2a}}}\\ {{I_{2a}}} \end{array}} \right]\)
\( \left[ {\begin{array}{*{20}{c}} {{V_1}}\\ {{I_1}} \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} {{A_a}}&{{B_a}}\\ { - {C_a}}&{{D_a}} \end{array}} \right]\left[ {\begin{array}{*{20}{c}} {{V_{2a}}}\\ { - {I_{2a}}} \end{array}} \right]\)

Answer 1

For network Na:-

V₁ = AV_2a - BI_2a

I₁ = CV_2a - DI_2a

\(\begin{bmatrix}V_1 \\\ I_1\end{bmatrix}=\begin{bmatrix}A&B \\\ C&D\end{bmatrix}\begin{bmatrix}V_{2a} \\\ -I_{2a}\end{bmatrix}\)