Two identical two-port networks having transmission matrix [[ *20c AB CD ]] are cascaded. What will be the resultant transmission matrix of the cascade?

[[ *20c A^2 + BCAB + BD AC + CDBC + D^2 ]]

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Network Theory and Analysis

Two identical two-port networks having transmission matrix \[\left[ {\begin{array}{*{20}{c}} {\text{A}}&{\text{B}} \\ {\text{C}}&{\text{D}} \end{array}} \right]\] are cascaded. What will be the resultant transmission matrix of the cascade?

A) \[\left[ {\begin{array}{*{20}{c}} {\text{A}}&{\text{B}} \\ {\text{C}}&{\text{D}} \end{array}} \right]\] B) \[\left[ {\begin{array}{*{20}{c}} {{\text{2A}}}&{{\text{2B}}} \\ {{\text{2C}}}&{{\text{2D}}} \end{array}} \right]\] C) \[\left[ {\begin{array}{*{20}{c}} {{{\text{A}}^2} + {\text{BC}}}&{{\text{AB}} + {\text{BD}}} \\ {{\text{AC}} + {\text{CD}}}&{{\text{BC}} + {{\text{D}}^2}} \end{array}} \right]\] D) \[\left[ {\begin{array}{*{20}{c}} {{{\text{A}}^2}}&{{{\text{B}}^2}} \\ {{{\text{C}}^2}}&{{{\text{D}}^2}} \end{array}} \right]\]

Answer & Solution

Correct Answer: Option C

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Two identical two-port networks having transmission matrix left begin array 20...

Two identical two-port networks having transmission matrix \[\left[ {\begin{array}{*{20}{c}} {\text{A}}&{\text{B}} \\ {\text{C}}&{\text{D}} \end{array}} \right]\] are cascaded. What will be the resultant transmission matrix of the cascade?

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