Chapter 5, Problem 5.1MCQ

Representing a transmission line by the two-port network, in terms of ABCD parameters, (a) express $V_S,$ which is the sending-end voltage, in terms of $V_R,$ which is the receiving-end voltage, and $I_R,$ the receiving-end current, and (b) express $I_S,$ which is the sending-end current, in terms of $V_R$ and $I_R.$

(a) $V_S=$

_________ (b) $I_S=$ ________

To determine

The sending end voltage in the form of receiving end parameters.

Answer to Problem 5.1MCQ

  $V_s=A{V}_R+B{I}_R$

Explanation of Solution

Given:

A two port network having ABCD parameter is shown below.

Calculation:

For transmission line, input-output terminal voltage and current in the form of

ABCD parameter is given by,

  $\left[\begin{array}{c}{V}_s\\ I_s\end{array}\right]=\left[\begin{array}{cc}A& B\\ C& D\end{array}\right]\left[\begin{array}{c}{V}_R\\ I_R\end{array}\right]$

Hence, from the above relation, sending end voltage is given by

  $V_s=A{V}_R+B{I}_R$

To determine

The sending end current in terms of receiving end parameters.

Answer to Problem 5.1MCQ

  $I_s=C{V}_R+D{I}_R$

Explanation of Solution

Given:

A two port network having ABCD parameter is shown below.

Calculation:

For transmission line, input-output terminal voltage and current in the form of

ABCD parameter in given by,

  $\left[\begin{array}{c}{V}_s\\ I_s\end{array}\right]=\left[\begin{array}{cc}A& B\\ C& D\end{array}\right]\left[\begin{array}{c}{V}_R\\ I_R\end{array}\right]$

Hence, from the above relation, sending end current is given by

  $I_s=C{V}_R+D{I}_R$