Question

Representing a transmission line by the two-port network, in terms of ABCDparameters, (a) express${\mathit{V}}_{\mathbf{S}}$, which is the sending-end voltage, interms of${\mathit{V}}_{\mathbf{R}}$, which is the receiving-end voltage, and${\mathit{I}}_{\mathbf{R}}$, the receiving-endcurrent, and (b) express${\mathit{I}}_{\mathbf{S}}$, which is the sending-end current, in termsof${\mathit{V}}_{\mathbf{R}}$and${\mathit{I}}_{\mathbf{R}}$.

(a)${\mathit{V}}_{\mathbf{S}\mathbf{=}}$

(b)role="math" localid="1653078165582" ${\mathit{I}}_{\mathbf{S}\mathbf{=}}$

Short answer

(a)The sending end voltage in terms of receiving end voltage and current is $V_s=A{V}_R+B{I}_R$

(b)The sending end current in terms of receiving end voltage and current is

$I_s=C{V}_R+D{I}_r$

Step-by-step solution

Determine the relation between sending end and receiving end quantities.

Draw the two-port network.

Write the relation between sending end and receiving end quantities.

Here, $A$, $B$, $C$ and $D$ are parameters that depends on transmission line parameters.

role="math" localid="1653078576310" ${\mathit{V}}_{\mathbf{S}}\mathbf{=}\mathit{A}{\mathit{V}}_{\mathbf{R}}\mathbf{+}\mathit{B}{\mathit{I}}_{\mathbf{R}}$ ……. (1)

role="math" localid="1653078586251" ${\mathit{I}}_{\mathbf{S}}\mathbf{=}\mathit{C}{\mathit{V}}_{\mathbf{R}}\mathbf{+}\mathit{D}{\mathit{I}}_{\mathbf{R}}$ ……. (2)

Here, $V_S$ and $V_R$ are sending end and receiving end voltages, $I_S$ and $I_R$ are sending end and receiving end currents.

Determine the answer.

The parameters$A$and $D$ are dimensionless.

The unit of $C$ is Siemens and the unit of $B$ is ohm.

Therefore, the sending end voltage and current in terms of receiving end voltage and current is obtained.