Question

Representing a transmission line by the two-port network, in terms of ABCDparameters, (a) express${\mathbf{V}}_{\mathbf{S}}$, which is the sending-end voltage, in terms of ${\mathbf{V}}_{\mathbf{R}}$, which is the receiving-end voltage, and${\mathbf{I}}_{\mathbf{R}}$, the receiving-end current, and (b) express${\mathbf{I}}_{\mathbf{S}}$, which is the sending-end current, in terms of${\mathbf{V}}_{\mathbf{R}}$androle="math" localid="1655355356933" ${\mathbf{I}}_{\mathbf{R}}$.

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

(b)${\mathbf{I}}_{\mathbf{S}}\mathbf{=}$

Short answer

(a)The sending end voltage in terms of receiving end voltage and current is ${\mathrm{V}}_{\mathrm{S}}={\mathrm{AV}}_{\mathrm{R}}+{\mathrm{BI}}_{\mathrm{R}}$

(b)The sending end current in terms of receiving end voltage and current is ${\mathrm{I}}_{\mathrm{S}}={\mathrm{CV}}_{\mathrm{R}}+{\mathrm{DI}}_{\mathrm{R}}$ .

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.

${\mathbf{V}}_{\mathbf{S}}\mathbf{=}{\mathbf{AV}}_{\mathbf{R}}\mathbf{+}{\mathbf{BI}}_{\mathbf{R}}$ ……. (1)

${\mathbf{I}}_{\mathbf{S}}\mathbf{=}{\mathbf{CV}}_{\mathbf{R}}\mathbf{+}{\mathbf{DI}}_{\mathbf{R}}$ ……. (2)

Here,${\mathrm{V}}_{\mathrm{S}}$ and ${\mathrm{V}}_{\mathrm{R}}$ are sending end and receiving end voltages, ${\mathrm{I}}_{\mathrm{S}}$ and ${\mathrm{I}}_{\mathrm{R}}$ are sending end and receiving end currents.

Determine the answer.

The parameters $\mathrm{A}$ and $\mathrm{D}$ are dimensionless.

The unit of $\mathrm{C}$ is Siemens and the unit of $\mathrm{B}$ is ohm.

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