Question

Express the no-load receiving-end voltage ${\mathit{V}}_{\mathbf{R}\mathbf{N}\mathbf{L}}$in terms of the sending endvoltage,role="math" localid="1653128768955" ${\mathit{V}}_{\mathbf{S}}$, and the ABCDparameters.

Short answer

Therefore, the answer is $V_{RNL}=\frac{V_s}{A}$.

Step-by-step solution

Determine the relation between sending end and receiving end quantities.

Write the relation between sending end and receiving end quantities in terms of transmission parameters.

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

${\mathit{I}}_{\mathbf{S}}\mathbf{=}\mathit{C}{\mathit{V}}_{\mathbf{R}}\mathbf{+}\mathit{D}{\mathit{i}}_{\mathbf{R}}$ ……. (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.

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

Determine the relation in no-load receiving end voltage in terms of the sending end voltage and the ABCD parameters.

For the no-load receiving end voltage, the output terminal will be open, so receiving end current will be zero, that is,

$I_R=0$

Substitute $0$for $I_R$ and $V_{RNL}$for in equation (1).

$$\begin{gathered} V_s=A{V}_{RNL}+B\left(0\right) \\ {V}_{RNL}=\frac{V_s}{A} \end{gathered}$$

Therefore, the no-load receiving-end voltage $V_{RNL}$ in terms of the sending end

voltage, $V_S$ , and the ABCDparameters is $V_{RNL}=\frac{V_S}{A}$.