Question

Derive the ABCDparameters for the T circuit shown in Figure 5.4.

Short answer

Therefore, the A,B,C,Dparameters are $\left(1+Y{Z}_1\right),\left(Z_1+Y{Z}_1{Z}_2+Z_2\right),Y\mathrm{and}\left(1+{\mathrm{YZ}}_2\right).$

Step-by-step solution

Determine the given data.

Draw the given circuit

Here, $V_s$is the sending end voltage, $V_R$is the receiving end voltage, $l_S$is the sending end current and $l_R$is the receiving end current.

Also, $Z_1$and $Z_2$are the impedance and Y is the admittance.

Determine the formulas of sending end voltage and current.

Write the formula of sending end voltage in terms of transmission line parameters.

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

Here, $V_s$is the sending end voltage, $V_R$is the receiving end voltage, and $l_R$is the transmission line current.

Write the formula of sending end current in terms of transmission line parameters.

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

Here, $l_S$is the sending end current, $V_R$is the receiving end voltage, and $l_R$is the receiving end current.

Determine the ABCD parameters.