To equalize the sending and receiving end voltages, impedance is connected at the receiving end of a transmission line having the following ABCD parameters A = D = 0.9 ∠0° B = 200 ∠90° Ω The impedance so connected would be

Concept:

ABCD parameters in a transmission line are represented as

V_S = AV_R + BI_R

I_S = CV_R + DI_R

To equalize the sending and receiving end voltage, V_S = V_R

⇒ V_R = AV_R + BI_R

\(\Rightarrow {I_R} = \frac{{1 - A}}{B}{V_R}\)

The impedance at the receiving end is

\(Z = \frac{{{V_R}}}{{{I_R}}} = \frac{B}{{1 - A}}\)

Calculation:

Given that,

A = D = 0.9∠0°, B = 200 ∠90° Ω

The impedance at receiving end

\(Z = \frac{{{V_R}}}{{{I_R}}} = \frac{B}{{1 - A}} = \frac{{200\angle 90^\circ }}{{1 - 0.9\angle 0^\circ }}\)

⇒ Z = 2000∠90° Ω