Question

A 200 Ω transmission line is to be matched to a computer terminal with ZL = (50 − j25) Ω by inserting an appropriate reactance in parallel with the line. If f = 800 MHz and r = 4, determine the location nearest to the load at which inserting:
A) A capacitor can achieve the required matching, and the value of the capacitor. PROBLEMS 131 B) An inductor can achieve the required matching, and the value of the inductor.

Answer 1

Answer:

The answer is below

Explanation:

a) To solve this problem, we are going to use the smith chart. After entering the value of Zo = 200 ohm and ZL = (50 − j25) Ω, this give us $z_L\ and\ y_L$, the intersection between $y_L$ and the SWR line gives:

$y(d)=1.026-j1.54\\\\We\ are\ using\ the\ imaginary\ part\ to calculate\ the\ capacitance,hence:\\\\wC=1.54*Y_o\\\\C=\frac{1.54}{Z_o*w}=\frac{1.54}{200*2\pi*800*10^6}=1.53*10^{-12}\\ \\C=1.53*10^{-12}F$

b) Also, we get:

$y(d)=1.0-j1.52\\\\We\ are\ using\ the\ imaginary\ part\ to\ calculate\ the\ inductance,hence:\\\\1/wL=1.52*Y_o\\\\L=\frac{Z_o}{1.52*w}=\frac{200}{1.52*2\pi*800*10^6}=2.6*10^{-8}\\ \\L=2.6*10^{-8}H$