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

The answer is below

Step-by-step 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=(1.54)/(Z_o*w)=(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=(Z_o)/(1.52*w)=(200)/(1.52*2\pi*800*10^6)=2.6*10^(-8)\\ \\L=2.6*10^(-8)H`