Question 4?

Question

A 300m long lossless tranmission line has a characteristic impedance of 75 ohm and a phase velocity of 220000km/s at the operating frequency of 3MHz.The line is terminated in an impedance of 150+J40Ohm.If the voltage across the receiving end is 50 V(rms) , determine the current through the load and the voltage input to the transmission line.

Answer 1

If this is lossless then R,G~=0

We're given Vp, and Z0, we need γ=α+jβ but lossless so α=0
and γ=jβ

Vp=ω/β==>
β=2πf/Vp=2π3E6/220E6=85.7E-3

next we need to find the input impedance with the Z0 and Zl given

Zi=Z0((Zlcosh(γl)+Z0sinh(γl))/(Z0cosh(γl)+Zlsinh(γl))

plugging in all the values we get

Zi=119<-32.73 (
Is=Vg/Zi (assume Zgenerator=0)

Is=50/119<-32.73=0.42<32.73


The current through the load is
i=v/r=50/(150+j40)=0.32<-14.9

the Vr=Zl/Zi*Vs=155.24<0.26/119<-32.73*50=65.26<1.57