- #1

timnswede

- 101

- 0

## Homework Statement

A 25-Ω antenna is connected to a 75-Ω lossless transmission line. Reflections back toward the generator can be eliminated by placing a shunt reactance Z at a distance l from the load (Fig. 1). Determine the values of Z and l.

## Homework Equations

Z(l)=Zo((ZL+jZotan(Bl))/(Zo+jZLtan(Bl))

## The Attempt at a Solution

My first intuition was to put a transmission line of length lambda/4 since the load impedance is just resistive, but the question asks for reactance which has me a bit stumped. I used a Smith chart and normalized the load to .33 ohms and found the conductance to be 3. Since I want a real part 1, I found the intersection of the constant vswr circle and the conductance equal to 1 circle. That point was 1+j1.15 and then I found the unnormalized reactance to be 65.2 ohms. I also got the length of l to be .083 lambda.

It's probably confusing to follow what I did on the Smith chart, but I just did the lumped element impedance matching. Apparently this is the right answer, but I'm having a hard time understanding why. The point of impedance matching is so that what the input impedance looks like (for this problem) at point B is 75 ohms. How can putting a complex component in shunt cause it to be 75 ohms? Is it because the transmission line from B to A is complex and it cancels that? I feel like I'm missing something fundamental.