Transmission Line Homework - Determine Input Impedance

[sandy.bridge]

Homework Statement

Attached is the problem. I am a little confused as to how I should be approaching this type of problem. If I Determine the input impedance for the first segment of transmission line and load impedance on the right, is that going to be in parallel with $Z_L$ on the left? I am assuming that "effective impedance" is referring to that total input impedance at the left of the diagram, but I am unsure.

 

[rude man]

1. What is the impedance looking into the 1/4 wave xfmr? (Pretend there's just the xfmr and end-termination).
2. So is that in parallel with the 1st 25 ohm resistor or ?
3. You should wind up with just a 50 ohm xmsn line and a yet-to-be-determined termination, from which you can come up with the reflection coefficient.
.

 

[sandy.bridge]

Number two is the very issue that I was having. I determined the input impedance of the 1/4 transformer and end impedance of 25 ohm to be $Z_i=(50Ω)^2/25Ω$. I believe this input impedance looking to the right would then be in parallel with $Z_L$ at the second termination on the left side and that results in 20Ω. Is that logical so far?

 

[rude man]

Number two is the very issue that I was having. I determined the input impedance of the 1/4 transformer and end impedance of 25 ohm to be $Z_i=(50Ω)^2/25Ω$. I believe this input impedance looking to the right would then be in parallel with $Z_L$ at the second termination on the left side and that results in 20Ω. Is that logical so far?

You are doing fine. I'm wondering why that isn't obvious to you. You're looking into the 1/4 wave xfmr and you see 100 ohms, and your end is in parallel with the first 25 ohm load.

 

[sandy.bridge]

Sorry this is all super new to me. It makes sense now. I get an effective impedance of 20ohms and a total reflection coefficient of -0.429

 

[rude man]

Sorry this is all super new to me. It makes sense now. I get an effective impedance of 20ohms and a total reflection coefficient of -0.429

Right on!