Transmission Line Homework - Determine Input Impedance

In summary: The impedance looking into the 1/4 wave xfmr is 100 ohms, and the end is in parallel with the first 25 ohm load. This results in an effective impedance of 20ohms and a total reflection coefficient of -0.429
  • #1
sandy.bridge
798
1

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 [itex]Z_L[/itex] 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.
 

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  • #2
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.
.
 
  • #3
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 [itex]Z_i=(50Ω)^2/25Ω[/itex]. I believe this input impedance looking to the right would then be in parallel with [itex]Z_L[/itex] at the second termination on the left side and that results in 20Ω. Is that logical so far?
 
Last edited:
  • #4
sandy.bridge said:
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 [itex]Z_i=(50Ω)^2/25Ω[/itex]. I believe this input impedance looking to the right would then be in parallel with [itex]Z_L[/itex] 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.
 
  • #5
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
 
  • #6
sandy.bridge said:
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!
 

FAQ: Transmission Line Homework - Determine Input Impedance

1. What is the purpose of determining input impedance in transmission line homework?

The input impedance of a transmission line is an important parameter that helps us understand how an electrical signal will behave as it passes through the line. It tells us how much resistance the line presents to the signal and how much of the signal will be reflected back. Knowing the input impedance can help us design and troubleshoot transmission line systems.

2. How is input impedance calculated?

Input impedance is typically calculated using the equation Zin = (Z0 * (ZL + jZ0*tan⁡(βl))) / (Z0 + jZL*tan(βl)), where Z0 is the characteristic impedance of the line, ZL is the load impedance, β is the propagation constant, and l is the length of the line. This calculation can be done by hand or with the help of specialized software or calculators.

3. What factors affect the input impedance of a transmission line?

The input impedance of a transmission line is affected by factors such as its length, the characteristic impedance of the line, the load impedance, and the frequency of the signal being transmitted. Changes in any of these parameters can result in a different input impedance.

4. Why is it important to match the input impedance in transmission line systems?

Matching the input impedance in a transmission line system is important because it minimizes signal reflections and maximizes the power transfer from the source to the load. This ensures that the signal is transmitted with minimal distortion and loss, which is crucial for the proper functioning of the system.

5. What are some common applications of transmission line systems?

Transmission line systems are used in a variety of applications, including telecommunications, radio and television broadcasting, power transmission, and high-speed data transmission. They are also used in electronic circuits, such as in antennas, filters, and impedance matching networks.

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