1. Notes 13 Transmission Lines (Impedance Matching)
ECE 3317
Applied Electromagnetic Waves
Prof. David R. Jackson
Fall 2018
Notes Transmission Lines (Impedance Matching)

2. Impedance Matching
Impedance matching is very important to avoid reflected power, which causes a loss of efficiency and interference. + -
We will discuss two methods:
Quarter-wave transformer
Single-stub matching

3. Quarter-Wave Transformer
Quarter-Wave Transformer: First consider a real load on a lossless line.
Hence

4. Quarter-Wave Transformer (cont.)
Set
Example:
Hence
This gives us

5. Quarter-Wave Transformer with Shunt Susceptance
Next, consider a general (complex) load impedance ZL.
Goal: determine Bs, Z0T
New model:

6. Quarter-Wave Transformer with Shunt Susceptance (cont.)
Summary of quarter-wave transformer matching method

7. Quarter-Wave Transformer with Shunt Susceptance (cont.)
Realization using a shorted stub:
(An open-circuited stub could also be used.)
Hence we have:

8. Quarter-Wave Transformer with Line Extension
In this method we use a line extension “d” instead of a shunt susceptance.
Goal: determine d, Z0T
We choose the length d to make the input impedance Zin (-d) real.
We then use a quarter-wave transformer to change the impedance to Z0.

9. Quarter-Wave Transformer with Line Extension (cont.)
Example

10. Quarter-Wave Transformer with Line Extension (cont.)
Wavelengths towards generator

11. Quarter-Wave Transformer with Line Extension (cont.)

12. Quarter-Wave Transformer with Line Extension (cont.)
Summary of Design

13. A parallel (shunt) susceptance is added at a distance d from the load.
Single-Stub Matching
A parallel (shunt) susceptance is added at a distance d from the load.
Goal: determine Bs, Z0T
1) We choose the distance d so that at this distance from the load
2) We then choose the shunt susceptance so that

14. Single-Stub Matching (cont.)
The feeding transmission line on the left sees a perfect match!

15. Single-Stub Matching (cont.)
Realization using a shorted stub
(An open-circuited stub could also be used.)
Goal: Find d and ls.

16. Single-Stub Matching (cont.)
We use the Smith chart as an admittance calculator to determine the distance d.
Convert the load impedance ZL to a load admittance YL.
Determine the distance d to make the normalized input conductance equal to 1.0.
Determine the required value of Bs to cancel Bin (Bs = - Bin).
Determine the stub length ls from the value of Bs.
Note: If desired, we can use the Smith chart to also find the stub length ls.

17. Single-Stub Matching (cont.)
Example

18. Single-Stub Matching (cont.)
Use this one
Smith chart scale:
Wavelengths toward load
Wavelengths toward generator

19. Single-Stub Matching (cont.)
Next, we find the length of the short-circuited stub:
Rotate clockwise from S/C to desired Bs value.
Note:
Here we have Z0s = Z0. Otherwise, we have to be careful with the normalization (see the note below).
0-j0.5
0-j1
0+j0.5
0+j1
0+j0
0+j2
0-j2
Note: In general,
Admittance chart

20. Single-Stub Matching (cont.)
From the Smith chart: X
Admittance chart
Analytically:

21. Single-Stub Matching (cont.)
Final Design

22. Single-Stub Matching (cont.)z
Unmatched
Crank Diagram
Recall: The stub is located at d = 

23. Single-Stub Matching (cont.)z
Unmatched
Matched z