1. Microwave Engineering
ECE
Microwave Engineering
Fall 2015
Prof. David R. Jackson
Dept. of ECE
Notes 3
Smith Chart
Examples

2. Example 1 a I (-d) + V (-d) - z z = 0 z = -d Find Z(-d)ZL
z = 0
I (-d)
z = -d
Find Z(-d)
Impedance chart a
 plane

3. Example 1 (cont.) b c I (-d) + V (-d) - z z = 0 z = -d Impedance chartZL
z = 0
I (-d)
z = -d c
Impedance chart
 plane

4. Example 2 a I (-d) + V (-d) - z Find Y(-d) z = 0 z = -dZL
z = 0
I (-d)
z = -d
Find Y(-d)
Admittance chart a
 plane

5. Example 2 (cont.) b c I (-d) + V (-d) - z z = 0 z = -dZL
z = 0
I (-d)
z = -d b c
Admittance chart
 plane

6. Þ Þ Which Chart to Use? Simple answer:
* When adding elements in series use Z-chart Þ ZA ZB ZC
* When adding elements in parallel use Y-chart YA YB YC Þ

7. Using Reactive Loads
Non-absorbing load (RL = 0)
 Use reactively loaded section of transmission line.
most common to use open or short load: or
Impedance chart
Reactance
V (-d) + - z ZL
z = 0
I (-d)
z = -d
 plane

8. Using Reactive Loads (cont.)
Susceptance
Admittance chart
V (-d) + - z ZL
z = 0
I (-d)
z = -d
 plane

9. Example 3
Use a short-circuited section of air-filled TEM, 50  transmission line
( = k0, g =0) to create an impedance of Zin = -j25  at f = 10 GHz.
Impedance chart L SC
50, k0
L = 1.28 cm
 plane

10. Example 4
Use an open-circuited section of 75  (Y0 = 1/75 S) air-filled transmission line at f = 10 GHz to create an admittance of :
Admittance chart L OC
75, k0
 plane

11. Matching Circuit Want to pick d and Ys such that Yin = Y0. d Z0 YS ZL
Zin, Yin d ZL YS YA Z0
Admittance chart
Want to pick d and Ys such that Yin = Y0.
Note: At d we have
 plane

12. Matching Circuit (cont.)
Zin, Yin d ZL YS YA Z0
We want
Choose:
 plane
Admittance chart

13. Example 5 ZL Z0 ls
Z0s d
In this example we will use the “usual” Smith chart, but as an admittance calculator.

14. (We’ll use the first choice.)
Example 5 (cont.)
Admittance chart
(We’ll use the first choice.) X OC SC X X
 plane
Smith chart scale:
wavelengths toward load
wavelengths toward generator

15. Example 5 (cont.) From the Smith chart: Analytically: Admittance chart
 plane
Analytically:

16. Quarter-Wave Transformer
At f0 :
For in = 0
Hence, we have

17. Match 100  load to 50  transmission Line at f0.
Example 6
Match 100  load to 50  transmission Line at f0.