1. ELEC 401 MICROWAVE ELECTRONICS Lecture on Matching
Instructor: M. İrşadi Aksun
Acknowledgements:

2. Outline
Chapter 1: Motivation & Introduction
Chapter 2: Review of EM Wave Theory
Chapter 3: Plane Electromagnetic Waves
Chapter 4: Transmission Lines & Smith Chart
Chapter 5: Microwave Network Characterization
Chapter 6: Impedance Matching
Chapter 7: Passive Microwave Components

3. Impedance Matching
Impedance matching or tuning is important, because it helps to
transfer maximum power to the network or load;
improve the signal-to-noise ratio of the system
Matching networks are ideally lossless, and
it is always possible to design such a matching network if the load has some non-zero real part 3

4. Impedance Matching I. Matching with lumped elements (L Networks):
L section uses two reactive elements to match an arbitrary load impedance to a TL;
There are two possible configurations;
is outside the 1+jX circle on the SC
is inside the 1+jX circle on the SC 4

5. Impedance Matching is outside the 1+jX circle on the SC
is inside the 1+jX circle on the SC 5

6. Impedance Matching
Comments on the use of lumped elements:
Actual lumped element capacitors and inductors can be used up to several GHz. However,
there is a large range of frequencies and circuit sizes where lumped elements cannot be realized.
This is considered to be the major limitation of the L-Section matching network. 6

7. Impedance Matching
Frequency response of a real lumped inductor: 7

8. Impedance Matching
Frequency response of a real lumped capacitor: 8

9. Impedance Matching
Realization of inductors and capacitors from TL sections
A small section of high impedance line is equivalent to a series inductance: 9

10. Impedance Matching
Realization of inductors and capacitors from TL sections
A small section of low impedance line is equivalent to a shunt capacitance: 10

11. Impedance Matching
Example: Design an L section matching network to match a load ZL=(100-j50)W to a 50 W line at 1.0 GHz.
is inside the 1+jX circle 11

12. Impedance Matching 1.
21. 3. 4.
22. 3. 4. 12

13. Impedance Matching 13

14. Impedance Matching II. Single Stub matching
In single stub tuning, the two adjustable parameters are the distance d from
the load to the stub position, and the length of the stub l. 14

15. Impedance Matching The basic idea is to select d so that and
to find the length of the stub l such that hence 15

16. Impedance Matching
Example: Design two single-stub shunt tuning networks to match
to a 50W line.
Solution:
- There are two approaches to solve such a problem; using Smith Chart and
using analytical expressions of TL.
- Solution with Smith Chart is more intuitive, and easier than solving the
problem analytically. 16

17. Impedance Matching Solution via Smith Chart: i)
ii) Draw the corresponding SWR circle or constant G circle.
iii)
Note that the SWR circle intersects the 1+jb circle at two points.
d2=0.5l-( )l
d1=( )l 17

18. Impedance Matching iv)
l1=0.147l
v) The first tuning solution requires a stub with
vi) The length of an open-
circuited stub that gives this susceptance can be found on the SC by starting at
l2=0.353l 18

19. Impedance Matching
Example: For a load impedance of ZL=(60-j45)Ω, design two single-stub matching networks that transform the load to a Zin=(75+j90)Ω input impedance. Assume that both stub and transmission line shown below have a chracteristic impedance of Z0=75Ω.
Microstrip realization 19

20. Impedance Matching 20

21. Impedance Matching Find the length d of the TL;
d1=( )l=0.266l
d2=( )l=0.066l 21

22. Impedance Matching Find the length l of the stub; l2=0.339l l1=0.067l
Starting from the open-circuit , one can move towards generator to reach 22

23. Impedance Matching II. Double-Stub matching
In double-stub tuning, the two adjustable parameters are the lengths of the stubs, l1 and l2.
Note that the distance between the two stubs d is usually set to a fixed value l/8 or 3l/8. 23

24. Impedance Matching The operation of this tuner: i. For a perfect match
point must be located on the circle. 24

25. Impedance Matching The operation of this tuner:
ii point must lie on the rotated circle
Forbidden
Region
circle is rotated towards load by the distance d. 25

26. Design of a double-stub matching network
It is assumed that in the double-stub matching network seen below, the lengths of the TLs are l1=λ/8 and l3=l2=3λ/8. Find the lengths of the short circuited stubs that match the load impedance ZL=(50+j50)Ω to a 50Ω input impedance. The chracteristic line impedance for all components is Z0=50Ω 26

27. 27

28. MAKE SURE THAT YD IS NOT INSIDE THE FORBIDDEN REGION
The difference between YD
and YC is:
Forbidden
Region
Therefore the length of
first stub is lS1 = 0.074λ.
The difference between YB
and YA is:
Therefore the length of
second stub is lS2 = 0.051λ. 28