ELEC 401 – Microwave Electronics
ELEC 401
MICROWAVE ELECTRONICS
Lecture on Matching
Instructor: M. İrşadi Aksun
Acknowledgements:
M. I. Aksun
Koç University
1/28
ELEC 401 – Microwave Electronics
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
M. I. Aksun
Koç University
2/28
ELEC 401 – Microwave Electronics
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
Z0
Matching
Network
Load
 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
M. I. Aksun
Koç University
3/28
ELEC 401 – Microwave Electronics
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;
jX
jX
Z0
jB
ZL
Z L is inside the 1+jX circle on the SC
M. I. Aksun
Koç University
Z0
jB
ZL
Z L is outside the 1+jX circle on the SC
4/28
ELEC 401 – Microwave Electronics
Impedance Matching
jX
Z0
jB
ZL
Z L is outside the 1+jX circle on the SC
jX
1  jX
Z0
jB
ZL
Z L is inside the 1+jX circle on the SC
M. I. Aksun
Koç University
5/28
ELEC 401 – Microwave Electronics
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.
M. I. Aksun
Koç University
6/28
ELEC 401 – Microwave Electronics
Impedance Matching
Frequency response of a real lumped inductor:
M. I. Aksun
Koç University
7/28
ELEC 401 – Microwave Electronics
Impedance Matching
Frequency response of a real lumped capacitor:
M. I. Aksun
Koç University
8/28
ELEC 401 – Microwave Electronics
Impedance Matching
Realization of inductors and capacitors from TL sections
 A small section of high impedance line is equivalent to a series
inductance:
Z 01
Z0
Z 02
Z L  Z 02
Z  jZ0 tan l
Z  jZ0l Z 0  Z L
Z in  Z 0 L
 Z0 L
   Z L  jZ0l
Z 0  jZ L tan l
Z 0  jZ Ll
Z l
Z in  Z L  j 0  Z L  jL
v
M. I. Aksun
Koç University
9/28
ELEC 401 – Microwave Electronics
Impedance Matching
Realization of inductors and capacitors from TL sections
 A small section of low impedance line is equivalent to a shunt
capacitance:
Z 01
Z0
Z 02
YL  Y02
Y  jY0 tan l
Y  jY0l Y0 YL
Yin  Y0 L
 Y0 L
  YL  jY0l
Y0  jYL tan l
Y0  jYLl
Yl
Yin  YL  j 0  YL  jC
v
M. I. Aksun
Koç University
10/28
ELEC 401 – Microwave Electronics
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.
Z L  2  j1 is inside the 1+jX circle
jX
Z0
jB
ZL
Y1  YL  jB YL  0.4  j 0.2
M. I. Aksun
Koç University
ZL
11/28
ELEC 401 – Microwave Electronics
Impedance Matching
1. Z L  2  j1  YL  0.4  j 0.2
21. Y1  YL  j 0.3  Z1  1  j1.2
3. Z in  Z1  j1.2  1.0
j 0.3
4. B  0.3; X  1.2
YL
jX
Z0
Z2
Y1
jB
ZL
ZL
Y1  YL  jB YL  0.4  j 0.2
Y2
Z1
22. Y2  YL  j 0.7  Z 2  1  j1.2
3. Z in  Z 2  j1.2  1.0
4. B  0.7; X  1.2
M. I. Aksun
Koç University
12/28
ELEC 401 – Microwave Electronics
Impedance Matching
B
6 10 3
3
Capacitive
3
B  0.3  B 
 6 10 / W  B  C  C 
 pF
50
2 1109 
60
30
Inductive

nH
X  1.2  X  X  50  60W  X  L  L 
9

2 110
jX
Z0
jB
ZL
Y1  YL  jB YL  0.4  j 0.2
B
1
50
L
H
9
L
0.7  2 110
X  1.2  X  X  50  60W  X 
1
1
C 
F
9
C
60  2 110
0.7
Inductive
B  0.7  B 
/ W   
50
Capacitive
M. I. Aksun
Koç University
13/28
ELEC 401 – Microwave Electronics
Impedance Matching
II. Single Stub matching
Yin
Ys
Y0
Y0
ZL
Y
Y0
Open Circuit
or
Short Circuit
d
l
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.
M. I. Aksun
Koç University
14/28
ELEC 401 – Microwave Electronics
Impedance Matching
 The basic idea is to select d so that Y  Y0  jB, and
 jB
jB
 to find the length of the stub l such that Ys   jB, hence Yin  Y
0

Y
Yin
M. I. Aksun
Koç University
Y0
ZL
Y
Y0
Open Circuit
or
Short Circuit
d
Ys
Y0
Ys
l
15/28
ELEC 401 – Microwave Electronics
Impedance Matching
 Example: Design two single-stub shunt tuning networks to match
Z L  (15  j10)W 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.
Yin
Ys
Y0
M. I. Aksun
Koç University
Y0
ZL
Y
Y0
Open Circuit
or
Short Circuit
d
l
16/28
ELEC 401 – Microwave Electronics
Impedance Matching
Solution via Smith Chart:
Z
(15  j10)
i) Z L  L 
 0.3  j 0.2
Z0
50
ii) Draw the corresponding SWR
circle or constant G circle.
iii) YL  2.2  j1.5
Note that the SWR circle intersects
the 1+jb circle at two points.
Y2
ZL
YL
d1  0.042 d2  0.385
Yin
Ys
Y0
Y0
ZL
Y1
Y
Y0
Open Circuit
or
Short Circuit
d
l
M. I. Aksun
Koç University
17/28
ELEC 401 – Microwave Electronics
Impedance Matching
iv) Y1  1.0  j1.33 Y2  1.0  j1.33
Ys  j1.33
v) The first tuning solution
requires a stub with Ys  j1.33
vi) The length of an opencircuited stub that gives this
susceptance can be found on
the SC by starting at
Y  0 (open  circuit )
l1  0.147 l2  0.353
Yin
d
Ys
Y0
Y
Y0
Open Circuit
Y 0
Y0
ZL
Ys   j1.33
l
M. I. Aksun
Koç University
18/28
ELEC 401 – Microwave Electronics
Impedance Matching

0
Z
Open
Circuit
Zin  (75  j90)W
Z L  60  j 45W
Ys
75
W
Zin  (75  j90)W
Z 0  75W
Z 0  75W
Z 0  75W
d
Z L  60  j 45W
 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.
l
Microstrip realization
M. I. Aksun
Koç University
19/28
ELEC 401 – Microwave Electronics
d
j 0.45  Ys1
Zin  (75  j90)W
Z 0  75W
Z in

W
75
Z
0
YL
Ys
Open
Circuit
l
 j1.6  Ys 2
ZL
Yin
ZL 
60  j 45
 0.8  j 0.6
75
75  j 90
 1.0  j1.2
75
YL  0.8  j 0.6
Z in 
Ys1  j 0.45
M. I. Aksun
Koç University
Ys 2   j1.6
20/28
Z L  60  j 45W
Impedance Matching
ELEC 401 – Microwave Electronics
Impedance Matching
d
YL  Ys1
Zin  (75  j90)W
Z 0  75W
YL
Open
Circuit
Yin
Y L  Ys 2
Z0

Ys
W
75
l
YL  Ys1  Yin
YL  Ys 2  Yin
M. I. Aksun
Koç University
d2=(0.416-0.35)=0.066
21/28
Z L  60  j 45W
 Find the length d of the TL;
ELEC 401 – Microwave Electronics
Impedance Matching
d
Zin  (75  j90)W
l1=0.067
Z 0  75W
Open
Circuit
Y 0
Z0

Ys
W
75
Z L  60  j 45W
 Find the length l of the stub;
Ys1  j 0.45
l
Starting from the opencircuit Y  0, one can move
towards generator to reach
Ys1  j 0.45
Ys1   j1.6
M. I. Aksun
Koç University
Ys 2   j1.6
22/28
ELEC 401 – Microwave Electronics
Impedance Matching
II. Double-Stub matching
YB YA
Yin YC
d
Y0
jB2
Y0
O.C or S.C.
l2
jB1
Y0
Y0
O.C or S.C.
Y0
YL
Y
l1
 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 /8 or 3/8.
M. I. Aksun
Koç University
23/28
ELEC 401 – Microwave Electronics
Impedance Matching
 The operation of this tuner:
i. For a perfect match Yin  1  YC  1  jB2 .
YC
point must be located on the G
 1 circle.
YB YA
Yin YC
d
G  1 Circle
Y0
jB2
Y0
Yin  1
M. I. Aksun
Koç University
O.C or S.C.
l2
jB1
Y0
Y0
O.C or S.C.
Y0
YL
Y
l1
24/28
ELEC 401 – Microwave Electronics
Impedance Matching
 The operation of this tuner:
ii. YB point must lie on the rotated G
 1 circle
YB YA
Yin YC
d
Y0
jB2
Y0
Yin  1
Forbidden
Region
O.C or S.C.
G  1 circle
l2
jB1
Y0
Y0
O.C or S.C.
YL
Y0
Y
l1
is rotated towards load by the distance d.
YB  YA  jB1.
M. I. Aksun
Koç University
25/28
ELEC 401 – Microwave Electronics
• 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
M. I. Aksun
Koç University
26/28
ELEC 401 – Microwave Electronics
Z L  1  j1W
YD  0.4  j 0.2S
0.125
Z D  2  j1W
M. I. Aksun
Koç University
27/28
ELEC 401 – Microwave Electronics
3 / 8 towards load
MAKE SURE THAT YD IS NOT INSIDE
THE FORBIDDEN REGION
YB  1 j3S
The difference between YD
and YC is:
YD  YC   j 2 S
 jBS1   j 2S
YD  0.4  j 0.2S
 jX S1  j 0.5W
YA  1S
Forbidden
Region
Therefore the length of
first stub is lS1 = 0.074λ.
The difference between YB
and YA is:
3 / 8 towards generator
YC  0.4  j1.8S
YB  YA   j3S
 jBS1   j 3S
 jX S1  j 0.33W
M. I. Aksun
Koç University
Therefore the length of
second stub is lS2 =28/28
0.051λ.