1THE UNIVERSITY OF QUEENSLAND
School of Information Technology
& Electrical Engineering
COMS4104/7104
Microwave Subsystems and Antennas
Practical 1
Impedance Transformers
2IMPEDANCE TRANSFORMERS
BINOMIAL TRANSFORMER-Design Equations
The input reflection coefficient, (), is given as
The individual reflection coefficients between
transmission line sections n and n+1 are
where the CnN are the binomial coefficients.
.)1()()1( 2 NjeA  
NNNjjNj AeeeA |)cos(|||2|||||||)(|)2(    
0
02|)(|2)3(
ZZ
ZZA
L
LNN

  
!)!(
!)4(
nnN
NAAC Nnn  n
n
nn
nn
n Z
Z
ZZ
ZZ 1
1
1 ln
2
1)5( 

 

(6)
3Exercise A: Binomial Transformer
Part I:
 Design a 3-section binomial transformer to match a load impedance of
ZL = 100 Ω to a transmission line with a characteristic impedance of
Z0 = 50 Ω at 5 GHz.
 Calculate the bandwidth for the maximum reflection coefficient m =0.05.
 Verify your design using ADS.
Part II: Repeat steps in Part I for
ZL = ZN+1= 190 Ω, Z0 = 50 Ω, Γm =0.1 and design at 5 GHz
Note that the solution to Part I is partially given on the following page.
4Binomial Transformer – Part I
the required characteristic in1pedances
n = 0:
n = 1:
n = 2:
N 3 ZL lnZ1 = lnZo + 2- C0 ln-
3 50 = ln 100 + 2- (1) ln
100
= 4.518,
Z1 = 91.7 Q;
N 3 ZL ln Z2 = ln Z 1 + 2- C 1 h1 -Zo
50
= ln91.7 + 2-3 (3) ln- = 4.26,
100
Z2 = 70.7 Q;
-N 3 ZL
ln Z3 = ln Z2 + 2 C2 h1 -
Zo
50
= ln 70.7 + 2-3 (3) ln- = 4.00,
100
Z3 = 54.5 Q.
5
Binomial Transformer – Part I
6Exercise A: Binomial Transformer
Your Report:
Part A-I:
 Get the ADS printout confirming the results shown in the previous page and
calculate the BW at m =0.05.
Part A-II:
 Get the values of Zn, BW,etc as in Part I and produce an ADS printout to
confirm the validity of your design.
Produce half- page comments on the results obtained in Part A-I and Part A-II.
7ADS
R
R1
R=100 Ohm
S_Param
SP1
Step=0.05 GHz
Stop=10.0 GHz
Start=1.0 GHz
S-PARAMETERS
Term
Term1
Z=50 Ohm
Num=1
TLIN
TL4
F=5 GHz
E=90
Z=91.7 Ohm
TLIN
TL3
F=5 GHz
E=90
Z=70.7 Ohm
TLIN
TL2
F=5 GHz
E=90
Z=54.5 Ohm
1 2 3 4 5 6 7 8 90 10
-60
-50
-40
-30
-20
-10
-70
0
freq, GHz
d
B
(
S
(
1
,
1
)
)
freq (0.0000Hz to 10.00GHz)
S
(
1
,
1
)
8IMPEDANCE TRANSFORMERS
CHEBYSHEV TRANSFORMER-Design Equations
The maximum allowable reflection coefficient magnitude
in the passband : m
Bandwidth:Reflection coefficient
between n and n+1 section:
9Exercise B: Chebyshev Transformer
Part I:
 Design a 3-section Chebyshev transformer to match a load impedance of
ZL = 100 Ω to a transmission line with a characteristic impedance of
Z0 = 50 Ω at 5 GHz.
 Calculate the bandwidth for the maximum reflection coefficient m =0.05.
 Verify your design using ADS.
Part II: Repeat steps in Part I for
ZL = ZN+1= 180 Ω, Z0 = 50 Ω, Γm =0.08 and design at 5 GHz.
Note that the solution to Part I is partially given in the following page.
10
Chebyshev Transformer – Part I
ZL =
11
Exercise B: Chebyshev Transformer
Your Report:
Part B-I:
 Get the ADS printout confirming the results shown in the previous page and
calculate the BW at m =0.05.
Part B-II:
 Get the values of Zn, BW,etc as in Part I and produce the ADS printout to
confirm the validity of your design.
Produce half- page comments on the results obtained in Part I-B and Part II-B.
12
ADS
TLIN
TL4
F=5 GHz
E=90
Z=87.0 Ohm
TLIN
TL2
F=5 GHz
E=90
Z=57.5 Ohm
R
R1
R=100 Ohm
Term
Term1
Z=50 Ohm
Num=1
TLIN
TL3
F=5 GHz
E=90
Z=70.7 Ohm
S_Param
SP1
Step=0.05 GHz
Stop=10.0 GHz
Start=0.0 GHz
S-PARAMETERS
1 2 3 4 5 6 7 8 90 10
-70
-60
-50
-40
-30
-20
-10
-80
0
freq, GHz
d
B
(
S
(
1
,
1
)
)
freq (0.0000Hz to 10.00GHz)
S
(
1
,
1
)
13
Submission Instructions:
1. The lab report must be typewritten.
2. All pages in the report should have page numbers (x/Total).
3. Include your name and student number on each page.
4. There is a 8-page limit for the report.
5. Include (in order) ADS printouts, sample calculations,final
numerical results, and all plots for each design.
6. Include a brief discussion and conclusion section.
7. Make sure to include a cover sheet. This is available at
https://student.eait.uq.edu.au/coversheets/.