Microwave-Circuit-Design.pptx

1. By
Professor Syed Idris Syed Hassan
Sch of Elect. & Electron Eng
Engineering Campus USM
Nibong Tebal 14300
SPS Penang
Microwave Circuit Design

2. Introduction
• 10 weeks lecture + 4 weeks ADS simulation
• Assessments :8 tests + 2 ADS assignments
+ 1 final examination
• Class : 9.00- 10.30 lecture
10.30-11.00 rest (tea break)
11.00-12.30 lecture
12.30- 1.00 test

3. Dates
• 06/04/02 Morning
• 20/04/02 Morning
• 27/04/02 Morning
• 04/05/02 Morning
• 11/05/02 Morning
• 18/05/02 Morning
• 25/05/02 Morning
• 08/06/02 Morning
• 15/06/02 Morning
• 22/06/02 Morning
• 29/06/02 morning
• 06/07/02 Morning
• 20/07/02 Morning
• 27/07/02 Morning

4. Syllabus
• Transmission lines
• Network parameters
• Matching techniques
• Power dividers and combiners
• Diode circuits
• Microwave amplifiers
• Oscillators
• Filters design
• Applications
• Miscellaneous

5. References
• David M Pozar ,Microwave Engineering- 2nd Ed.,
John Wiley , 1998
• E.H.Fooks & R.A.Zakarevicius, Microwave
Engineering using microstrip circuits, Prentice
Hall,1989.
• G. D. Vendelin, A.M.Pavio &U.L.Rohde, Microwave
circuit design-using linear and Nonlinear
Techniques, John Wiley, 1990.
• W.H.Hayward, Introduction to Radio Frequency
Design, Prentice Hall, 1982.

6. Transmission Line

7. Equivalent Circuit
R R
L L
C
G
z

C
L
Zo 
C
j
G
L
j
R
Zo





Lossy line
Lossless line
  
C
j
G
L
j
R 

 


LC

 

8. Analysis
L
j
R 

)
,
( t
z
I
dz
dI
z
I 

)
,
( t
z
V C
j
G 
 dz
dV
z
V 

z
dt
dI
L
z
RI
z
dz
dV


 


dt
dI
L
RI
dz
dV



z
dt
dV
C
z
GV
z
dz
dI


 


dt
dV
C
GV
dz
dI



From Kirchoff Voltage Law Kirchoff current law
z
dt
dV
C
z
GV
z
dz
dI
I
I 

 









z
dt
dI
L
z
RI
z
dz
dV
V
V 

 









(a) (b)

9. Analysis
Let’s V=Voejt , I = Ioejt
Therefore
V
j
dt
dV

 I
j
dt
dI


then
 I
L
j
R
dz
dV



  V
C
j
G
dz
dI




a b
Differentiate with respect to z
 
dz
dI
L
j
R
dz
V
d



 2
2
  V
C
j
G
L
j
R
dz
V
d

 


2
2
V
dz
V
d 2
2
2


 
dz
dV
C
j
G
dz
I
d



 2
2
  I
C
j
G
L
j
R
dz
I
d

 


2
2
I
dz
I
d 2
2
2



10. Analysis
The solution of V and I can be written in the form of
z z
Be Ae V
 
 
 
o
z z
Z
Be Ae
I
 
 


where









C
j
G
L
j
R
Zo


Let say at z=0 , V=VL , I=IL and Z=ZL
Therefore
B A V
L
 
o
L
Z
B A
I


and L
L
L
Z
I
V

e f
c d
  
C
j
G
L
j
R
j 



 




and

11. Analysis
Solve simultaneous equations ( e ) and (f )
2
o L L
Z I V
A


2
o L L
Z I V
B


Inserting in equations ( c) and (d) we have







 








 





2
2
)
(
z
z
o
L
z
z
L
e
e
Z
I
e
e
V
z
V











 








 





2
2
)
(
z
z
o
L
z
z
L
e
e
Z
V
e
e
I
z
I





12. Analysis







 


2
)
cosh(
z
z
e
e
z



But and







 


2
)
sinh(
z
z
e
e
z



Then, we have
)
sinh(
)
cosh(
)
( z
Z
I
z
V
z
V o
L
L 
 

)
sinh(
)
cosh(
)
( z
Z
V
z
I
z
I
o
L
L 
 

















)
sinh(
)
cosh(
)
sinh(
)
cosh(
)
(
)
(
)
(
z
Z
V
z
I
z
Z
I
z
V
z
I
z
V
z
Z
o
L
L
o
L
L




and
*
**

13. Analysis











)
sinh(
)
cosh(
)
sinh(
)
cosh(
)
(
z
Z
z
Z
z
Z
z
Z
Z
z
Z
L
o
o
L
o















)
tanh(
)
tanh(
)
(
z
Z
Z
z
Z
Z
Z
z
Z
L
o
o
L
o


Or further reduce
or
For lossless transmission line , = j since 0











)
tan(
)
tan(
)
(
z
jZ
Z
z
jZ
Z
Z
z
Z
L
o
o
L
o


)
cos(
)
cosh( z
z
j 
 
)
sin(
)
sinh( z
j
z
j 
 


14. Analysis
Standing Wave Ratio (SWR)
node
antinode
Ae-z
Bez
z
z
Ae
Be


 

 







 

1
z
z
z
L Ae
Be
Ae
V
 










1
o
z
o
z
z
L
Z
Ae
Z
Be
Ae
I
Reflection coefficient
Voltage and current in term of reflection coefficient
o
L
L
L Z
I
V
Z 













1
1













1
1
o
L
Z
Z
or

15. Analysis
For loss-less transmission line  = j
By substituting in * and ** ,voltage and current amplitude are
  2
/
1
2
)
2
cos(
2
1
)
( 


 


 z
A
z
V
  2
/
1
2
)
2
cos(
2
1
)
( 


 


 z
Z
A
z
I
o
Voltage at maximum and minimum points are
)
1
(
max 

 A
V )
1
(
min 

 A
V
and






1
1
s
VSWR
Therefore
For purely resistive load
o
L
Z
Z
s 
g
h

16. Analysis











o
L
o
L
Z
Z
Z
Z

o
o sZ
Z
I
V
Z 














1
1
min
max
max s
Z
Z
I
V
Z o
o 














1
1
max
min
min
Other related equations
From equations (g) and (h), we can find the max and min points

,
4
,
2
,
0
2 


 



z

,
3
,
2 


 


z
Maximum
Minimum

17. Important Transmission line equations




tanh
tanh
L
o
o
L
o
in
jZ
Z
jZ
Z
Z
Z



o
L
o
L
Z
Z
Z
Z









1
1
SWR
Zo
ZL
Zin

18. Various forms of Transmission
Lines
Two wire
cable Coaxial
cable
Microstripe
line
Rectangular
waveguide
Circular
waveguide
Stripline

19. Parallel wire cable
    d
a
for
a
d
or
a
d
L 

 
/
ln
2
/
cosh 1




   
d
a
for
a
d
or
a
d
C 

  /
ln
2
/
cosh 1




 
a
d
Zo 2
/
cosh
1 1





Where a = radius of conductor
d = separation between conductors

20. Coaxial cable
 
a
b
C
/
ln
2 


 
a
b
L /
ln
2


 
a
b
Zo /
ln
2
1




Where a = radius of inner conductor
b = radius of outer conductor
c = 3 x 108 m/s
r
c
c
ck
f


2

b
a
kc


2
a
b

21. Micro strip
w
he r
t
t=thickness of conductor
Substrate
Conducted strip
Ground

22. Characteristic impedance of
Microstrip line
 
h
w
w
h
Z
h
w
For e
e
eff
o /
25
.
0
/
8
ln
60
1
/ 



 
 
444
.
1
/
ln
667
.
0
393
.
1
/
377
1
/





h
w
h
w
Z
h
w
For
e
e
eff
o

   
 
2
5
.
0
/
1
04
.
0
/
12
1
2
1
2
1
h
w
w
h e
e
r
r
eff 





 



 
 
5
.
0
/
12
1
2
1
2
1 




 e
r
r
eff w
h











 1
2
ln
t
h
t
w
w e
e

t
h
he 2


Where
w=width of strip
h=height and
t=thickness

23. Microstrip width

















 

r
r
r
r
o
Z
A



 11
.
0
23
.
0
1
1
2
1
60
2
/
1
r
o
Z
B

 2
60

2
)
2
exp(
)
exp(
8
/


A
A
h
W
 
    














r
r
r B
lb
B
B
h
W




61
.
0
39
.
0
1
2
1
1
2
ln
1
2
/
For A>1.52
For A<1.52

24. Simple Calculation








2
377
h
w
Z
r
o

2
377
/ 

o
r Z
h
w

Approximation only

25. Microstrip components
• Capacitance
• Inductance
• Short/Open stub
• Open stub
• Transformer
• Resonator

26. Capacitance
Zo Zo
Zoc
1
c
Z
C
oc











1
2
sin
2
c
Z
C
oc


 s
m
c
r
/
10
3 8
1



For 8



For
8





27. Inductance
Zo Zo
ZoL

1
c
Z
L oL










1
sin
c
Z
L oL 


s
m
c
r
/
10
3 8
1



For 8



For
8




28. Short Stub
Zo
Z
Zo
Zo ZL


 
o
L Z
X /
tan 1



eff
o



360



tan
o
L
sc jZ
X
Z 



29. Open stub
Zo
Z
Zo
Zo ZL


 
o
c Z
X /
cot 1



eff
o



360



cot
o
c
oc jZ
X
Z 



30. Quarter-wave transformer
Zo Zo
ZT
/4
Zmx/min
ZL
x


 




o
L
o
L
Z
Z
Z
Z


2

x  in radian s
Z
x
Z o

max
)
(





1
1
s
s
Z
s
Z
Z
Z
Z
Z o
o
o
mx
in
T 

 .
At maximum point

31. Quarter-wave transformer


 




o
L
o
L
Z
Z
Z
Z



2


x  in radian
s
Z
x
Z o /
)
( min 





1
1
s
s
Z
s
Z
Z
Z
Z
Z o
o
o
in
T /
/
.
min 


at minimum point

32. Resonator
• Circular microstrip disk
• Circular ring
• Short-circuited /2 lossy line
• Open-circuited /2 lossy line
• Short-circuited /4 lossy line

33. Circular disk/ring
a
r
o
a



2
841
.
1

feeding
a


4

a
* These components usually use for resonators

34. Short-circuited /2 lossy line
n/2
Zin Zo 



o
Z
R 

o
o
Z
L


2

L
C
o
2
1







2
2




R
L
Q o



2

where
= series RLC resonant cct

35. Open-circuited /2 lossy line
n/2
Zin Zo 







2
2




RC
Q o
= parallel RLC resonant cct


o
Z
R 
o
o Z
C


2

C
L
o
2
1

 


2

where

36. Short-circuited /4 lossy line
/4
Zin Zo 




o
Z
R 
= parallel RLC resonant cct
o
o Z
C


4

C
L
o
2
1







2
4




RC
Q o



2

where

37. Rectangular waveguide
a
b
2
2
2
1














b
n
a
m
fcmn





Cut-off frequency of TE or TM mode
2
2
2
1
1
1
c
o
g 




o
g
TE
Z




g
o
TM
Z




  m
Np
a
b
b
a
R
o
o
g
s
c /
2 2
3
2
3





 

Conductor attenuation for TE10



2
o
s
R 

38. Example
Given that a= 2.286cm , b=1.016cm and 5.8 x 107S/m.
What are the mode and attenuation for 10GHz?
2
2
2
1














b
n
a
m
fcmn





Using this equation to calculate cutoff frequency of each mode

39. Calculation
GHz
fc
9
2
8
10 10
562
.
6
002286
.
0
2
10
3












TE10
a=2.286mm, b=1.016mm, m=1 and n=0 ,thus we have
Similarly we can calculate for other modes

40. Example
Mode fcmn
TE10 6.562 GHz
TE20 13.123GHz
TE01 14.764GHz
TE11 16.156GHz
TE10
TE20 TE01
TE11
6.562GHz 13.123GHz14.764GHz 16.156GHz
Frequency 10Ghz is propagating in
TE10.mode since this frequency is
below the 13.123GHz (TE20) and
above 6.561GHz (TE10)

41. continue


 026
.
0
2

o
s
R
1
2
05
.
158 








 m
a
o



  m
Np
a
b
b
a
R
o
o
g
s
c /
0125
.
0
2 2
3
2
3


 





m
dB
e
dB c
c /
11
.
0
log
20
)
( 

 

or

42. Evanescent mode
Mode that propagates below cutoff frequency of a wave guide is
called evanescent mode
2
2
1
1
2
o
c 


 

2
2
2
o
c
k 
 

Wave propagation constant is
Where kc is referred to cutoff frequency,  is referred to
propagation in waveguide and  is in space
   j =attenuation =phase constant
When f0< fc , 2
2
2
o
c
k 
 

But
Since no propagation then
The wave guide become attenuator

43. Cylindrical waveguide
a

 a
p
f nm
cnm
2
,

n p'n1 p'n2 p'n3
0 3.832 7.016 10.174
1 1.841 5.331 8.536
2 3.054 6.706 9.97
a
p
k nm
cnm
,

2
2
cnm
o
nm k

 

TE mode
Dominant mode is TE11
o
g
TE
Z















1
'2
11
2
2
11
p
k
a
R o
c
g
o
s
c






44. continue
a

 a
p
f nm
cnm
2
 a
p
k nm
cnm 
2
2
cnm
o
nm k

 

TM mode
g
o
TM
Z




n pn1 pn2 pn3
0 2.405 5.520 8.654
1 3.832 7.016 10.174
2 5.135 8.417 11.620
TM01 is preferable for long haul
transmission

45. Example
Find the cutoff wavelength of the first four modes of a circular waveguide
of radius 1cm
Refer to tables
n p'n1 p'n2 p'n3
0 3.832 7.016 10.174
1 1.841 5.331 8.536
2 3.054 6.706 9.97
TE modes TM modes
n pn1 pn2 pn3
0 2.405 5.520 8.654
1 3.832 7.016 10.174
2 5.135 8.417 11.620
1st mode
2nd mode
3rd &4th
modes
3rd &4th
modes

46. Calculation
nm
cnm
p
a


2


 a
p
f nm
cnm
2

1st mode Pnm= 1.841, TE11
m
c 0341
.
0
841
.
1
01
.
0
2
11 




2nd mode Pnm= 2.405, TM01
1st mode Pnm= 3.832, TE01 and TM11
m
c 0261
.
0
405
.
2
01
.
0
2
01 




m
c
c 0164
.
0
832
.
3
01
.
0
2
11
01 







47. Stripline
w
b
 
b
W
b
Z
e
r
o
441
.
0
30




  35
.
0
/
35
.
0 2




b
W
b
W
b
W
b
We
35
.
0


b
W
W
We

48. Continue
120
441
.
0
30


 o
r
o
r
Z
for
Z
b
W



120
441
.
0
30
6
.
0
85
.
0 











 o
r
o
r
Z
for
Z
b
W



On the other hand we can calculate the width of
stripline for a given characteristic impedance

49. Continue
 













120
16
.
0
120
30
10
7
.
2 3
o
r
o
s
o
r
o
r
s
c
Z
for
B
b
Z
R
Z
for
A
t
b
Z
R





 





 






t
t
b
t
b
t
b
t
b
W
A
2
ln
2
1

 











t
W
W
t
t
W
b
B


4
ln
2
1
414
.
0
5
.
0
7
.
0
5
.
0
1
Where
t =thickness of the strip