1. Microwave Circuit Design

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

3. 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.

4. Transmission Line

5. Equivalent Circuit R L R L C G
Lossy line
Lossless line

6. From Kirchoff Voltage Law
Analysis
From Kirchoff Voltage Law
Kirchoff current law
(a)
(b)

7. Analysis then Let’s V=Voejwt , I = Ioejwt Therefore b a
Differentiate with respect to z

8. Analysis The solution of V and I can be written in the form of c d
where
and
Let say at z=0 , V=VL , I=IL and Z=ZL
Therefore f e
and

9. Analysis Solve simultaneous equations ( e ) and (f )
Inserting in equations ( c) and (d) we have

10. Analysis
and
But
Then, we have * **
and

11. For lossless transmission line , g= jb since a=0
Analysis or
Or further reduce
For lossless transmission line , g= jb since a=0

12. Standing Wave Ratio (SWR)
Analysis
antinode
Standing Wave Ratio (SWR)
Reflection coefficient
node
Ae-gz
Begz
Voltage and current in term of reflection coefficient or

13. Analysis For loss-less transmission line g = jb
By substituting in * and ** ,voltage and current amplitude are g h
Voltage at maximum and minimum points are
and
Therefore
For purely resistive load

14. Analysis Other related equations
From equations (g) and (h), we can find the max and min points
Maximum
Minimum

15. Important Transmission line equations
Zin ZL Zo

16. Various forms of Transmission Lines

17. Parallel wire cable Where a = radius of conductor
d = separation between conductors

18. Coaxial cable b a Where a = radius of inner conductor
b = radius of outer conductor
c = 3 x 108 m/s

19. Micro strip Conducted strip t Substrate he er w Ground
t=thickness of conductor

20. Characteristic impedance of Microstrip line
w=width of strip
h=height and
t=thickness
Where

21. Microstrip width
For A>1.52
For A<1.52

22. Simple Calculation
Approximation only

23. Microstrip components
Capacitance
Inductance
Short/Open stub
Open stub
Transformer
Resonator

24. Capacitance
Zoc Zo Zo
For
For

25. Inductance
ZoL Zo Zo
For
For

26. Short Stub Zo Zo Zo ZL Z

27. Open stub Zo Zo Zo ZL Z

28. Quarter-wave transformer
l/4 x ZT ZL Zo Zo
Zmx/min
At maximum point
q in radian

29. Quarter-wave transformer
at minimum point
q in radian

30. Resonator Circular microstrip disk Circular ring
Short-circuited l/2 lossy line
Open-circuited l/2 lossy line
Short-circuited l/4 lossy line

31. * These components usually use for resonators
Circular disk/ring
feeding a a
* These components usually use for resonators

32. Short-circuited l/2 lossy line
Zin
= series RLC resonant cct Zo b a
=nl/2
where

33. Open-circuited l/2 lossy line
Zin
= parallel RLC resonant cct Zo b a
=nl/2
where

34. Short-circuited l/4 lossy line
Zin
= parallel RLC resonant cct Zo b a
=l/4
where

35. Rectangular waveguideb a
Cut-off frequency of TE or TM mode
Conductor attenuation for TE10

36. Using this equation to calculate cutoff frequency of each mode
Example
Given that a= 2.286cm , b=1.016cm and s=5.8 x 107S/m. What are the mode and attenuation for 10GHz?
Using this equation to calculate cutoff frequency of each mode

37. Calculation TE10 a=2.286mm, b=1.016mm, m=1 and n=0 ,thus we have
Similarly we can calculate for other modes

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

39. continue or

40. Evanescent mode
Mode that propagates below cutoff frequency of a wave guide is
called evanescent mode
Wave propagation constant is
Where kc is referred to cutoff frequency, g is referred to propagation in waveguide and b is in space
When f0< fc ,
But
g = a +jb
a=attenuation
b=phase constant
Since no propagation then
The wave guide become attenuator

41. Cylindrical waveguide
TE mode
Dominant mode is TE11

42. continue a
TM mode
TM01 is preferable for long haul
transmission

43. Example Refer to tables TM modes TE modes
Find the cutoff wavelength of the first four modes of a circular waveguide
of radius 1cm
2nd mode
Refer to tables
TM modes
TE modes
3rd &4th modes
3rd &4th modes
1st mode

44. Calculation 1st mode Pnm= 1.841, TE11 2nd mode Pnm= 2.405, TM01
1st mode Pnm= 3.832, TE01 and TM11

45. Stripline b w

46. Continue On the other hand we can calculate the width of
stripline for a given characteristic impedance

47. t =thickness of the strip
Continue
Where
t =thickness of the strip