1. MAXWELL’S EQUATIONS AND TRANSMISSION MEDIA CHARACTERISTICS
ENEE 482 Spring 2002
DR. KAWTHAR ZAKI

2. MICROWAVE CIRCUIT ELEMENTS AND ANALYSIS
Two conductor
wire
Coaxial line
Shielded
Strip line
Dielectric
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3. Common Hollow-pipe waveguides
Rectangular
guide
Ridge guide
Circular
guide
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4. STRIP LINE CONFIGURATIONSW
SINGLE STRIP LINE
COUPLED LINES
COUPLED STRIPS
TOP & BOTTOM
COUPLED ROUND BARS
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5. MICROSTRIP LINE CONFIGURATIONS
SINGLE MICROSTRIP
TWO COUPLED MICROSTRIPS
TWO SUSPENDED
SUBSTRATE LINES
SUSPENDED SUBSTRATE
LINE
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6. TRANSVERSE ELECTROMAGNETIC (TEM): COAXIAL LINES
TRANSMISSION MEDIA
TRANSVERSE ELECTROMAGNETIC (TEM):
COAXIAL LINES
MICROSTRIP LINES (Quasi TEM)
STRIP LINES AND SUSPENDED SUBSTRATE
METALLIC WAVEGUIDES:
RECTANGULAR WAVEGUIDES
CIRCULAR WAVEGUIDES
DIELECTRIC LOADED WAVEGUIDES
ANALYSIS OF WAVE PROPAGATION ON THESE
TRANSMISSION MEDIA THROUGH MAXWELL’S
EQUATIONS
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7. Electromagnetic Theory Maxwell’s Equations
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8. Auxiliary Relations:
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9. Maxwell’s Equations in Large Scale Form
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10. Maxwell’s Equations for the Time - Harmonic Case
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11. Boundary Conditions at a General Material Interfaceh
E1t
E2t
m1,e1
m2,e2
D1n
D2n h Ds
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12. Fields at a Dielectric Interface
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13. + + + n rs Js Ht
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14. The magnetic wall boundary condition
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15. Wave Equation
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16. Plane Waves
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17. ENEE482

18. H is perpendicular to E and to n. (TEM waves)z y E n H x
H is perpendicular to E and to n. (TEM waves)
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19. Plane Wave in a Good Conductor
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20. Boundary Conditions at the Surface of a Good Conductor
The field amplitude decays exponentially from its surface
According to e-u/ds where u is the normal distance into the
Conductor, ds is the skin depth
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21. Reflection From A Dielectric Interface
Parallel Polarization e x Er n2 e0 Et n3 q2 q3 q1 z n1 Ei
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22. ENEE482

23. Energy and Power Under steady-state sinusoidal time-varying
Conditions, the time-average energy stored in the
Electric field is
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24. ENEE482

25. Poynting Theorem
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26. ENEE482

27. ENEE482

28. Circuit Analogy L R I V C
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29. Potential Theory
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30. Solution For Vector PotentialJ
(x’,y’, z’) R
(x,y,z) r’ r
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31. Waves on An Ideal Transmission LineRg z
Lumped element circuit model for a transmission line
Ldz
I(z,t)+dI/dz dz
I(z,t)
V(z,t)
Cdz
V(z,t)+dv/dz dz
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32. ENEE482

33. Steady State Sinusoidal Waves
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34. Transmission Line ParametersC2 C1 S
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35. Terminated Transmission LineZL Zc Z
To generator
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36. ENEE482

37. Transmission Lines & Waveguides
Wave Propagation in the Positive z-Direction is Represented By:e-jbz
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38. Modes Classification: 1. Transverse Electromagnetic (TEM) Waves
2. Transverse Electric (TE), or H Modes
3. Transverse Magnetic (TM), or E Modes
4. Hybrid Modes
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39. TEM WAVES
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40. ENEE482

41. TE WAVES
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42. ENEE482

43. TM WAVES
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44. TEM TRANSMISSION LINES
Coaxial
Two-wire
Parallel -plate a b e
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45. COAXIAL LINES a b e
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46. THE CHARACTERISTIC IMPEDANCE OF A COAXIAL IS Z0
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47. Zc OF COAXIAL LINE AS A FUNCTION OF b/a1 10
100 20 40 60 80
120
140
160
180
200
220
240
260 = er Zo
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48. Transmission line with small losses
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49. ENEE482

50. Qc OF COAXIAL LINE AS A FUNCTION OF Zoer Zc
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51. Parallel Plate Waveguide
TEM Modes y d x w
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52. TM modes
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53. ENEE482

54. ENEE482

55. TE Modes
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56. ENEE482

57. COUPLED LINES EVEN & ODD
MODES OF EXCITATIONS
AXIS OF EVEN SYMMETRY
AXIS OF ODD SYMMETRY
P.M.C.
P.E.C.
ODD MODE ELECTRIC
FIELD DISTRIBUTION
EVEN MODE ELECTRIC
FIELD DISTRUBUTION
=ODD MODE CHAR.
IMPEDANCE
=EVEN MODE CHAR.
IMPEDANCE
Equal currents are flowing
in the two lines
Equal &opposite currents are
flowing in the two lines
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58. WAVEGUIDES HOLLOW CONDUCTORS RECTANGULAR OR CIRCULAR.
PROPAGATE ELECTROMAGNETIC ENERGY ABOVE A CERTAIN FREQUENCY (CUT OFF)
INFINITE NUMBER OF MODES CAN PROPAGATE, EITHER TE OR TM MODES
WHEN OPERATING IN A SINGLE MODE, WAVEGUIDE CAN BE DESCRIBED AS A TRANSMISSION LINE WITH C/C IMPEDANCE Zc & PROPAGATION CONSTANT g
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59. WAVEGUIDE PROPERTIES
FOR A W/G FILLED WITH DIELECTRIC er :
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60. PROPAGATION PHASE CONSTANT:
FOR RECTANGULAR GUIDE a X b, CUTOFF
WAVELENGTH OF TE10 MODES ARE:
: CUT OFF FREQUENCY IN GHz (lc INCHES):
FOR CIRCULAR WAVEGUIDE OF DIAMETER D
CUTOFF WAVE LENGTH OF TE11 MODE IS:
lc = D
DOMINANT MODES ARE TE10 AND TE11 MODE
FOR RECTANGULAR & CIRCULAR WAVEGUIDES
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61. RECTANGULAR WAVEGUIDE
MODE FIELDS y b z x a
CONFIGURATION
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62. TE modes
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63. TEmn MODES
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64. The dominant mode is TE10
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65. TMmn MODES
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66. TE Modes of a Partially Loaded Waveguidex
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67. ENEE482

68. CIRCULAR WAVEGUIDE MODESy r a f x z
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69. TE Modes
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73. TEnm MODES
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74. TMnmMODES
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75. Cutoff frequencies of the first few TE
And TM modes in circular waveguide
TE11
TE21
TE01
TE31 1
fc/fcTE11
TM01
TM11
TM21
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76. ATTENUATION IN WAVEGUIDES
ATTENUATION OF THE DOMINANT MODES (TEm0) IN
A COPPER RECTANGULAR WAVEGUIDE DIM. a X b, AND
(TE11) CIRCULAR WAVEGUIDE, DIA. D ARE:
WHERE f IS THE FREQUENCY IN GHz
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77. ATTENUATION IN COPPER WAVEGUIDES
DUE TO CONDUCTOR LOSS
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78. Higher Order Modes in Coaxial Line
TE Modes:
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79. Grounded Dielectric Slabx z
Dielectric
Ground plane
TM Modes
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80. ENEE482

81. Stripline y w b x z Approximate Electrostatic Solution: y b/2 a/2 -a/2
a/2
-a/2
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82. ENEE482

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84. ENEE482

85. Microstrip y w d
-a/2 x
a/2
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88. ENEE482

89. The Transverse Resonance Technique
TM Modes for the parallel plate waveguide y y d d w x
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90. ENEE482

91. MODES IN DIELTECTRIC LOADED WAVEGUIDEb
er1 a
er2
CATEGORIES OF FIELD SOLUTIONS:
TE0m MODES
TM0m MODES
HYBRID HEnm MODES
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92. BOUNDARY CONDITIONS FIELDS SATISFY THE WAVE EQUATION,
SUBJECT TO THE BOUNDARY CONDITIONS
Ez , Ef , Hz , Hf ARE CONTINUOUS AT r=b
Ez , Ef VANISH AT r=a
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93. WHERE A IS AN ARBITRARY CONSTANT
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94. Characteristic equation
Where z=x1a is the radial wave number in er
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95. ENEE482

96. For n = 0, the Characteristic Equation Degenerates in two
Separate Independent Equations for TE and TM Modes:
For TE Modes
And:
For TM Modes
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97. COMPLEX MODES COMPLEX PROPAGATION CONSTANT : g = a +jb
ONLY HE MODE CAN SUPPORT COMPLEX WAVES
PROPAGATION CONSTANT OF COMPLEX MODES
ARE CONJUGATE :
COMPLEX MODES DON’T CARRY REAL POWER
COMPLEX MODES CONSTITUTE PART OF THE
COMPLETE SET OF ELECTROMAGNETIC FIELD
SPACE
COMPLEX MODES HAVE TO BE INCLUDED IN THE
FIELD EXPANSIONS FOR CONVERGENCE TO
CORRECT SOLUTIONS IN MODE MATCHING
TECHNIQUES.
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98. OPTICAL FIBER 2a e1 IN CIRCULAR CYLINDRICAL COORDINATES:
Step-index fiber
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99. For the symmetric case n=0, the solution break into Separate
TE and TM sets. The continuity condition for Ez1= Ez2
and Hf1= Hf2 at r=a gives for the TM set:
The continuity condition for Hz1= Hz2
and Ef1= Ef2 at r=a gives for the TE set:
If n is different from 0, the fields do not separate into TM
and TE types, but all the fields become coupled through
continuity conditions.
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100. Parallel Plate Transmission Lineb c er
Partially loaded parallel
Plate waveguide y x
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104. Low Frequency Solution
When the frequency is low,
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105. y c b er a x -W W
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110. High Frequency Solution:
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111. Microstrip Transmission Linew y H x
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114. Boundary conditions:
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