TRANSMISSION MEDIA

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TRANSMISSION MEDIA

• MAXWELLS EQUATIONS AND
• TRANSMISSION MEDIA CHARACTERISTICS

ENEE 482 Spring 2002 DR. KAWTHAR ZAKI
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MICROWAVE CIRCUIT ELEMENTS AND ANALYSIS
Dielectric
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Common Hollow-pipe waveguides
Rectangular guide
Ridge guide
Circular guide
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STRIP LINE CONFIGURATIONS
W
SINGLE STRIP LINE
COUPLED LINES
COUPLED STRIPS TOP BOTTOM
COUPLED ROUND BARS
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MICROSTRIP LINE CONFIGURATIONS
SINGLE MICROSTRIP
TWO COUPLED MICROSTRIPS
TWO SUSPENDED SUBSTRATE LINES
SUSPENDED SUBSTRATE LINE
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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 MAXWELLS
• EQUATIONS

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Electromagnetic Theory
Maxwells Equations
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Auxiliary Relations
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Maxwells Equations in Large Scale Form
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Maxwells Equations for the Time - Harmonic Case
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Boundary Conditions at a General Material
Interface
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Fields at a Dielectric Interface
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Js
Ht
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The magnetic wall boundary condition
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Wave Equation
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Plane Waves
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n
H
x
H is perpendicular to E and to n. (TEM waves)
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Plane Wave in a Good Conductor
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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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Reflection From A Dielectric Interface
Parallel Polarization
e
x
Er
n2
e0
Et
n3
q2
q3
z
q1
n1
Ei
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Energy and Power
Under steady-state sinusoidal time-varying
Conditions, the time-average energy stored in
the Electric field is
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Poynting Theorem
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Circuit Analogy
C
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Potential Theory
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Solution For Vector Potential
(x,y,z)
(x,y, z)
R
J
r
r
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Waves on An Ideal Transmission Line
Rg
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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Steady State Sinusoidal Waves
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Transmission Line Parameters
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Terminated Transmission Line
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Transmission Lines Waveguides Wave
Propagation in the Positive z-Direction is
Represented Bye-jbz
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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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TEM WAVES
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TE WAVES
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TM WAVES
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TEM TRANSMISSION LINES
Coaxial
Two-wire
Parallel -plate
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COAXIAL LINES
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• THE CHARACTERISTIC IMPEDANCE OF A COAXIAL IS Z0

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Zc OF COAXIAL LINE AS A FUNCTION OF b/a
er

Zo
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Transmission line with small losses
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Qc OF COAXIAL LINE AS A FUNCTION OF Zo
er
Zc
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Parallel Plate Waveguide
TEM Modes
y
d
x
w
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TM modes
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TE Modes
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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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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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WAVEGUIDE PROPERTIES

• FOR A W/G FILLED WITH DIELECTRIC er

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• 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 1.706 D
• DOMINANT MODES ARE TE10 AND TE11 MODE
• FOR RECTANGULAR CIRCULAR WAVEGUIDES

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RECTANGULAR WAVEGUIDE MODE FIELDS
y
b
z
x
a
CONFIGURATION
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TE modes
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TEmn MODES
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The dominant mode is TE10
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TMmn MODES
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TE Modes of a Partially Loaded Waveguide
y
x
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CIRCULAR WAVEGUIDE MODES
y
r
a
f
x
z
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TE Modes
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TEnm MODES
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TMnmMODES
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Cutoff frequencies of the first few TE And TM
modes in circular waveguide
TE11
TE01
TE21
TE31
1
0
fc/fcTE11
TM01
TM11
TM21
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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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ATTENUATION IN COPPER WAVEGUIDES DUE TO CONDUCTOR
LOSS
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Higher Order Modes in Coaxial Line
TE Modes
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Grounded Dielectric Slab
TM Modes
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Stripline
y
w
b
x
z
Approximate Electrostatic Solution
y
b/2
0
a/2
-a/2
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Microstrip
y
w
d
x
-a/2
a/2
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The Transverse Resonance Technique
TM Modes for the parallel plate waveguide
y
y
d
d
0
x
w
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MODES IN DIELTECTRIC LOADED WAVEGUIDE
b
er1
a
er2

• CATEGORIES OF FIELD SOLUTIONS
• TE0m MODES
• TM0m MODES
• HYBRID HEnm MODES

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BOUNDARY CONDITIONS
FIELDS SATISFY THE WAVE EQUATION, SUBJECT TO THE
BOUNDARY CONDITIONS Ez , Ef , Hz , Hf ARE
CONTINUOUS AT rb Ez , Ef VANISH AT ra
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WHERE A IS AN ARBITRARY CONSTANT
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Characteristic equation
Where zx1a is the radial wave number in er
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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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COMPLEX MODES

• COMPLEX PROPAGATION CONSTANT
• g a jb
• ONLY HE MODE CAN SUPPORT COMPLEX WAVES
• PROPAGATION CONSTANT OF COMPLEX MODES
• ARE CONJUGATE

• COMPLEX MODES DONT 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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e1
OPTICAL FIBER
2a
IN CIRCULAR CYLINDRICAL COORDINATES
Step-index fiber
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For the symmetric case n0, the solution break
into Separate TE and TM sets. The continuity
condition for Ez1 Ez2 and Hf1 Hf2 at ra gives
for the TM set
The continuity condition for Hz1 Hz2 and Ef1
Ef2 at ra 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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Parallel Plate Transmission Line
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Low Frequency Solution
When the frequency is low,
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y
c
b
er
a
x
-W
W
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High Frequency Solution
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Microstrip Transmission Line
w
y
H
x
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Boundary conditions
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