EE 30358 Electromagnetic Fields and Waves II

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EE 30358 - Electromagnetic Fields and Waves II
FIRST MAN SAW LIGHT (but its electromagnetic
nature was hidden for him), and BODIES looked
like NEUTRAL (negative and positive charges were
hidden.
We intend to think that GRAVITATIONAL FORCE is
the dominating FORCE. .
The spacetime bodyforce model describes the
dynamics of the universe.
Geometrical space and time set the theater.
Bodies collide, forces interfere.
Consider a FORCE like gravitation which varies
inversely as the square of the distance, but
BILLION-BILLION-BILLON-BILLION times stronger.
And there are two types of matter, positive and
negative, and like kinds repel, unlike kinds
attract, unlike gravity where there is only
attraction. What would happen?
A bunch of positives would repel with an enormous
force, and spread out in all directions. A bunch
of negatives would do the same. But an evenly
mixed bunch of positives and negatives would do
something different.
The opposite pieces would be pulled together by
the enormous attractions.
The terrific forces would form tight mixtures of
positive and negative, and between two separate
bunches of these mixtures there would be
practically no attraction or repulsion at all.
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There is such a force the ELECTRICAL or
COULOMB FORCE). .
And all matter is a mixture of POSITIVCE PROTONS
and NEGATIVE ELECTRONS.
THE BALANCE ON THE MACRO SCALE IS PERFECT!
Atoms are made of positive protons and negative
electrons Why do they remain separate?
Because of QUANTUM PHYSICS Quantum effects.
What holds the NUCLEUS together?
NUCLEAR PHYSICS Nuclear forces keep the nuclei
together.
BILLION-BILLION-BILLION-BILLION TIMES STRONGER
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Physics of Electromagnetism
Least sophisticated Geometrical optics
Rays
Electromagnetic Waves
Most sophisticated
Photons Quantum Optics
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FUNDAMENTAL LAWS OF ELECTROMAGNETIC FIELDS AND
WAVES MAXWELLS EQUATIONS -
EM FIELD STORES ENERGY AND HAS MOMENTUM
CONSERVATION OF ENERGY IN ELECTROMAGNETIC FIELDS
CONDITIONS FOR UNIQUE SOLUTION OF MAXWELLS
EQUATIONS
Inside a closed volume the ELECTRIC AND MAGNETIC
FIELDS ARE KNOWN at a given moment of time t
t0 (INITIAL CONDITIONS), the GENERATORS are
known from t0 to t, , AND either the TANGENTIAL
ELECTRIC or the TANGENTIAL MAGNETIC fields are
given at the SURFACE enclosing the volume from t0
to t (BOUNDARY CONDITIONS),.

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MAXWELLS EQUATIONS
Gausss Law for Electric Field
Gausss Law for Magnetic Field
Faradays Law
Amperes Law
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BOUNDARY CONDITIONS
CONTINUITY EQUATION
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Time Harmonic Fields and Their Phasor
Representation
IN LINAR TIME-INVARIANT MATERIALS
DO NOT DEPEND ON THE FIELDS AND ON TIME
IN THIS CASE MAXWELLS EQUATIONS ARE LINEAR,
i.e. sinusoidal time variations of source
functions of a given frequency produce
steady-state sinusoidal time variations of the
field vectors (E, D, B, H) of the same
frequency.
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MAXWELLS EQUATIONS
Monochromatic (phasor, single frequency
sinusoidal, harmonic) form
Local (differential) form
Integral form
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MEDIA
Free space
Lossless (conservative) medium
Conductive medium
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EE 30358 - Electromagnetic Fields and Waves II
IN NATURE
PLANE WAVE PROPAGATION, REFLECTION,
REFRACTION LINEAR, CIRCULAR, ELLIPTIC
POLARIZATION PROPGATION IN CONDUCTIVE MEDIUM
GUIDED EM WAVES
ENERGY PROPGATES IN THE DIELECTRIC, NOT IN
WIRES TRANSMISSION LINES, WAVEGUIDES,
DISCONTINUITIES
RADIATION ANTENNAS
ACCELERATED CHARGE RADIATES, RETARDED
POTENTIALS HERTZ-DIPOLE, LINEAR WIRE ANTENNAS,
ARRAYS
CIRCUIT REPRESENTATION OF EM FIELDS AND WAVES
MAXWELLS EQUS.
KIRCHHOFFS EQUS.
IMPEDANCE ADMITTANCE SCATTERING
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ELECTROMAGNETIC WAVES IN NATURE
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ELECTROMAGNETIC WAVES - OUTLOOK
Gamma-rays
PHz
THz
GHz
MHz
kHz
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Uniform Plane Wave Propagation in a Medium
MAXWELLS EQUATIONS
Propagation in z direction
GENERAL SOLUTION FOR PHASORS IN SPACE
Descartes coordinates
In general ELLIPTIC POLARIZATION
Special cases CIRCULAR or LINEAR POLARIZATION
GENERAL SOLUTION IN SPACE-TIME
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Polarization of Plane Waves
LINEAR POLARIZATION
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LINEAR POLARIZATION
CIRCULAR POLARIZATION
ELLIPTICAL POLARIZATION
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Uniform Plane Wave Propagation in Conductive
Medium
MEDIUM OF PROPAGATION IS HOMOGENEOUS, LINEAR AND
ISOTROPIC
FREE SPACE
CONDUCTIVE MEDIUM
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REFLECTION AND TRANSMISSION AT MULTIPLE
INTERFACES
Region 1
Region 2
Region 3
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PLANE WAVE PROPAGATION AT ARBITRARY ANGLE in
lossless medium
Direction of propagation
Propagation constant
Wave impedance of the medium
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E in plane of Incidence
E Normal to plane of Incidence
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Given
Snells Laws
Frensel Equations
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COMPARISON BETWEEN REFLECTION COEFFICIENTS FOR
PARALLEL AND PERPENDICULAR POLARIZATIONS
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Brewster angle
Brewster angle
No reflection !
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TOTAL REFLECTION AT CRITICAL ANGLE OF INCIDENCE
At the critical angle
Total internal reflection
Total reflection EXISTS for BOTH POLARIZATIONS
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DIELECTRIC SLAB WAVEGUIDE
only discrete values of
For a given
and
for which guiding takes place
SELF CONSISTANCY CONDITION FOR GUIDANCE
At a point in space only a single value of phase
can occur.
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RAY TRACING
GEOMETRICAL OPTICS
REFRACTIVE INDEX
Fermat principle of geometric optics
Either minimum or maximum
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GUIDED ELECTROMAGNETIC WAVES
TRANSMISSION LINES
WAVEGUIDES
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Propagation constant
TELEGRAPHERS EQUATIONS
Characteristic impedance
General solution
TIME-DOMAIN
PHASOR-DOMAIN
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ANALOGY BETWEEN A NORMALLY INCIDENT, LINEARLY
POLARIZED PLANE WAVE AND WAVE ALONG A
TRANSMISSION LINE
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WAVE GUIDES
TEM mode
PLANE WAVE
TRANSEVERSAL ELECTRIC-MAGNETIC FIELD
Two-wire wave guides
Single-wire wave guides
TEM mode propagation is possible
Is propagation in TEM mode possible ?
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TMmn modes in rectangular wave guides
TEmn modes in rectangular wave guides
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It is true in general that modes are orthogonal
to each other
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We can assign an ortho-normal set of modal
functions to every waveguide cross section
Example TE10, TEm0
Mutatis mutandis
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The orthonomral set of modal functions is
complete Every field can be expanded as a
linear combination os modal fields
The coefficients in the expansion are MODAL
VOLTAGES and MODAL CURRENTS
WAVE GUIDE SECTION
TRANSMISSION LINES
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A WAVE GUIDE IS EQUIVALENT TO A SET OF UNCOUPLED
MODES
MODES ARE EXCITED AT THE BOUNDARIES OF THE
WAVE GUIDE SECTION
First, let us look at the excitation of a
semi-infinite wave guide
If we prescribe
, it always can be expanded as
where
are the mode excitations
and e.g.
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Because
Because of orthonormality
Only those modes will be excited which are
present in the feeding field
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Cut-off frequency
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