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Introduction to electromagnetics
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Electromagnetic phenomena
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Steady state current (simple DC circuit)
The globe lights up due to the work done by electric current (moving charges).
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Radiation by oscillating charges
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Generation of electromagnetic wave
Oscillating voltage source forces
electrons to be accelerated,
which generates electromagnetic
wave
Oscillator circuit
Output voltage
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Electromagnetic wave : radio communication
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Moving charges on the antenna generate electromagnetic waves.
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Electromagnetic wave : automotive radar
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Moving charges on the antenna generate electromagnetic waves.
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Electromagnetic wave : ground penetrating radar
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The EM wave from the transmitter refracts into the ground and is
reflected back by the underground facilities.
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Electromagnetic wave generation : antennas
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Many kinds of antennas are built and
utilized.
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Electromagnetic wave : signal propagation
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The electrical signal propagate along
the line trace at the speed of light.
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Importance of electromagnetic theory
•
•
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EM theory helps understand how electrical signals propagate along
conductors as well as free space.
Predicts voltages and currents using the concept of electric and magnetic
field.
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Electromagnetic theory
EM-theory
Material
Electric field (E)
Sources (q, J)
Magnetic field (H)
Electro-magnetic field (E,H )
Material (ε, μ)
Mathematics
Coordinate systems
Vector calculus
(divergence, curl,
gradient)
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Contents
1.
Electric field
① Coulomb’s law
② Gauss’s law (divergence)
③ Electric potential (gradient)


1.
④ Capacitance
⑤ Ohm’s law
2.
2.
Magnetic field
① Biot-Savart law
② Ampere’s law (curl)

Sources
①
Charge
②
Current
Material
①
Conductor (semi-conductor,
lossy material)
②
Dielectric (insulator)
③
Magnetic material
③ Inductance
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3.
Electro-magnetic field
① Faraday’s law
② Displacement current
③ Maxwell’s equations
④ Plane wave
⑤ Reflection/transmission
4.
Transmission lines
① Impedance matching
② Smith chart
③ Waveguides
5.
Radiation
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Mathematics -Glossary
• Scalar : a quantity defined by one number (eg. Temperature, mass, density, voltage, ... )
• Vector : a quantity defined by a set of numbers. It can be represented by a magnitude and a
direction. (velocity, acceleration, …)
• Field : a scalar or vector as a function of a position in the space. (scalar field, vector field, …)
Scalar field
Vector field
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Example of a vector field
Ek
+q
q1
r
2
rˆ
•Magnitudes and directions of
vectors change with positions.
•The electric field is a field quantity
because its magnitude and direction
changes with positions.
Electric field generated by a charge (+q1)
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Usefulness of the field concept
Fk
+q
-q
E
+q
-q
q 1q 2
r
2
rˆ
This equation states only the forces
between the two charges +q and –q. It
does not state about the interactions that
occur between them. It is misleading that
this equation may imply that the
interaction occurs instantaneously.
q1
F
E
 k 2 rˆ
q2
r
F  q2 E
The electric field due to +q spread into the
space. Then (–q) feels the attractive force by
way of the electric field.
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Analogy to the mechanical law
Newton’s law of gravity :
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Gm1m2
F
r̂12
2
r
Point-to-point reaction
(action at a distance)
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Gravitational field
F
GM
G    2 rˆ
m
r
Moon
F
GMm
rˆ
2
r
Earth
Gravitational field mediates interactions
between the earth and the moon.
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Coulomb’s law
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•
This law is discovered by Coulomb experimentally.
•
In the free space, the force between two point charges is proportional to the charges of
them, and is inversely proportional to the square of the distance between those charges.
Fk
q 1q 2
r
2
k  9  109 [ Nm2C2 ] 
rˆ
1
40
ε0 : permittivity of vacuum.
If q1, q2 have the same
polarity, the force is
repulsive.
+q1
+q2
 

R  R 2  R1

R2

R1
Coulomb’s law only states that
the force between two charge is
related to the distance between
them and their charges. It does
not tells us how the interaction
occurs.
O
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Fk
q 1q 2
r
2
rˆ
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Definition of electric field
q1 ˆ
F

R
2
q2 0 q
40 r
2
E  lim
+q1
+q2
Electric field is measured by the force divided by charge
quantity with the amount infinitesimally small. This limit
process is necessary for not disturbing the original electric
field by q1.
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Simple circuit example
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Electrical signal transmission means the propagation of the
electromagnetic field, not the movement of charges.
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Generation of charges : friction charging
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Friction charging
Contact
Electrons “lost”
Separation
Electrons “gained”
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Induction charging
Metallic sphere
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Generation of charges : battery
An amount of positive charges are generated such that the terminal voltages are
sustained.
Electrons(-) are absorbed.
(+) charges are generated
Electrons(-) are generated.
(+) charges are absorbed.
2NH 4  2e   2 NH3  H 2
Zn  Zn 2  2e 
Electrons are generated via
electro-chemical reaction.
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Charge transport example : battery with open wire
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Charges in a wire are moved by diffusion and electromagnetic laws.
Positive charges are plenty.
Diffusion
Charge movement by
diffusion
Negative charges are plenty.
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Contention between diffusion and Coulomb’s law
Movement by
diffusion
Repelling force by
Coulomb’s law
•
•
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Positive charges are accumulated.
The accumulated charges repel
charge movement by diffusion
Attracting force by
Coulomb’s law
•
Movement by
diffusion
Repelling force by
Coulomb’s law
•
Net charge flow becomes zero only
when the voltage difference between
the wires is equal to the voltage
between the battery terminals.
The accumulated charges repel
charge movement by diffusion
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Electric field distribution near charged plates
E
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If a charge is brought into the plates, it will be accelerated
along the direction of electric field.
F  ma  qE
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Magnetic field
A charged particle in
motion generates magnetic
field nearby.
In the same way, currents
generate magnetic field
nearby.
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Motion of a charge in a magnetic field
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F  qv  B
Charged particles in motion are influenced by
magnetic fields
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Biot-Savart law
ˆ
Ids  R
dH 
4R 2
Current
segment
Id s
r'
R  r r'
r
Direction of
H-field
The generated magnetic field can be predicted
by Biot-Savart’s law
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Electromagnetic law – Maxwell equations
Maxwell equations
B
E  
t
D
H  J 
t
D  
B  0
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1. Electromagnetic phenomena are explained
by the four Maxwell equations.
2. Through the equations, electric field and
magnetic field are coupled to each other.
3. Quantities on the right hand side are the
source terms.
4. Quantities on the left side are the resulting
phenomena.
5. The independent variables are current
density vector J and charge density .
E: electric field
D: electric displacement flux density
H: magnetic field
B: magnetic flux density
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Ampere’s law
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E
H  J 
t
Current or increase of
electric field strength
E,J
H
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Faraday’s law
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  E  
H
H
t
Increase of
magnetic field
E
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Faraday’s law
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The time-varying magnetic
field generates electric field
nearby.
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Gauss’ law
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E   /
E
+Q
-Q
Electric field lines emanate from positive
charges and sink into negative charges.
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H  0
Magnetic field lines always form
closed loops
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Example – Hertzian dipole antenna
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spheres for storing electric charges
Heinrich Hertz (1857-1894)
arc monitoring
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Schematic diagram of Hertz experiment
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Transformer for high voltage generation
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Propagation of electromagnetic wave
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Electric field : red
Magnetic field : blue
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Radio communication
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Reception of EM wave
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current
E
Transmitting
antenna
V
Receiving
antenna
The charges on the receiving antenna move
toward the antenna terminal, which causes
voltage drop across them.
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Example – Signal propagation over a line trace
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V
H-field due to
moving charges
t
E
V


H


E
H  J 
t


ZL

H
  E  
t
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