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Antennas: from Theory to Practice
1. Basics of Electromagnetics
Yi HUANG
Department of Electrical Engineering & Electronics
The University of Liverpool
Liverpool L69 3GJ
Email: [email protected]
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Objectives of this Chapter
• Review the history of RF engineering and
antennas;
• Lay down the foundation of mathematics
required for this course;
• Examine the basics of electromagnetics and
• introduce Maxwell’s equations to establish
the link between the fields and sources.
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1. 1
The First Successful Antenna Experiment
It was conducted by Hertz
in 1887
Experimental set-up
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1.2
Radio Systems
• Compared with a wired system, radio systems can
offer the following advantages:
– Mobility
– Good coverage over an area
– Low path-loss over a long distance
A typical radio system
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1.3
Necessary Mathematics
• Complex numbers
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• Vectors
– A vector has both a magnitude and a direction
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• Vector addition and subtraction
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• Vectors multiplication:
– dot product:
– cross product:
Cross product doesn’t obey
the commutative law!
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An Example
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• Cartesian and spherical coordinates
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1.4
Basics of Electromagnetics
l (m)
f (Hz)
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Radio Frequency Bands
Frequency Band Wavelength Applications
•
•
•
•
•
•
•
•
•
3-30 kHz
30-300kHz
0.3-3 MHz
3-30 MHz
30-300MHz
0.3-3 GHz
3-30 GHz
30-300GHz
0.3-3 THz
VLF
LF
MF
HF
VHF
UHF
SHF
EHF
100-10 km
10-1 km
1-0.1 km
100-10 m
10-1
m
1-0.1 m
100-10mm
10-1 mm
1-0.1 mm
Navigation, sonar, fax
Navigation
AM broadcasting
Tel, Fax, CB, ship comms
TV, FM broadcasting
TV, mobile, radar, satellite
Radar, microwave links
Radar, wireless comms
Sub-millimetre application
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dB
• Logarithmic scales are widely used in RF
engineering and antennas community since the
signals we are dealing with change significantly
but
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The Electric Field
• The electric field (in V/m) is defined as the force
(in Newtons) per unit charge (in Coulombs). From
this definition and Coulomb's law, the electric field
E created by a single point charge Q at a distance r
is
e is the electric permittivity, also called dielectric constant
In free space:
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• The product of permittivity and the electric field is
called the electric flex density (also called the
electric displacement), D which is a measure of
how much electric flux passes through a unit area,
i.e.,
The complex permittivity can be written as
The ratio of the imaginary part to the real part is called
the loss tangent
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Relative permittivity of some materials
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• The electric field E is related to the current density J
(in A/m2), another important parameter, by Ohm’s
law:
J  E
 is the conductivity which is the reciprocal
of resistivity. It is a measure of a material’s ability to
conduct an electrical current and is expressed in
Siemens per metre (S/m).
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Conductivity of some materials
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The Magnetic Field
• The magnetic field, H (in A/m), is the vector field
which forms closed loops around electric currents
or magnets. The magnetic field from a current
vector I is given by the Biot-Savart law as
H
I  rˆ
4r 2
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• Like the electric field, the magnetic field exerts a
force on electric charge. But unlike an electric field,
it employs force only on a moving charge, and the
direction of the force is orthogonal to both the
magnetic field and charge's velocity
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Relative permeability of some materials
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Qv can actually be viewed as the current vector I and
the product of is called the magnetic flux density
B (in Tesla), the counterpart of the electric flux
density.
When we combine the electric and magnetic fields,
the total force:
This is called the Lorentz force. The particle will
experience a force due to the electric field of QE,
and the magnetic field Qv × B
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1.5
Maxwell’s Equations
Maxwell’s equations describe the interrelationship
between electric fields, magnetic fields, electric
charge, and electric current
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• Faraday's Law of Induction
The induced electromotive force is proportional to the rate of
change of the magnetic flux through a coil. In layman's terms,
moving a conductor through a magnetic field produces a
voltage or a time varying magnetic field can generate an
electric fields!
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• Amperes’ Circuital Law
It shows that both the current (J) and time varying
electric field can generate a magnetic field.
• Gauss' Law for Electric Fields
It means that charges () can generate electric fields, and
it is not possible for electric fields to form a closed loop.
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• Gauss’ Law for Magnetic Fields
It means that the magnetic field lines are closed loops,
thus the integral of B over a closed surface is zero
• Integral form
The partial
differential form
applies to a point
But this is for
an area/volume!
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1.6
Boundary Conditions
Tangential components of an electric field are continuous
across the boundary between any two media.
The change in tangential component of the magnetic field
across a boundary is equal to the surface current density.
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Applying these boundary conditions on a perfect conductor
Field distribution around a two-wire transmission line:
E-field is orthogonal to the line surface and H-field (loops).
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