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Radiation Pattern Definitions
Normalized field pattern:
Power pattern:
In dB scale
Examples
Ideal dipole:
Line current:
Main lobe (major lobe, main beam)
Side lobe (minor lobe)
Maximum side lobe level:
Half-power beamwidth:
Pattern types: Broadside, Intermediate, Endfire.
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Directivity
Solid angle:
Radiation intensity:
where
Directivity:
Beam solid angle:
Power Gain (Gain)
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or
Radiation efficiency:
Referenced Gain:
dBi: referenced to isotropic antenna.
dBd: referenced to dipole antenna.
The origin of radiation – short dipoles.
Phasor retarded potential
and
,
Consider an infinite small short dipole
pointing in z direction and
located at origin, where is a line current, and
is the length, i.e.,
or at
then,
,
since
.
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In spherical coordinate
and
that is
Near Field:
The same as the static magnetic field calculated by Biot-Savart’s law
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since
.
The same as the static electric field generated by dipole moment .
Far field:
Spherical TEM wave
,
Propagating in
In general,
Summary:
,
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1.
All radiation of finite current distribution is spherical TEM wave
at far field.
2.
Both
and
Half-wave dipole
varies as
at far field.
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Poynting vector:
Power radiated:
Radiation resistance:
Importance of half-wave dipole:
1. consider the dipole as an open transmission line, then
. At
,
,...,
. Which means zero
reactance. In reality, the length is a little be shorter. Since a good
transmission’s intrinsic impedance is near pure real, this allows
matching to transmission lines.
2.
The efficiency is the best at
.
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Antenna Arrays
Suppose there are N identical antennas each located at location
, then
where
Thus,
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where
is called array factor,
is the vector potential of single
element located at origin.
General Uniform Linear Arrays
Let
, and
where
then the normalized array factor,
,
then
1.
Main-beam direction. Maximum occurs when
a.
Broadside array,
b.
Endfire array,
, i.e.,
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2.
Null locations:
3.
Side lobe locations:
Pattern Multiplication
Example: Two-Collinear, Half-Wavelength Spaced Short Dipoles
Parameters:
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Example: Two Parallel, Half-Wavelength Spaced Short Dipoles
Since
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Antenna in Communication Systems
Open circuit voltage:
polarization match.
for ideal dipole receiving antenna and
When
Maximum power transfer:
Power density:
Maximum effective aperture
For a dipole
In general,
Effective aperture:
Available power:
In general,
or
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Aperture efficiency:
, where
is the physical aperture size.
Communication Links
Power delivered to the load
: polarization mismatch factor,
: impedance mismatch factor,
In dB form
or
where dBm is power in decibels above a milliwatt.
EIRP: effective (equivalent) isotropically radiated power
ERP: effective radiated power by a half-dipole
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Other Antenna Types
1.
Traveling wave antennas
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2.
Helix
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3.
Yagi-Uda
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4.
Broadband antennas
a. Spiral
b. log-periodic
5.
Aperture
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6.
Patch