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Antennas 1
Antennas
! Grading policy.
" Weekly Homework 40%.
" Midterm Exam 30%.
" Project 30%.
! Office hour: 3:10 ~ 4:00 pm, Monday.
! Textbook: Warren L. Stutzman and Gary A. Thiele,
“Antenna Theory and Design, 2nd Ed.”
! Matlab programming may be needed.
! Contents
" Electromagnetics and Antenna Fundamentals
" Simple Antennas
" Arrays
" Resonant Antennas
" Broadband Antennas
" Aperture Antennas
" Antenna Synthesis
" Numerical Techniques
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Overview of Antennas! Antenna performance parameters
" Radiation pattern: Angular variation of
radiation power or field strength around the
antenna, including: directive, single or multiple
narrow beams, omnidirectional, shaped main
beam.
" Directivity : ratio of power density in the
direction of the pattern maximum to the
average power density at the same distance
from the antenna.
" Gain : Directivity reduced by the losses on
the antenna.
" Polarization: The direction of electric fields.
- Linear
- Circular
- Elliptical
" Impedance
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" Bandwidth
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! Antenna types
" Electrically small antennas: The extent of the
antenna structure is much less than a
wavelength.
- Properties
# very low directivity
# Low input resistance
# High input reactance
# Low radiation efficiency
- Examples
# Short dipole
# Small loop
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" Resonant antennas: The antenna operates well
as a single of selected narrow frequency bands.
- Properties
# Low to moderate gain
# Real input impedance
# Narrow bandwidth
- Examples
# Half wave dipole
# Microstrip patch
# Yagi
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" Broadband antennas:
- Properties
# Low to moderate gain
# Constant gain
# Real input impedance
# Wide bandwidth
- Examples
# Spiral
# Log periodic dipole array
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" Aperture antennas: has a physical aperture
(opening) through which waves flow.
- Properties
# High gain
# Gain increases with frequency
# Moderate bandwidth
- Examples
# Horn
# Reflector
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James Clerk Maxwell 1831-1879
Maxwell Equations
! Important Laws in
Electromagnetics
" Coulomb’s Law
" Gauss’s Law
" Ampere’s Law
" Ohm’s Law
" Kirchhoff’s Law
" Biot-Savart Law
" Faradays’ Law
! Maxwell Equations (1873)
: electric field intensity.: electric flux density: magnetic field intensity
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: magnetic flux density: electric current density: magnetic current density
: electric charge density: magnetic charge density
: permittivity: permeability
! Constituent Relationship
! Continuity Equations
! Boundary Conditions
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! Time-Harmonic Fields
Time-harmonic:
: a real function in both space and time.: a real function in space.
: a complex function in space. A phaser.
Thus, all derivative of time becomes.
For a partial deferential equation, all derivative of timecan be replace with , and all time dependence of can be removed and becomes a partial deferentialequation of space only.
Representing all field quantities as
,then the original Maxwell’s equation becomes
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! Power Relationship
! Poynting vector:
! Solution of Maxwell’s EquationsNote all the field and source quantities are functions ofspace only. The wave equations of potentials becomes
,
where is called the wave number. The aboveequations are called nonhomogeneous Helmholtz’sequations. The Lorentz condition becomes
Also
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The wave functions for electric and magnetic fields insource free region becomes
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The Ideal Dipole
Purpose: Investigate the fundamental properties of anantenna.
Short Dipole:
Therefore
Since
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We have
.
And
As or , then
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E-plane pattern: plane containing E-fields.H-plane pattern: plane containing H-fields.Radiated power,
To sum up, at far field1. Spherical TEM waves.2. Wave impedance equal the intrinsic impedance
.
3. Real power flow.
Radiation from Line Currents
For a general straight line source located at origin,.
At far field, and , thus
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.
Since,
At neglecting high order terms of ,
Similarly,
and.
Far Field Conditions
To sum up:
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1. At fixed frequency, .
2. At fixed antenna size,
3. At various frequency and antenna size scaled,
Example 1-1
Radiation Pattern DefinitionsNormalized field pattern:
Power pattern:
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In dB scale
ExamplesIdeal 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:
Example 1-2 Directivity of an Ideal Dipole
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or
Example 1-3 Directivity of a Sector OmnidirectionalPattern
Power Gain (Gain)
or
Radiation efficiency:
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Referenced Gain:
dBi: referenced to isotropic antenna.dBd: referenced to dipole antenna.
Antenna Impedance
Ideal dipole:
When the conductor is thicker than skin depth
where
Considering the effect of continuity at the end of thedipole, use triangular current distribution
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Example 1-4: Radiation Efficiency of an AM Car RadioAntenna.
Radius Dipole Length Frequency 1 MHz.
For short dipole,
Example 1-5: Input Reactance of an AM Car RadioAntenna of Example 1-4.
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Polarization
Cases1. Linear polarization: 2. Circular polarization:
3. Others: Ellipse.
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Half-wave Dipole
Image Theory
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Monopole
Small Loop Antenna
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Duality: due to symmetry of Maxwell’s Eqs.
For a magnetic dipole
Ferrite rod antenna:
Inductance:Small circular loop of radius b for :
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Small rectangular loop of :
Example 2-1: A Small Circular Loop AntennaLoop circumference Wire radius Frequency
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Antenna in Communication Systems
Open circuit voltage: for ideal dipole receivingantenna and polarization match.
When
Maximum power transfer:
Power density:
Maximum effective aperture
For an ideal dipole
In general, or
Effective aperture: Available power:
In general,
Aperture efficiency: , where is the physical
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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 radiatedpowerERP: effective radiated power by a half-dipole
Example 2-3: Direct Broadcast Satellite ReceptionReceiving disk antenna: size 0.46 m in diameter,
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Arrays• Phased array: electronic scan. Radars, smart
antennas.• Active array: each antenna element is powered
individually.• Passive array: all antenna elements are powered by
one source.Array type by positioning:1. Linear arrays,2. Planar arrays,3. Conformal arrays.
Examples
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Array Factor
In general the radiation pattern is
where is the excitation current of n-th antenna, thelocation vector, and the field pattern.If all antenna elements are the same
AF is called array factor. It is determine only by twoparameters: the excitations and the locations of theantennas.
Equal Space Linear Array
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If the excitation has a linear phase progression, i.e.
Then
where .
If the amplitude of the excitation is the same, that is,
then
Neglecting the phase factor,
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Normalized AF: .
Maximum at Main beam at . This is the scanning effect.
Broadside: Endfire:
Summary:• N increases as the main lobe beamwidth decreases.• Number of side lobes: N-2.• Number of nulls: N-1.• Side lobe width: . Main lobe width: .• Side lobe peaks decrease with increasing N.• is symmetric about .
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BWFN of Broadside Array ( )First null occurs when , or
Then, for long array
Similarly, half power beamwidth near
broadside.
BWFN of Endfire ArrayFirst null occurs when , or
Similarly, half power beamwidth
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Example 3-5 Four-Element Linear ArrayParameters: , ,
Main beam
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Single Mainbeam Oridinary Endfire ArrayOridinary Endfire: main beam at exactly or .Range of : Half-width of a grating lobe:
Choose to eliminate most of the grating lobe,
or
Example 3-6 Five-Element Ordinary Endfire LinearArrayParameters:
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Hansen-Woodyard Endfire Array
Purpose: increase directivity by increasing to reducethe visible region of the main beam.Choose to reduce main beam width.Choose to prevent back lobe to becomelarger than main lobe.Maximum directivity for large array: .
Simpler Formula for :
Example 3-7 Five-Element Hansen-Woodyard EndfireLinear ArrayParameters: ,
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Pattern Multiplication
Example 3-8 Two-Collinear, Half-Wavelength SpacedShort Dipoles
Parameters:
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Example 3-9 Two Parallel, Half-Wavelength SpacedShort Dipoles
Since
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Directivity of Uniformly Excited, Equal SpacedLinear Arrays
For and ,
For broadside, isotropic array, for .
For ordinary endfire, isotropic array, for .
For Hansen-Woodyard endfire, isotropic array
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Directivity as a function of scan anglesCombining element pattern:
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Nonuniformly Excited, Equally Spaced LinearArrays
Let , then the array factor
is a polynomial of 1. Binomial distribution:
Properties: no sidelobe, broader beam width, lowerdirectivity.2. Dolph-Chebyshev distribution:
Properties: equal sidelobe levels, narrower beamwidth, higher directivity. Sidelobe level can bespecified.
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General expression of directivity of non-equal spacedand non-uniform excitation:
where is the current amplitude of k-th element, theposition, and .For equal space, broadside array, , , we have
Furthermore, if , we have
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Issue of Array
1. Mutual Couplinga. Effect impedancesb. Effect radiation patternsc. Scan Blindness
2. Feed networka. Increase lossb. Effect bandwidthc. Increase space
Feed Network
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2-Dimensional Equal Space Progressive PhaseArrays
From the general equation,
where
Thus,
where
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