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Antennas 1
Antennas
! Grading policy.
" Weekly Homework 40%
" Midterm exam, final exam 30% each.
! Office hour: 2:10 ~ 3:00 pm, Thursday.
! 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
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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 : ration 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
" 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 weel
as a single of selectd 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 phsical 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 density.: electric flux density: magnetic field density
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: electric flux density: electric current density: magnetic flux 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. Aphaser.
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:1. At fixed frequency, .
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2. At fixed antenna size,
3. At various frequency and antenna size scaled,
Example 1-1
Radiation Pattern Definitions
Normalized field pattern:
Power pattern: In dB scale
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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 1-2Example 1-3
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Power Gain (Gain)
or
Radiation efficiency:
Referenced Gain:
dBi: referenced to isotropic antenna.dBd: referenced to dipole antenna.
Antenna Impedance
Ideal dipole:
When the conductor is thinker than skin depth
where
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Considering the effect of continuity at the end of thedipole, use triangular current distribution
Example 1-4
For short dipole,
Example 1-5
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Polarization
Cases1. Linear polarization:
2. Circular polarization:
3. Others: Ellipse.
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Half-wave Dipole
Monopole
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Small Loop Antenna
Duality: due to symmetry of Maxwell’s Eqs.
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For a magnetic dipole
Example 2-1
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Antenna in Communication Systems
For ideal dipole receiving antenna andpolarization match.When
Maximum power transfer:
Power density:
Maximum effective aperture
For a dipole
In general, or
Effective aperture:
Available power:
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In general,
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 radiatedpowerERP: effective radiated power by a half-dipole
Example 2-3
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Arrays
Phased array: electronic scan. Radars, smart antennas.Active array: each antenna element is poweredindividually.Passive array: all antenna elements are powered by onesource.
Array type by positioning:1. Linear arrays,2. Planar arrays,3. Conformal arrays.
Array Factor
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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
If the excitation has a linear phase progression, i.e.
Then
where .
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If the amplitude of the excitation is the same, that is,
then
Neglecting the phase factor,
Normalized AF: .
Maximum at
Main beam at . This is the scanning effect.
Broadside: Endfire:
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homework #1 1.7-4,1.8-7,1.8-10,1.9-4, 3/5homework #2 1.10-1, 2.2-5,2.5-13
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BWFN of Broadside ArrayFirst null occurs when , or
Then, for long array
Similar\y, 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.Formula:
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 boradside, isotropic array
For ordinary endfire, isotropic array
For Hansen-Woodyard endfire, isotropic array
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Directivity as a function of scan angles
Combining 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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