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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, 2 nd 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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### Transcript of Antennas 1 Antennas - cag.dat.demokritos.gr

I:\cgu\Antenna\antenna.wpd! Textbook: Warren L. Stutzman and Gary A.
Thiele, “Antenna Theory and Design, 2nd Ed.”
! Matlab programming may be needed.
! Contents
radiation power or field strength around the
antenna, including: directive, single or
multiple narrow beams, omnidirectional,
from the antenna.
the antenna.
- Linear
- Circular
- Elliptical
" Impedance
" Bandwidth
wavelength.
- Properties
as a single of selectd narrow frequency bands.
- Properties
(opening) through which waves flow.
- Properties
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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. A phaser.
Thus, all derivative of time becomes .
For a partial deferential equation, all derivative of time can be replace with , and all time dependence of can be removed and becomes a partial deferential equation of space only.
Representing all field quantities as
, then the original Maxwell’s equation becomes
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! Power Relationship
! Poynting vector:
,
where is called the wave number. The above equations are called nonhomogeneous Helmholtz’s equations. The Lorentz condition becomes
Also
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The wave functions for electric and magnetic fields in source free region becomes
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Short Dipole:
E-plane pattern: plane containing E-fields. H-plane pattern: plane containing H-fields. Radiated power,
.
.
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Similarly,
and
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3. At various frequency and antenna size scaled,
Example 1-1
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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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dBi: referenced to isotropic antenna. dBd: referenced to dipole antenna.
Antenna Impedance
Ideal dipole:
where
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Considering the effect of continuity at the end of the dipole, use triangular current distribution
Example 1-4
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Maximum power transfer:
aperture size.
Power delivered to the load : polarization mismatch factor, : impedance mismatch factor,
In dB form or
EIRP: effective (equivalent) isotropically radiated power ERP: 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 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.
Array Factor
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In general the radiation pattern is
where is the excitation current of n-th antenna, the location vector, and the field pattern. If all antenna elements are the same
AF is called array factor. It is determine only by two parameters: the excitations and the locations of the antennas.
Equal Space Linear Array
Then
where .
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If the amplitude of the excitation is the same, that is ,
then
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Then, for long array
Similarly, half power beamwidth
Main beam
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Single Mainbeam Oridinary Endfire Array Oridinary Endfire: main beam at exactly or . Range of :
Half-width of a grating lobe:
Choose to eliminate most of the grating
lobe, or
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Hansen-Woodyard Endfire Array
Purpose: increase directivity by increasing to reduce the visible region of the main beam. Formula:
Example 3-7 Five-Element Hansen-Woodyard Endfire Linear Array Parameters:
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Pattern Multiplication
Parameters:
Since
For and ,
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Combining element pattern:
Let , then the array factor
is a polynomial of 1. Binomial distribution:
Properties: no sidelobe, broader beam width, lower directivity. 2. Dolph-Chebyshev distribution:
Properties: equal sidelobe levels, narrower beam width, higher directivity. Sidelobe level can be specified.
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General expression of directivity of non-equal spaced and non-uniform excitation:
where is the current amplitude of k-th element, the position, and . For equal space, broadside array, , , we have
Furthermore, if , we have
Issue of Array
1. Mutual Coupling a. Effect impedances b. Effect radiation patterns c. Scan Blindness
2. Feed network a. Increase loss b. Effect bandwidth c. Increase space
Feed Network
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From the general equation,