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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
Antennas 2
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
Antennas 3
! 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
Antennas 4
" 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
Antennas 5
" Broadband antennas:
- Properties
# Low to moderate gain
# Constant gain
# Real input impedance
# Wide bandwidth
- Examples
# Spiral
# Log periodic dipole array
Antennas 6
" Aperture antennas: Has a phsical aperture
(opening) through which waves flow.
- Properties
# High gain
# Gain increases with frequency
# Moderate bandwidth
- Examples
# Horn
# Reflector
Antennas 7
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
Antennas 8
: electric flux density: electric current density: magnetic flux density: electric charge density: magnetic charge density
: permittivity: permeability
! Constituent Relationship
! Continuity Equations
! Boundary Conditions
Antennas 9
! 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
Antennas 10
! 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
Antennas 11
The wave functions for electric and magnetic fields insource free region becomes
Antennas 12
The Ideal Dipole
Purpose: Investigate the fundamental properties of anantenna.
dBi: referenced to isotropic antenna.dBd: referenced to dipole antenna.
Antenna Impedance
Ideal dipole:
When the conductor is thinker than skin depth
where
Antennas 20
Considering the effect of continuity at the end of thedipole, use triangular current distribution
Example 1-4
For short dipole,
Example 1-5
Antennas 21
Polarization
Cases1. Linear polarization:
2. Circular polarization:
3. Others: Ellipse.
Antennas 22
Half-wave Dipole
Monopole
Antennas 23
Small Loop Antenna
Duality: due to symmetry of Maxwell’s Eqs.
Antennas 24
For a magnetic dipole
Example 2-1
Antennas 25
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:
Antennas 26
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
Antennas 27
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
Antennas 28
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 .
Antennas 29
If the amplitude of the excitation is the same, that is,