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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