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 : 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

" 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

! 5 dB or less

" Electrically small antennas

" Loops

" Dipoles/monopoles

! 5 dB to 8 dB

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" Microstrip Patches

" Planar frequency-independent antennas (e. g.

Spirals)

! 8 dB to 15 dB

" Yagi-Uda

" Helix (axial mode)

" Log periodic dipole array

! 15 dB and more

" Aperture antennas (Horns, Reflectors)

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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. 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

E-plane pattern: plane containing E-fields.H-plane pattern: plane containing H-fields.Radiated power,

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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

.

Since,

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At neglecting high order terms of ,

Similarly,

and

.

Far Field Conditions

To sum up:1. At fixed frequency, .

2. At fixed antenna size,

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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 1-2 Directivity of an Ideal Dipole

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or

Example 1-3 Directivity of a Sector OmnidirectionalPattern

Power Gain (Gain)

or

Radiation efficiency:

Referenced Gain:

dBi: referenced to isotropic antenna.

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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 :

Small rectangular loop of :

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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 dipolereceiving antenna 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, the

location 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 Array

Parameters: ,

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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, the

position, 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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