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Antennas

Theory, characteristics, and implementations

Chris Allen (callen@eecs.ku.edu)

Course website URL people.eecs.ku.edu/~callen/823/EECS823.htm

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TopicsRole of antennasTheoryAntenna typesCharacteristics

– Radiation pattern – beamwidth, pattern solid angle– Directivity, gain, effective area– Bandwidth

Friis’ transmission formulaImplementations

– Dipole, monopole, and ground planes– Horn– Parabolic reflector– Arrays

Terminology

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The role of antennasAntennas serve four primary functions• Spatial filter

directionally-dependent sensitivity

• Polarization filterpolarization-dependent sensitivity

• Impedance transformertransition between free space and transmission line

• Propagation mode adapterfrom free-space fields to guided waves

(e.g., transmission line, waveguide)

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Spatial filterAntennas have the property of being more sensitive in one direction than in another which provides the ability to spatially filter signals from its environment.

Directive antenna. Radiation pattern of directive antenna.

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Polarization filter

Dipole antenna

Incident E-field vector

z

xy

0EzE V = h E0

+_

EhV

hzh

Incident E-field vector

0EyE

z

xy

V = 0+_

Dipole antenna

EhV

hzh

Antennas have the property of being more sensitive to one polarization than another which provides the ability to filter signals based on its polarization.

In this example, h is the antenna’s effective height whose units are expressed in meters.

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Impedance transformerIntrinsic impedance of free-space, E/H

Characteristic impedance of transmission line, V/I

A typical value for Z0 is 50 .

Clearly there is an impedance mismatch that must be addressed by the antenna.

7.376

120000

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Propagation mode adapterIn free space the waves spherically expand following Huygens principle:each point of an advancingwave front is in fact thecenter of a fresh disturbanceand the source of a new train of waves.

Within the sensor, the waves are guided within a transmission line or waveguide that restricts propagation to one axis.

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Propagation mode adapterDuring both transmission and receive operations the antenna must provide the transition between these two propagation modes.

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Antenna typesAntennas come in a wide variety of sizes and shapes

Horn antenna Parabolic reflector antennaHelical antenna

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TheoryAntennas include wire and aperture types.Wire types include dipoles, monopoles, loops, rods, stubs, helicies, Yagi-Udas, spirals.Aperture types include horns, reflectors, parabolic, lenses.

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TheoryIn wire-type antennas the radiation characteristics are determined by the current distribution which produces the local magnetic field.

Helical antennaYagi-Uda antenna

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Theory – wire antenna example

Some simplifying approximations can be made to take advantage the far-field conditions.

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Theory – wire antenna exampleOnce E and E are known, the radiation characteristics can be determined.Defining the directional function f () from

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Theory – aperture antennasIn aperture-type antennas the radiation characteristics are determined by the field distribution across the aperture.

Horn antenna Parabolic reflector antenna

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Theory – aperture antenna example

Where Sr is the radial component of the power density, S0 is the maximum value of Sr, and Fn is the normalized version of the radiation pattern F()

The far-field radiation pattern can be found from the Fourier transform of the near-field pattern.

zyzx

D4

77.00

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TheoryReciprocityIf an emf is applied to the terminals of antenna A and the current measured at the terminals of another antenna B, then an equal current (both in amplitude and phase) will be obtained at the terminals of antenna A if the same emf is applied to the terminals of antenna B.

emf: electromotive force, i.e., voltage

Result – the radiation pattern of an antenna is the same regardless of whether it is used to transmit or receive a signal.

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Three-dimensional representation of the radiation pattern of a dipole antenna

Characteristics

Radiation patternRadiation pattern – variation of the field intensity of an antenna as an angular function with respect to the axis

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Characteristics

Radiation patternSpherical coordinate system

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Characteristics

Radiation pattern

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Characteristics

Radiation pattern

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Characteristics

Radiation pattern

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Characteristics

Radiation pattern

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Characteristics

Radiation pattern

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Characteristics

Beamwidth and beam solid angle

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np d,F

The beam or pattern solid angle, p [steradians or sr] is defined as

where d is the elemental solid angle given by ddsind

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Characteristics

Directivity, gain, effective area Directivity – the ratio of the radiation intensity in a given direction from the antenna to the radiation intensity averaged over all directions.

[unitless]

Maximum directivity, Do, found in the direction (, ) where Fn= 1

Given Do, D can be found

and or

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Characteristics

Directivity, gain, effective area

t

ol P

P

olo DG

Gain – ratio of the power at the input of a loss-free isotropic antenna to the power supplied to the input of the given antenna to produce, in a given direction, the same field strength at the same distance

Of the total power Pt supplied to the antenna, a part Po is radiated out into space

and the remainder Pl is dissipated as heat in the antenna structure. The

radiation efficiency l is defined as the ratio of Po to Pt

Therefore gain, G, is related to directivity, D, as

And maximum gain, Go, is related to maximum directivity, Do, as

,, DG l

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Characteristics

Directivity, gain, effective area

paeff AAD

220

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yzxzpeffA

22

yyz l

Effective area – the functional equivalent area from which an antenna directed toward the source of the received signal gathers or absorbs the energy of an incident electromagnetic wave

It can be shown that the maximum directivity Do of an antenna is related to an

effective area (or effective aperture) Aeff, by

where Ap is the physical aperture of the antenna and a = Aeff / Ap is the aperture

efficiency (0 ≤ a ≤ 1)

Consequently

For a rectangular aperture with dimensions lx and ly in the x- and y-axes, and

an aperture efficiency a = 1, we get

xxz l

[m2]

[rad] [rad]

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Characteristics

Directivity, gain, effective area Therefore the maximum gain and the effective area can be used interchangeably by assuming a value for the radiation efficiency (e.g., l = 1)

zyzxeffAG

4420

effl AG 20

4

4

2

0GAeff

Example: For a 30-cm x 10-cm aperture, f = 10 GHz ( = 3 cm)

xz 0.1 radian or 5.7°, yz 0.3 radian or 17.2°

G0 419 or 26 dBi

(dBi: dB relative to an isotropic radiator)

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Characteristics

BandwidthThe antenna’s bandwidth is the range of operating frequencies over which the antenna meets the operational requirements, including:

– Spatial properties (radiation characteristics)– Polarization properties– Impedance properties– Propagation mode properties

Most antenna technologies can support operation over a frequency range that is 5 to 10% of the central frequency

(e.g., 100 MHz bandwidth at 2 GHz)

To achieve wideband operation requires specialized antenna technologies

(e.g., Vivaldi, bowtie, spiral)

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Friis’ transmission formulaAt a fixed distance R from the transmitting antenna, the power intercepted by the receiving antenna with effective aperture Ar is

where Sr is the received power density (W/m2), and Gt is the peak gain of the transmitting antenna.

rtt

rri AGR

PASP

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Friis’ transmission formulaIf the radiation efficiency of the receiving antenna is r, then the power received at the receiving antenna’s output terminals is

Therefore we can write

which is known as Friis’ transmission formula

rrtt

irr AGR

PPP

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22

2

4 R

AAGG

RP

P rtrtrt

t

r

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Friis’ transmission formulaas Friis’ transmission formula can be rewritten to explicitly represent the free-space transmission loss, LFS

which represents the propagation loss experienced in transmission between two lossless isotropic antennas.With this definition, the Friis formula becomes

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R

LFS

FS

rt

t

r

L

GG

P

P

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Friis’ transmission formulaFinally, a general form of the Friis’ transmission formula can be written that does not assume the antennas are oriented to achieve maximum power transfer

where (t, t) is the direction of the receiving antenna in the transmitting antenna coordinates, and vice versa for (r, r).

An additional term could be included to represent a polarization mismatch between the transmit and receive antennas.

rrrtttt

r GGRP

P

,,4

2

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ImplementationDipole, monopole, and ground planes

Horns

Parabolic reflectors

Arrays

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Implementation

Dipole, monopole, and ground planeFor a center-fed, half-wave dipole oriented parallel to the z axis

2

2

20

sin

cos2

cos15

r

ISr

Tuned half-wave dipole antenna

(V/m)rkj0 e

sin

cos2

cos

r

I60jE

(W/m2)

dB15.264.1D0

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2

2

nn sin

cos2

cosF,F

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Dipole antennas

Versions of broadband dipole antennas

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Dipole antennas

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Monopole antenna

Groundplane

Mirroring principle creates image of monopole, transforming it into a dipole

Radition pattern of vertical monopole above ground of (A) perfect and (B) average conductivity

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Ground planeA ground plane will produce an image of nearby currents. The image will have a phase shift of 180° with respect to the original current. Therefore as the current element is placed close to the surface, the induced image current will effectively cancel the radiating fields from the current.

The ground plane may be any conducting surface including a metal sheet, a water surface, or the ground (soil, pavement, rock).

Horizontal current element

Current element image

Conducting surface(ground plane)

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Implementation

Horn antennas

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Implementation

Horn antennas

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Implementation

Parabolic reflector antennasCircular aperture with uniform illumination. Aperture radius = a.Ap = a

2

qa

qaJe

r

AEjqE rkjp

2

22 10

2

10 2

22

qa

qaJSqSr

where sinq

where 22

220

0 20

r

AESS p

r

J1( ) is the Bessel function of the first kind, zero order

20

4

pAD

a221

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Antenna array composed of several similar radiating elements (e.g., dipoles or horns).

Element spacing and the relative amplitudes and phases of the element excitation determine the array’s radiative properties.

Implementation

Antenna arrays

Linear array examples

Two-dimensional array of microstrip patch antennas

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Implementation

Antenna arraysThe far-field radiation characteristics Sr(, ) of an N-element array

composed of identical radiating elements can be expressed as a product of two functions:

Where Fa(, ) is the array factor, and Se(, ) is the power directional pattern

of an individual element.

This relationship is known as the pattern multiplication principle.

The array factor, Fa(, ), is a range-dependent function and is therefore

determined by the array’s geometry.

The elemental pattern, Se(, ), depends on the range-independent far-field

radiation pattern of the individual element. (Element-to-element coupling is ignored here.)

,S,F,S ear

2

1

0

N

i

rkjia

ieA,F

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Implementation

Antenna arraysIn the array factor, Ai is the feeding coefficient representing the

complex excitation of each individual element in terms of the

amplitude, ai, and the phase factor, i, as

and ri is the range to the distant observation point.

ijii eaA

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Implementation

Antenna arraysFor a linear array with equal spacing d between adjacent elements, which approximates to

For this case, the array factor becomes

Note that the e-jkR term which is common to all of the summation terms can be neglected as it evaluates to 1.

2

1N

0i

cosdkijjiaa eeaF,F i

cosdiRri

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Implementation

Antenna arraysBy adjusting the amplitude and phase of each elements excitation, the beam characteristics can be modified.

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Implementation

Antenna arrays

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Implementation

Antenna arrays

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ImplementationExample: 2-element array

Isotropic radiators

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ImplementationExample: 2-element array

Isotropic radiators

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ImplementationExample: 2-element array

Half-wave dipole radiators

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ImplementationExample: 2-element array

Half-wave dipole radiators

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ImplementationExample: 6-element array

Half-wave dipole radiators

grating lobes

d ≥ produces two grating lobes

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Antenna arraysBeam steering effects

Inter-element separation affects linear array gain and grating lobes

• The broadside array gain is approximately

where d is the inter-element spacing and N is the number of elements in the linear array

• To avoid grating lobes, the maximum inter-element spacing varies with beam steering angle or look angle, , as

5~Nfor,GdN2

G elementarray

sin1

dmax

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Antenna arraysBeamwidth and gain

An 2-D planar array with uniform spacing, N x M elements in the two dimensions with inter-element spacing of /2 provides a broadside array gain of approximately

The beamwidth of a steered beam from a uniform N-element array is approximately (for N > ~5)

where b is the window function broadening factor (b = 1 for uniform window function) andd is the inter-element spacing

5M,Nfor,GMNG elementarray

1800forradians,dN

b

sin

866.0

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ConclusionsAntennas play an important role in microwave

remote sensing systems.

There are both art and science aspects to antennas.

Antenna arrays enable the radiation characteristics to be changed electronically (i.e., very rapidly) unlike conventional mechanically-steered antennas.

Digital beamforming (dedicated transmit or receive electronics for each element) enable simultaneous realization of multiple antenna beams and/or multiple independent signals.

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TerminologyAntenna – structure or device used to collect or radiate electromagnetic waves

Array – assembly of antenna elements with dimensions, spacing, and illumination sequency such that the fields of the individual elements combine to produce a maximum intensity in a particular direction and minimum intensities in other directions

Beamwidth – the angle between the half-power (3-dB) points of the main lobe, when referenced to the peak effective radiated power of the main lobe

Directivity – the ratio of the radiation intensity in a given direction from the antenna to the radiation intensity averaged over all directions

Effective area – the functional equivalent area from which an antenna directed toward the source of the received signal gathers or absorbs the energy of an incident electromagnetic wave

Efficiency – ratio of the total radiated power to the total input power

Far field – region where wavefront is considered planar

Gain – ratio of the power at the input of a loss-free isotropic antenna to the power supplied to the input of the given antenna to produce, in a given direction, the same field strength at the same distance

Isotropic – radiates equally in all directions

Main lobe – the lobe containing the maximum power

Null – a zone in which the effective radiated power is at a minimum relative to the maximum effective radiation power of the main lobe

Radiation pattern – variation of the field intensity of an antenna as an angular function with respect to the axis

Radiation resistance – resistance that, if inserted in place of the antenna, would consume that same amount of power that is radiated by the antenna

Side lobe – a lobe in any direction other than the main lobe