Antennas for Wireless Communications

– Basic Principles and System Applications

Warren Stutzman and Bill DavisVirginia Tech Antenna Group

June 9, 2006antenna.ece.vt.edu

OUTLINE1. Introduction Stutzman

2. Antenna Fundamentals Davis

3. Antenna Elements Davis

4. Array Antennas Stutzman

break

5. System Considerations Davis

6. Wireless Applications Both

7. Photo presentation Stutzman

1. INTRODUCTION

• The Speakers• Self Introductions of Class• Wireless versus Wireline• History of Communications• The Spectrum• Antenna Performance Parameters

Warren Stutzman

• Professor at VT for 37 years• Fellow of the IEEE• Past President of IEEE Ant

& Prop. Society• Distinguished alumnus of U

of Illinois• Founder of Virginia Tech

Antenna Group• Served as ECE Dept Head

twice

Bill Davis

• Professor at VT for 28 years

• Director of Virginia Tech Antenna Group

• Past Commission Chair –USNC/URSI Commission A

• URSI Meetings Coordinator• Vice Chair 2005 IEEE

APS/URSI Symposium

Wireless versus Wireline

• Fields of Application– Communications– Sensing and Imaging

• Active – Radar• Passive – Radiometry

– Industrial• Control Ex.: garage door opener• Medical• Heating, cooking, drying, ...

• Communications– Antennas must be used for:

• Mobile communications• Very long distances

– Space– Remote terrestrial locations

– Antennas are preferred for • Broadcast and point-to-multipoint comm.• Long distance communications• Thin routes• Portable and personal communications

– The physics of wireless vs. wireline• Loss in wireline is (e-αr)2• Loss in wireless is 1/r2

ReferencesW. Stutzman and G. Thiele, “Antenna Theory and Design,” 2e, Wiley, 1998.T. Rappaport, “Wireless Communications: Principles and Practice,”

Prentice-Hall, 1996.K. Siwiak, “Radiowave Propagation and Antennas for Personal

Communications,” Sec. Ed., Artech House, 1998.

The History of CommunicationsPre-modern civilization

Optical communications: Smoke signals, flags, ....Acoustical communications: Drums

[note – all are forms of digital communications]1844

Telegraph (Morse)1864

Maxwell’s equations – principles of radio waves1876

Telephone (Bell)1887

First antenna (Hertz)1897

First radio systems (Marconi, Popov)

1901

First transatlantic radio (Marconi)

World War II

Development of radar

1960

Fiber optics

1980s

Wireless reinvented

Wireless RadioWireless

⎥ ⎥⎥ ⎥1900 2000

The Spectrum

• Wavelength λ (m) = 300 / f(MHz) λ (cm) = 30 / f(GHz)

• Frequency bands

1 mm1 cm 30 GHz3 GHzSHF

10 cm1 m3 GHz300 MHzUHF

1 m10 m300 MHz30 MHzVHF

10 m100 m30 MHz3 MHzHF

100 m1 km3 MHz300 kHzMF

1 km10 km300 kHz30 kHzLF

10 km100 km30 kHz3 KHzVLF

Wavelengths

FrequenciesBand

Antenna Performance Parameters

• Radiation pattern F(θ,φ)The angular variation of radiation around an antenna

Pattern types:Directive (narrow main beam)OmnidirectionalShaped beamLow side lobe

• Directivity DRatio of power density in the direction of pattern maximum to the Average power density at the same distance from the antenna;i.e. how much more focused the power is than if isotropicallydistributed.

• Gain GDirectivity reduced by losses on the antenna

• PolarizationThe figure traced out with time by the instantaneous electricfield vector.

Types:Linear, circular, elliptical, dual (for diversity and reuse)

• ImpedanceInput impedance at the antenna terminals

• BandwidthRange of operating frequencies for which performance parameters are acceptable.

• ScanningMovement of the radiation pattern in angular spaceTypes: electronic, mechanical, hybrid

• MechanicalSize, weight, RCS, aerodynamics

• Cost

2. ANTENNA FUNDAMENTALS

• What is an antenna?• Connecting to the antenna• Basic properties

– Impedance– Gain– Pattern– Polarization

• Fundamental Limits

What is an antenna?

• Collection of metal/material objects– Wire– Plates (reflector, dish)– EM Bandgap Materials …

• Absence of metal– Slots– Waveguide apertures

Transformation from Electronics to Space

Determining the Radiation

• Start with the current (assume)– Wire: Approximate sinusoid/traveling wave

– Plate: Physical Optics approximation or image current

• Giving for example (dipole):

)()()cos(ˆ),( yxzIzrJ δδβω =rr

To the Fields

Current

Vector Potential

∫ •−

=V

rrjrj

dverJr

erA ')'(

4)( 'ˆ

rrrrr ββ

πμ

HErr

,

The Fields (far field)

• Electric Field

• Magnetic Field

)ˆ(1

ArjHrr

×−= βμ

)ˆ(ˆ rArAjHrE −−=×−=rrr

ωη

Far-Field Conditions

• Wavelength

• Distance

• Size

λ>>r

Drr =>> )'max(

16

2 2 λλ

<⇒> phaseD

r

Far Field

Projection ~ replace distance

Antenna

Observation

Distance

Diameter D

Example – Short Dipole

• Current

• Vector Potential

• Magnetic Field

• Electric Field

• Poynting Vector

)(ˆ~ rIzJ z

rrδΔ

z

rj

Izr

eA Δ=

−

ˆ4π

μβr

φθπ

ββ

ˆsin4 z

rj

Ir

ejH Δ=

−r

θθηπ

ββ

ˆsin4 z

rj

Ir

ejE Δ=

−r

πηβ

θπ

ηβ

12

sin16

ˆ2

1

2

1

22

2

222

22

2*

z

z

IP

r

IrHES

Δ=

Δ=×=

rrr

Radiation Resistance – Short Dipole

• EQUATE– Input Power &

Radiation Power

22

2

240

321 λ

πλ

ηπ zzradrad

I

PR

Δ≈

Δ⇒=

Radiation Pattern

• Variation of Fields with Elevation (θ) and Azimuth (φ)

• Variations:– Spherical– E-plane & H-plane (or Elevation & Azimuth)– Conical

dipoleshort for ,sinmax

),(),(

,

θϕθ

ϕθϕθ

==E

EF

Patterns

0.5

1

30

210

60

240

90

270

120

300

150

330

180 0

y = 0 or φ = 0° Cut

θ

0.5

1

30

210

60

240

90

270

120

300

150

330

180 0

x = 0 or φ = 90° Cut

θ

Linear, Principal-Plane Cuts

0.5

1

30

210

60

240

90

270

120

300

150

330

180 0

z = 0 or θ = 90° Cut

φ

Half-Power Beamwidth

Efficiency

• Loss

– Radiation Resistance

• Mismatch

• Total

lossrad

rad

RR

Re

+==

InputPower

RadiatedPower

dsRJI

R surface

S

Sloss

2

2

1∫=r

Real ,4

12

2

o

oAnt

Anto ZZZ

RZq

+=Γ−=

qeEfficiency =

Directivity & Directive Gain

∫ Ω==

φθ

φθπφθ

,

2

2

2

2

),(

4

)(),(

dF

F

FAverage

FD

)],(max[ φθDD =

A

DΩ

=π4

Angle Solid Beam,

2 =Ω=Ω ∫φθ

dFA

Directivity

θ

dΩ = sin θ dθ dφ

sin θ dφ

dθ

(a) Actual pattern (b)

UmUm

ΩA

Figure 1-17

Element of solid angle dΩ.

Figure 1-18

Antenna beam solid angle ΩA.

Open Circuit Voltage& Effective Length

• Open Circuit Voltage

• Effective Length

EhVOCrr

•−= *

Irej

E

dverJI

rrh

rjrad

Ant

rrj

)4/(

')'(1

ˆˆ),( 'ˆ

πωμ

φθ

β

β

−

•

−=

××−= ∫r

rrr r

Polarization

• Linear, Circular, Elliptical

• Polarization Factor

)cos(ˆcosˆ 21 δωω ++= tEytExE

222/ EhEhp

rrrr•=

-180° -135° -90° -45° 0° +45° +90° +135° +180°

Right-handed Left-handed

Counter-clockwise

Clockwise

0

1

2

1

2

∞

E

E2

1

jwt j( t + )ˆ ˆ ˆ ˆ = E + E = E e + E e ω δx y 1 2E x y x y

Figure 2-37 Polarization ellipses as a function of the ratio E2/E1 and phase angle δwith wave approaching. Clockwise rotation of the resultant E corresponds toleft-handed polarization (IEEE definition) while counterclockwise correspondsto right-handed polarization.

Gain & Realized Gain

• Gain

• Realized Gain

• Partial Realized Gain

eDG =qeDGR =

pqeDpGg RR ==

A Communication Link

• Friis’ Trans. Formula2

2

)4( R

GGPP RTXmitRcv π

λ=

Effective Area

),(4

),(2

φθπλφθ RR GA =

24 R

AGPP RTXmitRcv π

=

To Give

Transient Link

t

ti

c

Rth

Rthv trOC ∂

∂∗⎟⎠⎞

⎜⎝⎛ −⎟

⎠⎞

⎜⎝⎛•=

∗ )(

4)(

rr

πμ

Connections

• Connectors (coax, twin-lead)• Balanced vs Unbalanced

– Balun

• Feed Network (Arrays)– Phased– True Time-Delay

• Filtering & Impedance Transformation– Circuit & loading– Tapering

Properties

• Impedance– Treat as a circuit

element– By Reciprocity:

– Induced EMF Z

XmitRcv ZZ =

∫ Ω•=Ant

dJEJI

Z )(1

2

rrr

Properties

• Patterns

XmitRcv FF =

Pattern Reciprocity

Fundamental Limits• A bit of Controversy

– Chu (1948) – McLean

)1(

122233

22

++

=aa

aQ

βββ

aaQ

ββ11

33+=

0 0.5 1 1.5 2 2.510

-1

100

101

102

ka

Rad

iatio

n Q

Antenna Fundamental Limit

Dipole

Goubau

Inverted F

Dual Inverted F

Planar Inverted F

Patch

Foursquare

Wideband, Compact, Planar Inverted F

McLeanGrimesChu

2. ANTENNA ELEMENTS

• The Four Antenna Types– Electrically Small Antennas– Resonant Antennas– Broadband Antennas

• Frequency Independent• Ultra Wideband

– Aperture Antennas

The Four Antenna Types• Electrically Small Antennas

Examples

Short dipole Small loop

PropertiesLow directivityLow input resistanceLow efficiency and gain

• Resonant Antennas

Examples

Dipole Microstrip antenna Yagi

PropertiesLow to moderate gainReal input impedanceLow efficiency and gain

Monopoles and Images

• Broadband AntennasExamples (Frequency Independent)

Spiral Log Periodic Dipole Array

PropertiesLow to moderate gainReal input impedanceLow efficiency and gain

There are two types of broadband antennas, ones that havefrequency independent performance and ones that preserve signal properties in the time domain (UWB)

• Aperture Antennas

Examples

Horn antenna Parabolic reflector antenna

PropertiesLow to moderate gainReal input impedanceLow efficiency and gain

3. ANTENNA ARRAYS

A. Array Basics

B. Arrays of Isotropic Elements

C. Inclusion of Element Effects

D. Mutual Coupling

E. Phased Arrays

Def.: Array Antenna. An antenna comprised of a number of identical radiating elements in a regular arrangement and excited to obtain a prescribed radiation pattern.

Advantages of arrays:

• Many small antenna elements instead of one large mechanical structure

• Scanning at electronic speeds is possible

• Multiple user (target) tracking is possible

• Many geometries, including conformal, are possible

Problems:

• A feed network is required with its losses and bandwidth limitations

• Mutual coupling between elements affects performance and complicates design

• Computer control may be necessary

Receiver

Phase shifter

AttenuatorFeednetwork

⎧⎪⎪⎨⎪⎪⎩

Figure 3-1 A typical linear array. The symbols and indicate variable phase shifters and attenuators. The output currents are summed before entering the receiver

General array configuration with feed network

A. Array Basics

B. Linear Arrays of Isotropic Elements

• General array configuration of isotropic elements

Figure 3-2 Equivalent configurationof the array in Fig. 3-1 for determiningthe array factor. The elements of thearray are replaced by isotropic pointsources.

Wavefronts

Rays

Referencewavefront

Array factor

Phase = 0ξ 1ξnξ

θ

nξ = phases at element n due to incoming wave

= complex current representing the feed network amplitude and phase at element n

nI

0 1 2j j jI I I ...ξ ξ ξ= + + +0 1 2AF e e e

je 1ξ1je 0ξ1 nje ξ1

nIPh ( )

nI

jI e 0ξ0

jI e 1ξn njI e ξ

n

(3-3)

δ

0° 45° 90° 135° 180°

d λ=1

8

d λ=1

4

d λ=3

8

d λ=1

2

d λ=5

8

d λ= 1

φ

dI1 I δ∠1

Elements

From [Kraus]

• Two element arrays of isotropic elements of various spacingsand phasings

Figure 3-7 Equally spaced linear array of isotropic point sources.

θ

θz

r

d d

0 1 2

d cos θ

Nj d j d j nd

n

I I e I e I eβ θ β θ β θ−

= + + + = ∑1

cos 2 cos cos0 1 2 n

=0

AF L

where the n + 1th element leads the nth element in phase by a. Then (3-14) becomes

Define

Then

jnan nI A e=

Now consider the array to be transmitting. If the current has a linear phase progression(i.e., relative phase between adjacent elements is the same), we can separate the phase explicitly as

(3-14)

(3-15)

( )N

jn d an

n

A e β θ−

+

=∑

1cos

0

AF = (3-16)

Njn

nn

A e ψ−

=∑

1

0

AF =

d aψ β θ= cos + (3-17)

(3-18)

• General uniformly excited, equally spaced linear array (UE,ESLA)

Universal array factor

Properties of the universal array factor

• The array factor is periodic in 2π

• Visible region extent:

• Exactly one period of the array factor appears in the visible region when the element space is λ/2.

Proof: Width of the visible region = 2βdAF period = 2πFor one period visible:

2π = 2βd = 2(2π/λ)dd = λ/2

For d > λ/2, grating lobes may appear in the visible region depending on α.

For d ≥ λ, grating lobes will appear in the visible region

Proof: ( ) ( )

( )

jn 2n

jn jn2 jnn n

AF 2 A e

A e e A e

AF

ψ π

ψ π ψ

ψ π

ψ

++ =

= =

=

∑∑ ∑

180° θ 0

1 < cos θ < 1

βd < βd cos θ < βd

α βd < < α βd+ψ

≥ ≥ °−−−

The general array factor expression for a UE,ESLA

( ) ( )( )

Njn

n

j N

A A A

A e

NA e

ψ

ψ ψψ

−

=

−

= = =

=

∑

0 1 2

1

00

1 /20

AF =

sin /2

sin /2

L

( ) ( )A A Nψ = =0 0AF = 0 1+1 + +1L

( ) ( )( )

N

f UE, ESLAN

ψψ

ψsin /2

sin /2

The expression is maximum for ψ = 0

This is the normalized array factor for an N element UE, ESLA that is centered aboutthe coordinate origin.

(3-33)

Figure 3-11 Array factor of an equally spaced, uniformly excited linear array for a few array numbers. (a) Three elements. (b) Five elements. (c) Ten elements.

(b)

1.0

00

ψ

( )f ψ

N = 5

0.4π 0.8π 1.2π 1.6π 2π

(c)

1.0

00

ψ

( )f ψ

N = 10

2π1.6π 1.8π1.4π1.2π0.2π 0.4π 0.6π 0.8π π

(a)

1.0

00

ψ

( )f ψ

N = 3

2ππ23

π43

Universal array factors for N = 3, 5, 10

1z

ψ

z

( )je π /21 je π1 ( )j 3e π /21d

1.0( )f

ψψ ψ=

sin 2

4 sin2

π-π 2ππ

−2

π2

π3

2

θo = 120°

βd = ππ

α =2

θ

(a)

(b)

(c)

Figure 3-12 Array factor for afour-element, uniformly excited,equally spaced phased array(Examples 3-5). (a) The arrayexcitations. (b) Universal patternfor N = 4. (c) Polar plot for d = λ/2 and α = π/2.

Example 3-5 Four-element array steered to 120°

• Scanning the pattern of a linear array in space

The main beam maximum occurs for ψ = 0. Let θo be the value of θ in the directionof the beam maximum. Then o

o

ψ = 0 = βd cos θ +α

α = βd cos θ

This element-to-element phase shift will scan the main beam peak to θ = θ0.

Often, we express ψ asoψ = βd (cos θ - cosθ )

(3-36)

(3-38)

• Beamwidth of the main beam

( )

o

For Nd >> (Nd L length of the array)

HP 0.886( /Nd) csc near broadside

HP 2 0.886 /Nd at endfire

≅

⎡ ⎤≅ ⎣ ⎦1/2

λ = =

λ θ

λ

( ) ( )( )

[ ] ( )o

1/2

o

Example N 20 d /2

0.886 /Nd 0.886 / 20 /2 0.0886 radians

90 HP 0.0886 r 0.0886 180/ 5.1°

0 HP 2 0.0886 0.595 180/ 34.1°

π

π

⎡ ⎤= =⎣ ⎦= ° =

= ° =

= = λ

λ λ λ

θ = =

θ = =

(3-45)

(3-46)

• Directivity of Uniformly Excited, Equally Spaced Linear Arrays

( )( )

/2

/2N

m

N

ND

N mm d m

N N m d

δδπ

α−

=

= =Ω + ∑

14

21

sin

sin41 2 -

sin β cos β

λ= 0

2If , d n

D NThen

α=

=

L Nd

D broadside≈ =2 2λ λ

(3-78)

Figure 3-20 Directivity as a function of element spacing for a broadside array of isotropic elements for several element numbers N.

The directivity of a broadside array of isotropic elements is approximated by

where L = Nd is the array length. This is a straight-line approximation to the curves

Dir

ecti

vity

(D

)

d

λ

α= 0δ = 0

for L

D N= =2 10λ

N = 109876

543

2.01.51.00.500

5

10

15

20

(3-80)

• Nonuniformly excited, ESLA N-1

jnn

n=0

AF A e βd cosψ ψ θ α= = +∑

1.0

1.0

1.0

1.0

1.0

0.5

0.5

0.5

0.5

00

0

0

0

00

0

λ

λ

λ

λ

λ

2λ

2λ

2λ

2λ

2λ

z

z

z

z

z

1/2λ

1/2λ

1/2λ

1/2λ

1/2λ

3/2λ

3/2λ

3/2λ

3/2λ

3/2λ

An

An

An

An

An

(a)

(b)

(c)

(d)

(e)

Uniform

1: 1 : 1 : 1 : 1

Triangular

1 : 2 : 3 : 2 : 1

Binomial

1 : 4 : 6 : 4 : 1

Dolph-Chebyshevfor a side lobe level of -20dB

1 : 1.61 : 1.94 : 1.61 : 1

Dolph-Chebyshevfor a side lobe level of -30dB

1 : 2.41 : 3.14 : 2.41 : 1

Figure 3-24 Current distributionscorresponding to the patterns ofFig. 3-23. The current phases arezero (α = 0). Currents are normal-ized to unity at the array center.(a) Uniform. (b) Triangular.(c) Binomial. (d) Dolph-Chebyshev (SLL = -20 dB).(e) Dolph-Chebyshev.

Figure 3-23 Patterns of several uniform phase (θo = 90°), equally spaced (d = λ/2) linear arrays with various amplitude distributions. The currents are plotted in Fig. 3-24.

180°

(a) Uniform currents, 1 : 1 : 1 : 1 : 1. (b) Triangular current amplitudedistribution, 1 : 2 : 3 : 2 : 1.

(c) Binomial current amplitudedistribution, 1 : 4 : 6 : 4 : 1.

D 5

HP 20.5

SLL 12 dB

== °

= −

180°180°0° 0° 0°

1.00 1.00 1.000.75 0.75 0.75

0.250.250.25 0.500.500.50

D 4.26

HP 26.0

SLL 19.1 dB

== °

= −

D 3.66

HP 30.3

SLL dB

== °

= −∞

180° 0°

1.000.75

0.250.50

(d) Dolph-Chebyshev

Current amplitude distribution, 1 : 1.61 : 1.94 : 1.61 : 1for a side lobe level of -20 dB.

(e) Dolph-Chebyshev

Current amplitude distribution,1 : 2.41 : 3.14 : 2.41 : 1, with a side

lobe level of -30 dB.

D 4.22

HP 26.4

SLL 30 dB

== °

= −

180° 0°

1.000.75

0.500.25

D 4.68

HP 23.6

SLL 20 dB-

== °

=

Fig. 3-23 (continued)

We can draw a general conclusion from the foregoing examples that applies to antennas in general:

As amplitude taper increases:

Beamwidth increases

Directivity decreases (as a consequence of beamwidth increasing)

Sidelobes decrease

Current envelope:

Pattern:

Directivity of nonuniformly excited, isotropic element arrays

General case of unequally spacings and nonuniform phasings

Equal spacings and broadside operation

(3-91)

(3-92)

Spacings a multiple of a half-wavelength and broadside

(3-93)

( ) ( )( )

m p

N

k

N Nm pj

m pm p m p

A

Dsin z z

A A ez z

k

α α β

β

−

− −−

⎛ ⎞⎜ ⎟⎝ ⎠=

⎡ ⎤−⎣ ⎦−

∑

∑∑

21

=0

1 1

=0 =0

( )( )

0,

N

kk

n nN N

m pm p

A

D z ndm p d

A Am p d

αβ

β

−

− −

⎛ ⎞⎜ ⎟⎝ ⎠= = =

⎡ ⎤−⎣ ⎦−

∑

∑∑

21

=0

1 1

=0 =0

sin

( ) , . . .

N

nn

N

nn

A

D d ,A

λλ

−

−

⎛ ⎞⎜ ⎟⎝ ⎠= =∑

∑

21

=01

2

=0

2

C. Inclusion of Element EffectsPrinciple of Pattern Multiplication: The pattern of an array (array pattern, F) consisting of similar elements is the product of the pattern of one of the elements (the element pattern, ga) and the pattern f the array of isotropic elements with the same locations, relative amplitudes and phases as the original array (the array factor, f).

Pattern F

Element pattern ga

Array factor f

F(θ,φ) = ga (θ,φ) f(θ,φ) (3-36)

Collinear elements

Example: Two collinear short dipoles

λ

2I Io = =11 1

| |z

θ

(a) The array.

Figure 3-17 Array of two half-wavelength spaced, equal amplitude, equal phase, collinear short dipoles (Example 3-8).

Figure 3-18 A linear array of parallel line sources.

Elementpattern

Arrayfactor

Totalpattern

(b) The pattern.

Parallel elements

θsinπ

θ⎛ ⎞⎜ ⎟⎝ ⎠

cos cos2

π

θ θ⎛ ⎞⎜ ⎟⎝ ⎠

sin cos cos2

x

z

γ

θ

y

Parallel half-wave dipoles

For a half-wave dipole along z-axis

z

For an array of parallel half-wave dipoles it is best to orient the elements along the x-axis. Then the element pattern is expressed as

x

z

(2-8)

(3-68)

(3-69)

( ) half wave dipole

π θθ

⎡ ⎤⎣ ⎦ −cos /2 cos

sin

( ) ( )

( )( )

a

a

g

cos

g ,

π γγ

γ

γ θ φ γ θ φ

π θ φθ φ

θ φ

⎡ ⎤⎣ ⎦=

=

⎡ ⎤⎣ ⎦=

2 2

2 2

cos /2 cos

sin

sin cos sin = 1- sin cos

cos /2 sin cos

1- sin cos

Prob. 3.3-2

From (2-7) ( )

π⎛ ⎞⎜ ⎟⎝ ⎠=a

cos cosθ2

g θsinθ

From (3-13)

So

(Fig. 2-5b) (Fig. 3-6c)

ga x f F

z z z

=

π2

1 1λ

( ) ( )f π=θ cos cosθ

( ) ( ) ( ) ( )

π

π θ

⎛ ⎞⎜ ⎟⎝ ⎠= =a

cos cosθ2

F θ g θ f θ cos cossinθ

• Method used in practice to produce a single endfire beam

Problem 3.7-7 uses array theory to find the patterns

x y

z

Ground plane

λ

4

Image theory solution The array factor is that of Example 3-2

-1 -11 1

x y

λd =

2λ

d =2

yz-plane (arrayfactor)

xz-plane (includingλ/2 dipole effect)

There is no general exact formula for the directivity of arrays includingthe element pattern. The following often- quoted approximate directivityformula must be used with caution

( ) ( )e iD D D≈ = =1.5 4 6

e

e

i

D D D

D directivity of a single element

D directivity of the array with isotropic elements

≈

=

=

i

Example: 4-element, broadside array of collinear short dipoles with spacing d = λ/2

(3-83) gives D = 5.6, an exact answer

• Directivity of arrays of real elements

d 0.72λ=

L2λ

= ( )

e i

From code

D 7.75 dBi d 0.72

5.6 dBd

Approximate directivity

D D D 1.64(5.4) 8.9, using Fig. 3-20

9.5 dB 7.3 dBd

= =

=

=

λ

≈ = =

=

• Base Station Collinear Arrays

The tower enhances the gain by making

pattern more directive

Base station with elements in opposing pairs and clocked90 degrees around the towerto produce nearly anomnidirectional pattern

Feed network

1 2 m N

D. Mutual Coupling

There are three mechanisms responsible for mutual coupling:Direct free space coupling between elements

Indirect coupling due to scattering by nearby objects

Coupling through the feed network

In many arrays the elements are impedance matched to the feed network and feed coupling can be ignored. Then the array can be modeled with independent generators, leading to the conventional circuit N port representation.

where the mutual impedance is

and reciprocity has been assumed through Zmn = Znm

Figure 3-26 (a) Mechanisms for coupling between elements of an array.

1 11 1 12 2 1N N

2 12 1 22 2 2N N

N 1N 1 1N 2 NN N

V Z I Z I Z I

V Z I Z I Z I V Z I Z I Z I

= + + +

= + + +••

= + + +

K

K

K

mmn

m

VZ

I iwith I 0 for all i except i = n= =

The input impedance of the mth element in an array with all elements activeand mutual coupling included is

m 1 2 Nm m1 m2 mN

m m m m

V I I 1Z Z Z Z

I I I 1⋅⋅⋅⋅⋅⋅⋅⋅= = + + + (3-103)

Note that active impedance depends on mutual impedances between elementsas well as the excitations of all elements. This dependence includes the

current phases and thus scan angle in phased arrays.

The effects of mutual coupling include:

• The impedance of an element in an array differs from its free space value and dependson that array scan angle (element phases) and the element location.

• The pattern of an element is changed from its isolated pattern and depends on arrayposition.

• Polarization characteristics deteriorate.

mV

mZmI

gmV

gmZ

This is often called active impedance or driving point impedance.

Current generatorVoltage generator (loaded)

0

-10dB

-20

φ = 180° φ = 0°

Figure 10-27 Linear array pattern with main beam steered to φo = 45° and ideal current generators (solid curve) compared to patterns from an array with voltage generators for 72-Ω loaded voltage generator excitations (dashed curve).

Also see: D. Kelley and W. Stutzman, “Array antenna pattern modeling methods that include mutual coupling effects,” IEEE Trans. On Ant. And Prop., Dec. 1993.

Example: Mutual coupling effect on a 12-element, half-wave spaced linear array

y

z

x

x

180° 0°

θo= 90°90°

0.250.50

0.751.00

(a) θo= 90°

z

(b) θo= 90°

180° 0°

θo= 75°90°

0.250.50

0.751.00

(c) θo= 75°

180° 0°

θo= 30°90°

0.250.50

0.751.0

(d) θo = 30° (bifurcated pattern)

180° 0°

θo= 0°90°

0.250.50 0.75

1.0

(e) Endfire (θo = 0°)

z

(f) Endfire (θo = 90°)

Figure 3-32 Example of phase-scanned patterns for a five-element linear array alongthe z-axis with elements equally spaced at d = 0.4λ and with uniform current magnitudes for various main beam pointing angles θo.

E. Phased Arrays

Important point to remember:The array factor scans inside the envelope of the fixed element pattern

Example: Linear array of four broadside elements spaced 0.7λ apart. The elementpattern is g(θ) = (cos θ)2.

Broadside operation Scanned 30° off broadsideFmag(θ)

g(θ)

1

0.8

0.6

0.4

0.2

0-90-80-70 -60-50 -40-30-20 -10 0

1

0.8

0.6

0.4

0.2

0-90-80-70 -60-50 -40-30-20 -10 0 4010 20 30 50 60 70 80 90 4010 20 30 50 60 70 80 90

θ θ

• Basic Feed Types

(a) Parallel, or corporate, feed. (b) Series feed.

Primarytransmittingantenna

Pickupantenna

Secondarytransmittingantenna

(c) Space feed. (d) Parallel-series feed.

Figure 3-33 Types of array feed networks.

Mounted on top of aircraft such as E-3A, E-2C for aerial surveil-lance and detection of bombers and low flying fighters coming inover north pole

First operational radar antenna with very low sidelobes: -40 dBSlotted waveguide array with 4000 slotsScanned in vertical plane using ferrite phase shiftersRotated for azimuth coverageNext generation: phased array conforming to the aircraft

Phased array example: AWACS (Airborne Warning and Control System)

E-2C

• Beam switched scanning

1 x 4 Switch

1 x 4 Switch

RotmanLens or

Butler Matrix

ERP = PTGT = GePs

(a)

(b) (c)

43 2 1

Switched antenna system vs linear array configurations: (a) switched antennas;(b) multiple-beam array; (c) steered-beam array.

[Microwave Journal, January 1987]

oGe sP P=

sP

sPsP

oG

1 2 3 4

eP oG se

PP

4=

se

PP

4=

T T o o

10 Log N 6 dB for N 4

ERP P G NG NP

=

=

+=

= ⋅

s s4G P=

• Digital Beam Forming

ReceivingAntenna

Array

Beams

CalibrationTone

WeightsController

DigitalBeamformer

RX

RX

RX

ADC

ADC

ADC

Directions of Look

. .

1 1.5 2 2.5 30

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

90

41.8

25.4

14.5

6.4

0

Max

imum

Sca

n A

ngle

Nor

mal

ized

Ele

men

t Spa

cing

(d/λ)

Bandwidth (f/f )L

1

Sinuous

Foursquare

Spirals

• Scanning arrays of wideband elements[Stutzman and Buxton, Microwave Journal, Feb. 2000.]

• The future for phased arrays- Wideband, multifunctional arrays will be used- Intelligence will be integrated with arrays, creating “smart arrays” that can

adapt to changing conditions and faults- Radiating elements will be printed, giving low cost and uniform geometrical

construction (see figure)- Feed networks will make use of integrated fabrication techniques

such as MMIC.- Elements and feeds will be integrated together- Beam steering:

Low cost phase shifters: MEMS, Ferroelectric, . . .Photonic feedsDigital beam forming will be very popular as RF and DSP module

performance and cost improve

2x2 array of Foursquare elements

capable of 2:1 bandwidth and dual polarization

Fourpoint element

5. SYSTEM CONSIDERATIONS

• Friis Transmission Equation• Propagation in real links• Factors in selecting an operating

frequency

• Factors in operating frequency selection

– Propagation and link budget considerations• VHF and below for long distance, narrow bandwidth• UHF and above for wide bandwidth• Above 10 GHz, atmospheric losses are high

– Antenna considerations• Very long distance point-to-point communications

require high frequencies to enable large antenna gains

– Regulatory issues• Must use allocated bands• Licensed vs. unlicensed bands

6. WIRELESS APPLICATIONS

• Base Station Antennas for Land Mobile

• Antennas for Satellite Communications

• Vehicle Antennas

• Antennas for Personal Communications

• UWB– Some Concepts

• Radiation Safety

Base Station Antennas for Land Mobile Radio

• Cell Coverage Types

OmnidirectionalSectorized

Smart antenna thatforms beams on users

• Omnidirectional pattern base station antennas

– Pattern is constant in azimuth and narrow in elevation

– Usually realized with collinear array of dipoles

Example: Cellular base station

Antel Cellular Base Station Antenna

870-970 MHzCollinear dipoles136 in long10 dBd gain1.25 deg downtilt

• Sector base station antennasTypical 120 deg sectors, VP

Polarization diversity120 deg sectors, dual slant 45 deg LP

• Sector (“panel”) antennas– Elements

• Dipoles in front of a ground plane• Log periodic dipole (LPDA) and LPDA vees• Patches• Fourpoint antenna (VT) covers both cellular and PCS

with dual polarization

– Considerations• Bandwidth (VSWR<2)• Power handling• Intermodulation products

DB Products LPDA vee antenna

• A new wideband base station antenna developed at

VTAG:– Minimum number of antennas on tower

– Dual-polarized for diversity

– Multi-functional capability (800 ~ 2200 MHz)

– Low profile and compact

– Printed antenna on a PCB

Front view Tuning plate on back

Fourpoint Antenna Data

AMPS, GSM, DCS, PCS, etc

Measured Radiation PatternsMeasured Radiation Patterns

900 MHz 1800 MHz• HPBW: 60° ~ 80 °• Low cross-pol, less than -30 dB

E-planeH-plane

• Satellite communications antennas

Satellite servicesFSS – Fixed Satellite Service

[gateways, VSATs]BSS – Broadcast Satellite Service (DBS, DTH)Mobile (Iridium, Orbcom, Inmarsat)

Gain of spacecraft antenna Global coverage 19 dBUS coverage 34 dB

Ground station antennasReflectors are used above a few GHz

Small offset reflectors for VSATLarge, dual reflectors for gateways

Direct Broadcast systemfrom DirecTV manual________________________12.2 -12.7 GHz downlink

to user17.3-17.8 GHz uplink from

gatewayDual circularly polarized

Vehicular Antennas • Broadcast reception

Traditional 31” (0.003 λ at AM) fender mount whip antennais vanishing.

New cars have mostly on-glass antennas

Example of a Ford rear windowglass antenna

• Two-way land mobile vehicle antennasVHF and below

Short monopoleQuarter-wave

monopole

Example quarter-wavemonopole

UHF Quarter-wave monopole5/8 over ¼ wavelength

Example 5/8 over¼ wavelength

• Aircraft antennas

Example: Commercial MD-80 airplane

• Antennas for fixed wireless– Access points and terminals

Omnidirectional antennasCollinears for access pointsStubby or planar antennas for terminals

High gain (20 dB or more) – reflectorsModerate gain

YagiStub loaded helix antenna

75% volume reductionCircularly polarized

Example; Stub loadedhelix antennawww.frc-corp.com

• Antennas for personal communicationsVHF

Short monopoleLoops, small and/or loadedNormal mode helix

UHFMonopoleNormal mode helixPatchInverted-L Planar inverted-LEmbedded

Perhaps the most popular antenna for cell phones is the stubby antenna with an extendable wire antenna

Nokia Patent5,612,704

• Inverted-L family of antennas

Inverted-LInverted-F Dual

Inverted-F

PlanarInverted-F

43WC PIFA

12Dipole

8PIFA

4DIFA

2IFA

1Patch

Bandwidth

(%)

AntennaWideband Compact PIFA

VT patent 6,795,028

UWB Antennas

TEM Horn Ridged Horn BiCone

Tapered Slot (Vivaldi) Impulse Radiating Antenna (IRA)

Half-Disk

PICA & VSWR

2 4 6 8 10 12 14 16 18 201

1.5

2

2.5

3

3.5

4

4.5

5S imulation Meas urement

Typical Responses – TEM Horn

0 2 4 6 8 10 12 14 16 18 20-40

-30

-20

-10

0Return Loss

Frequency (GHz)

Am

plitu

de (

dB)

0 2 4 6 8 10 12 14 16 18 20-400

-200

0

200Phase - Delay Phase

Frequency (GHz)

Pha

se (

degr

ees)

0 2 4 6 8 10 12 14 16 18 20-100

-50

0

Frequency Response s21

Frequency (GHz)

s 21 (

dB)

0 2 4 6 8 10 12 14 16 18 20-1

0

1

2x 10

9 Impulse Response s21

Time (nsec)

Am

plitu

de (

s-1)

Reflection Transmission Link

Phase Transient Transmission

Radiation Safety & Interference

• SAR – Specific Absorption Rate– Power per area absorption

• HAC – Hearing Aid Compatibility– Buzzing and related noise in Hearing Aid

• System Interference and Cross-Modulation

Facilities

INSTRUMENTATION

•ANTCOM 7+1 axis near field –far field scanner

•Agilent 8510, 8511, 8530 Network Analyzer

Measured Near Field Pattern

Calculated Far Field Pattern

For those interested in an in-depth antennas short course

ANTENNAS: Principles, Design, and Measurements

July 17-20Albuquerque, NM

antennacourse.com