ael.chungbuk.ac.krael.chungbuk.ac.kr/lectures/graduate/antenna-engineering/... · 2018. 11. 24. ·...

Antenna Array Design Techniques using Electromagnetic Simulation

Ing. Jan Eichler, Ph.D., CST Computer Simulation Technology GmbH

Abstract: Antenna arrays have long been ideal choice for wide range of applications such as radar, remote sensing, wireless communication and others. In these applications it is desired to control properties of radiation pattern such as directivity or side lobe level or electronically steer the beam. Antenna arrays have also perspective in car-to-car communication or millimeter wave communications proposed e.g. in 5G cellular networks. While antenna arrays offer high performance and flexibility, their cost is higher (especially for larger phased arrays) and the design process is more complicated compared to single antenna.

The presentation will give an introduction to antenna array theory – array multiplication principle, active/embedded element pattern, active reflection coefficient, scan blindness etc. A workflow of using electromagnetic field simulation for phased array design including the effects of mutual coupling will be presented. In the last part of the presentation, an example of phased array design for Ku band satellite communication will be shown in CST STUDIO SUITE®. The design will focus on optimization of the array radiation and elements reflection coefficient for multiple scan angles at multiple frequencies.

Date: October 05, 2017

Time: 16:00 to 17:30

Location: CTU in Prague Faculty of Electrical Eng. Technicka 2 Prague 6 Room: T2:B2-80

For details, please contact: Tomas Korinek [email protected] +420 224352910

Jan Eichler received the M.Sc. degree in electrical engineering and Ph.D. in radioelectronics from the Czech Technical University in Prague in 2010 and 2014 respectively. He joined CST in 2014 as an application engineer where his main area of work involves high frequency applications including antenna design and simulation, antenna arrays or electrically large structures. His interests also lies in the field of material characterization based on measured data. Second main area of his work is EMC/EMI simulation in particular emissions simulation of power electronics (e.g. converters, LED drivers).

mailto:[email protected]

IEEE New Hampshire SectionRadar Systems Course 1Antennas Part 2 1/1/2010 IEEE AES Society

Radar Systems EngineeringLecture 9Antennas

Part 2 - Electronic Scanning and Hybrid Techniques

Dr. Robert M. O’DonnellIEEE New Hampshire Section

Guest Lecturer

Radar Systems Course 2Antennas Part 2 1/1/2010

IEEE New Hampshire SectionIEEE AES Society

Block Diagram of Radar System

Transmitter

WaveformGeneration

PowerAmplifier

T / RSwitch

Antenna

PropagationMedium

TargetRadarCross

Section

Photo ImageCourtesy of US Air ForceUsed with permission.

PulseCompressionReceiver Clutter Rejection

(Doppler Filtering)A / D

Converter

General Purpose Computer

Tracking

DataRecording

ParameterEstimation Detection

Signal Processor Computer

Thresholding

User Displays and Radar Control



Antenna Functions and the Radar Equation

• “Means for radiating or receiving radio waves”*– A radiated electromagnetic wave consists of electric and

magnetic fields which jointly satisfy Maxwell’s Equations• Direct microwave radiation in desired directions, suppress

in others• Designed for optimum gain (directivity) and minimum loss

of energy during transmit or receive

Pt G2 λ2 σ

(4 π )3 R4 k Ts Bn LS / N =

TrackRadar

Equation

Pav Ae ts σ

4 π Ω R4 k Ts LS / N =

SearchRadar

Equation

G = Gain

Ae = Effective Area

Ts = System NoiseTemperature

L = Losses

ThisLecture

RadarEquationLecture

* IEEE Standard Definitions of Terms for Antennas (IEEE STD 145-1983)



Radar Antennas Come in Many Sizes and Shapes

Mechanical ScanningAntenna Hybrid Mechanical and Frequency

Scanning AntennaElectronic Scanning

Antenna

Hybrid Mechanical and FrequencyScanning Antenna

Electronic ScanningAntenna

Mechanical ScanningAntenna

PhotoCourtesy

of ITT CorporationUsed withPermission

Courtesy of RaytheonUsed with Permission

Photo Courtesy of Northrop GrummanUsed with Permission

Courtesy US Dept of Commerce

Courtesy US Army Courtesy of MIT Lincoln LaboratoryUsed with Permission



Outline

• Introduction

• Antenna Fundamentals

• Reflector Antennas – Mechanical Scanning

• Phased Array Antennas– Linear and planar arrays– Grating lobes– Phase shifters and array feeds – Array feed architectures

• Frequency Scanning of Antennas

• Hybrid Methods of Scanning

• Other Topics

PartOne

PartTwo



• Multiple antennas combined to enhance radiation and shape pattern

Arrays

Array Phased ArrayIsotropicElement

PhaseShifter

Σ

CombinerΣ Σ

Direction

Res

pons

e

Direction

Res

pons

e

Direction

Res

pons

e

Direction

Res

pons

e

Array

Courtesy of MIT Lincoln LaboratoryUsed with Permission



Two Antennas Radiating

Horizontal Distance (m)

Vert

ical

Dis

tanc

e (m

)

0 0.5 1 1.5 2-1

0

-0.5

0.5

1

Dipole1*

Dipole2*

*driven by oscillatingsources

(in phase)Courtesy of MIT Lincoln LaboratoryUsed with Permission



Array Beamforming (Beam Collimation)

Broadside Beam Scan To 30 deg

• Want fields to interfere constructively (add) in desired directions, and interfere destructively (cancel) in the remaining space




Controls for an N Element Array

• Geometrical configuration– Linear, rectangular,

triangular, etc

• Number of elements

• Element separation

• Excitation phase shifts

• Excitation amplitudes

• Pattern of individual elements

– Dipole, monopole, etc.

Array FactorAntenna Element

ElementNumber

ElementExcitation

1

4

3

2

NNj

N ea φ

3j3 ea φ

4j4 ea φ

2j2 ea φ

1j1 ea φ

N

D

na

nφ

D

ScanAngle




The “Array Factor”

• The “Array Factor” AF, is the normalized radiation pattern of an array of isotropic point-source elements

rrkjN

1n

jn

nn eea),(AF ⋅

=

φ∑=φθr

Position Vector

Excitation njna e Φ

Source Element n:

nnn1 zzyyxxr ++=r

Observation Angles (θ,φ):Observation Vector

θ+φθ+φθ= coszsinsinycossinxr

Free-SpacePropagation Constant c

f22k π=

λπ

=

NIsotropicSources

Observe at (θ, φ)

1rr

Nrr2rr 3rr

r

z

y

x



Array Factor for N Element Linear Array

∑∑∑−

=

θψ−

=

β+θ⋅

=

φ− ===φθ −−

1N

0n

)(nj1N

0n

)cosdk(njrrkjN

1n

j1n eAeAeea),(AF 1n1n

rd

θ

4321 1N − N

Where : and,

It is assumed that:

Phase progression is linear, is real.

Using the identity:

β+θ=θψ cosdk)(

nnjj a,ee n βφ =

The array is uniformly excited Aan =

1c1cc

N1N

0n

n

−−

=∑−

=

( )( )2/SinN

2/Nsin),(AFψψ

=φθThe Normalized Array Factor becomes :

Main Beam Location

0cosdk =β+θ=ψ

( ) π±=β+θ=ψ mcosdk

21

2



Properties of N Element Linear Array

• Major lobes and sidelobes– Mainlobe narrows as increases– No. of sidelobes increases as increases– Width of major lobe = – Height of sidelobes decreases as increases

• Changing will steer the peak of the beam to a desired– Beam direction varies from to– varies from to

• Condition for no grating lobes being visible:

N

N

NN/2π

β

ocos11d

θ+<

λ

π0oθ=θ

β+− kdψ β+kd

oθ = angle off broadside

Note how is defined.θ



-20 0 20 40 60 80

Array and Element Factors

• Total Pattern = Element Factor X Array Factor

• Element Factor

• Array Factor Adapted fromFrank in Skolnik

Reference 2

Ten Element Linear Array – Scanned to 60 °

Angle (degrees)

Total Pattern

Element Factor

Array Factor

Rel

ativ

e Fi

eld

Stre

ngth

0.2

0.8

0.6

1.0

0.4

2/λ

ElementSpacing

)(E)(E)(E ae θ×θ=θ

θ=θ cos)(Ee

( )( )( )866.0sin2/sin10

866.0sin5sin)(Ea −θπ−θπ

=θ

0.707



Array Gain and the Array Factor

ArrayFactorGain

ArrayGain(dBi)

Array FactorGain(dBi)

ElementGain(dBi)

= +

Individual Array Elements are Assumed to Be Isolated

The Overall Array Gain is the Product of the Element Gain and the Array Factor Gain

RAD

2

AF P),(AF4

),(Gφθπ

=φθ

φθθφθ= ∫ ∫π π

ddsin),(AFP2

0 0

2RAD



Homework Problem – Three Element Array

• Student Problem:

– Calculate the normalized array factor for an array of 3 isotropic radiating elements. They are located along the x-axis (center one at the origin) and spaced apart. Relevant information is 2 and 3 viewgraphs back.

– Use the results of this calculation and the information in viewgraph 28 of “Antennas Part 1’ to calculate the radiation pattern of a linear array of three dipole, apart on the x-axis.

2/λ

2/λ



Increasing Array Size byAdding Elements

• Gain ~ 2N(d / λ) for long broadside array

N = 10 Elements N = 20 Elements

Gai

n (d

Bi)

Angle off Broadside (deg)

Linear Broadside ArrayIsotropic Elements

Element Separation d = λ/2No Phase Shifting

-90 -60 -30 0 30 60 90-30

-20

-10

0

10

20

N = 40 Elements

10 dBi 13 dBi 16 dBi

Angle off broadside (deg)

Figure by MIT OCW.

-90 -60 -30 0 30 60 90Angle off broadside (deg)

-90 -60 -30 0 30 60 90




Increasing Broadside Array Size bySeparating Elements

Limit element separation to d < λ to preventgrating lobes for broadside array

Limit element separation to d < λ to preventgrating lobes for broadside array

d = λ/4 separation d = λ/2 separation d = λ separation

Gai

n (d

Bi)

GratingLobes

-30

-20

-10

0

10

20

10 dBi7 dBi

10 dBi

L = (N-1) d

Figure by MIT OCW.

N = 10 ElementsMaximum at

Design Goal Required Phase

Angle off Broadside (deg) Angle off Broadside (deg)Angle off Broadside (deg)-90 -60 -30 0 30 60 90 -90 -60 -30 0 30 60 90 -90 -60 -30 0 30 60 90

0=β

0cosdk90

=β+θ=ψ=θ o

o90=θ




Ordinary Endfire Uniform Linear Array

• No grating lobes for element separation d < λ / 2• Gain ~ 4N(d / λ) ~ 4L / λ for long endfire array without grating lobes

Gai

n (d

Bi)

GratingLobe

GratingLobes

-30

-20

-10

0

10

20d = λ/4 separation d = λ/2 separation d = λ separation

10 dBi 10 dBi 10 dBi

Figure by MIT OCW.

L = (N-1) dN = 10 Elements

Required Phase

Angle off Broadside (deg) Angle off Broadside (deg)Angle off Broadside (deg)-90 -60 -30 0 30 60 90 -90 -60 -30 0 30 60 90-90 -60 -30 0 30 60 90

Maximum at

Design Goal

0cosdk90

=β+θ=ψ=θ o

o90=θ 0=β




Linear Phased ArrayScanned every 30 deg, N = 20, d = λ/4

To scan over all space without grating lobes, keep element

separation d < λ / 2

-30

-20

-10

0

10

20

Gai

n (d

Bi)

Broadside: No Scan Scan 30 deg Scan 60 deg Endfire: Scan 90 deg

10 deg beam 12 deg beam 22 deg beam 49 deg beam

10 dBi 10.3 dBi10 dBi 13 dBi

Angle off Broadside (deg)Angle off Broadside (deg) Angle off Broadside (deg)Angle off Broadside (deg)-90 -60 -30 0 30 60 90-90 -60 -30 0 30 60 90 -90 -60 -30 0 30 60 90-90 -60 -30 0 30 60 90

Maximum at

Design Goal

At Design Frequency

Required Phase

2o ok c fπ=

ofoθ=θ

oo cosdk θ−=β

0cosdk oo =β+θ=ψc/f2k oo π=




Uniform Planar Array

Figure by MIT OCW.

xxx cossinkd β+φθ=ψwhere

yyy sinsinkd β+φθ=ψ

( )oo ,φθ

ooxx cossinkd φθ−=β

ooyy sinsinkd φθ−=β

:

( )

⎪⎪⎭

⎪⎪⎬

⎫

⎪⎪⎩

⎪⎪⎨

⎧

⎟⎟⎠

⎞⎜⎜⎝

⎛ ψ

⎟⎟⎠

⎞⎜⎜⎝

⎛ ψ

⎪⎪⎭

⎪⎪⎬

⎫

⎪⎪⎩

⎪⎪⎨

⎧

⎟⎠⎞

⎜⎝⎛ ψ

⎟⎠⎞

⎜⎝⎛ ψ

=φθ

2sin

2N

sin

N1

2sin

2Msin

M1,AF

y

y

x

x

n

Progressive phase to scan to

Two Dimensional Planar array(M x N Rectangular Pattern)

• To scan over all space without grating lobes: dx < λ / 2 and dy < λ / 2



Uniform Planar Array

Figure by MIT OCW.

xxx cossinkd β+φθ=ψwhere

yyy sinsinkd β+φθ=ψ

( )oo ,φθ

ooxx cossinkd φθ−=β

ooyy sinsinkd φθ−=β

:

( )

⎪⎪⎭

⎪⎪⎬

⎫

⎪⎪⎩

⎪⎪⎨

⎧

⎟⎟⎠

⎞⎜⎜⎝

⎛ ψ

⎟⎟⎠

⎞⎜⎜⎝

⎛ ψ

⎪⎪⎭

⎪⎪⎬

⎫

⎪⎪⎩

⎪⎪⎨

⎧

⎟⎠⎞

⎜⎝⎛ ψ

⎟⎠⎞

⎜⎝⎛ ψ

=φθ

2sin

2N

sin

N1

2sin

2Msin

M1,AF

y

y

x

x

n

Progressive phase to scan to

• To scan over all space without grating lobes: dx < λ / 2 and dy < λ / 2

Beam pattern at broadside(25 element square array)



Change in Beamwidth with Scan Angle

• The array beamwidth in the plane of scan increases as the beam is scanned off the broadside direction.

– The beamwidth is approximately proportional to – where is the scan angle off broadside of the array

• The half power beamwidth for uniform illumination is:

• With a cosine on a pedestal illumination of the form:

– And the corresponding beamwidth is:

• In addition to the changes in the main beam, the sidelobes also change in appearance and position.

ocos/1 θ

oB cosdN

886.0θλ

≈θ

[ ]o1o

B a/a2(636.01cosdN886.0

+θλ

≈θ

)N/n2(cosa2aA 1o π+=

oθ



Time Delay vs. Phase Shifter Beam Steering

• Time delay steering requires:– Switched lines

• It is a relatively lossy method• High Cost• Phase shifting mainly used in phased array radars

d d

oθoθosind θ

osind θ

Phase Shift =Time Shift =( ) osin/d2 θλπ( ) osinc/d θ

Time Delay Steering Phase Shifter Steering

Adapted from Skolnik, Reference 1



Phased Array Bandwidth Limitations

• The most prevalent cause of bandwidth limitation in phased array radars is the use of phase shifters, rather than time delay devices, to steer the beam

– Time shifting is not frequency dependent, but phase shifting is.

d d

oθoθosind θ

osind θ

Phase Shift =Time Shift =( ) osin/d2 θλπ( ) osinc/d θ

Time DelaySteering

Phase ShifterSteering




Phased Array Bandwidth Limitations

• With phase shifters, peak is scanned to the desired angle only at center frequency

• Since radar signal has finite bandwidth, antenna beamwidth broadens as beam is scanned off broadside

• For wide scan angles ( 60 degrees):– Bandwidth (%) ≈ 2 x Beamwidth (3 db half power) (deg)

oθ

Angle

Squi

nted

Bea

m P

atte

rn

MINfMAXf of

( ) θλπ=φΔ sin/d2 o

φΔ−=φ

off =oθoff <

0=φ φΔ+=φ



Thinned Arrays

• Attributes of Thinned Arrays

– Gain is calculated using the actual number of elements

– Beamwidth – equivalent to filled array

– Sidelobe level is raised in proportion to number of elements deleted

– Element pattern same as that with filled array, if missing elements replaced with matched loads

4000 Element Grid with 900 Elements

Angle (degrees)0 20 40 60 80

Rel

ativ

e po

wer

(dB

) 0

-10

-30

-20

-40

Example – Randomly Thinned Array

NG π=

Ave Sidelobe Level31.5 dB

Adapted from Frank in Skolnik, see Reference 2



Amplitude Weighting of Array Elements

• These days, Taylor weighting is the most commonly used illumination function for phased array radars

– Many other illumination functions can be used and are discussed in “Antennas-Part 1”

• Low sidelobe windows are often used to suppress grating lobes

• Amplitude and phase errors limit the attainable level of sidelobe suppression

• Phased array monopulse issues will be discussed in Parameter Estimation Lecture Adapted from Mailloux, Reference 6

Angle (degrees)

16 Element Array with Two Different Illumination Weights

Angle (degrees)

Uniformly Illuminated 40 dB Taylor patternn=5

0 30 60 90 0 30 60 90

Rel

ativ

e Po

wer

(dB

)

0

- 10

- 20

- 30

- 40

- 50

0

- 10

- 20

- 30

- 40

- 50

Rel

ativ

e Po

wer

(dB

)



Effects of Random Errors in Array

• Random errors in amplitude and phase in element current• Missing or broken elements• Phase shifter quantization errors• Mutual Coupling effects

Rad

iatio

n (d

B)

0 10 20 30 40 50 60

Rad

iatio

n (d

B)

Angle (degrees)0 10 20 30 40 50 60

100 Element Linear ArrayNo-Error

40 dB Chebyshev Pattern

100 Element Linear Array40 dB Chebyshev Pattern

Peak Sidelobe Error - 37 dBRMS Amplitude Error 0.025

RMS Phase Error 1.44 degrees

Angle (degrees)

Adapted from Hsiao in Skolnik, Reference 1

The Effect on Gain and Sidelobes of These DifferentPhenomena Can Usually Be Calculated

0

-20

-40

-60

0

-20

-40

-60



Outline

• Introduction






• Other Topics



Sin (U-V) Space

Spherical Coordinate SystemFor Studying

Grating Lobes

Projection of Coordinate SystemOn the X-Y Plane

( view from above Z-axis)

Direction Cosinesφθ=φθ=

sinsinvcossinu

o270=φφ

y

x Unit Circle

Unit Circle

θ

z Directionof Array

Main Lobe

o0=θ

o90=θ

o180=φo0=φ

o90=φv

u



Grating Lobe Issues for Planar Arrays

Rectangular Grid of ElementsTriangular Grid of Elements

xd

yd

xdyd

Lobes at ( )q,p

yoq

xop

dqvv

dpuu

λ+=

λ+=

UnitCircle

v

u-3 -2 -1 0 1 2 3

1

2

-1

-2



Grating Lobe Issues – λ/2 Spacing

Square Grid of Elements

xd

yd

Triangular Grid of Elements

xdyd

For 2/dd yx λ==Lobes at ( ) ( )q2,p2v,u qp =

Lobes at ( )q,p

yoq

xop

dqvv

dpuu

λ+=

λ+=

UnitCircle

v

u-3 -2 -1 0 1 2 3

1

2

-1

-2No visible grating lobes



Grating Lobe Issues – λ Spacing


xd

yd

UnitCircle

v

u-3 -2 -1 0 1 2 3

1

2

-1

-2


xdyd

For λ== yx ddLobes at ( ) ( )q,pv,u qp =

Lobes at ( )q,p

yoq

xop

dqvv

dpuu

λ+=

λ+=

Grating Lobes will be seen with beam pointing broadside



Grating Lobe Issues – Scanning of the Array


xd

yd

UnitCircle

v

u-3 -2 -1 0 1 2 3

1

2

-1

-2

UnitCircle

v

u-3 -2 -1 0 1 2 3

1

2

-1

-2

0,0 =θ=φ Beam Scanned oo 90,0 =θ=φ

For 2/dd yx λ==

Lobes at ( ) ( )q2,p20.1v,u qp +=

Grating lobes visible as pattern shifts to right



Grating Lobe Issues

• Triangular grid used most often because the number of elements needed is about 14 % less than with square grid

– Exact percentage savings depends on scan requirements of the array

– There are no grating lobes for scan angles less than 60 degrees

• For a rectangular grid, and half wavelength spacing, no grating lobes are visible for all scan angles

•


xdyd

Lobes at ( )q,p

yoq

xop

dqvv

dpuu

λ+=

λ+=



Mutual Coupling Issues

Do All of these Phased Array Elements Transmit and Receive without Influencing Each Other ?

Courtesy of Eli BrooknerUsed with Permission

Courtesy of spliced (GNU)

BMEWS Radar, Fylingdales, UK Photo from Bottom of Array Face



Mutual Coupling Issues


Courtesy of National Archives

COBRA DANE RadarShemya, Alaska Close-up Image Array Face

Do All of these Phased Array Elements Transmit and Receive without Influencing Each Other ?



Answer- No …..Mutual Coupling

• Analysis of Phased Arrays based on simple model – No interaction between radiating elements

• “Mutual coupling” is the effect of one antenna element on another

– Current in one element depends on amplitude and phase of current in neighboring elements; as well as current in the element under consideration

• When the antenna is scanned from broadside, mutual coupling can cause a change in antenna gain, beam shape, side lobe level, and radiation impedance

• Mutual coupling can cause “scan blindness”

Z Z

~

AntennaElement

m

AntennaElement

n

~

Drive Both AntennaElements

In addition ... mutual coupling can sometimes be exploitedto achieve certain performance requirements

Adapted from J. Allen, “Mutual Coupling in Phased Arrays”MIT LL TR-424



Outline

• Introduction



• Phased Array Antennas– Linear and planar arrays– Grating lobes– Phase shifters and radiating elements – Array feed architectures



• Other Topics



• If the phase of each element of an array antenna can be rapidly changed, then, so can the pointing direction of the antenna beam

– Modern phase shifters can change their phase in the order of a few microseconds !

– This development has had a revolutionary impact on military radar development

Ability to, simultaneously, detect and track, large numbers of high velocity targets

– Since then, the main issue has been the relatively high cost of these phased array radars

The “quest” for $100 T/R (transmit/receive) module

Phase Shifters - Why

TRADEXRadar

Patriot RadarMPQ-53

Time to move beam ~20°

order of magnitudemicroseconds

Time to move beam ~20°

order of magnitudeseconds

Courtesy of NATOCourtesy of MIT Lincoln LaboratoryUsed with Permission



Phase Shifters- How They Work

• The phase shift, , experienced by an electromagnetic wave is given by:

– f = frequency, L = path length v = velocity of electromagnetic wave– Note: v depends on the permeability, μ, and the dielectric constant, ε

• Modern phase shifters implement phase change in microwave array radars, mainly, by two methods:

– Changing the path length (Diode phase shifters) Semiconductors are good switching devices

– Changing the permeability along the waves path (Ferrite phase shifters)

EM wave interacts with ferrite’s electrons to produce a change in ferrite’s permeability

μεπ=π=φ Lf2v/Lf2

φ



Examples of Phase Shifters

• Diode phase shifter implementation– Well suited for use in Hybrid MICs and MMICs– At higher frequencies:

Losses increase Power handling capability decreases

• Ferrite Phase Shifter Implementation– At frequencies > S-Band, ferrite phase shifters often used

Diode phase shifters may be used, above S-Band On receive- after low noise amplifier (LNA) Before power amplifier on transmit

( )λ16/5Total Phase Shift

Drive Wires

Four Bit Latching Ferrite Phase Shifter

22 1/2° BitToroid

45° BitToroid

90° BitToroid

180° BitToroid

Microwave Power In

16/λ 8/λ 4/λ 2/λ

Four Bit Diode Phase Shifter

Individual22 1/2 ° Phase

Bit

MICMicrowaveIntegrated

CircuitMMIC

MonolithicMicrowaveIntegrated

Circuit




Radiating Elements for Phased Array Antennas

Metal Strip Dipole

Transmission Line

Printed Circuit Dipole

Stripline

RadiatingEdge Slot

CouplingStructure

Slot Cut in Waveguide

Notch Radiatorin Stripline

Rectangular PatchRadiator

Open EndWaveguideNotch

GroundPlane

Substrate

MetalPatch




Outline

• Introduction






• Other Topics



Phased Array Architectures

• How is the microwave power generated and distributed to the antenna elements?

• Passive vs. Active Array– Passive Array - A single (or a few) transmitter (s) from which

high power is distributed to the individual array elements– Active Array – Each array element has its own transmitter /

receiver (T/R) module T/R modules will be discussed in more detail in lecture 18

• Constrained vs. Space Feed– Constrained Feed Array– Space Fed Array



Feed Systems for Array Antennas

• Concepts for feeding an array antenna :

– Constrained Feed Uses waveguide or other microwave transmission lines

Convenient method for 2-D scan is frequency scan in 1 dimension and phase shifters in the other (more detail later)

– Space Feed Distributes energy to a lens array or a reflectarray Generally less expensive than constrained feed

no transmission line feed network Not able to radiate very high power

– Use of Subarrays The antenna array may be divided into a number of subarrays to

facilitate the division of power/ receive signal to (and from) the antenna elements

The AEGIS radar’s array antenna utilizes 32 transmit and 68 receive subarrays



Phased Array Antenna Configurations(Active and Passive)

Duplexer

Receiver &Signal

Processor

High PowerTransmitter

Suba

rray

Suba

rray

Suba

rray

Suba

rray

Passive Array

Suba

rray

Suba

rray

Suba

rray

Suba

rray

T/RT/RT/R

T/R

T/R

T/RT/RT/R

T/R

T/R

T/RT/RT/R

T/R

T/R

T/RT/RT/R

T/R

T/R

Low Power Transmit Pulse to

T/R Module

Receiver Output toA/D and Processing

Active Array Phase ShifterIn Each T/R Module

PhaseShifter




Examples – Active Array Radars

Suba

rray

Suba

rray

Suba

rray

Suba

rray

T/RT/RT/R

T/R

T/R

T/RT/RT/R

T/R

T/R

T/RT/RT/R

T/R

T/R

T/RT/RT/R

T/R

T/R


T/R Module



UHF Early Warning Radar

THAAD X-Band Phased Array Radar





More Examples – Active Array Radars

Suba

rray

Suba

rray

Suba

rray

Suba

rray

T/RT/RT/R

T/R

T/R

T/RT/RT/R

T/R

T/R

T/RT/RT/R

T/R

T/R

T/RT/RT/R

T/R

T/R


T/R Module



Counter Battery Radar (COBRA)Courtesy of Thales GroupUsed with Permission

APG-81 Radar for F-35 Fighter

Courtesy of Northrop GrummanUsed with Permission



Examples – Passive Array Radars

Duplexer

Receiver &Signal

Processor

High PowerTransmitter

Suba

rray

Suba

rray

Suba

rray

Suba

rray

Passive ArrayPhaseShifter

S- Band AEGIS Radar

L- Band COBRA DANE RadarCourtesy of US Air Force

Courtesy of U S Navy



Space Fed Arrays Reflectarrays and Lens Arrays

Curved PhaseFrom Offset Feed

Curved PhaseFrom Feed

Phase front after Steering by

Lens Array

Phase front after Steering by

Reflectarray

OffsetFeed

Reflectarray Configuration Lens Array Configuration

ShortCircuit

PhaseShifter



Example: Space Fed - Lens Array Radar

MPQ-39Multiple Object Tracking Radar

(MOTR)

8192 phase shifters (in a plane) take the place of the dielectric lens. The spherical wave of microwave radiation is phase shifted appropriately to form a beam and point it in the desired direction

MOTR Space Fed Lens Antenna

Courtesy of Lockheed MartinUsed with Permission

Courtesy of Lockheed MartinUsed with Permission



Examples: Space Fed - Lens Array Radars

Patriot Radar MPQ-53S-300 “30N6E” X-Band Fire Control Radar*

• * NATO designation “Flap Lid” – SA-10• Radar is component of Russian S-300 Air Defense System

Courtesy of MDA

Courtesy of L. Corey, see Reference 7



Example of Space Fed - Reflectarray Antenna

S-300 “64N6E” S-Band Surveillance Radar*

• * NATO designation “Big Bird” – SA-12• Radar is component of Russian S-300 Air Defense System

• Radar system has two reflectarray antennas in a “back-to-back”configuration.

• The antenna rotates mechanically in azimuth; and scans electronically in azimuth and elevation

Radar System and Transporter Radar Antenna

Courtesy of Martin RosenkrantzUsed with Permission

Courtesy of Wikimedia / ajkol



Two Examples of Constrained Feeds(Parallel and Series)

• Parallel (Corporate) Feed– A cascade of power splitters, in parallel, are used to create a tree like structure– A separate control signal is needed for each phase shifter in the parallel feed

design• Series Feed

– For end fed series feeds, the position of the beam will vary with frequency– The center series fed feed does not have this problem– Since phase shifts are the same in the series feed arraignment, only one control

signal is needed to steer the beam• Insertion losses with the series fed design are less than those with the

parallel feed

Parallel (Corporate) Feed

2/1 PowerSplitter

2/1 PowerSplitter

2/1 PowerSplitter

φ φ2

MicrowavePower φ

End Fed - Series Feed

φ φ φ

φ3 φ4



Outline

• Introduction



• Phased Array Antennas



• Other Topics



Frequency Scanned Arrays

• Beam steering in one dimension has been implemented by changing frequency of radar

• For beam excursion , wavelength change is given by:

• If = 45°, 30% bandwidth required for , 7% for

λπ=π=φ /L2v/Lf2

The phase difference between 2 adjacent elements is

where L = length of line connecting adjacent elements and v is the velocity of propagation

L Serpentineor

“Snake” Feed”

Main BeamDirection

1θ

TerminationStub

AntennaElements

D

( ) 1o sinL/D2 θλ=λΔ1θ±

1θ 5L/D = 20L/D =Adapted from Skolnik, Reference 1



Example of Frequency Scanned Array

• The above folded waveguide feed is known as a snake feed or serpentine feed.

• This configuration has been used to scan a pencil beam in elevation, with mechanical rotation providing the azimuth scan.

• The frequency scan technique is well suited to scanning a beam or a number of beams in a single angle coordinate.

Planar Array Frequency Scan Antenna




Examples of Frequency Scanned Antennas

SPS-52

SerpentineFeed

SPS-48E

Courtesy of US NavyCourtesy of ITT CorporationUsed with Permission

SerpentineFeed



Outline

• Introduction





• Example of Hybrid Method of Scanning

• Other Topics



ARSR-4 Antenna and Array Feed

• Joint US Air Force / FAA long range L-Band surveillance radar with stressing requirements

– Target height measurement capability– Low azimuth sidelobes (-35 dB peak)– All weather capability (Linear and Circular Polarization)

• Antenna design process enabled with significant use of CAD and ray tracing

ARSR-4 Antenna ARSR-4 Array Feed

OffsetArrayFeed

10 elevation Beams

Array Size17 x 12 ft

23 rowsand

34 columnsof elements

Courtesy of Northrop GrummanUsed with Permission

Courtesy of Frank SandersUsed with Permission



Phased Arrays vs Reflectors vs. Hybrids

• Phased arrays provide beam agility and flexibility – Effective radar resource management (multi-function capability) – Near simultaneous tracks over wide field of view– Ability to perform adaptive pattern control

• Phased arrays are significantly more expensive than reflectors for same power-aperture

– Need for 360 deg coverage may require 3 or 4 filled array faces– Larger component costs– Longer design time

• Hybrid Antennas – Often an excellent compromise solution– ARSR-4 is a good example array technology with lower cost

reflector technology– ~ 2 to 1 cost advantage over planar array, while providing

very low azimuth sidelobes



Outline

• Introduction






• Other Antenna Topics



Printed Antennas

Spiral Antenna

Log - Periodic AntennaCircular Patch Array inAnechoic Chamber




Antenna Stabilization Issues

• Servomechanisms are used to control the angular position of radar antennas so as to compensate automatically for changes in angular position of the vehicle carrying the antenna

• Stabilization requires the use of gyroscopes , GPS, or a combination, to measure the position of the antenna relative to its “earth” level position

• Radars which scan electronically can compensate for platform motion by appropriately altering the beam steering commands in the radar’s computer system



Radomes

• Sheltering structure used to protect radar antennas from adverseweather conditions

– Wind, rain, salt spray

• Metal space frame techniques often used for large antennas– Typical loss 0.5 dB

• Inflatable radomes also used – Less loss, more maintenance, flexing in wind

ALCOR COBRA GEMINI

MMW

Courtesy of US Navy





Summary

• Enabling technologies for Phased Array radar development– Ferrite phase shifters (switching times ~ few microseconds)– Low cost MMIC T/R modules

• Attributes of Phased Array Radars– Inertia-less, rapid, beam steering– Multiple Independent beams– Adaptive processing– Time shared multi-function capability– Significantly higher cost than other alternatives

• Often, other antenna technologies can offer cost effective alternatives to more costly active phased array designs

– Lens or reflect arrays– Reflectors with small array feeds, etc.– Mechanically rotated frequency scanned arrays



Acknowledgements

• Dr. Pamela R. Evans• Dr. Alan J. Fenn



References

1. Skolnik, M., Introduction to Radar Systems, New York, McGraw-Hill, 3rd Edition, 2001

2. Skolnik, M., Radar Handbook, New York, McGraw-Hill, 3rd Edition, 2008

3. Balanis, C.A., Antenna Theory: Analysis and Design, 3nd Edition,New York, Wiley, 2005.

4. Kraus, J.D. and Marhefka, R. J., Antennas for all Applications, 3nd

Edition, New York, McGraw-Hill, 2002.5. Hansen, R. C., Microwave Scanning Antennas, California,

Peninsula Publishing, 1985.6. Mailloux, R. J., Phased Array Antenna Handbook, 2nd Edition,

Artech House, 2005.7. Corey, L. E. , Proceedings of IEEE International Symposium on

Phased Array Systems and Technology, ”Survey of Low Cost Russian Phased Array Technology”, IEEE Press, 1996

8. Sullivan, R. J., Radar Foundations for Imaging and Advanced Concepts, 1st Edition, SciTech, Raleigh, NC, 2004



Homework Problems

• Skolnik, Reference 1

– 9.11, 9.13, 9.14, 9.15, 9.18, and 9.34

– For extra credit Problem 9.40

IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 65, NO. 6, JUNE 2017 2983

Design of a Phased Array in Triangular Grid Withan Efficient Matching Network and ReducedMutual Coupling for Wide-Angle Scanning

Bijan Abbasi Arand, Member, IEEE, Amir Bazrkar, and Amir Zahedi

Abstract— In this paper, a wide-scan angle planar patch phasedarray is proposed. The proposed array is composed of widebandprobe-fed microstrip patches placed 0.087λh(λh is the wavelengthof highest frequency) above individual ground planes and inter-laced with parasitic decoupling walls. In order to cancel the feedprobe inductance, the array elements comprise additional degreesof freedom to introduce controllable capacitance. Concurrently,individual ground planes and parasitic decoupling walls areproposed as an effective structure to considerably increase theE-plane scanning angle of the phased array by reducing the mag-nitude of near-field mutual coupling. A 544-element phased arrayprototype of the proposed element was designed, manufactured,and validated experimentally. The experimental results agree wellwith the numerical simulation ones and indicate effectiveness ofthe proposed design for mutual coupling reduction and wide-angle scanning. Because of the modifications, the measuredmutual coupling between adjacent elements is reduced to lowerthan −32 dB at the center frequency. The proposed phased arrayhas almost a constant active input impedance (active VSWRless than 2 over 20% bandwidth) up to scan angle of 65° inE-plane and 60° in H-plane, with a realized gain reduction ofabout 3.5 dB.

Index Terms— Microstrip phased array, mutual coupling,planar scanning antennas, wide-angle scanning.

I. INTRODUCTION

PLANAR microstrip arrays have received a lot of attentionin the past few decades thanks to their attractive features

of being low profile, low cost, compact size, and lightweight.In practical large phased arrays, inevitable mutual couplingamong array elements causes the active input impedance ofthe elements substantially changes as a function of beamscanning angle. The input impedance variation and mismatchmake the transmitted power return to the receivers and reducethe realized gain of the array antenna [1]. Therefore, a keyaspect in the design of a wide-scan angle phased array antennais to achieve wide-angle impedance matching and eliminatepossibility of scan blindness occurrences. Some techniqueshave been proposed to diminish magnitude of the mutual

Manuscript received March 10, 2016; revised January 14, 2017; acceptedMarch 10, 2017. Date of publication April 4, 2017; date of current versionMay 31, 2017. (Corresponding author: Bijan Abbasi Arand.)

B. Abbasi Arand and A. Zahedi are with the Department of Electrical andComputer Engineering, Tarbiat Modares University, Tehran 14115-111, Iran(e-mail: [email protected]; amir.zahedy@ modares.ac.ir).

A. Bazrkar is with the Department of Electrical and Electronic Engi-neering, Shiraz University of Technology, Shiraz 71946-84471, Iran (e-mail:[email protected]).

Color versions of one or more of the figures in this paper are availableonline at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TAP.2017.2690903

coupling among patch elements in an array environment.That is why the considerable attention has been surprisinglygiven to substrate modifications and baffles [2], using periodicstructures such as electromagnetic bandgap structures [3]–[5],defected ground structures [6]–[8], adding shorting pins under-neath the radiating patch [9], or enclose microstrip elementby a cavity [10]–[12]. The mutual coupling can be assignedto the three phenomena [13]: 1) near-field coupling due to thedirect interaction of electric charges between closely spacedelements [11], [15]; 2) far-field coupling due to the radiationof patch along the ground plane; and 3) surface-wave couplingdue to the surface mode excitation in dielectric slab [14].The far-field coupling can be efficiently reduced only ifthe antenna radiation in horizontal directions is suppressed.A patch antenna excites surface waves which are guided by thesubstrate and the ground plane [14] and consequently, whentwo patch elements are printed on a common high permittivitysubstrate, the surface wave can be significant. Thereby, if thesubstrate between elements is truncated, the propagation ofthe surface wave is suppressed. Near-field coupling is themost dominant coupling for very closely spaced elementswhereas surface waves are dominant for large separation, dueto their radial variations [16]. Based on these three basicstatements, two simple mutual coupling reduction techniquesare proposed. Two representative simple designs are depictedin Fig. 1. The first design is a pair of conventional patchelements placed in a conventional environment and the secondone is the same pair of patches, which are placed in a modifiedstructure with truncated substrate, separated ground plane, anda decoupling wall. In the following section, the proposedtechniques are investigated by comparing the magnitude ofmutual couplings between two patches of designs #1 and #2.

According to the proposed configuration in Fig. 1(b) anda novel impedance matching network, in this paper, a planarantenna array design, which have the following specifications,is presented: 1) low-profile with wide-angle scanning andwide impedance matching over 20% of operational fractionalbandwidth; 2) modularity and robustness which accommodateit to be mounted on a planar phased array structure; 3) highpower handling capability which allows for high power phasedarray systems; and 4) low cost because of using low costprinted circuit board fabrication technology.

This paper is organized as follows. The next section intro-duces the effectiveness of the aforementioned techniques inreduction of mutual coupling between two simple patchesand describes the design necessities of the antenna array.

0018-926X © 2017 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

2984 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 65, NO. 6, JUNE 2017

Fig. 1. Two-element patch array antennas with d = 0.6λ0, s = 0.32λ0,h = 0.08λ0, h1 = 0.1λ0, g = 0.15λ0 , L1 = 0.4λ0, and εr = 2.4.(a) Conventional two-element array geometry. (b) Modified two-element arraygeometry.

In Section III, the design details of the novel patch elementand the parametric study of its performance is provided.A choice of the patch and matching network parameters arethen selected to achieve the most proper broadside active inputimpedance. Experimental demonstrations using a 544-elementphased array prototype are explored in Section IV. Finally,a conclusion is given in Section V.

II. INVESTIGATION OF THE PROPOSED TECHNIQUES

AND THE PHASED ARRAY NECESSITIES

A. Proposed Techniques

When the antenna elements are placed along principalE-plane, the mutual coupling is significantly stronger and inputimpedance of the array elements changes more rapidly withscan angle [17], [18]. As can be seen in Fig. 1, the tworepresentative patch elements are placed along the E-plane andthe coupling between them is investigated.

Design #1 was first investigated to evaluate the mutualcoupling between the patches. As it has been pointed out

Fig. 2. Scattering parameters of the conventional and modified two-elementarrays (w → with and w/o → without).

Fig. 3. Magnitude of mutual coupling coefficient between two patches ofdesign #2 for various decoupling structure geometric parameters.

in the previous section, the destructive effect of mutual cou-pling on the active input impedance of the elements duringelectronically scanning of the beam can be compensated byintroducing proper modifications in the structure of the array.The truncated substrate cannot support surface wave mode andeliminates any possibility of it on the mutual coupling [19].In order to diminish surface wave as well as a reduction ofthe far-field horizontal radiation of the patches, the patchesin design #2 are backed by two separated low permittivitysubstrates. The purpose of introducing the separated groundplane and decoupling wall is to diminish near-field couplingbetween the two patch elements.

Fig. 2 shows the simulated results of reflection and mutualcoupling coefficients between the elements of the two-elementarrays. As can be seen in Fig. 2, the proposed techniqueshave been significantly decreased the magnitude of mutualcoupling with a negligible effect on reflection coefficient.Fig. 3 shows the magnitude of the mutual coupling as afunction of frequency for different gap and decoupling walldimensions. In design #2, the near-field interaction between

ABBASI ARAND et al.: DESIGN OF A PHASED ARRAY IN TRIANGULAR GRID WITH AN EFFICIENT MATCHING NETWORK 2985

two adjacent patches is reduced significantly due to theseefficient decoupling modifications.

As can be seen in Fig. 3, the more the distance of thegap is, the more the decoupling is. This phenomenon is dueto alleviation of interaction between charges on the arrayground plane when the patches are resonating. This modi-fication causes the electrical distance between two adjacentpatches to increase and subsequently the mutual conductancedeclines dramatically. Meanwhile, introducing the decouplingwall causes the TM configured fields at the equivalent radiatingslots of the patch not to be coupled directly to the adjacentpatch. As can be seen in Fig. 2, minimum magnitude of mutualcoupling is achieved when both the gap and the decouplingwall are applied to the design #2.

Since the decoupling walls between the elements of anarray remain thin, during H-plane scan the array of decouplingwalls will not affect the H-plane scan [18]. Therefore, it isexpected that by applying these two mutual coupling reductiontechniques, a significant improvement in a phased array scanperformance is obtained. As can be seen in Fig. 3, the effectof the introduced decoupling techniques entirely depends onthe size of the gap and decoupling wall. Thus, these geometricparameters should be determined for each specific design.

B. Design Requirements

The specifications of the array considered in this paper areas follows.

1) Center Frequency: f0 (at S-band).2) Operational Bandwidth: About 20% (0.9–1.1 f0).3) Active VSWR: < 2.4) Maximum Scan Range: ±65° (E-plane) and ±60°

(H-plane).5) No grating lobes in the field of visible space.6) No scan blindness in the field of scan volume.7) Polarization: Linear.8) Minimum Element Spacing: 0.53λh .9) Maximum Array Aperture Height: 0.5λ0.

10) The elements should be modular, robust, and capable ofhigh power handling.

11) Application: Antenna of an active phased array.

The first step is design of a proper array configuration to meetthe phased array system requirements. A way to reduce thecost is use element spacing greater than a half wavelengthwhich leads to less transmit/receive modules. Triangular gridsprovide another way to reduce element count whereas main-taining scan performance properly [1]. Hence, in order to avoidgrating lobes in visible space, an equilateral triangular grid hasbeen chosen with spacing 0.61λh . The grating lobe diagramfor this arrangement is shown in Fig. 4, and compared to thecorresponding result obtained for the same element spacing(0.61λh) in a rectangular grid.

The next step is selection of a proper single element to fulfillthe array requirements.

The microstrip patch seems to be a proper choice to meetthe system requirements, because of their low cost, ease offabrication, wideband, and wide-angle radiation characteris-tics. Fig. 5 shows an illustration of a 16-element array of the

Fig. 4. Grating lobe diagram comparison between the equilateral triangulargrid (0.61λh in E-plane and 0.53λh in H-plane) and rectangular grid (0.61λhin y-direction and 0.53λh in x-direction) for phased arrays.

Fig. 5. Illustration of 16-element array in the triangular grid with d = 0.61λhand d ′ = 0.53λh .

TABLE I

DESIGN PARAMETERS OF THE PATCH ANTENNA ELEMENT (unit: λ0)

proposed patch elements, where the center to center spacingbetween elements is denoted as d = 0.61λh . As depictedin Fig. 6, for this design the patch is etched on a 20 milthick low loss RO4003 substrate with a relative permittivityof 3.55 and tan δ = 0.0012. The printed patch is placedover a hollowed poly tetra fluoro ethylene insulator with arelative permittivity of 2.1. In order to improve the fractionalbandwidth and furthermore diminish gain of the antennaelement in horizontal direction along the ground plane, eachpatch is placed 0.087λh above an individual ground plane. Thededicated area per element of the array is Acell = (0.61λh)2×sin 60° and the total height of the antenna element, includingthe radome, is 0.22λ0. The dimensions of the proposed elementare summarized in Table I.

III. STUDY OF THE PROPOSED ARRAY ELEMENT

The proposed element is depicted in Fig. 6. As shownin Fig. 6(b), the feed probe is passed through the grounded


Fig. 6. Proposed patch element. (a) Top view. (b) Cross-sectional view.(c) Exploded view.

metallic cylinder. Increasing the probe length leads to moreinductive reactance of the feed which limits the impedancebandwidth of patch antennas [21]. As it is obvious, the longprobe length underneath a patch can also acts as a monopoleand because of its current direction, the cross-polarized field ofthe antenna would be increased. The novel proposed cylinderhelps for better control of the probe inductance of the feed

and also makes the electrical length of the probe shorter.As depicted in Fig. 6(c), in order to match the antenna

to the characteristic impedance of the feed line and broadenits bandwidth, precisely underneath the patch the probe isconnected to a capacitive disk, and it is soldered at its endto the patch strip. It should be mentioned that the disk and thepatch strip are electrically connected to each other througha via. The space between top surface of the cylinder andthe disk acts as a controllable stub and is tuned to diminishthe inductive reactance of the input impedance of the antennaelement.

To eliminate the possibility of existence of any scan blind-ness over the scan range, the proposed aforementioned decou-pling techniques is introduced into the array element unitcell. Finally, the antenna structure is covered by a low lossradome. Individual ground planes of the array elements wouldimply undesired backward radiation. As depicted in Fig. 5,to compensate this undesired effect, the patch elements havebeen mounted above a metallic plate. This metallic plateeliminates the backward radiation of the array as well aspreparing a modular fixture for antenna elements to mount onthe phased array structure. The metallic plate has been placedin a proper distance from the patches to reflect backward wavesin a manner to add in-phase to the forward radiation.

The antenna element is characterized by its most cru-cial parameters: g (distance between cylinder and disk),r2 (the cylinder radius), and L1 (length of the ground). In thefollowing, a parametric investigation of these three parametersof the proposed array element in unit cell environment iscarried out. As beginning point, the following parameters arechosen: g = 0.064λ0, r2 = 0.025λ0, and L1 = 0.3λ0.All simulations are executed for infinite array analysis withthe commercial software CST MICROWAVE STUDIO infrequency domain.

The first parameter to investigate is the gap betweentop surface of the cylinder and the disk, g. As depictedin Fig. 7, with g = 0.064λ0, reactance is inductive andif g decreases gradually, the reactance is desirably reduced.However, the resistance is affected in a minor manner. Wheng decreases, the introduced capacitance which is in series withthe inductance of the feed probe is increased and consequently,the reactance of the input impedance will be reduced. There-fore, for a proper g = 0.025λ0, the input reactance will beabout zero. If g decreases more than 0.025λ0, the reactancewill be capacitive and it is not a desirable effect.

The next parameter to be considered was the radius of thematching cylinder. As depicted in Fig. 8, as r2 increases,the input resistance and reactance are reduced in the samemanner. It is evident that as r2 increases, due to the largercapacitive area between the disk and the cylinder, the inductiveeffect of the feed network is decreased. This, of course, leadsto the desired effect of decreasing the center of operationalfrequency bandwidth. As such, the cylinder radius is animportant parameter used to match the array element radiationresistance to the specific system impedance.

The last parameter that should be considered is the length ofthe ground plane, L1. Fig. 9 shows the impedance curves ver-sus frequency for L1 = 0.3λ0, 0.35λ0, 0.4λ0, and 0.43λ0. It is


Fig. 7. Active resistance (solid) and reactance (dashed) of the proposed patchelement at broadside with the g varied. All other parameters are kept constantas shown in Table I.

Fig. 8. Active resistance (solid) and reactance (dashed) of the proposedpatch element at broadside with the r2 varied. All other parameters are keptconstant as shown in Table I.

observed that as L1 increases, resistance below f0 is increasedwhereas the resistance above f0 is decreased. Therefore, as L1increases, the steep curve of the resistance versus frequency isgetting smoother and at a proper length L1 it reaches approx-imately about the constant 50� characteristic impedance overthe frequency bandwidth. Therefore, the reactance decreasesspecifically around the center frequency and at a proper L1 itreaches to zero over the entire frequency bandwidth. As such,L1 is a critical parameter to increase bandwidth and matchthe proposed element to the 50� characteristic impedance.According to the input impendence graphs, the following para-meters were selected for the proposed phased array element:g = 0.021λ0, r2 = 0.05λ0, and L1 = 0.45λ0. This providesa reasonably constant input impedance of about 50� with asmall capacitive reactance. For this case, the simulated E- andH-plane active reflection coefficient of the patch element ininfinite array environment is depicted in Figs. 10 and 11,respectively. Of importance is the remarkable scanning perfor-mance of this array. As depicted in Figs. 10 and 11, the arrayelement maintains an active reflection coefficient less than−10 dB over frequency bandwidth whereas scanning up to65° in the E-plane and 60° in the H-plane.

Fig. 9. Active resistance (solid) and reactance (dashed) of the proposedpatch element at broadside with the L1 varied. All other parameters are keptconstant as shown in Table I.

Fig. 10. Simulated E-plane active reflection coefficient of the proposed arrayelement over multiple scan angles.

Fig. 11. Simulated H-plane active reflection coefficient of the proposed arrayelement over multiple scan angles.

In the following, the simulation and measured resultsof a 544-element array prototype will verify the perfor-mance of the proposed array element for enhancement of the


Fig. 12. 544-element linear polarized phased array prototype.

E-plane scanning characteristic, and furthermore will revealthat the modifications also improve the D- and H-plane scan-ning characteristics of the considered phased array.

IV. 544-ELEMENT PHASED ARRAY

EXPERIMENTAL RESULTS

The performance improvements of the array are experi-mentally verified through the manufacturing of 544-elementarray antenna. A photograph of the array prototype is shownin Fig. 12. The prototype array was manufactured to examinesome of the fabrication challenges and verify the proposedstructure effectiveness.

The concept of N-port reciprocal microwave networks [22]which includes the incident voltage vector [V +], the reflectedvoltage vector [V −], and the scattering matrix [S] is applied tocalculate the active reflection coefficient of the central elementof the fabricated 544-element array for E-, H-, and D-planescanning. This is simply done by adding the measured complexself- and mutual coupling coefficients together. As depictedin Fig. 13, the antenna element under test is denoted aselement No.1. In that case, the element No.1 was connectedto port 1 of a network analyzer and one of the neighboringelements of the central element was connected to port 2 ofthe network analyzer, while the other elements were match-ended by 50� terminations. Thus, self-coupling and all mutualcoupling coefficients between the element No.1 and the otherelements were measured and a set of complex coefficientswere obtained. Therefore, the calculated active reflection coef-ficients are derived and expressed as follows:

⎡⎢⎢⎢⎣

V −1

V −2

...

V −N

⎤⎥⎥⎥⎦ =

⎡⎢⎢⎢⎣

S11 S12 · · · S1N

S21 S22 · · · S2N...

.... . .

...SN1 SN2 · · · SN N

⎤⎥⎥⎥⎦

⎡⎢⎢⎢⎣

V +1

V +2

...

V +N

⎤⎥⎥⎥⎦ (1)

where Sij is defined as:V −

i

V +j

|Vk=Terminated

|S11−active| = 20 log10

∣∣S11e jk(x11u+y11v) + S21e jk(x21u+y21v)

+ · · · + SN1e jk(xN1u+yN1v)∣∣ (2)

Fig. 13. Schematic front view of the 544-element array and triangular grid.

where u = sin θ × cos ϕ and v = sin θ × sin ϕ. In thiscase, the mutual coupling coefficients with magnitude lessthan −55 dB were not brought in the calculation of theactive reflection coefficient of element No.1 and, thus, only100 neighboring elements around the element No.1 wereincluded in the calculations.

The digitally calculated magnitude of broadside activereflection coefficient of the element No.1 and mutual couplingcoefficients between element No.1 and some of its neighboringelements are depicted in Fig. 14. It is evident that the measuredmutual coupling between element No.1 and its adjacent ele-ments is lower than −32 dB at the center frequency. A usefulfigure of merit in evaluating the scan performance of an arrayand determining how far the main beam can be scanned beforethe scan blindness occurs, is the broadside conjugate matchedreflection coefficient [23]

S11−active(θ, ϕ) = Z in(θ, ϕ) − Z in(0, 0)

Z in(θ, ϕ) + Z∗in(0, 0)

. (3)

The cutoff point for acceptance of maximum scan angle istaken to be |S11−active| < −10 (dB). The phases of themeasured complex reflection coefficients and mutual couplingsare assigned according to the specified scanning angle (θ ,ϕ) ofthe phased array in the E-, H-, and D-plane using MATLAB.Fig. 15 shows the active reflection coefficient of the elementNo.1 regarding three principal scanning planes. The scanblindness in the array can occur at the angles corresponding tothe peaks in the active reflection coefficient graph. As can beseen in Fig. 15, there is no scan blindness in the operationalfrequency range. As shown in Figs. 14 and 15, the operationalbandwidth covers the frequency band from 0.9 f0 to 1.1 f0.It is noticeable that there is a very good agreement betweensimulated results of Figs. 10 and 11, achieved in an infinitearray and measured results achieved with the 544-elementarray prototype. The minor discrepancies between simulatedresults of infinite array and the measured ones can be relatedto the following. First, the discontinuity at the boundary of theground plane introduces electrical field diffraction at the edgeof the antenna array. Second, finite number of elements in themanufactured array in comparison with the infinite number of


Fig. 14. Measured and simulated broadside active reflection coefficient ofelement No.1 and the mutual coupling between the central element and itsneighboring elements.

Fig. 15. E-, H-, and D-plane measured broadside-matched reflectioncoefficients versus scan angle for central element of the 544-element arrayprototype.

elements in the simulation is another reason for discrepancy.Third, the coupling coefficients among the antenna elements(Sk1, k = 2, 3, …, N) are very difficult to be measuredaccurately, because of the high-isolation of the array elements,with a maximum magnitude of about −32 dB.

In addition, the measured self-coupling and all the mutualcoupling coefficients between the element No.1 and the otherelements of the array are used to calculate the realized elementefficiency [24]. The element efficiency in an array is definedas one minus the ratio of power radiated to free space by anelement in the array environment divided by power available,when only that element is excited. This ratio is equal to powerreturned to all generators when only one generator is excited.Thus the calculated element efficiency is derived from themeasured complex self- and mutual coupling coefficients asfollows:

Element efficiency = 1 − Preturned

Pinput= 1 − {|S11|2 + |S21|2

+· · · + |SN1|2}. (4)

Fig. 16. Measured normalized AEPs in E- and H-planes for the elementNo.1 at center frequency ( f0) compared to the ideal cos(θ) pattern.

Fig. 17. Measured and computed broadside copolarized and cross-polarizedrealized gain of the 544-element array.

Therefore, using (4), the central element efficiency at f0 isabout 94.2%.

Fig. 16 shows the normalized measured active elementpattern (AEP) of element No.1 in both E- and H-planes and theideal cos(θ) pattern. The AEP is related to the active reflectioncoefficient and the angle of scan blindness occurrence [25].Also, the AEP includes the element pattern in array environ-ment with all mutual coupling accounted for. As can be seenin Fig. 16, it is obvious that the corresponding E-plane AEP ofthe element No.1 in comparison with the ideal cos(θ) patternhave no significant power reflection in the field of scanningangle and it is free from any scan blindness, thanks to theproposed modifications applied to the patch. From Fig. 16,it can be found that the E-plane AEP is similar to the idealcos(θ) pattern for θ = 65°, but at grazing angles the E- andH-plane patterns deviate significantly due to the cancelationof radiated fields associated with ground plane image currentand structure of the patch element.

The realized gain of a large array antenna is also related tothe AEP and active reflection coefficient of the array elements


Fig. 18. Measured broadside H-plane radiation patterns of the 544-elementphased array antenna at f0 before and after calibration.

Fig. 19. Measured and simulated H-plane radiation patterns of the544-element phased array antenna at f0 scanned to θ = 0°, θ = 30°,and θ = 60°.

by [24]

GAEP(θ, ϕ) = 4π Acell

λ2 [1 − |(θ, ϕ)|2] cos θ (5)

GArray(θ, ϕ) = NGAEP(θ, ϕ). (6)

Therefore, the realized gain of 544-element array is com-puted utilizing measured AEP where Acell is area of the ele-ment unit cell in array environment and N is 544. As depictedin Fig. 17, the computed gain is compared to the simu-lated directivity and the direct measured realized gain of the544-element phased array antenna. As can be seen in Fig. 17,the simulated directivity and direct measured gain of the arrayare reasonably similar with a minor discrepancy due to theerrors in the calibration process, dielectrics losses, and finiteground plane diffraction.

To demonstrate the importance of the calibration procedureof the phased array antennas, the measured RX radiationpatterns of the array at center frequency are depicted in Fig. 18.Also, to demonstrate the wide-angle scanning performanceof the array, the measured and simulated H-plane radiation

Fig. 20. Measured and simulated E-plane radiation patterns of the544-element phased array antenna at f0 scanned to θ = 0°, θ = 30°,and θ = 65°.

patterns at center frequency are shown in Fig. 19. Similarly, theE-plane radiation patterns which are scanned to the broadside,30° and 65°, are depicted in Fig. 20. Indeed, good agree-ment between simulated and measured patterns is observed.Additionally, the measured cross-polarized component remains19 dB below the copolarized component when the beam isscanned to θ = 60° in E- or H-plane. The radiation patternsin the other frequencies show similar agreement and wereomitted for brevity. As can be seen in Figs. 19 and 20, gaindegradation of the scanned beams has a behavior similar tothe AEPs in Fig. 16. Finally, it should be mentioned thatto avoid manufacturing complexity and radiation losses, it isrecommended to take advantage of the proposed structure infrequencies from L- to X-band.

V. CONCLUSION

A novel array element with integrated matching networkwas presented as the array element of an active phasedarray antenna. The array element is placed 0.078λh over aground plane and it made several degrees of freedom toallow cancelation of the inductance caused by the feed probeand ground plane. Several parametric sweeps were presentedto control the array impedance. In order to achieve wide-angle scanning performance, two decoupling techniques wereintroduced to the array element and consequently, the mutualcoupling between adjacent elements diminished significantly.The results indicate the suitability of the proposed approachin achieving a phased array antenna with relatively widebandwidth and wide-angle scanning performance. The pro-posed array is capable of scanning up to 65° in E-planeand 60° in both D- and H-planes with an active VSWRless than 2 over 20% operational bandwidth. The proposedmutual coupling reduction techniques can provide a degree offreedom in other types of array elements to achieve widebandwide-angle scanning performance. Finally, a finite 544-elementarray was fabricated and validated by extensive computationsand experiments. A very good agreement between the sim-ulated and measured results was obtained over several scanangles.


ACKNOWLEDGMENT

The authors would like to thank the anonymous reviewers ofthis paper for their valuable comments and suggestions, whichhave greatly improved the quality of this paper.

REFERENCES

[1] N. Amitay, V. Galindo, and C. P. Wu, Theory and Analysis of PhasedArray Antennas. Hoboken, NJ, USA: Wiley, 1972.

[2] M. Davidovitz, “Extension of the E-plane scanning range in largemicrostrip arrays by substrate modification,” IEEE Microw. Guided WaveLett., vol. 2, no. 12, pp. 492–494, Dec. 1992.

[3] L. Zhang, J. A. Castaneda, and N. G. Alexopoulos, “Scan blindnessfree phased array design using PBG materials,” IEEE Trans. AntennasPropag., vol. 52, no. 8, pp. 2000–2007, Aug. 2004.

[4] G. Donzelli, F. Capolino, S. Boscolo, and M. Midrio, “Elimination ofscan blindness in phased array antennas using a grounded-dielectric EBGmaterial,” IEEE Antennas Wireless Propag. Lett., vol. 6, pp. 106–109,2007.

[5] F. Yang and Y. Rahmat-Samii, “Microstrip antennas integrated withelectromagnetic band-gap (EBG) structures: A low mutual couplingdesign for array applications,” IEEE Trans. Antennas Propag., vol. 51,no. 10, pp. 2936–2946, Oct. 2003.

[6] C.-Y. Chiu, C.-H. Cheng, R. D. Murch, and C. R. Rowell, “Reductionof mutual coupling between closely-packed antenna elements,” IEEETrans. Antennas Propag., vol. 55, no. 6, pp. 1732–1738, Jun. 2007.

[7] H. Moghadas, A. Tavakoli, and M. Salehi, “Elimination of scanblindness in microstrip scanning array antennas using defected groundstructure,” AEU-Int. J. Electron. Commun., vol. 62, no. 2, pp. 155–158,Feb. 2008.

[8] D. B. Hou, S. Xiao, B. Z. Wang, L. Jiang, J. Wang, and W. Hong,“Elimination of scan blindness with compact defected ground structuresin microstrip phased array,” IET Microw., Antennas Propag., vol. 3,no. 2, pp. 269–275, Mar. 2009.

[9] M. M. Nikolic, A. R. Djordjevic, and A. Nehorai, “Microstrip antennaswith suppressed radiation in horizontal directions and reduced cou-pling,” IEEE Trans. Antennas Propag., vol. 53, no. 11, pp. 3469–3476,Nov. 2005.

[10] N. C. Karmakar, “Investigations into a cavity-backed circular-patch antenna,” IEEE Trans. Antennas Propag., vol. 50, no. 12,pp. 1706–1715, Dec. 2002.

[11] M. H. Awida, A. H. Kamel, and A. E. Fathy, “Analysis and designof wide-scan angle wide-band phased arrays of substrate-integratedcavity-backed patches,” IEEE Trans. Antennas Propag., vol. 61, no. 6,pp. 3034–3041, Jun. 2013.

[12] M. C. van Beurden, A. B. Smolders, M. E. J. Jeuken,G. H. C. van Werkhoven, and E. W. Kolk, “Analysis of wide-bandinfinite phased arrays of printed folded dipoles embedded in metallicboxes,” IEEE Trans. Antennas Propag., vol. 50, no. 9, pp. 1266–1273,Sep. 2002.

[13] L. B. Felsen and N. Marcuvitz, Radiation and Scattering of Waves.Englewood Cliffs, NJ, USA: Wiley, 1973.

[14] R. E. Collin, Foundations for Microwave Engineering. New York, NY,USA: McGraw-Hill, 1992.

[15] R.-L. Xia, S.-W. Qu, P.-F. Li, D.-Q. Yang, S. Yang, and Z.-P. Nie,“Wide-angle scanning phased array using an efficient decoupling net-work,” IEEE Trans. Antennas Propag., vol. 63, no. 11, pp. 5161–5165,Nov. 2015.

[16] N. Alexopoulos and I. Rana, “Mutual impedance computation betweenprinted dipoles,” IEEE Trans. Antennas Propag., vol. AP-29, no. 1,pp. 106–111, Jan. 1981.

[17] D. M. Pozar, “Input impedance and mutual coupling of rectangularmicrostrip antennas,” IEEE Trans. Antennas Propag., vol. AP-30, no. 6,pp. 1191–1196, Nov. 1982.

[18] S. Edelberg and A. A. Oliner, “Mutual coupling effects in large antennaarrays II: Compensation effects,” IRE Trans. Antennas Propag., vol. 8,no. 4, pp. 360–367, Jul. 1960.

[19] J.-G. Yook and L. P. B. Katehi, “Micromachined microstrip patchantenna with controlled mutual coupling and surface waves,” IEEETrans. Antennas Propag., vol. 49, no. 9, pp. 1282–1289, Sep. 2001.

[20] E. Sharp, “A triangular arrangement of planar-array elements thatreduces the number needed,” IRE Trans. Antennas Propag., vol. 9, no. 2,pp. 126–129, Mar. 1961.

[21] H. Malekpoor, A. Bazrkar, S. Jam, and F. Mohajeri, “Miniaturized trape-zoidal patch antenna with folded ramp-shaped feed for ultra-widebandapplications,” Wireless Pers. Commun., vol. 72, no. 4, pp. 1935–1947,Oct. 2013.

[22] J. A. Dobrowolski, Microwave Network Design Using the ScatteringMatrix. Miami, FL, USA: Artech House, 2010.

[23] J. T. Aberle and F. Zavosh, “Analysis of probe-fed circular microstrippatches backed by circular cavities,” Electromagnetics, vol. 14, no. 2,pp. 239–258, Apr./Jun. 1994.

[24] P. Hannan, “The element-gain paradox for a phased-array antenna,”IEEE Trans. Antennas Propag., vol. 12, no. 4, pp. 423–433, Jul. 1964.

[25] D. M. Pozar, “A relation between the active input impedance and theactive element pattern of a phased array,” IEEE Trans. Antennas Propag.,vol. 51, no. 9, pp. 2486–2489, Sep. 2003.

Bijan Abbasi Arand (M’15) received the B.Sc.degree from Shiraz University, Shiraz, Iran, in 1995,and the M.S. and Ph.D. degrees in telecommunica-tion engineering from Tarbiat Modares University,Tehran, Iran, in 1997 and 2003, respectively.

From 2003 to 2005, he was a Researcher withthe Electromagnetic Propagation Department, IranTelecommunication Research Center, North Kargar,Iran. In 2005, he joined the Satellite communica-tion Laboratory, Tarbiat Modares University, Tehran,Iran, as a Post-Doctoral Researcher. Since 2010,

he has been an Assistant Professor with the Faculty of Electrical andComputer Engineering, Tarbiat Modares University. He has published morethan 35 papers and publications in journals and conferences.

Amir Bazrkar was born in Tehran, Iran, in 1985.He received the B.Sc. degree in electronics engineer-ing from the University of Guilan, Rasht, Iran, andthe M.S. degree in communication engineering fromthe Shiraz University of Technology, Shiraz, Iran.

His current research interests include phased arrayantennas design, meta-materials, electromagneticband gaps, and their applications at microwave fre-quencies.

Amir Zahedi was born in Rasht, Iran, in 1988.He received the B.Sc. degree in electrical engineer-ing from Mehrastan University, Astaneh Ashrafieh,Iran, and the M.Sc. degree in electrical engineeringfrom Tarbiat Modares University, Tehran, Iran.

His current research interests include antennaand propagation, microwave passive circuits, andoptimization methods applied to electromagneticproblems.

Mr. Zahedi has been a member of the MembershipDevelopment Committee in the IEEE Iran Sectionsince 2014.

Hindawi Publishing CorporationInternational Journal of Antennas and PropagationVolume 2009, Article ID 624035, 10 pagesdoi:10.1155/2009/624035

Research Article

Sunflower Array Antenna with Adjustable Density Taper

Maria Carolina Vigano,1 Giovanni Toso,2 Gerard Caille,3 Cyril Mangenot,2 and Ioan E. Lager1

1 International Research Centre for Telecommunications and Radar (IRCTR), Delft University of Technology,Mekelweg 4, P.O. Box 5031, 2628 GA Delft, The Netherlands

2 European Space Agency, ESA-ESTEC, 2200 AG Noordwijk, The Netherlands3 Thales Alenia Space, 26 Avenue J. F. Champollion, 31037 Toulouse, Cedex 1, France

Correspondence should be addressed to Maria Carolina Vigano, [email protected]

Received 24 September 2008; Accepted 5 January 2009

Recommended by Stefano Selleri

A deterministic procedure to design a nonperiodic planar array radiating a rotationally symmetric pencil beam pattern with anadjustable sidelobe level is proposed. The elements positions are derived by modifying the peculiar locations of the sunflower seedsin such a way that the corresponding spatial density fits a Taylor amplitude tapering law which guarantees the pattern requirementsin terms of beamwidth and sidelobe level. Different configurations, based on a Voronoi cell spatial tessellation of the radiativeaperture, are presented, having as a benchmark the requirements for a typical multibeam satellite antenna.

Copyright © 2009 Maria Carolina Vigano et al. This is an open access article distributed under the Creative Commons AttributionLicense, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properlycited.

1. Introduction

Communication satellites use multiple beam antennas pro-viding downlink and uplink coverages over a field of viewfor high data rate, multimedia, or mobile personal com-munication applications. High gain, multiple overlappingspot beams, using both frequency and polarization reuse,provide the needed coverage. In order to generate high gainspot beams, electrically large antenna apertures are required.These apertures may be generated by either reflectors orphased arrays. Phased arrays would be a natural choice togenerate multiple beams but up to now the poor efficiency,the high cost, and the deployment complexity of activearrays have been their main drawbacks, limiting their useonboard satellites. These drawbacks are mainly due to therequired distributed and tapered power amplification whichis inducing poor power efficiency.

Aperiodic arrays with equiamplitude elements permit tomitigate these limitations and represent a valid alternative totraditional periodic phased arrays with amplitude tapering.Resorting to aperiodic arrays with equiamplitude fed ele-ments is particularly effective for the design of large arraysworking in transmission. This type of antenna architecture isconsidered extremely promising for achieving a multibeamcoverage on the Earth from a geostationary satellite [1–4].

Unequally spaced arrays have several interesting char-acteristics and may offer some potential advantages withrespect to periodic arrays [2]. Firstly, aperiodic arrays allowthe reduction of the sidelobe level (SLL) without resortingto an amplitude tapering. A second useful property ofaperiodic arrays is the possibility to reduce the number ofelements in one assigned aperture without major impact onthe beamwidth. The reduction in the number of elements,with respect to the corresponding periodic array, dependson the required aperture efficiency and on the field of viewwhere the assigned sidelobe level is imposed (based onthe desired scanning range and regulatory aspects). Thirdly,sparse arrays can effectively be employed for spreading outthe energy that would otherwise accumulate in grating lobes(GL) due to the wide interelement spacing.

In terms of limitations, nonperiodic arrays exhibit areduced aperture efficiency when identical, non-equispacedelements are used. As a consequence, a reduced maximumequivalent isotropically radiated power (EIRP) is obtainedif not compensated by an increase of the power radiated byeach active chain. Furthermore, implementation constraints,as a nonregular lattice, may jeopardize the use of genericbuilding blocks, with consequences on the costs. Thisparticular drawback may be mitigated by implementing a setof different types of subarrays to fill the whole aperture.

2 International Journal of Antennas and Propagation

Up to now, sparse and thinned arrays have been rarelyused, essentially because of the complexity of their analysisand synthesis with a reduced knowledge, as a consequenceof their radiative properties. The main concern in the designof sparse arrays is to find an optimal set of element spacingto meet the array specifications, while assuming a uniformexcitation for practical convenience.

The synthesis of aperiodic arrays is a known problem inthe antenna community [5–22]. It is interesting to observethat while in the 1960s and 1970s mainly deterministic solu-tions have been proposed, in the last years procedures basedon statistic global optimization techniques have been mainlypresented. Recently, in [22], the simple and elegant spatialtapering deterministic solution introduced in the papers ofDoyle [11] and Skolnik [17], and qualitatively in the work ofWilley [7], has been revisited and improved. Deterministicsolutions present two important advantages with respect tostatistical algorithms: they allow obtaining results in real timeand offer a solution with a controllable accuracy. Moreover,the results obtained applying deterministic solutions maybe directly used or adopted as starting point for a furtheroptimization based on a numerical technique which cantake into account other constraints (like maximum andminimum spacing between the radiators, etc.).

The problem of aperiodic arrays has recently gaineda renewed interest especially for the design of multibeamsatellite antennas [1–4]. Most of the techniques presented forthe design of aperiodic arrays deal with the case of lineararrays. When approaching the planar case, the designer hasa higher number of degrees of freedom but the problemincreases also in complexity. In some papers, an aperiodicplanar lattice organized in rings has been proposed [12–14]. Arrays organized in rings permit having a patternwith good symmetry properties, allow the reduction andcontrol of GL, and their design is simplified because theelements positions can be expressed as the product oftwo functions one controlling the angular position of theelements and one controlling the distance of the rings fromthe center.

In this paper, the equiamplitude elements constitutingthe aperiodic array are placed on a lattice reproducingthe positions of the sunflower seeds, opportunely adjustedaccording to a desired amplitude tapering. This type of latticeis selected essentially because it guarantees a really goodradial and azimuthal spreading in the element positions. As aconsequence, the pattern in the sidelobes and grating lobesregion tends having a plateau-like shape [9, 16], avoidingthe presence of high narrow peaks. Moreover, by adjustingthe element positions using a simple parametric equation,a beamwidth can be selected and the SLL kept under anassigned value.

An aperiodic planar array with the elements organizedaccording to a sunflower lattice has been already proposedin [23]. However, the spatial density of the elements in[23] is uniform. As a consequence, since the elements areequiamplitude, the equivalent amplitude tapering is uniformas well so that this type of array guarantees only a goodsuppression of the GL, without the ability of controlling theSLL.

The hereby proposed sunflower lattice is completelyadjustable in order to follow stringent requirements on thebeamwidth and the SLL without using any amplitude taper.This planar array can be considered in the design of a trans-mitting direct radiating array for a satellite communicationantenna on a geostationary satellite.

The paper now proceeds as follows. In Section 2 theradiation pattern is introduced for a generic array, inSection 3 the definition of the element density functionis given and discussed for the uniform case. In Section 4a procedure to adjust the spatial density according to aTaylor amplitude tapering is presented. In Section 5 therequirements of a typical telecommunication multibeamantenna are introduced. Finally, in Section 6 some numericalresults, in order to test the functionality of the proposedconfiguration, are presented. Additionally, the appendixesprovide more general information on spirals and discuss thenormalized element density that is used in the course of theelement placement.

2. Array Radiation Pattern

The antenna radiation pattern of a planar array is given by

E(θ,φ) =N∑

n=1

anFn exp(jk[xn sin(θ) cos(φ)

+ yn sin(θ) sin(φ)])

,

(1)

where N is the total number of elements, an represents theexcitation coefficient for the nth element and Fn its radiationpattern, xn and yn are the nth element positions in the xOyplane, θ is the elevation angle measured from the Oz axis,and φ is the azimuth angle measured in the xOy planewith respect to the Ox axis. Because the variables to bederived (xn and yn) appear inside an exponential function,the optimization problem is not linear. Moreover, Fn, unlikein periodic arrays, can change from element to element if arequirement on the minimum aperture efficiency (hence onthe minimum gain) is enforced.

In the following section, a particular spiral configurationwill be introduced as a starting point before the space taperis applied.

3. Spiral Array with Uniform Spatial Density

A well-known spiral is the Fermat one (see Figure 12) whichhas the property of enclosing equal areas within each turn.This spiral is often found in nature, as indicated in theappendix. The elements are placed along this spiral accordingto the following equations:

ρn = s√n

π, for n = 1, . . . ,N + 1, (2)

φn = 2πnβ1, for n = 1, . . . ,N + 1, (3)

where ρn is the distance from the spiral center to the nthelement, the parameter β1 controls the angular displacementφ between two consecutive elements, and the parameter s

International Journal of Antennas and Propagation 3

denotes the distance between the elements in the xOy plane.Assume a sparse array deployed on a circular aperture ofradius Rap along the Fermat spiral, with element locationsgiven by (2) and (3). Note that ρN is taken to correspondto Rap, whereas ρN+1 is a virtual element places outside theaperture, its use is becoming obvious in what follows.

Let us now introduce a normalized element densityfunction:

d(ρn) =

(R2n − R2

n−1

)min(

R2n − R2

n−1

) , for n = 1, . . . ,N , (4)

where Rn−1 and Rn are the inner and outer radii of theannular rings enclosing the nth element, respectively, withR0 being always taken as zero (see the appendix) for ajustification for this choice of defining the normalizeddensity function). Here, a choice is made to take the radiiRn as

R2n =

ρ2n+1 + ρ2

n

2for n = 1, . . . ,N. (5)

As recognizable from (4), the normalized density functioncorresponds to the current of a single element divided by thearea of the relevant annular ring.

The lattice in [23] (see Figure 1) is characterized by auniform density. On account of (5) and (2), it can be easilyshown that

d(ρn) = 2

(R2n − R2

n−1

)min(

ρ2n+1 − ρ2

n−1

) =πR2

ap

Ns2= 1. (6)

This property is attractive when the interest focuses onavoiding GL only, without a control of the SLL. As for theSLL, it remains around 17 dB, irrespective of the numberof elements in the array and the spacing factor s. Thisis consistent with the element distribution replicating auniform current distribution on a circular aperture.

It is now clear that the only possibility to control the SLLas well is by introducing a density taper. In the followingsection, it will be demonstrated how, by translating a Tayloramplitude tapering law [24] into a corresponding spatialdensity law, the SLL can be drastically reduced.

4. Spiral Array with Density Tapering

The spiral aperiodic lattice with a uniform element densityintroduced in the previous section is an excellent startingpoint to apply a space tapering process. The spreading of theelements in the spiral arms guarantees an optimal behaviorin terms of GL even when the interelement spacing is largerthan λ. In order to be able to control the SLL, it is possible tovary the elements positions with respect to the array center,thus obtaining an effect similar to an amplitude taper.

The space taper technique presented here consists ofchoosing a reference amplitude distribution whose patternsatisfies the assigned requirements and emulates it by varyingthe radiator distance from the center. Concretely, a Tayloramplitude taper law with a certain SLL and n [24] is selectedas a reference. The locations of the elements in the sparse

−60

−40

−20

0

20

40

60

λ

−60 −40 −20 0 20 40 60

λ

xz

y

Figure 1: Distribution of the 250 elements in the uniformsunflower array antenna, as reported in [23].

−60

−40

−20

0

20

40

60

λ

−60 −40 −20 0 20 40 60

λ

xz

y

Figure 2: Distribution of the 250 elements in the tapered sunflowerarray antenna.

array are determined by means of a simple, 2 step algorithm:firstly N circles of increasing radii ρn, n = 1, 2, . . . ,N areselected by sequentially applying the relations

2π∫ ρn

Rn−1

A(r)r dr = 2π2N

∫ Rap

0A(r)r dr, (7)

2π∫ Rn

Rn−1

A(r)r dr = 2πN

∫ Rap

0A(r)r dr, (8)

starting from R0 that is taken to be 0. Here, A(r) denotes theTaylor amplitude taper and Rap is the radius of the complete


−2.4

−1.2

0

1.2

2.4

deg

(Nor

d)

−3.6 −1.8 0 1.8 3.6

deg (Est)

Figure 3: European multibeam coverage in a 1 : 4 frequency re-usescheme from a geostationary satellite.

circular aperture. Note that (7) emulates the desired taperby equating the surface integral over the annular ringdelimited by Rn−1 and ρn to half of the Nth part of the totalaperture excitation. Subsequently, the element positions aredetermined by choosing their pertaining azimuth angle φnaccording to (3). The result of this placement strategy isillustrated in Figure 2 where a 56 λ aperture is filled with 250elements distributed in a manner such to obtain a patternsimilar to the one achievable with a Taylor amplitude lawcharacterized by SLL = 32 dB and n = 4. A total numberN = 250 is selected as a good compromise between theperformance in scanning and the cost. The choice for thesevalues will be clearer in the following sections.

5. Typical Requirements for a MultibeamSatellite Application

The transmitting antenna considered in this study is operat-ing in Ka-band (19.7–20.2 GHz) and may have a maximumdiameter of 1.3 m. The starting point considers the circulardirect radiating array with dimensions deemed as sufficientto provide the required maximum gain and beamwidth. Thearray must generate 64 spot beams. The total frequency bandis divided into 4 subbands, and each of them being assignedto a set of beams so that there are no adjacent pencil beamsusing the same resource. Figure 3 shows the footprint on theEarth of the 64 pencil beams.

In the last 3 rows of Table 1, the maximum sidelobe levelin three different regions has been specified. The value indBi has been preferred to the dB one as the configurationsanalyzed in Section 5 have different maximum directivityvalues.

In Figure 4, the array factor of the configurations pre-sented in Figures 1 and 2, respectively, is plotted for twodifferent φ cuts. In both uniform and tapered sunflowerconfigurations, the array factor is remarkably stable in φ,resulting in the area of interest, in practically rotationallysymmetric radiation patterns. The array factor in Figure 4(b)is following the expected behavior until a certain θ angleat which the effects of the first pseudograting lobe (the

−50

−45

−40

−35

−30

−25

−20

−15

−10

−5

0

dB

−10 −5 0 5 10

θ◦

(a)

−50

−45

−40

−35

−30

−25

−20

−15

−10

−5

0

dB

−10 −5 0 5 10

θ◦

(b)

Figure 4: Array Factor, two different φ cuts (φ = 0◦ in red dottedline and φ = 90◦ in black), for the array configuration in Figures 1and 2, respectively.

Table 1: Mission requirements.

Number of spots 64

Spot diameter 0.65◦

Inter-spot distance 0.56◦

Rx band 29.5–30.0 GHz

Tx band 19.7–20.2 GHz

Frequency reuse 1 : 4

EOC gain 43.8 dBi

SLL in the first ∓4◦ 20 dBi



energy of which being spread over a wider θ interval dueto the nonperiodic placement) become visible. Consideringthe previous example in which the maximum interelement


−60

−40

−20

0

20

40

60

λ

−60 −40 −20 0 20 40 60

λ

Figure 5: The Voronoi tessellation consisting of the cells enclosingthe chosen phase centers.

−60

−40

−20

0

20

40

60

λ

−60 −40 −20 0 20 40 60

λ

Figure 6: Subarray allocation and aperture subdivision corre-sponding to the Voronoi tessellation in Figure 5.

distance Dmax = 8.43 λ, the first contribution of the gratinglobe is expected at

θGL = sin−1(

1Dmax

)= 6.81◦. (9)

In fact, in Figure 4(b), the pattern starts exceeding theimposed SLL around this θGL.

0

5

10

15

20

25

30

35

40

45

50

(dB

i)

−10 −5 0 5 10

θ◦

Figure 7: Array pattern for the configuration depicted in Figure 6.The beam is scanned to boresight. The red line corresponds to therequirement mask.

2

4

6

8θ

90120

150

180

210

240270

300

330

0

φ

30

60

Figure 8: Array pattern for the configuration depicted in Figure 6.The beam is pointing at Europe edges. The red line represents theiso-level curves at 43.8 dBi, and the blue ones the iso-level curves at20 dBi. The black circles represent the interfering area.

6. Validation of the Technique

The locations provided by the space taper process (seeFigure 2) have been used as phase centers of the radiators ina planar array. Two different techniques are used to select theradiators.

6.1. First Approach: Using the Entire Aperture. The circularaperture with a maximum radius of 56 λ is completely filledwith patches disposed on a regular lattice. The triangulargrid is chosen because of its better performances comparedto the regular rectangular one. The analytical equations in[25] are used to express the field of the elementary patchantenna, radiating on a ground plane, with side lengthsequaling 0.42 λ and a rectangular cell surrounding it withside lengths 0.8 λ × 0.85 λ. In order to cover the complete


−60

−40

−20

0

20

40

60

λ

−60 −40 −20 0 20 40 60

λ

Figure 9: Hexagonal subarray positions and dimension afterpostprocessing.

aperture, with this patch choice, more than 15 thousandspatches are required. These patches are then collected intosubarrays.

The positions of the phase centers of the subarraysfor N = 250 are derived with the formulation presentedin the previous section following a Taylor taper with SLL= 32 dB and n = 4. The subarray positions are thensuperimposed on the uniform array, as indicated in Figure 6.Each patch center is assigned to the closest subarray centerthat can be interpreted as assigning the relevant patchto the Voronoi cell [26] corresponding to the computedphase center. Note that the Voroni surface division (seeFigure 5) provides an optimum tessellation of the availablereal estate.

To obtain the total radiation pattern, each radiationpattern of the subarray Fn has been calculated and multipliedby the exponential that takes into account the positions of thephase center of that subarray given in (1).

Since the Voronoi cell shapes are close to circularones, the subarray patterns result to be almost rotationallysymmetric. This is an important property when the beam isscanned.

In Figure 7, the pattern for the beam pointing atboresight is plotted for 360 φ cuts (one at every degree). Thered line in this figure indicates the mask requirements givenin Table 1. Figure 8 represents the radiation pattern when thebeam is pointed at the Europe’s edges: the blue and red linesare iso-level curves at 20 dBi and 43.8 dBi, respectively, whilethe black circles enclose the regions of the coverage in whichthe same resource is used. As it can be seen from Figure 8,even when the beam is pointed at the Europe’s edges, thepattern remains complaint with the requirements given in[1].

0

5

10

15

20

25

30

35

40

45

50

(dB

i)

−10 −5 0 5 10

θ◦

Figure 10: Array pattern for the configuration depicted in Figure 9.The beam is scanned to boresight. The red line corresponds to therequirement mask.

2

4

6

8θ

90120

150

180

210

240270

300

330

0

φ

30

60

Figure 11: Array pattern for the configuration depicted in Figure 9.The beam is pointing at Europe edges. The red line represents theiso-level curves at 43.8 dBi, and the blue ones the iso-level curves at20 dBi. The black circles represent the interfering area.

With this method, the entire surface available is usedmaintaining at the same time a very small number of controls(one for each subarray).

6.2. Second Approach: 4 Different Types of Subarrays. In thiscase, a more technology-oriented approach is considered:the aperture is filled as much as possible with predefinedhexagonal subarrays. A limited number of these subarraysis selected as a compromise in order to keep the complexityand the cost limited while offering good performances.Four subarrays with different sizes have been selected andused to fill the array aperture. All the subarrays have ahexagonal shape and consist of 2, 3, 4, or 5 rings of elementssurrounding the central one on a regular triangular lattice.The patches used in the subarrays are the same as the onesdescribed in the previous subsection.


−2

−1.5

−1

−0.5

0

0.5

1

1.5

2

−2 −1 0 1 2

y

x

r

φ

Figure 12: The Fermat spiral and its associated coordinate system.

The procedure consists of computing for each cell theradius of the maximum circle that can be inscribed in it.According to this value, the best hexagonal sub-array amongthe four available is selected and placed in the cell (seeFigure 9). After this first step, a postprocessing is carried outin which every subarray is replaced by its larger version ifno overlapping with its neighbor occurs. In the followingcase, 117 of the 250 subarrays were substituted during thepostprocessing and this is the reason why the subarrayplacement in the array is not clearly divided into annularareas around the array center enclosing the same type ofsubarrays. The postprocessing allows increasing the aperturefilling from 44.4% up to 60.9%.

In Figure 9, the subarrays have been plotted in differentcolors depending on their size. Since the element placementis more dense in the center, smaller subarray dimensionsare needed in the array middle while at the periphery largerhexagonal subarray can be accommodated improving thedirectivity but, depending on the maximum dimension,allowing for a limited beam scan only.

With the first approach, the results were exceeding therequirements but the physical implementation of the arraywould be too demanding since every subarray is differentand has to be designed and tested individually. With thesecond approach proposed here, only 4 subarrays need tobe generated and moreover, the feeding network will beeasier to implement. The boresight radiation pattern for thisconfiguration is depicted in Figure 10. As it can be noticed,the SLL is still within the specifications; the maximum gaindrops by approximately 2 dB but the EOC gain is enforced.As a drawback, the array performance is optimal only whenthe beam is pointing at boresight. When the beam is scannedto the Europe edges, it is possible to maintain the SLLunder the prescribed value in the area of interest but therequirement on the EOC gain cannot be reached as shownin Figure 11.

1

2

3

4

5

6

7

89

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

−6

−4

−2

0

2

4

6

λ

−6 −4 −2 0 2 4 6

λ

(a)

1

2

3

4

5

6

7

89

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

−6

−4

−2

0

2

4

6

λ

−6 −4 −2 0 2 4 6

λ

(b)

Figure 13: Sunflower array configuration: the elements are num-bered starting from the center. In this case, 5 clockwise Fibonaccispirals appear, red line, and 8 anticlockwise, in blue line. Theinterval of identificative numbers between elements on the sameFibonacci spiral is always equal to the number of spirals occurring,in this figure notice 22− 14 = 14− 6 = 8 and 24− 19 = 19− 14 = 5.

7. Conclusions

A deterministic procedure to design aperiodic planar arrayswhich guarantees the control of SLL, GL, and beamwidthwithout using any amplitude tapering has been introduced.Starting from an array characterized by a uniform spatialdensity of the elements, the density function has been


modified in order to fit a reference amplitude tapering.The design technique has been applied for the preliminarydesign of a Direct Radiating Array for a multibeam satellitecommunication mission.

Appendices

A. Fibonacci Spirals

Spirals are one of the most common regular shapes in nature:from the snail shell to the sunflower seed placement, tothe Milky way arms. Different kinds of spirals are knownin literature. Using a spiral placement for the elements ofa planar array guarantees a good spreading of the energyassociated to the side and grating lobes. Furthermore, aspiral lattice permits obtaining a quite uniform filling of agiven aperture compared to other planar lattices like the onesorganized in rings. A well-known spiral is the Fermat spiral(Figure 12) which has the property of enclosing equal areaswithin every turn. Its equation can be expressed in polarcoordinates as

ρ = a√φ, (A.1)

where ρ is the distance from the spiral center, and φ is theangle that identifies the point position respect to the x axis;the parameter a controls the distance between the spiralturns.

This spiral is quite often found in nature. In particular,there are leafs and seeds whose positions can be obtained bysampling a Fermat spiral equation, that is,

ρ = √nb,

φ = 2πnc

,(A.2)

and when it is important having a uniform subdivision of thespace the parameters b and c are closely related to the GoldenRatio, also known as Fibonacci number since it represents thesolution of the Fibonacci quadratic equation. For instance,the leaves around a stem use this positioning to share in anoptimal way the space and the light [27].

The Fibonacci sequence is known since 1202 d.C., thanksto Leonardo son of Bonaccio from Pisa and his bookLiber Abaci. This sequence has been widely analyzed andapplied in different fields: from the description of particularplants to computer science, from crystallography to electricalengineering. By solving the Fibonacci quadratic equation[28]:

β2An = βAn + An, (A.3)

the following two roots are obtained:

β1 =√

5 + 12

= τ,

β2 = 1−√52

= −1τ.

(A.4)

In most of the applications, the first value has been used,but to characterize the spiral, both of them are usable. Thedivergence angle, also referred to as the golden angle, isdefined as

golden angle = 360◦

β21= 360◦ − 360◦

β22. (A.5)

Because this value is irrational, it is impossible to have twoor more elements in the spiral array characterized by thesame φ angle. The element packing results to be efficient.Interesting Fermat spirals could be also the ones with otherirrational coefficients like

√2. In the patent [23], β1 is used

for the element disposition along the spiral according to theformulation presented in (2) and (3). As it can be easilynoticed, the positions of the elements in the sunflower arraydepend only on n via a trivial equation.

The second type of spirals employed in this study isthe Fibonacci one, namely, a particular kind of logarithmicspiral, where the ratio between radii evaluated at each 90◦ isrelated to the golden ratio number. It is interesting to notethat in a sunflower array configuration, when the elementsare placed on a Fermat spiral at every β1 degrees, the elementsform sets of clockwise and anticlockwise Fibonacci spirals.The number of spirals in each set are two consecutive termsof the Fibonacci series as it can be seen in Figures 13(a) and13(b). Another particular characteristic of this configurationis that in order to obtain for example the 5 clockwise spirals,it is sufficient to connect the elements on the Fermat spiralwhose numbers difference is exactly 5.

B. Normalized Element Density Function

Assume the case when a continuous, strictly positive,rotationally symmetric, normalized current amplitude dis-tribution A(r) on a circular aperture of radius Rap needsto be mimicked by means of N equiamplitude elementslocated at monotonically increasing distances ρn, n = 1, . . . ,N .(All distances r or radii R employed in this appendix areconsidered with respect to the aperture center.) Let Rn (n =0, . . . ,N) be N + 1 radii chosen such that Rn−1 < ρn < Rnfor n = 1, . . . ,N , with R0 being taken to be zero. Note thatfor reasons that will be elaborated upon later, RN may be,and in most cases is, taken to be (slightly) larger than Rap.The monotonic increasing of the values ρn combined withthe choice for the radii Rn ensures that inside in each annularring of inner radius Rn−1 and outer radius Rn there is onlyone radiator. With these prerequisites, an equivalent discreteamplitude density function can be defined by means of theexpression

d(ρn) = K

π(R2n − R2

n−1

) , for n = 1, . . . ,N , (B.1)

where the K denotes the constant excitation of each of theN elements. In view of ensuring the consistency of thisdefinition, the radii Rn−1 and Rn are chosen such that

∫ Rn

Rn−1

A(r)r dr = K , for n = 1, . . . ,N. (B.2)


Furthermore, in view of ensuring identical aggregate excita-tion over the aperture, the constant K is adopted as

K = 1N

∫ Rap

0A(r)r dr. (B.3)

By now invoking the mean function theorem, the area ofthe annular ring in the denominator of (B.1) can be rewrittenas

π(R2n − R2

n−1

) = 1A

(ξn)∫ Rn

Rn−1

A(r)r dr

= K

A

(ξn), for n = 1, . . . ,N ,

(B.4)

with ξn (n = 1, . . . ,N) being an unspecified point in theintervals [Rn−1,Rn]. Substituting (B.4) in (B.1) then yields

d(ρn) = A

(ξn), for n = 1, . . . ,N. (B.5)

Due to the choice for ρn and ξn, the distance |ρn − ξn| isbounded above by Rn − Rn−1, which, in view of complyingto (B.3) and of the continuity of A(ρ), becomes arbitrarilysmall for arbitrarily large N-s. Consequently, the (discrete)amplitude density function can be made to approximate witharbitrary accuracy of the original current density.

In order to prevent possible above unit values of thediscrete amplitude density d(ρn) that may occur in the casewhenN is small, this quantity is now normalized to its largestvalue. By accounting for the fact that max[d(ρn)]|n=1,...,N

corresponds to the minimum R2n−R2

n−1 difference, it is foundthat

d(ρn) = min

(R2n − R2

n−1

)|n=1,...,N

R2n − R2

n−1, for n = 1, . . . ,N ,

(B.6)

which is the expression that was used in Section 3.Some remarks are due with respect to the hereby dis-

cussed choice for a (normalized) discrete amplitude densityfunction. Firstly, in view of the correspondence between ρnand Rn, it is obvious that RN exceeds ρN . In many cases,the aperture will be construed as the area effectively coveredby individual radiators, a choice that allows mapping thebeamwidth requirement on a maximum element to centerspacing. In that case, ρN = Rap and, thus, RN > Rap,as anticipated above. This fact does not conflict with thedefinition of the density function, the continuous A(ρ)being amenable to extrapolation beyond Rap, while the

normalization in (B.6) recalibrates the maximum d(ρn) to 1.Secondly, the determination of the radii Rn according to

the condition to yield equal surface integrals of A(ρ) overthe relevant annular rings can be easily carried out when theamplitude density is known, as demonstrated in Section 4.However, the handling of the converse situation, when thelocation of the elements is known and the (equivalent)amplitude density needs being calculated is less evident.To circumvent this difficulty, the radii Rn were chosen inSection 3 based on the intrinsic properties of the Fermatspiral, a choice that eventually allowed verifying that the

amplitude density function d(ρn) is, indeed, constant.

References

[1] Y. Cailloce, G. Caille, I. Albert, and J. M. Lopez, “A Ka-banddirect radiating array providing multiple beams for a satellitemultimedia mission,” in Proceedings of the IEEE InternationalSymposium on Phased Array Systems and Technology, pp. 403–406, Dana Point, Calif, USA, May 2000.

[2] G. Toso, C. Mangenot, and A. G. Roederer, “Sparse andthinned arrays for multiple beam satellite applications,” inProceedings of the 2nd European Conference on Antennas andPropagation (EuCAP ’07), pp. 1–4, Edinburgh, UK, November2007.

[3] M. C. Vigano, G. Toso, S. Selleri, C. Mangenot, P. Angeletti,and G. Pelosi, “GA optimized thinned hexagonal arrays forsatellite applications,” in Proceedings of the IEEE Antennasand Propagation International Symposium, pp. 3165–3168,Honolulu, Hawaii, USA, June 2007.

[4] G. Caille, Y. Cailloce, C. Guiraud, D. Auroux, T. Touya, and M.Masmousdi, “Large multibeam array antennas with reducednumber of active chains,” in Proceedings of the 2nd EuropeanConference on Antennas and Propagation (EUCAP ’07), pp. 1–9, Edinburgh, UK, November 2007.

[5] H. Unz, “Linear Arrays with arbitrarily distributed elements,”IRE Transactions on Antennas and Propagation, vol. 8, no. 2,pp. 222–223, 1960.

[6] Y. T. Lo and S. W. Lee, “A study of space-tapered arrays,” IEEETransactions on Antennas and Propagation, vol. 14, no. 1, pp.22–30, 1966.

[7] R. E. Willey, “Space tapering of linear and planar arrays,” IEEETransactions on Antennas and Propagation, vol. 10, no. 4, pp.369–377, 1962.

[8] R. Harrington, “Sidelobe reduction by nonuniform elementspacing,” IRE Transactions on Antennas and Propagation, vol.9, no. 2, pp. 187–192, 1961.

[9] A. Ishimaru, “Theory of unequally-spaced arrays,” IRE Trans-actions on Antennas and Propagation, vol. 10, no. 6, pp. 691–702, 1962.

[10] H. Schjaer-Jacobsen and K. Madsen, “Synthesis of nonuni-formly spaced arrays using a general nonlinear minimaxoptimisation method,” IEEE Transactions on Antennas andPropagation, vol. 24, no. 4, pp. 501–506, 1976.

[11] W. Doyle, “On approximating linear array factors,” Tech. Rep.RM-3530-PR, RAND Corporation, Santa Monica, Calif, USA,February 1963.

[12] T. A. Milligan, “Space-tapered circular (ring) array,” IEEEAntennas and Propagation Magazine, vol. 46, no. 3, pp. 70–73,2004.

[13] M. Vicente-Lozano, F. Ares-Pena, and E. Moreno, “Pencil-beam pattern synthesis with a uniformly excited multi-ringplanar antenna,” IEEE Antennas and Propagation Magazine,vol. 42, no. 6, pp. 70–74, 2000.

[14] R. L. Haupt, “Optimized element spacing for low sidelobeconcentric ring arrays,” IEEE Transactions on Antennas andPropagation, vol. 56, no. 1, pp. 266–268, 2008.

[15] G. Toso, M. C. Vigano, and P. Angeletti, “Null-matching forthe design of linear aperiodic arrays,” in Proceedings of the IEEEAntennas and Propagation International Symposium, pp. 3149–3152, Honolulu, Hawaii, USA, June 2007.

[16] Y. Chow, “On grating plateaux of nonuniformly spacedarrays,” IEEE Transactions on Antennas and Propagation, vol.13, no. 2, pp. 208–215, 1965.


[17] M. I. Skolnik, “Nonuniform arrays,” in Antenna Theory, PartI, F. J. Collin and R. E. Zucker, Eds., chapter 6, pp. 207–234,McGraw-Hill, New York, NY, USA, 1969.

[18] J. Sahalos, “The orthogonal method of nonuniformly spacedarrays,” Proceedings of the IEEE, vol. 62, no. 2, pp. 281–282,1974.

[19] R. L. Haupt, “Thinned arrays using genetic algorithms,” IEEETransactions on Antennas and Propagation, vol. 42, no. 7, pp.993–999, 1994.

[20] A. Trucco, “Synthesis of aperiodic planar arrays by a stochas-tic approach,” in Proceedings of the MTS/IEEE Conference(OCEANS ’97), vol. 2, pp. 820–825, Halifax, Canada, October1997.

[21] S. Holm, A. Austeng, K. Iranpour, and J. F. Hopperstad,“Sparse sampling in array processing,” in Sampling Theory andPractice, F. Marvasti, Ed., chapter 19, Springer, New York, NY,USA, 2001.

[22] O. M. Bucci, M. D’Urso, T. Isernia, P. Angeletti, and G.Toso, “A new deterministic technique for the design ofuniform amplitude sparse arrays,” in Proceedings of the 30thESA Workshop on Antennas for Earth Observation, Science,Telecommunication and Navigation Space Missions, Noordwijk,The Netherlands, May 2008.

[23] D. W. Boeringer, “Phased array including a logarithmic spirallattice of uniformly spaced radiating and receiving elements,”US patent no. 6433754 B1, Silver Spring, Md, USA, April 2002.

[24] T. Taylor, “Design of circular apertures for narrow beamwidthand low sidelobes,” IRE Transactions on Antennas and Propa-gation, vol. 8, no. 1, pp. 17–22, 1960.

[25] J. L. Volakis, Antenna Engineering Handbook, McGraw-Hill,New York, NY, USA, 4th edition, 2007.

[26] A. Okabe, B. Boots, K. Sugihara, and S. N. Chiu, SpatialTessellations: Concepts and Applications of Voronoi Diagrams,John Wiley & Sons, Chichester, UK, 2nd edition, 1999.

[27] P. Atela, C. Gole, and S. Hotton, “A dynamical system for plantpattern formation: a rigorous analysis,” Journal of NonlinearScience, vol. 12, no. 6, pp. 641–676, 2002.

[28] R. A. Dunlap, The Golden Ratio and Fibonacci Numbers, WorldScientific, Singapore, 1997.

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2017 Progress In Electromagnetics Research Symposium — Spring (PIERS), St Petersburg, Russia, 22–25 May

Beam Steering Performance of Wideband Cavity-backed PatchAntenna Array Element

Artem Vilenskiy, Vladimir Litun, Konstantin Lyulyukin, and Vladimir MitrokhinBauman Moscow State Technical University, Moscow, Russia

Abstract— The paper presents some development results of a low-profile linearly polarizedradiator intended for operation as an element of a planar wideband antenna array. The design isbased on a rectangular pin-fed patch antenna with an additional U-shaped slot on a single layersubstrate. This ordinary structure was modified by means of introducing a low depth rectangularair cavity into a metallic base underneath the patch element. The entire structure was optimizedusing Floquet channel model taking into account an array lattice structure with a goal to achievea minimal input reflection coefficient magnitude in 12% relative bandwidth and 40◦ conical beamsteering sector. An experimental array fragment comprising 7 by 6 antenna elements was designedand manufactured. Key results of the design process and a comparison between simulated andmeasured characteristics are shown.

1. INTRODUCTION

Phased antenna arrays (PAA) based on printed radiating elements are widespread in a field ofvarious purpose radar design. Patch antennas are one of the most applicable for 2D planarPAA [1, 2]. Generally, this popularity stems from their structural simplicity, technological effec-tiveness, lightweight and low cost.

Wideband (WB) and ultra-wideband systems design is one of the major directions of radardevelopment in recent years. This fact has an influence on PAA operating frequency band require-ments. One of the basic printed resonant antennas’ drawbacks is their narrow relative bandwidth,which depends generally on matching with feed lines [3]. This problem can be solved not only bymeans of substrate modification but also by resonator structure complicating [4, 5]. In the firstcase, the effect is usually obtained by increasing the substrate thickness, thereby reducing theresonator Q-factor. This approach has some specific restriction in PAA design applications. Thesubstrate thickness growth results in higher intensity of surface waves excitation in a shielded pla-nar layered dielectric structure. In its turn, this leads to augmentation of mutual coupling betweenPAA elements [6, 7]. A strong radiators coupling causes an intense variation of array element inputimpedance during a beam steering, stipulating PAA gain reduction and, for some cases, PAA scanblindness.

Several ways of printed array element bandwidth extension are known, including topology mod-ification by introducing additional resonant [5] or reactance compensating elements [3]. To obtaina WB matching in the first case, it’s still required to use a thick substrate for the vast majority ofstructures. In the second case, the design process is limited by manufacturing restrictions includingrealized topology tolerances, a minimal width of conductors and gaps.

Thereby, an optimal PAA design solution should be considered as a tradeoff, combining a WBoperation capability, wide-angle beam steering sector and a feasible lightweight low-cost structure.

This paper is devoted to PAA printed element development with a goal to achieve the bestelements matching for 40◦ conical beam steering sector in 12% relative operating bandwidth bymeans of minimal number of radiators per PAA aperture area.

2. ARRAY ELEMENT STRUCTURE

As explained earlier, WB requirements for printed PAA are hard to implement in the whole wide-angle beam steering sector. A high level of mutual coupling between resonant patches locatedon a single substrate causes a considerable reflection coefficient growth even for small values ofsteering angles. Therefore, the problem under discussion comes to challenge of printed array elementdevelopment with both low intrinsic Q-factor and suppressed mutual coupling with surroundingradiators.

Many researchers have encountered similar problems earlier. In [8–10] authors exploited a cavity-backed patch design. The patch is located in the upper cavity plane with an additional shieldingbelt. It was shown that a decrease of cavity filling material permittivity and closer shielded volume

3340


border allocation result in a considerable beam steering performance enhancement [10]. On theother hand, these steps lead to operating frequency bandwidth narrowing.

On the strength of the gathered information, a WB patch antenna array element design (Fig. 1)was devised for isosceles triangular array grid in C-band [11]. Other authors earlier have also dis-cussed performance of a similar array element [12], but they limited the array analysis by broadsideradiation regime without beam steering for square grid.

θ

ϕX

Y

Z M(R,θ,ϕ)

R

Py

0.5Px0.5Px

Figure 1: Antenna array element and grid structures.

The proposed array element structure consists of pin-fed planar double-resonant patch on asingle-layer substrate and metal base with a rectangular air cavity underneath. The first elementresonance corresponds to the eigenmode of the basic rectangular patch, the second is conditionedby the U-shaped slot excitation. Low substrate thickness causes a minor level of neighbor elementsmutual coupling. The air cavity has a small depth compared to the operating wavelength andits planar dimensions exceed the patch area. It extends the operating bandwidth by means ofdecreasing the Q-factor at both resonant frequencies. An increase of cavity depth entails furtherreduction of Q-factor but also causes the increase of a spurious inductance of the pin element.Thus, the cavity depth should be chosen rationally. To improve manufacturability of the structurearray elements can be grouped in rows on common substrate strips and separated from each otherwith air gaps (Fig. 1). It also makes possible to design various types of skew-angular grid PAAsusing topologically identical base linear units. In addition, a PAA aperture can be developed as acompleted subassembly using coaxial connectors’ pins for element feeding.

The current paper does not concern the performance of the isolated radiator, because it wasalready done in [12]. Results of [12] evidence that the single antenna can have up to 15% bandwidthwith a reflection coefficient magnitude being less than 0.33.

3. PAA GRID STRUCTURE

A lot of PAA characteristics depend on a lattice structure. It’s reasonable to minimize a numberof array elements fulfilling the requirements for beam steering angular sector, realized gain andreflection coefficient magnitude values in the operating frequency band. In other words, the arraymust be as sparse as possible. However, inter-elements spacing growth is limited by grating lobesoccurrence and feedline matching deterioration. In fact, these effects are related [13] and appearin printed PAAs more often than in waveguide structures [14]. It is known that a triangular gridallows using less array elements in comparison with a rectangular lattice for the same aperture areaand beam steering angular sector [13]. Thus, an isosceles triangular grid was chosen for the furtherdevelopment. The grid structure is shown in Fig. 2 in xOy-plane of the same coordinate system asin Fig. 1. Thus, the radiators’ coordinates are attached to the skew-angular grid (xy′z -axes) withinter-element spacings Px and P ′

y and grid angle α; Py is a rows spacing.When general radiating field structure of the infinite uniform array is of the interest, the PAA

can be analyzed in terms of propagating eigenmodes of the corresponding periodic grid. For thispurpose the Floquet modal function analysis [13, 14] capable of grating lobes appearance predic-tion is employed. A grating lobe arises when at least one higher order Floquet mode becomes

3341


Figure 2: Antenna array lattice structure. Figure 3: Grating lobes appearance boarders at sev-eral frequencies: 1 — 1.00f0, 2 — 1.04f0, 3 —1.06f0, 4 — 1.08f0.

propagating:

Re (γmn) ≥ 0, Im (γmn) = 0, m �= 0 and n �= 0 simulataneously. (1)

Here γmn is a wave number along z-axis of mn-th Floquet mode (2):

γmn =

√(2π

λ

)2

−(

φx + 2πm

Px

)2

−(

φ′y + 2πn

P ′y sin (α)

− φx + 2πm

Px tan (α)

)2

, m, n = 0,±1,±2, . . . , (2)

where λ is a free-space wavelength at the operating frequency f , φx and φ′y depend on the beam

steering direction (θs, ϕs) as

φx =2π

λPx sin (θs) cos (ϕs) ,

φ′y =

2π

λP ′

y sin (θs) cos (ϕs − α) .

(3)

Therefore, it is possible to find a grating lobes free angular area using the Equations (1)–(3)for the given grid structure. This method was applied to check the beam steering capabilities ofisosceles triangular lattice structure with Px = 0.61λ0, Py = 0.53λ0 (α = 66.4◦). The resultedgrating lobe appearance boarders at several frequencies are shown in Fig. 3.

The results confirm that the proposed grid structure provides grating lobes free beam steeringin a conical angular sector up to θs ≈ 51◦ for ϕs = 0 . . . 360◦ at 1.06f0. The sector is larger thanrequired, but it gives the structure some reserve by keeping it away from possible scan blindnessangles appearance.

4. ELEMENT STRUCTURE OPTIMIZATION

For the chosen PAA grid structure a Floquet-channel model of the array element was considered toinvestigate and optimize its performance. Influence of all structure geometrical parameters (Fig. 4)was examined using finite element analysis in Ansoft HFSS. The optimization goal was to achievethe minimal input reflection coefficient (Γ) magnitude in 12% relative bandwidth over the entire40◦ conical beam steering sector. The structure is based on RO4350B (εr = 3.66, tan δe = 0.004)substrate.

Feeding pin is situated in the center of both air cavity and patch. Resulting values for theoptimal design (normalized to λ0 and rounded off to one hundredth): patch length Lp = 0.25λ0 andwidth Wp = 0.37λ0; slot dimensions Ls1 = 0.10λ0, Ls2 = 0.16λ0, Ws1 = 0.02λ0, Ws2 = 0.02λ0 anddisplacement from patch border ds = 0.01λ0; substrate thickness hs = 0.03λ0 (standard for laminatetype) and laminate strip width Wps = 0.47λ0; air cavity transverse dimensions Lc = 0.30λ0,Wc = 0.40λ0 and depth hc = 0.03λ0.

3342


(a) (b)

Figure 4: PAA element geometry: (a) top view, (b) cross-section.

Figure 5: Input reflection coefficient magnitude of the optimized structure.

(a) (b)

Figure 6: Active PAA element gain pattern at central frequency: (a) co-polarized component, (b) cross-polarized component.

Simulation results for |Γ| over the frequency range for several beam steering directions are shownin Fig. 5(a): curve 1 — broadside radiation (θs = 0◦); curve 2 — θs = 40◦, ϕs = 0◦; curve 3 —θs = 40◦, ϕs = 30◦; curve 4 — θs = 40◦, ϕs = 60◦; curve 5 — θs = 40◦, ϕs = 90◦. It should benoted that no scan blindness were found for any beam steering direction inside the angular sectorof interest.

An active PAA element gain pattern can be easily extracted from Floquet-channel simula-tion [14]. In Fig. 6 patterns are shown for several azimuth cross-sections at f0 for co- and cross-

3343


polarized components (Ludwig-3 basis is employed): 1 — xOz -plane (ϕ = 0◦), 2 — diagonal plane(ϕ = 45◦), 3 — yOz -plane (ϕ = 90◦). It is interesting to note that before the first grating lobeappearance in yOz -plane (θs ≈ 57◦) array demonstrates a sharp co-polarized gain drop with thesteep cross-polarization level increase. This phenomenon is attributed to array co-polarized scanblindness caused by the periodic structure surface wave excitation. Also, from the given results wecan see that up to θs = 40◦ the relative cross-polarization level is below −17 dB.

5. EXPERIMENTAL STUDY

Optimized PAA printed element structure was used as the basis for prototype development. Thedesign presents an assembly of 7 laminate strips, each of them containing 6 patch elements, on asingle metal base (Fig. 7(a)). This 7 × 6 subarray could be applied as a base unit for a scalablemodular PAA. The experimental study objective was to estimate |Γ| over the wide-angle beamsteering sector from measured elements S-parameters [14]. All examined couples of elements wereparticularly chosen inside the subarray to minimize edge effects and eventually to compile 3 sur-rounding rings model (Fig. 7(b)). The following measured data arrangement ensures high-accuracyΓ computation based on mutual coupling between the central element and its neighbors (with 36surrounding elements in total).

The results obtained after the post-processing are depicted in Fig. 8 as a family of curves forθs = 0 . . . 40◦, ϕs = 0 . . . 360◦ (thin grey lines). These results are in good agreement with the

1 2 3 4 5 61

2

3

4

5

6

7

str.\el.

3,14 3,15

2,10

1,5 1,6

1,11,4

1,3 1,2

0,1

3,11

3,12

3,13

3,9

3,8

3,7 3,4

3,3

3,2

3,16

3,17

3,18

3,13,10 2,7

2,8

2,9 2,11

2,12

2,1

2,6

2,5 2,3

2,2

3,6 3,5

2,4

(a) (b)

Figure 7: Experimental study of array prototype: (a) fabricated subarray, (b) post-processing scheme,including 3 surrounding rings.

Figure 8: Calculated input reflection coefficient magnitude set of curves for θs = 0 . . . 40◦, φs = 0 . . . 360◦

and Floquet-channel results.

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(a) (b)

Figure 9: Post-processed |Γ| in 12% relative bandwidth: (a) maximal, (b) averaged.

element performance predicted by Floquet-channel simulation (in Fig. 8: curve 1 — broadsideradiation (θs = 0◦), measured; curve 2 — θs = 40◦, ϕs = 90◦, measured; curve 3 — broadsideradiation (θs = 0◦), simulated; curve 4 — θs = 40◦, ϕs = 90◦, simulated).

Also, from the system design point of view it is interesting to get the maximal and the averagedover the operating 12% relative frequency band |Γ| as functions of beam steering direction (θs, ϕs)(Fig. 9). Summarizing the results, it can be concluded that the element performance fully meetsgiven requirements. Thus, prototype measurements have fully verified that the proposed printedradiator design can be successfully used as the element of WB wide-angle beam steering PAA.

6. CONCLUSIONS

In this paper the comprehensive electromagnetic analysis of the printed patch radiator intendedfor operation as an element of planar wideband PAA is presented. The basic element structurecomprised of the double-resonant patch with the additional air-filled cavity in the metal base isdescribed in details. The simulated and measured results are in good agreement and verify elementWB performance. The measured element averaged reflection coefficient magnitude is less than 0.4in 12% relative bandwidth for 40◦ conical beam steering sector. It is reasonable to consider methodsof higher array elements mutual coupling suppression in the future research.

REFERENCES

1. Hansen, R. C., Phased Array Antennas, Wiley, 2009.2. Volakis, J. L., Antenna Engineering Handbook, 4th Edition, Mc Grow Hill, 2007.3. Kumar, G. and K. P. Ray, Broadband Microstrip Antennas, 432, Artech House, 2003.4. Volakis, J., C.-C. Chen, and K. Fujimoto, Small Antennas: Miniaturization Techniques &

Applications, McGraw-Hill, 2010.5. Lau, K. L., K. M. Luk, and K. F. Lee, “Wideband U-slot microstrip patch antenna array,”

IEE Proceedings — Antennas, Microwaves and Propagation, Vol. 148, No. 1, 41–44, 2001.6. Pozar, D. and D. Schaubert, “Scan blindness in infinite phased arrays of printed dipoles,”

IEEE Transactions on Antennas and Propagation, Vol. 32, No. 6, 602–610, 1984.7. Hansen, V., “Finite array of printed dipoles with dielectric cover,” IEEE Proceedings, Vol. 134,

Pt. H, No. 3, 261–269, 1987.8. Davidovitz, M., “Extension of the E-plane scanning range in large microstrip arrays by sub-

strate modification,” IEEE Microwave and Guided Wave Letters, Vol. 2, No. 12, 492–494,1992.

9. Zavosh, F. and J. T. Aberle, “Infinite phased arrays of cavity-backed patches,” IEEE Trans-actions on Antennas and Propagation, Vol. 42, No. 3, 390–398, 1994.

10. Awida, M. H. and A. E. Fathy, “Design guidelines of substrate-integrated cavity-backed patchantennas,” IET Microwave, Antennas and Propagation, Vol. 6, No. 2, 151–157, 2012.

11. Awida, M. H., S. H. Suleiman, and A. E. Fathy, “Substrate-integrated cavity-backed patcharrays: A low-cost approach for bandwidth enhancement,” IEEE Transactions on Antennasand Propagation, Vol. 59, No. 4, 1155–1163, 2011.

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12. Lyulyukin, K. V., V. I. Litun, and A. A. Rogozin, “The wide-band cavity backed patch ir-radiator for a phased array antenna” Proceedings of 25th International Crimean Conference“Microwave and Telecommunication Technology (CriMiCo)”, 457–458, Sevastopol, Crimea,September 2015.

13. Amitay, N., V. Galindo, and C. P. Wu, Theory and Analysis of Phased Array Antennas,Wiley-Interscience, 1972.

14. Bhattacharyya, A. K., Phased Array Antennas — Floquet Analysis, Synthesis, BFNs andActive Array Systems, Wiley, 2006.

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