Electronically Scanned Arrays MATLAB® Modeling and Simulation

229 Pages·2012·16.84 MB·English

by  Arik D. Brown

Electrical Engineering B Electronically
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n
Scanned Arrays
Electronically Scanned Arrays
MATLAB® Modeling and Simulation E
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e MATLAB Modeling Simulation
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“[Contains] more lengthy mathematical derivations than most {comparable r
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books] … for arrays, provides for a unique, stand-alone mathematical descrip-
n
tion that can be adopted by anyone trying to communicate the theoretical i Edited by Arik D. Brown
c
foundation for their array design…has insights from a practitioner that are a
unique. The MATLAB® scripts alone are worth the price.” l
l
y
—Daniel C. Ross, PhD, Northrop Grumman Corporation
S
c
Electronically Scanned Arrays: MATLAB® Modeling and Simulation is considered
a
the first book to provide comprehensive modeling/simulation programs used to design n
and analyze Electronically Scanned Arrays (ESA), a key technology international in n
e
scientific and engineering communities. d

A
Several books have been written about ESAs, but most cover only fundamental r
r
theory. Few, if any, provide the insightful, easy-to-use simulation tools found in this a
book. Obviously, MATLAB is one of the greatest tools available for exploring and y
s
understanding science and engineering concepts, and we use MATLAB functions
to easily and instantly calculate ESA patterns. However, to achieve a truly insightful M
A
and in-depth analysis of subarray architectures, conformal arrays, etc., it is T
imperative that users first develop a firm grasp of ESA fundamentals. L
A
B
®
Covers largely unexplored topics, such as reliability aspects and the application

M
of ESAs in space
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d
This volume helps readers build an elemental understanding of how ESAs work. It also e
l
provides code to run as an aid, so that readers don’t have to start from scratch. The i
n
book expands on ESA principles and provides a modeling framework using MATLAB to g

model applications of ESAs (i.e., pattern optimization, space-based applications and a
n
reliability analysis). Presented code serves as an excellent vehicle to help readers d
master the analysis and simulation of ESAs.
S
i
m
Exploring how difficult problems can be simplified with short, elegant solutions, this is
u
an invaluable resource for students and others new to ESAs, as well as experienced l
a
practicing engineers who model ESAs at the systems level. t
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n
K12849
ISBN: 978-1-4398-6163-9
90000
9 781439 861639

Electronically
Scanned Arrays
®
MATLAB Modeling Simulation
and
Edited by Arik D. Brown
Boca Raton London New York
CRC Press is an imprint of the
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not warrant the accuracy of the text or exercises in this book. This book’s use or discussion of MAT-
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of a particular pedagogical approach or particular use of the MATLAB® software.
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Dedication
I dedicate this to the Lord, who gave me the inspiration to write
this book; to my wonderful wife, Nadine, who has never faltered
in her belief in my abilities; and to my two children, Alexis and
Joshua, whom I hope this will inspire to fulfill their purpose and
destiny in life.

Contents
Preface................................................................................................................vii
Acknowledgments.............................................................................................ix
Contributors........................................................................................................xi
Chapter 1 Electronically Scanned Array Fundamentals—Part 1 .........1
Arik D. Brown
Chapter 2 Electronically Scanned Array Fundamentals—Part 2 .......35
Arik D. Brown
Chapter 3 Subarrray Beamforming..........................................................81
Arik D. Brown
Chapter 4 Pattern Optimization .............................................................109
Daniel Boeringer
Chapter 5 Spaceborne Application of Electronically Scanned
Arrays ........................................................................................149
Timothy Cooke
Chapter 6 Electronically Scanned Array Reliability ..........................177
Jabberia Miller
Appendix.A:.Array.Factor.(AF).Derivation................................................197
Appendix.B:.Instantaneous.Bandwidth.(IBW).Derivation.......................201
Appendix.C:.Triangular.Grating.Lobes.Derivation...................................203
v

Preface
During.the.course.of.my.career.at.Northrop.Grumman,.I.have.had.the.plea-
sure.of.teaching.several.internal.classes.in.addition.to.mentoring.young.
engineers.new.to.the.company..Several.years.ago.one.of.the.things.I.noticed.
was.that.many.of.our.talented.new.employees.were.lacking.the.insight.that.
comes.from.understanding.the.fundamentals..I.often.saw.antenna.analy-
sis.performed.with.no.real.insight.into.key.concepts.for.understanding.
and.students.tackling.more.difficult.problems.with.no.textbook.solution..
It.is.widely.known.that.an.electronically.scanned.array.(ESA).pattern.can.
be.calculated.by.simply.typing.in.the.fft.function.in.MATLAB®,.and,.in.
the.blink.of.an.eye.you.have.before.you.a.beautifully.colored.ESA.pattern..
However,.when.it.comes.to.analyzing.subarray.architectures,.conformal.
arrays,.etc.,.it.is.imperative.that.the.fundamentals.of.an.ESA.are.known—
as.opposed.to.how.to.type.the.word.fft.or.fftshift.in.MATLAB..One.of.the.
goals.of.this.book.is.to.provide.a.vehicle.whereby.those.who.are.new.to.
ESAs.can.get.a.fundamental.understanding.of.how.they.work,.and.also.to.
provide.code.to.run.as.an.aid.without.having.to.start.from.scratch.
Several.years.ago.I.had.the.honor.and.privilege.of.taking.the.reins.of.
an.ESA.course.that.was.being.given.to.customers.who.were.unfamiliar.
with.ESA.technology,.and.who.might.not.understand.some.of.the.funda-
mental.concepts..One.of.my.mentors,.Bill.Hopwood,.was.the.originator.of.
this.course,.and.it.has.proven.quite.beneficial.in.educating.new.customers.
on.our.ESA.expertise.at.Northrop.Grumman..I.also.wanted.this.book.to.be.
a.reference.that.I.could.refer.to.those.who.had.an.interest.in.learning.more.
about.ESAs.and.wanted.more.than.just.a.cursory.top-level.introduction.
Last,.this.book.is.intended.to.serve.as.both.a.textbook.in.a.college/uni-
versity.setting.as.well.as.a.reference.for.practicing.engineers..MATLAB.
is.one.of.the.best.tools.available.for.exploring.and.understanding.science.
and.engineering.concepts..The.code.provided.within.this.book.is.a.great.
vehicle.for.understanding.the.analysis.and.simulation.of.ESAs.
This.book.is.comprised.of.six.chapters..Chapters.1.and.2.deal.pri-
marily.with.the.fundamentals.of.ESA.theory.that.should.be.a.part.of.the.
knowledge.base.of.anyone.who.is.serious.about.ESAs..Concepts.such.as.
beamwidth,.grating.lobes,.instantaneous.bandwidth,.etc.,.are.covered.in.
vii
viii Preface
detail..Chapter.1.focuses.solely.on.one-dimensional.ESAs,.while.Chapter.
2.delves.into.two-dimensional.ESA.analysis.and.includes.coordinate.
definitions,.sine.space,.and.pattern.analysis.
Chapters.3.and.4.build.upon.the.fundamental.ESA.topics.covered.
in.Chapters.1.and.2,.and.advances.to.subarrays.and.pattern.optimi-
zation..Chapter.3.focuses.on.subarray.architectures.and.the.nuances.
involved.with.subarrayed.architectures,.such.as.phase.vs..time.delay.
steering,.instantaneous.bandwidth.considerations,.and.the.utility.of.
digital.beamforming..The.chapter.concludes.with.the.analysis.of.over-
lapped.subarrays.
Chapter.4.was.written.by.my.colleague,.Dr..Daniel.Boeringer..It.
focuses.on.pattern.optimization..Developing.methodologies.for.optimiz-
ing.the.spatial.distribution.of.sidelobes.is.of.great.importance,.and.this.
chapter.provides.an.introduction.to.pattern.optimization.and.the.added.
capability.it.provides.
Chapters.5.and.6.cover.topics.that.have.not.been.explored.as.thor-
oughly,.if.at.all,.by.other.books.in.regard.to.ESAs..Presenting.this.infor-
mation.is.extremely.exciting.and.I.think.it.will.be.of.great.benefit.to.the.
reader..Chapter.5.focuses.on.the.application.of.ESAs.in.a.space.environ-
ment..This.chapter.was.written.by.an.extremely.talented.system.engineer,.
Timothy.Cooke..The.chapter.focuses.on.pattern.projections,.translation.
of.sine.space.to.latitude/longitude.coordinates.for.ESAs.operating.in.an.
orbital.regime,.and.covers.some.basic.astrodynamics.principles.that.are.
necessary.to.understand.when.analyzing.space-based.applications.for.
ESAs.
Chapter.6.concludes.with.reliability.aspects,.which.are.quite.frankly,.
often.overlooked.when.it.comes.to.analyzing.ESAs..The.material.in.this.
chapter.is.based.primarily.on.a.technical.memo.authored.by.one.of.
Northrop’s.retired.senior.system.architects,.Bill.Hopwood..My.colleague.
Dr..Jabberia.Miller.formalized.the.notes.and.has.provided.a.most.useful.
chapter.on.reliability.analysis.and.its.impact.on.ESA.performance.
MATLAB®.is.a.registered.trademark.of.The.MathWorks,.Inc..For.pro-
duct.information,.please.contact:
The.MathWorks,.Inc..
3.Apple.Hill.Drive.
Natick,.MA.01760-2098.USA.
Tel:.[phone].
Fax:.[phone].
E-mail:[e-mail].
Web:.www.mathworks.com.