INVESTIGATIONS ON MICROSTRIP PEANO LINE ANTENNA THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENT FOR THE DEGREE OF MASTER OF ELECTRONICS AND TELECOMMUNICATION ENGINEERING JADAVPUR UNIVERSITY (MAY 2011) BYARKAPROVO DAS UNIVERSITY REGISTRATION NUMBER: 108453 OF 2009-2010 EXAMINATION ROLL NUMBER: M4ETC11-01 CLASS ROLL NUMBER: 000910702001 UNDER THE SUPERVISION OF PROF. BHASKAR GUPTA DEPARTMENT OF ELECTRONICS AND TELECOMMUNICATION ENGINEERING JADAVPUR UNIVERSITY KOLKATA 700032 INDIA FACULTY OF ENGINEERING AND TECHNOLOGY JADAVPUR UNIVERSITY ThisistocertifythatthedissertationtitledInvestigationson MicrostripPeanoLineAntennahasbeencarriedoutbyArkaprovoDas (UniversityRegistrationNo.:108453of2009-10)undermyguidanceand supervisionandbeacceptedinpartialfulfillmentoftherequirementforthe degreeofMasterofElectronics&TelecommunicationEngineering.The researchresultspresentedinthethesishavenotbeenincludedinanyother paper submitted for the award of any degree to any other University or Institute. CERTIFICATE ________________________ Prof. Bhaskar Gupta Head of the Department Electronics and Telecommunication Engineering, Jadavpur University, Kolkata- 700032. ___________________________________ Prof. Niladri Chakraborty Dean Faculty of Engineering and Technology, Jadavpur University, Kolkata- 700032. ___________________________________ Prof. Bhaskar Gupta Project Supervisor Department of Electronics and Telecommunication Engineering, Jadavpur University, Kolkata-700032 FACULTY OF ENGINEERING AND TECHNOLOGY JADAVPUR UNIVERSITY CERTIFICATE OF APPROVAL* Theforegoingthesisisherebyapprovedasacreditablestudyofan engineeringsubjectcarriedoutandpresentedinamannersatisfactoryto warrantitsacceptanceasapre-requisitetothedegreeforwhichithasbeen submitted. Itisunderstoodthatbythisapprovaltheundersigneddonotendorseor approve any statement made, option expressed or conclusion drawn therein but approve the thesis only for the purpose for which it is submitted. Committee on final examination for the evaluation of the thesis ________________________ (Signature of the Examiner) _________________________ (Signature of the Supervisor) *Only in case the thesis is approved FACULTY OF ENGINEERING AND TECHNOLOGY JADAVPUR UNIVERSITY DECLARATION OF ORIGINALITY AND COMPLIANCE OF ACADEMIC ETHICS IherebydeclarethatthisthesistitledINVESTIGATIONSON MICROSTRIPPEANOLINEANTENNAcontainsliteraturesurveyand originalresearchworkdonebytheundersignedcandidate,asapartofhis degree of Master of Electronics and Telecommunication Engineering studies. Allinformationinthisdocumenthavebeenobtainedandpresentedin accordance with academic rules and ethical conduct. Ialsodeclarethat,asrequiredbytheserulesandconduct,Ihavefully cited and referenced all material and results that are not original to this work. Name : ARKAPROVO DAS Examination Roll Number: M4ETC11-01 Thesis Title : INVESTIGATIONS ON MICROSTRIPPEANO LINE ANTENNA Signature with date: Iwouldliketotakethisopportunitytothankafewindividuals,directlyorindirectly involved with me, for the successful completion of this project. ACKNOWLEDGEMENT Firstandforemost,Iwouldliketoconveymysinceregratitudetowardsmyproject supervisorProf.BhaskarGupta,HeadoftheDept.ofElectronics&Telecommunication Engg., Jadavpur University for his constant guidance, support and best wishes, without which this work would not have been initiated. Most importantly, I would like to thank him for the faith he has shown in me to take up this work and proceed further. Working with him during the entire tenure was indeed an absolute pleasure. IamalsogratefulandthankfultomyteachersatJadavpurUniversity,tonameafew, Prof.D.R.Poddar,Dr.SudhabinduRoy,Prof.AsimKarfortheirfullsupportand cooperationduringmystayattheinstitute.Theirlectureswereimmenselybeneficialwhich helped me strengthen my knowledge base for pursuing research work. Imustconveyspecialthankstomyfriendandsenior,Mr.SayantanDhar,whohas helped me out from all sorts of difficulties that I faced while working on my project. I would certainly like to mention that all the discussions I had with him on technical issues, helped me grow my analytical thinking capacity to a great extent.Mywhole-heartedthankstomyseniorcolleaguesMs.SanghamitraDasgupta,Mr. RajendraPrasadGhosh,Mr.S.Sankaralingam,Mr.SudiptaMaity,Mr.AvraKunduandto myfriendsSantanu,Amrita,Sonali,RahulandAnkitaforprovidingtheirsupportand unforgettable moments which I shall certainly cherish throughout my life. I also thank all my other seniors and colleagues whom I could not mention in this section. I cannot ever forget the contribution of my fatherMr. Anupam Das, and my mother Mrs. MinaDastowardsmyproperupbringingandforalltheencouragementandsupportthey renderedmeforpursuinghigherstudiesandresearch.Inaddition,Iwouldcertainlyliketo thankmyrelativesandwell-wishers.Lastly,IdedicatethisthesistomygrandfatherLate Prafulla Kumar Sarkar,whocertainlywould have been very happy on seeing the successful completion of this dissertation. Above all, I thank the Almighty and pray for everyones wellbeing. Arkaprovo Das CONTENTS 1.INTRODUCTION 1-2 1.1Preface1 1.2Objective of the thesis1 1.3Organization of the thesis2 2.What is RFID and what are the Antennas Used 3-9 2.1Outline of the chapter 3 2.2RFID3 2.3Components of RFID systems4 2.3.1RFID tag or transponder4 2.3.2RFID reader 4 2.4RFID frequency bands and applications 52.5RFID antennas5 2.5.1Near-field systems6 2.5.2Far-field systems7 2.6Design criteria for RFID tag antennas8 2.7Summary9 References9 3.An Introduction to Space-filling Curves 10-16 3.1Outline of the chapter 10 3.2Fractals10 3.3Space-filling curves10 3.4Fractal Dimension12 3.5Hilbert curves 13 3.6Peano curves14 3.7Process of generating 2nd order Peano curves15 3.8Summary16 References16 4.Peano Line Antennas 17-24 4.1Outline of the chapter 17 4.2Concept of miniaturization17 4.3Electrically small antennas17 4.4Miniaturization of wire antennas18 4.5Peano line wire antennas18 4.6Miniaturization of microstrip antennas19 4.7Microstrip Peano line antennas20 4.8Summary23 References23 5.A Brief Review of Peano Line Antenna 25-30 5.1Outline of the chapter 25 5.2Advancements in miniaturization of antennas25 5.3Review of Peano line antennas26 5.4Summary29 References29 6.RFID Tag Antenna Design Using Peano Curves 31-57 6.1Outline of the chapter 31 6.2RFID frequency bands31 6.3Design Goal31 6.4Design Procedure32 6.5Design prototype32 6.6Design approaches34 6.6.1Approach 1: Increase of path length of the antenna35 6.6.2Approach 2: Higher permittivity substrate42 6.6.3Approach 3: Input impedance match using quarter wavetransformer44 6.6.4Approach 4: Use of different dielectric materials for feed andantenna46 6.6.5Approach 5: Use of stacked dielectric layers 46 6.6.6Approach 6: Modification of the structure described inapproach 547 6.6.7Approach 7: Single stub matching51 6.7Discussions56 6.8Summary56 References56 7.Probe Feed Optimization 58-65 7.1Outline of the chapter 58 7.2Antenna parameters58 7.3Variation in probe feed position58 7.4Observations from the optimization process64 7.5Radiation Pattern for the fundamental mode64 7.6Summary65 8.Lumped Circuit Model Analysis 66-83 8.1 Outline of the chapter 66 8.2 Brief description of the antennas modeled66 8.3 Antenna modeling procedure67 8.3.1Segmentation of the antenna67 8.3.2Modeling of line segments68 8.3.3Modeling of right-angled bends71 8.3.4Modeling of the open end72 8.3.5Cascading of the equivalent circuit73 8.4Implementation of the lumped equivalent circuit model74 8.4.1Meander line antenna74 8.4.2Peano line antenna78 8.5Discussions82 8.6Summary83 References83 9.Conclusion and Scope for Future Works 84-85 9.1Conclusion84 9.2Scope for future research works84 References85 Chapter 1 Introduction Introduction 1 Chapter 1Introduction1.1Preface Inmathematicalanalysis,aspace-fillingcurveisacurve,whichhelpsinfillingupa two-dimensional space.Giuseppe Peano(1858-1932) was thefirst to discover one,which is commonly known as Peano curve. A few space-filling curves, other than the Peano curves are Hilbertcurve,Moorecurve,Sierpinskicurveetc.Thesespace-fillingcurvesfindimmense applicationinthefieldofantennaengineering.Whenthewireitselftakestheshapeofa space-filling curve, and radiates in free space, they are referred to as space-filling curve wire antennas.Again,incaseofmicrostripantennas,thepatchcanbemeanderedbytracingthe shapeofspace-fillingcurves,whicharethenreferredtoasspace-fillingcurvemicrostrip antennas.Whileextensiveresearchworkintermsofantennaperformancehasbeen performedtilldateintheformercategory,thelattercategoryisarelativelynewerfieldof study,andrequiresgreaterattention.Thisthesisdealswithsomeinvestigationsandstudies on microstrip Peano line antennas, where the patch of the microstrip antenna traces the shape of a Peano curve. This configuration is still newer among the latter category stated above, and hence calls for extensive research work. 1.2Objective of the thesis Thepastdecadehasseenphenomenaladvancesinportableelectronicstechnologylike mobilephones,RFIDtagsandMP3players.ThishasledtothedevelopmentofSystemin Package(SiP)whichcombinesallthenecessarycomponentsintoasinglepackage. MiniaturizationofRFcircuittechnologyhasresultedintheneedforminiaturizedantennas. Antennasbasedonspacefillingcurvesaremainlyusedwherecompactnessand miniaturizationarethekeyobjectives.Consideringthatpurpose,microstripPeanoline antennas have been explored in the following chapters.This thesis highlights the applications, where these antennas are used.It also provides a brief theory, both from graphical point of view, as well as from the viewpoint of antennas. It enumerates in detail the approaches towards a particular design problem, and the variation in input impedance characteristics with varying probe feed position. Most importantly, a simple lumpedcircuitequivalentmodeloftheantennaisderivedandpresented,whichformsthe most important part of the thesis. Introduction 2 1.3Organization of the thesis This thesis is divided into nine chapters. Chapter 2 deals with an introduction to RFID, andtheantennasusedforminiaturization.HerethecontextualapplicationofPeanoline antennas is also presented. Chapter3givessomeinsightonthegraphicaltheoryofPeanocurves,whilethebasic theory of Peano line antenna is briefly presented in Chapter 4. Chapter 5 highlights the historical background of Peano line antennas, and the research work that has been carried out in this field in the recent years. The next three chapters describe mainly the research work done during the M.E. project. Chapter6highlightsaparticulardesignproblem,andtheproblemsfacedtherein.In addition, the problems faced are modified with better alternatives, and are studied. TogetfurtherideaonmicrostripPeanolineantennas,Chapter7dealswithafew studies on variation of probe feed location along the antenna, where the patch traces a second iteration Peano curve. InChapter8,asimplelumpedequivalentcircuitmodeloftheantennaisderivedand presented. In addition to that, the same for microstrip meander line antenna is also presented, and a comparison for both the cases is described. Finally,Chapter9summarizestheentireproject,withaconcludingnoteonscopefor future works, and a suggestion for a way forward.

Chapter 2 What is RFID and what are the Antennas Used What is RFID and what are the Antennas Used 3 Chapter 2What is RFID and what are the Antennas Used 2.1Outline of the chapter This chapter presents a very brief introduction to RFID technology and the antennas used forit.Theusefulnessofminiaturizedantennasisalsomentionedinthisregard.Theentire discussionisqualitativeonly,anddetailedmathematicalformulationsforthischapterare beyond the scope of this thesis. 2.2RFID RFIDisanabbreviationforRadioFrequencyIdentification,arapidlygrowing technology, which uses RF signals for automatic identification of objects. RFID systems are shortranged-normallydigital,wirelesssystems.Examplesofapplicationsincludeanimal tagging,assettracking,electronicpassports,smartcardsandshopsecurityetc[1].A simplified diagram of RFID system is shown in Fig. 2.1.

Fig. 2.1 A simplified RFID system [1] What is RFID and what are the Antennas Used 4 2.3Components of RFID systems There are two main components of an RFID system. They are: Tag or transponder Reader 2.3.1RFID tag or transponder As shown in Fig. 2.1, at one end of the system is the RFID tag or transponder, a system that is placed on the objects to be identified. The tag contains an integrated circuit (IC), and anantennatoreceiveEMwavesfromthereaderforitsidentification.Thetagshavean ElectronicProductCode(EPC)label,whichisanalogoustotheUniversalProductCode (UPC)formatusedbyBarcodes.Thetagsarealsoprogrammableandcancontainuser-specific information, i.e. they contain some user memory. a) Passive tags: These are the tags, which needsto be powered by the RFID reader, i.e. the fieldsfromthereaderservesasenergyexcitationforthesetagstobeoperational.Theyare comparatively cheaper in cost. Types of RFID tags: b)Semi-activetags:Semi-activetagshavelimitedpowersupply,andhenceallowsfaster operation than the passive tags. c)Activetags:Theyhaveinbuiltbatterypowersupplywhichmakesthemfunctional, without relying on external aid. They are used in high data rate communications. 2.3.2RFID reader An RFID reader or interrogator on the other hand, prompts communication with the tags. However, contrary to its name, a reader can also write or transfer data to the tag. The reader is usually connected to a host network or a computer. a)Mono-staticreaders:Inthiscase,thetransmissionandreceptionofEMsignalusesthe same antenna. Types of RFID readers: What is RFID and what are the Antennas Used 5 b)Bi-staticreaders:Inbi-staticreaders,theantennasandtheassociatedcircuitryare different. The scheme is shown in Fig. 2.1, where the second optional antenna is also used. 2.4RFID frequency bands and applications [2] 125-134.2KHzand140-148.5KHz(LF)canbeusedgloballywithoutalicense, often used in vehicle identification. 6.765-6.795 MHz (MF) inductive coupling. 13.553-13.567MHz(HF)-oftencalled13.56MHzband,usedforelectronic ticketing, garment tracking, access control, contactless payment etc. 26.957-27.283MHz(HF)Inductivecoupling,usedforspecialapplications,bio-medical applications. 433 MHz (UHF) Backscatter coupling, used for remote car keys. 858-930MHz(UHF)Restrictedusage,usedforassetmanagement,container tracking, baggage tracking, work in progress tracking etc. 2.4-2.483 GHz (SHF) Backscatter coupling, only used in USA/Canada. 2.446-2.454GHz(SHF)Backscattercoupling,usedforlong-rangetrackingand with active tags, AVI (Automatic Vehicle Identification). 5.725-5.875 GHz (SHF) Backscatter coupling, not so widely used. 2.5RFID antennasIn general, the antenna for the RFID tag is a balanced one, to suit the differential inputs of the tag IC. It is a linearly polarized electrically small antenna. The reader antenna is generally electrically larger than the tag antenna, and may be either balanced or unbalanced.Readerantennas are often circularlypolarized when the orientation of the tag is unknown. It is because; a circularly polarized wave can be decomposed into two mutuallyorthogonal,verticalandhorizontallinearlypolarizedcomponents,andthus eliminatesanylikelihood ofcompletepolarizationmismatchatthetag.Thisisimportantin tagging applications where high reliability is required. However, there is a 3-dB loss between What is RFID and what are the Antennas Used 6 circularlyandlinearlypolarizedantennasandhencemaximumpowertransferbetweenthe reader and tag cannot be achieved. LFandHFsystemsusenearfieldcouplingbetweenthereaderandthetagantennas. Generally, the coupling is inductive; however, it may also be capacitive. When the coupling is inductive, multi-turn coils are used as tag and reader antennas. The effect is more like that ofatransformer,thanthatofanantenna,withthecoilinthereaderservingastheprimary winding, while that in the tag serving as the secondary. The coupling between the antennas is dependentontheirseparation,andalwaysoccursinthenear-fieldregion.Thisnear-field couplingmethodisusedinapplications,wherethetagcanbeplacedonalossydielectric such as an animal or a solid object etc. Far-fieldcouplingisusedgenerallyforUHFsystems,wherethetransferofenergy between the reader and the tag is determined by Friis equation [3]. 2.5.1Near-field systems Near-field systems use coil/loop antennas for communication between the reader and the tag. The reader and tag loop antennas are shown in Fig. 2.2. The reader and tag antennas with radii a & b respectively are separated by a distance d. Fig. 2.2 Simplified Reader and Tag loop antennas [1] What is RFID and what are the Antennas Used 7 The magnetic field produced due to the coil antennas is greatest along the axis of the loop, i.e. alongthez-axis.Thetagantennasizeandgeometryisgovernedbytheapplication.For instance,creditcarddimensionsareoftenusedforsmartcards.Multi-turnloopsarealso often employed in order to increase the mutual inductance. A typical rectangular tag antenna isshowninFig.2.3,whileFig.2.4depictsthephotographofanexampleofacommercial coil antenna- used in a European passport. The antenna in Fig. 2.4 has five turns using thin wires. The IC is connected to the strap prior to being connected to the coil. 2.5.2Far-field systems Systems with carrier frequencies greater than 100 MHz generally operate by transferring powerinthefarfield.ISMbandcenteredaround2.45GHz,alsousesthismethodofRFID communication. A typical far field system is shown in Fig. 2.5. A wide variety of antennas is possibleinthefarfieldsystems,thoughcoilantennasareveryrarelyused.Dipoles,PIFAs andpatchesareamongtheoptionsatthereader.Patchesareoftenusedtoprovidecircular polarization (shown in Fig. 2.5). Modified dipoles are commonly used as tag antennas. Fig. 2.3 Rectangular Tag coil [1] Fig. 2.4 Coil antenna used within passport [1] Fig. 2.5 Typical far field reader and tag antennas [1] What is RFID and what are the Antennas Used 8 ThetransferofenergybetweenthereaderandthetagisgovernedbyFriistransmission equation as stated below [3] R TTRG Gd PP24= (2.1) where, PR is the power received by the tag, PT is the power transmitted bythe reader, GT& GR are the gains for reader (Transmitter) and tag antennas (Receiver)respectively, separated d distance apart, being the wavelength corresponding to the frequency of signal transmitted.Amongthewireandmicrostripantennaconfigurations,meanderlineantennas,orother antennasbasedonspace-fillingcurvesarebeingusedlately,inordertofacilitate miniaturization.ThoseRFIDsystems,whichareusedforbiomedicalapplications,require miniaturized RFID circuitry, and hence affirm the need for miniaturized antennas. 2.6Design criteria for RFID tag antennasTherequirementsthatlargelydeterminethedesignofanRFIDtagantennaare enumerated below [4]: 1.Frequencyband:thedesiredfrequencybanddependsontheregulationsformulatedby the country, where the tag is to be used. 2. Size and form: The size and form of the tags depend on the applications, where it is to be used. 3.Readrange:ThemaximumdistanceatwhichtheRFIDreadercandetectthe backscattered signal from the tag is defined as the read range. The read range depends on: EIRP: Effective Isotropic Radiated Power is determined by local country regulations. Objects: Tag performance changes when placed on different objects. Orientation:Readrangedependsonantennaorientation.Someapplicationsrequire tagstohaveaspecificdirectivepattern,suchasomnidirectionalorhemispherical coverage. 4.Applicationswithmobility:Incaseofmobiletagapplications,Dopplershiftmustbe accounted for, in the computations. What is RFID and what are the Antennas Used 9 5. Cost: Theantennas should be of lowcost, so as toreduce the total cost of the RFID tag. This puts restriction on the choice ofantenna structure, and the choice of materials usedfor its construction. 2.7Summary AbriefaccountonRFIDtechnologyhasbeenportrayedinthischapter.Theantennas used for this technology were also illustrated briefly, and their characteristics were discussed. Aspresentedinearliersections,itisevidentthat,thistechnologyisagrowingtechnology, due to the applications on which it is used. As this technology does not require Line of Sight (LOS) propagation, it is replacing the optical Bar code technology very rapidly. References [1]Y.HuangandK.Boyle,AntennasfromTheorytoPractice,JohnWiley&SonsLtd, 2008[2]http://www.radio-electronics.com/info/wireless/radio-frequency-identification-rfid/low-high-frequency-bands-frequencies.php [3]H.T.Friis,Anoteonasimpletransmissionformula,ProceedingsIRE,41,pp.254-256, 1946 [4]K.V.SeshagiriRao,P.V.Nikitin,S.F.Lam,AntennaDesignforUHFRFIDTags:A ReviewandaPracticalApplication,IEEETransactionsofAntennaand Propagation, Vol. 53, No. 12, December 2005 Chapter 3 An Introduction to Space-filling curves An Introduction to Space-filling Curves 10 Chapter 3An Introduction to Space-filling Curves 3.1Outline of the chapter This chapter presents a very brief description of the space-filling curves in general. Few ofthespace-fillingcurvesarealsoexplainedin thetext.However,Peanocurvesconstitutes the most important part of this chapter, since the antennas described in the later chapters, are patternedonthiscurve.Processofgeneratingastandard2nditerationPeanospace-filling curve is also explained. 3.2Fractals Afractalisdefinedasaroughorfragmentedgeometricshapethatcanbesplitinto parts,eachofwhichis(atleastapproximately)areduced-sizecopyofthewhole,"[1]a propertycalledself-similarity.Inotherwords,fractalformsapartofnon-Euclidean geometricalshapes,thatisrepeatedateven-smallerscalestoproduceirregularshapesand surfacesthatcannotberepresentedbyclassicalgeometry.Thetermfractalwascoinedby Benoit Mandelbrot in 1975 and was derived from the Latin word fractus meaning "broken" or "fractured"[2].Afractalshapeisgeneratedusingrecursivealgorithms.Twoimportant propertiesoffractalshapesareself-similarityandscale-invariance.Fractalsconsistof identical and similar elements repeated in different magnifications, orientations and positions, often in inter-connected fashion to obtain the final structure. One important feature of fractal geometryin2-dimensionis,afterinfinitenumbersofrecursiveiterations,thelengthofthe curvetracedbecomesinfinite,yetthecurveoccupiesafinitearea.Thispointisexplained later. 3.3Space-filling curves Space-filling curves are subset of a broader class of fractals. As the name suggests, these curves effectively aid in filling up a particular space (in 2-D), or a particular volume (in 3-D), as the iteration order increases. In simpler words, the property of a space-filling curve may be explained as: if a particular geometrical curve occupies a definite area in 2-dimensional space inits1stiteration,theninhigheriterations,itoccupiesthesamearea,withreduced magnification, and many repetitive patterns. Thus, as the iterationorder increases, thecurve An Introduction to Space-filling Curves 11 traces more path,yetconfined in a definite area, and helping in compression. The repetitive pattern brings in the concept of self-similarity as described earlier. Examples:Someofthecommontypesofspace-fillingcurvesareMoorecurves,Peano curves,Hilbertcurves,Wunderlichcurvesetc.ThefirstsixiterationsforHilbertcurveare shown in Fig. 3.1. Fig 3.1 Six iterations of the Hilbert curve construction [3] Construction: The first iteration is the unit cell, the repetition of which generates the higher iterations.Asseenfromthefigureabove,thefirstiterationcurveisusedinthesecond iteration with reduced size, either rotated by 90 degrees clockwise/anticlockwise, or keeping itintact.Theunitcelloffirstiterationisrepeated4times(2-rotated,2-intact)tofillthe samespaceinseconditeration.Additionallinesegmentsareaddedinordertoensure continuity of the curve.Now, this second iteration Hilbert curve is the unit cell for the third iteration. This process is a recursive one, and goes on with increasing iteration orders. 1st iteration2nd iteration3rd iteration 4th iteration5th iteration6th iteration An Introduction to Space-filling Curves 12 3.4Fractal Dimension Fractaldimensionisanimportantparametertoquantifythespace-fillingabilityofa space-fillingcurve.Foraspace-fillingcurvetoeffectivelyfilla2-Dspace,thefractal dimension must approach 2. Similarly, the same parameter must approach a value of 3 so as to effectively fill a 3-D volume. To illustrate the above point, some examples are considered.Letusconsideralinesegmentoflengthl.Whenthelineisequallyhalved,eachofthe segments is of length l/2. Alternatively, each of those smaller line segments when magnified byafactor2,yieldstheoriginallinesegment.Similarly,ifalinesegmentisdividedinto threeparts,eachofthemmaybemagnifiedbyafactorof3togettheoriginalsegment. Therefore,ingeneral,ifalineisdividedequallyintonself-similarsmallerlinesegments, each one of them when magnified by a factor n yields the original line segment. Let us now consider the case of a square, with sides of length l. If we now assume a smaller squarewitheachsideoflengthl/2,then4suchsmallersquaresarerequiredtofillinthe spacebytheoriginalbiggersquare.Thus,thebiggersquarecanbedividedinto4smaller self-similar squares, each with magnification 2. Similarly, if l/3 be the length of each side of the smaller squares, then it would require 9 such squares to fill the bigger square of length l. For this case, we can sayeach of the smaller 9 squares havea magnificationfactor 3, i.e. if the sides of any of the 9 smaller squares be trebled, it would produce the bigger square. Similar examples may be taken for the case of cubes.For the first case of a straight line, it can be divided equally into any numbers of smaller self-similar segments. Let it be n. Hence, it can be expressed as unit power of n, i.e. n = n1, or, more generally, n = ND, where for this case, N = n, and D = 1. Intheaboveexpressions,nisthenumberofsmallerlinesegments,Nisthemagnification factor, and D is the dimension. D = 1 indicates, a straight line is one-dimensional. Thesecondcaseofasquaresuggeststhat,thebiggersquarecanbedividedequallyinton numberofsmallerself-similarsquares,nbeingaperfectsquarenumber.Asseenabove,it can be divided into 4, 9, 16 etc. number of smaller squares. An Introduction to Space-filling Curves 13 So, if a square is divided into 9 smaller squares, then 9 = 32, where n = 9, N = 3, D = 2 Whichclearlysuggests,thedimensionofasquareis2,i.e.itoccupiesadefiniteareain2-dimensional plane. Therefore, for any general D-dimensional space, the following relation holds true: n = ND (3.1) Forregulargeometries,Disthedimension,whileforfractalgeometries;Disdefinedas Fractal Dimension. Taking logarithm on both sides of (3.1), we get, log n = D log N, or, D = log n / log N (3.2) Therefore, dimension or fractal dimension is defined as the ratio of the logarithm of number of self-similar pieces to the logarithm of the magnification factor. ForaKochfractalcurve,themaximumattainablefractaldimensionD=1.26,whilefora Hilbert curve, maximum value of D = 2. This clearly suggests that, as the iteration number of aHilbertcurveincreases,itfillsthe2-DspacemoreeffectivelythanasimilarorderKoch curve. 3.5Hilbert curves The basic pictorial representation of Hilbert curves is depicted in Fig. 3.1. In this section, the values of the dimensions of its line segments are provided (Fig. 3.2). Dimensions: (a) Iteration - 1 (b)Iteration - 2 Fig. 3.2 Hilbert curve l d = l d=l/3 l An Introduction to Space-filling Curves 14 Let l be the side dimension of the Hilbert curve, with d being the length of each smallest unit of line segment. Let the total length of the curve be S, and n be the iteration order. Then, for a Hilbert curve, 1 2 =nld; and S = ( 22n 1 ) d = ( 2n + 1 ) l 3.6Peano curves The first space-filling curve was discovered by Giuseppe Peano in the year 1890. It was named after him as Peano curve. There are different types of Peano curves the standard first Peano curve, minimal N-shaped curve etc. The first Peano curve is the most commonly used oneforantennadesignpurposes,anditisshowninFig.3.3.APeanocurvehasafractal dimension of the value 2. Dimensions: For a Peano curve, the dimensions of the curves are given as follows: 1 3 =nld; and S = ( 32n 1 ) d = ( 3n + 1 ) l Comments:IfweobservethelengthdimensionsfortheHilbertandPeanocurves,wefind thatforadefinitefootprintareaandfixediterationorder,thepathlengthScoveredbya Peano curve, is greater than that covered by a Hilbert curve. This suggests that, a Peano curve offersmorecompressionandspace-fillingpropertythanasimilarHilbertcurve.This (a) First iteration(b) Second iteration (c) Third iteration Fig. 3.3 Peano curves [3] An Introduction to Space-filling Curves 15 contrastingpropertyisbeneficial,especiallyincaseofantennadesign,whichassertsPeano line antennas as better candidates for miniaturization. 3.7Process of generating 2nd order Peano curves Step 1: First, consider the first iteration, and its mirror image. They are depicted below: Step 2: Reduce the scale of the size of first iteration curve and its mirror image Step 3: Divide the square space to be filled (i.e. space containing the first iteration curve) into 9 equal squares. Step4:Goonfillingthesmallersquaresinthenumberedorderstatedabove,alternatively with the reduced Peano 1st iteration curve and its mirror image. The square number 1 contains reduced1stiterationcurve,squarenumber2containsitsmirrorimage,andsoon,tillwe arrive at square number 9 Original Curve Mirror image

1 2 34 5 6 9 8 7 An Introduction to Space-filling Curves 16 Step 5: Add extra line segments to ensure the continuity of the curve. The generated curve is the second iteration Peano curve. The same process, taking the second order Peano curve and itsmirrorimageforaunitcell,canberepeatedtoproduceathirdorderPeanocurve.This process is a recursive one, and can be applied to generate any higher iteration. 3.8Summary Thischapterpresentedanoverviewofthespace-fillingcurvesingeneralandits concepts,whileemphasizingmainlyontheHilbertandPeanocurves.Alsotheprocessof generatingasecondorderPeanocurvehasbeendiscussed,thatcanbeappliedtogenerate any higher order of the same curve. References [1]B.B. Mandelbrot, The Fractal Geometry of Nature, New York: W.H. Freeman & Co.,1983 [2]http://en.wikipedia.org/wiki/Fractal [3]http://en.wikipedia.org/wiki/Space-filling_curve Chapter 4 Peano Line Antennas Peano Line Antennas 17 Chapter 4Peano Line Antennas 4.1Outline of the chapter In chapter 3, a brief idea on Peano space-filling curves has been presented. This chapter presentstheapplicationofthesamecurveinantennaengineering.Inthatcontext,thebasic theory regarding miniaturization of antennas is also discussed. 4.2Concept of miniaturization Miniaturization of an antenna can be thought of from two different viewpoints. Although they mean the same thing, yet they may be considered separately: Frequency Reduction: Compared to a particular conventional antenna design, if anyotherdesigncanreducetheresonantfrequencyoftheantenna,yetnot exceeding the total physical size, then the new design can be considered to be as a miniaturized one. Size miniaturization: The above concept can be rephrased in a different manner. Sincethedesignofaresonantantennadependsontheeffectivewavelength, hence a lower frequency antenna design requires the physical size of the antenna to be much larger. However, as explained in last point, if the antenna can realize a lowerresonantfrequency,withoutexceedingtheantennasize,thenitcertainly aids in size reduction, as compared to the conventional design at lower frequency, where in terms of effective wavelength, the size is much larger. 4.3Electrically small antennas Anantennaissaidtobesmallwhenitssizeismuchsmallerthantheoperating wavelength.SmallAntennaLimit(SAL)determinesthecriteriaforanantennatobe electrically small. It is defined as the upper frequency boundary, at which an antenna may be consideredaselectricallysmall[1].InthecontextofSAL,Wheelerdefinedanelectrically small antenna as one whose maximum dimension is less than /2 [2]. This relation is often expressed as: ka < 1 (4.1) Peano Line Antennas 18 where, k = 2/, is the free space wavelength, a is the radius of a sphere circumscribing the maximum physical dimension of the antenna. A sphere of radius a = 1/k = /2 is defined as the radiansphere. Therefore, when an antenna can be enclosed into a radiansphere of radius a, it is said to be an electrically small antenna. From (4.1), it can be inferred that, an antenna is electrically small for a particular frequency of interest. It follows directly that, a frequency reduction, causes an antenna to be electrically small, thus helping in miniaturization. 4.4Miniaturization of wire antennas Wireantennascanbeminiaturizediftheantennalengthofaconventionaldipoleor monopole design is extended following a particular meandering pattern, called meander line antenna,orbyfollowinganyotherspace-fillingcurve.Thecompressionpropertyofspace-filling curves has been discussed in chapter 3. Thus, when the wire traces a space-filling curve, the current path over it followsanextendedpath,andhencecausesareductionin theresonantfrequencyoftheantenna,withoutexceeding thephysicalsizelimits.Oneparticularsimple configurationofameanderlinewireantennaisshownin Fig.4.1.Inthefigure,thewiretakesmeanderingturnsto reducetheresonantfrequency,andthewholeantennais placed over a ground plane in a monopole like fashion. 4.5Peano line wire antennas In Fig. 4.1, if the meander pattern of the wire is replaced by a Peano curve pattern, then it formsaPeanolinewireantenna.Asshowninchapter3,thePeanocurvemaybeofany iterationorder.Astheiterationorderincreases,thespace-fillingpropertyofthecurve increases,andhenceitresultsinmorefrequencyreductionfortheantenna,leadingto miniaturization.Thoughthesespace-fillingwireantennasresultinminiaturization,yetthey sufferfromcertaindrawbacks.Whenusedasaverticalmonopoleantenna,justlikethat Fig. 4.1 Meander line wire antenna Ground Plane Peano Line Antennas 19 showninFig.4.1,theseantennasrequirealargehorizontalgroundplane,whicheventually increases the total size of the package, and thus hampers our original goal for miniaturization. Secondly, the antenna is fed at the end as a monopole, and hence, the input impedance cannot be changed by changing the feed position. Therefore, the problem of impedance matching is a seriousconcern.Forthesereasons,weswitchovertomicrostripconfigurationantennas, where the space-filling property of the curves is utilized for miniaturization. 4.6Miniaturization of microstrip antennas With growing demands for miniaturized circuitry in todaysworld, smaller and cheaper antennasare required tobe integrated intoelectronic devices. Thiscalls for the introduction ofminiaturizedplanerantennasinmostoftheapplications.Themicrostrippatchantennas have a significant number of advantages over conventional antennas. Nevertheless, the length of the patch required for an operation at lower frequency range at its fundamental mode is too high,sincethelengthisoftheorderofhalfoftheeffectivewavelength.Insuchcases, different methods are to be employed to reduce the size of the antennas. They are: Use of high permittivity substrate: Rectangular patch antennas are operated at a resonant frequency fr, where fr is given by [3]: rrLcf 2=(4.2) where c is the speed of light in free space, L is the length of the patch and r is the permittivity of the substrate used. Thus (4.2) implies that the resonant length L is proportionalto r1atafixedresonantfrequency.Hence,ahighpermittivity substrate results in smaller antenna length. Use of shorting pins: Use of edge shorted patch, or shorting pins at the vicinity ofacoaxialfeedarewellknowntechniquesforsizereductionofamicrostrip antenna [4-7]. The shorting post or pin adds an extra path for the current to flow, thus increasing the magnetic field associated with it, whicheffectively increases the inductive effect. This reduces the resonant frequency of the antenna. Peano Line Antennas 20 Insertionofslots:Insertingsuitableslotsintheradiatingpatchisalsoan important technique for reducing the dimensions of the patch antenna [8-9]. The slots introduce parasitic capacitance, and extended path for surface current, which tends to reduce the resonant frequency of the antenna.Useofspace-fillingcurve:Miniaturizationcanalsobeeffectedbythe introduction of space-filling curves [10-12]. If the patch of the microstrip antenna traces a space-filling curve without increasing the original physical footprint area, thenitgreatlyhelpsinfrequencyreduction,andhenceminiaturization.This technique is used in the thesis, and the space-filling curve that is implemented in microstrip form is the 2nd order Peano curve. 4.7Microstrip Peano line antennas Fig. 4.2 shows the geometry of a microstrip Peano line antenna, while the photograph of a fabricated Peano line antenna is shown in Fig. 4.3. ThepatchofthemicrostripantennatracesasecondorderPeanocurve.Thefabricated photograph shows a Peano line antenna fabricated on a Duroid substrate and separated from the ground plane using foam. Frequency Reduction:The convoluting nature of the patch as shown in figures above suggests that the surface currentthatflowsoveritfollowsagreatlymeanderedpath.Duetotheextendedpathover whichthesurfacecurrentflows,ascomparedtoitspathonarectangularpatchwithsimilar footprintarea,extrainductiveeffectcomesintopicture.Inaddition,thecloselyplaced Fig. 4.2 Geometry of Microstrip Peano line antenna [13] IEEE 2007 Fig. 4.3 A fabricated 2nd order Peano line antenna [13] IEEE 2007 Peano Line Antennas 21 adjacentlinesfacilitateselectromagneticcouplingbetweenthem,whichaccountsforextra capacitiveeffectaswell.Astheinductiveandcapacitiveeffectsincreases,theresonant frequency (fr) of the antenna falls, following the relation: LCfr 21= (4.3) provided,the effective inductanceL andcapacitance C of the antenna equivalent circuit can be represented as a series resonant circuit.Radiation Mechanism:Theradiationfromtheantennamainlyoccursduetothediscontinuitiesinherentwithin the structure itself. As the current over the antenna traverses a convoluted path, the electrons or the charges encounter sharp discontinuities, where they are accelerated or decelerated. This causesradiationtooccurfromthediscontinuities.Inthiscontext,itisnoteworthythatthe fringingfieldsfromboththeopenendscontributeverylittletotheeffectiveradiation.Itis because, the width of the microstrip line forming a Peano line antenna is very small, and thus providesverysmallradiatingedgesforthefringingfieldstooccur.Thisisthemainreason for these antennas not complying with the conventional design rule of l = eff/2, where l is the lengthoftheantenna,andefftheeffectivewavelength.Theaboveruleisvalidonlyfor microstrip rectangular patch antenna, where the resonance occurs for an antenna length equal tohalftheeffectivewavelength.Whenthelengthofthepatchfollowstheaboverule,the fringingfieldsfromboththeopenendsisexactlyoppositelydirected.Thevertical components of those fields cancel out each other, leaving only the horizontal components as effective radiating slots separated by a distance of half the effective wavelength, resulting in maximumradiationinthebroadsidedirection.ButincaseofPeanolineantennas,radiation occursfromthediscontinuitiesandnotduetothefringingfields,andthereforethedesign rule is not followed. This fact is verified in Chapter 6 by the simulation results. The radiation pattern of this antenna is depicted in Chapter 7.Comparison with Hilbert antennas: In Chapter 3, it has been mentioned that since the path length of the curve as occupied by a2ndorderPeanocurveisgreaterthanthatcoveredbya2ndorderHilbertcurve,therefore Peano curves provide better compression properties. Thus when the patch follows a 2nd order Peano curve, the surface current on it traverses more path length than that caused due to a 2nd Peano Line Antennas 22 order Hilbert curve within the same footprint area. Therefore, microstrip Peano line antennas provide better miniaturization and more frequency reduction properties than a similar Hilbert antenna. Comparison with Meander line antennas: Asfarasminiaturizationisconcerned,boththeantennasalmostprovidesimilar miniaturizationcharacteristics.However,acomparisonmaybedrawnconsideringthe structureofthetwo.Thestructureofonlythepatchesformicrostripmeanderlineantenna, andmicrostripPeanolineantennahasbeen showninFig.4.4.Boththeantennascover similarpathlengths,andoccupyequal footprintarea.The3-dimensionalfiguresare not shown for simplicity. As evident from the figures,therearemorenumbersof discontinuities in Peano line antennas, than in meanderlineantennas.Soiftheradiation fromthediscontinuitiesaddup constructively,Peanolineantennacan providemoreradiationgainthanthecorrespondingmeanderlineantennaofsameantenna lengthandsamefootprintarea.TheworkofFukusakoetal.[11]reportedsuchan observation. Anotherimportantpointinthisregardisthatincaseofmeanderlineantennas,the currentsintheparalleladjacentlyplacedlinesegmentsbeingoppositelydirectedhelpsin cancellationofradiationduetothematthefarfield,whilethesmallerlinesegments comprisesoftheeffectiveradiatingelements.However,byvirtueofitsstructure,complete cancellation of radiation due to parallel adjacent line segments is impossible in case of Peano line antennas. Quality factor, Bandwidth & Radiation efficiency: Duetocloselyplacedlinesegments,thereisahugeamountelectromagnetic coupling between them, which helps in storage of a lot of energy in the near field of the antenna. This enhances the quality factor (Q) of the antenna (a) (b) Fig. 4.4 (a) Microstrip meander line antenna (b) Microstrip Peano line antenna Peano Line Antennas 23 As bandwidth is inversely proportional to the quality factor, therefore microstrip Peanolineantennasuffersfromlowerbandwidth.Thisisthecasewithall antennas based on space-filling curves. Application of space-filling curves, effectively increases the antenna path length, henceincreasestheconductorlossoftheantenna.Thisenhancestheloss resistanceoftheantenna,whichresultsinreductionofantennaradiation efficiency. 4.8Summary Thischapterexplainedthebasicprinciplesofminiaturization,withanemphasison electricallysmallantennas.ThefocushasbeenputmainlyonPeanolineantennasfor miniaturization,andinthatcontextthebasicprinciplesofPeanolineantennashasbeen discussed.Asdescribedinthechapter,Peanolineantennasareadvantageousintermsof frequencyreductionascomparedtoHilbertantennas,andintermsofradiationgain,as compared to meander line antennas. However, they suffer from drawbacks, which is common to all antennas based on space-filling curves. References [1]S.R.Best,ADiscussiononthePropertiesofElectricallySmallSelf-ResonantWire Antennas, IEEE Antennas and Propagation Magazine, Vol. 46, No. 6, December 2004 [2]H.A.Wheeler,FundamentalLimitationsofSmallAntennas,ProceedingsIRE, pp.1479-1484, December 1947 [3]R.Garg,P.Bhartia,I.Bahl,A.Ittipiboon,MicrostripAntennaDesignHandbook, Arctec House Inc., 2001 [4]N.Fayyaz,E.Shin,S.Safavi-Naeini,Anoveldual-bandpatchantennaforGSM band, Antennas and Propagation for Wireless Communications, pp. 156159, 1998 [5]R. Waterhouse, Small microstrip patch antenna, Electron. Lett. 31, 604605, April 13, 1995 [6]S. Dey and R. Mittra, Compact microstrip patch antenna, Microwave Opt. Technol. Lett. 13, 1214, Sept. 1996 [7]M. Sanad, Effect of the Shorting Posts on Short Circuit Microstrip Antennas, IEEE International Symposium on Antennas and Propagation, Vol. 2, pp.794-797, 1994 [8]G.Kosiavas,A.Papiernik,J.P.Boisset,M.Sauvan,TheC-Patch:ASmall Microstrip Element, Electronics Letters, Vol. 25, pp. 253254, 1989 [9]K.L.WongandK.P.Yang,Smalldual-frequencymicrostripantennawithcross slot, Electron. Lett. Vol. 33, pp.19161917, Nov 1997 Peano Line Antennas 24 [10]H.Y.WangandM.J.Lancaster,Aperture-CoupledThin-FilmSuperconducting Meander Antennas, IEEE Transactions on Antennas and Propagation, Vol.47, No.5, May 1999 [11]T.Fukusako,T.Terada,K.Iwata,Designandcomparativestudyonplanarsmall antennasusingmeanderandpeanolinestructure,InternationalSymposiumon Antennas and Propagation Society, pp. 2451-2454, 2007 [12]X.Chen,S.Safavi-Naeini,Y.Liu,ADown-SizedPrintedHilbertAntennaforUHF Band,IEEEAntennasandPropagationSocietyInternationalSymposium,Vol.2, pp.581-584, 2003 [13]J.McVayandA.Hoorfar,Miniaturizationoftop-loadedmonopoleantennasusing Peano-curves, Radio and Wireless Symposium, IEEE, pp. 253-256, 2007

Chapter 5 A Brief Review of Peano Line Antennas A Brief Review of Peano Line Antenna 25 Chapter 5A Brief Review of Peano Line Antenna 5.1Outline of the chapter This chapter briefly highlights the research works that has been carried out in the field of Peano line antennas over the years. As mentioned in Chapter 1, this field is a relatively newer fieldofstudyinthebranchofantennaengineering.Thechronologicaladvancementsinthe development of Peano line antennas have been elucidated in the following sections. 5.2Advancements in miniaturization of antennas The methods for miniaturization of antennas have been discussed in the previous chapter. Theelectricalsizeofanantennahasbeenanimportantfieldforresearchwork,rightfrom 1947, when H.A.Wheeler published a paper on small antennas [1]. In the very next year, L.J. Chuinhisjournalformulatedafundamentallimit,popularlyknownasChulimit[2].Also, there has been several other researchers in this field over the years [3-4]. In addition, a lot of thoughtprocessonminiaturizationtechniqueshastakenplace.Someofthemhavebeen discussedinChapter4,andthereviewofthoseworksisnotthefocusofattentioninthis thesis. Forminiaturizationpurposes,theconceptoffractalsisalsointroducedinthefieldof antennas.ThewiremayfollowdifferentfractalshapeslikeKoch,Minkowskietc.[5]to reducetheresonantfrequencyoftheantenna.Inaddition,fractalgeometrycanalsobe applied to microstrip configuration, where the edges of the patch are protruded in the form of the fractal shapes, to result in miniaturization.Nevertheless,themostpopularlyusedantennaforthesepurposesarethemeanderline antennas [6-7]. They may be in wire configuration, or in microstrip form. This concept paved the way for the introduction of graph theory in antenna engineering. Therefore, space-filling curveslikeHilbertcurves,Moorecurves,Wunderlichcurves,Peanocurvesetc.werethus studiedingreaterdetail.Although,Hilbertcurveantennas[8-9]bothinwireconfiguration and in microstrip form have attracted several researchers due to its simplicity, the others are a bitlessexplored.Hence,itcallsformoreandmorestudiesontheotherspacefillingcurve antennas.TheadvancementsinthefieldofPeanolineantennasisdescribednext,whilethe review of other space filling curve antennas are beyond the scope of this thesis. A Brief Review of Peano Line Antenna 26 5.3Review of Peano line antennas AlthoughGiuseppePeanodiscoveredthePeanocurvealongtimeearlier(1890),yetit wasalateintroductioninthefieldofantennaengineering.Thoughtherewereafewpapers onbroadbandarraysusingPeano-Gospercurve,yetthestandardfirstPeanocurvevariant was not yet implemented. It was in the year 2003 that Jose M. Gonzalez-Arbesu et al. investigated the effectiveness of space-filling curves as small antennas [10]. The importance of space-filling geometries, as optimalorefficientcurvesforsmallantennadesignwasassessedinthisworkusingbi-dimensional wire monopoles. Several variants of space-filling curves were taken in the form of monopole wires in his comparative study, which included three different variants of Peano monopolesinfirsttwoiterations.Theimportantconclusionwas,thoughtheyweresuitable forreachinghigherminiaturizationratiosthanconventionalquarter-wavemonopoles,they store a lot of energy in the near field of the antenna and have higher ohmic losses, resulting in high quality factor and lower radiation efficiencies. In 2004, J.Zhu et al. [11] investigated the characteristics of a single antenna made of thin wire, patterned after Peano space-filling curve. The same team had earlier worked on similar investigationforHilbertcurvewireantennas.Thisstudymainlyfocusedonthefeedpoint effects,currentdistributionpattern,crosspolarization,impedancebandwidthandother radiation characteristics. The study revealed that when the feed point was placed at the point ofsymmetry,therealpartofinputimpedancewasverylow.However,itwaspossibleto locateanoff-centrefeed,wheretherewasaperfect50-ohmor75-ohminputimpedance match.Thoughthesizereductionwassubstantial,yettheimpedancebandwidthwasquiet poor as compared to similar order Hilbert antenna. The magnitude of the current distribution wasreportedtobealmostsymmetric,whilethephasevariedveryslowlyalongthewire length.Theradiationpatternoftheantennaatitsfundamentalresonantfrequencyinthe planesof=0and=90almostresembledthepatternsofalineardipole.Otherthan frequencyreduction,themainadvantageofthisantennacomparedtoHilbertantennawas lowercrosspolarizationlevel.Lastly,theradiationefficiencywasreportedtobedecreasing with increasing iteration order. Inthesameyear,X.Chenetal.reportedthefirstworkonprintedPeanolineantenna [12].Thisworkwasageneralizedoneonafewspace-fillingprintedantennas,thePeano antenna being one of them. The input impedance and current distribution of all the antennas A Brief Review of Peano Line Antenna 27 werecalculatedusingMethodofMoment(MOM)withMixedPotentialIntegralEquation (MPIE) formulation. The resonant frequencies were obtained by searching for the roots of the imaginarypartofinputimpedance.Thefeedstructurewasmodeledasadelta-gapvoltage source.Amongtheantennasmodeled,theschematicstructureofthepatchofPeanoline antenna, which was taken for analysis, is shown in Fig. 5.1a. The magnitude and phase of the current distribution along the same antenna is depicted in Fig. 5.1b. Fig. 5.1 (a) Printed 2nd order Peano antenna (b) Current distribution along the antenna [12] IEEE 2004 J. Mc Vay and A. Hoorfar in their paper [13] in 2006 investigated the characteristics of utilizingplanermetallicpathintheformofPeanocurveandHilbertcurvetoprovidetop loading properties to electrically short monopole antenna elements. This antenna focused on planerspace-fillingcurveconfigurationwithamuchlowerprofile,andutilizedprobefeed andshortingpostssothatitcouldbematchedtoa50-ohmsourceoverawidebandwidth. Fig.5.2showstheschematicdiagramoftheantenna,VSWRcharacteristicsandradiation pattern. Fig. 5.2 (a) Geometry of the antenna (b) VSWR characteristics (c) Gain patterns [13] IEEE 2006 (a) (b) (a) (b) (c) A Brief Review of Peano Line Antenna 28 The role of shorting posts was to reconfigure the structure into radiating like a matched top-loaded monopole with vertical polarization. In2007,E.El-Khoulyetal.[14] proposedahighdirectivityantennausing Peanospace-fillingcurve.Thiswasthefirst instance of a broadband, high gain Peano line antenna,butatthecostofgreatersize dimensions.Theantennawasproposedin microstripconfiguration,withthreedifferent designs. In the three designs, gains of 15.7dB, 17.2dBand17.5dBwereobtained.The antenna used six 180-phase shifters to orient the current distribution throughout the antenna, oversamedirection.Asallthelinesegmentshadcurrentdistributionorientedoversame direction, the directivity of the antenna increased substantially. The proposed design is shown in Fig. 5.3. Inthesameyear,J.McVayandA.HoorfaragainpublishedapaperonPeanoline antennaandHilbertcurveantenna[15],thistimetheworkbeingbasedonmicrostrip configurationwithdielectricsubstrates,unliketheirpreviousworkin2006.ThePeano antenna geometry and the fabricated photograph of the antenna are shown in Fig. 4.2 and Fig. 4.3respectivelyinchapter4.Againofabout4.6dBiwasobtainedusingthisdesign.The VSWR characteristics and the radiation pattern for the Peano line antenna are shown in Fig. 5.4. Fig. 5.3 Proposed antenna design [14] IEEE 2007 (a)(b) Fig. 5.4 (a) VSWR characteristics (b) Radiation pattern [15] IEEE 2007 A Brief Review of Peano Line Antenna 29 However,thefirstRFID design specific work in the field of microstrip Peano line antenna wasreportedintheyear2007, byateamofFukusakoetal. fromKumamotoUniversity, Japan[7].Theworkreporteda designofmeanderlineaswell asPeanolineantennafora centrefrequencyof1GHz,for RFIDapplications.Themost interestingaspectinthisdesignwastheapplicationofasecondorderPeanocurve,butina modified form. Normal second order Peano curve was not used; instead, an extended version to the second order curve was implemented. This enhanced the miniaturization of the antenna largely,whichoccupiedafootprintareaofassmallas/50X/100.Theantennastructure and its measured VSWR characteristics are shown in Fig. 5.5. The details of this antenna are consideredinChapter6,whereitisusedasthedesignprototypeforaparticulardesign problem. AsimilardesignwasproposedbyateamofT.Teradaetal.[16]fromKumamoto University,Japanintheyear2008.Theteamfabricatedandmeasuredtheimpedanceand radiationcharacteristicsofasmallandlowprofileprintedantennausingPeanoline.An antenna gain of -7.9dBi was reported, and the polarization was investigated to be elliptical. 5.4Summary In this chapter, a brief historical background of Peano line antennas has been presented. AlthoughHilbertcurveantennahasbeenexploredbymanyresearchers,veryfewpapers havebeenreportedintheliterature,whicharedevotedtoPeanolineantennas.Bothfrom design as well as analysis point of view, this branch is quiet open for the researchers willing to make a contribution in this field. References (a) (b) Fig. 5.5 (a) Antenna structure (b) VSWR characteristics [16] IEEE 2007 A Brief Review of Peano Line Antenna 30 [1]H.A.Wheeler,FundamentalLimitationsofSmallAntennas,ProceedingsIRE, pp.1479-1484, December 1947 [2]L. J. Chu, Physical limitations on omni-directional antennas, J. Appl. Phys., vol. 19, pp. 11631175, Dec. 1948 [3]H.A. Wheeler, Small Antennas, IEEE Transactions on Antennas and Propagation, Vol. AP-23, No. 4, pp.462-469, 1975 [4]R.C.Hansen,FundamentallimitationsinAntennas,ProceedingsIEEE,Vol.69, No.2, Feb.1981 [5]J.P.Gianvittorio,Y.R-Samii,FractalAntennas:ANovelAntennaMiniaturization Technique, and Applications, IEEE Antennas and Propagation Magazine, Vol. 44, No. 1, February 2002 [6]H.Y.WangandM.J.Lancaster,Aperture-CoupledThin-FilmSuperconducting Meander Antennas, IEEE Transactions on Antennas and Propagation, Vol.47, No.5, May 1999 [7]T.Fukusako,T.Terada,K.Iwata,Designandcomparativestudyonplanarsmall antennasusingmeanderandpeanolinestructure,InternationalSymposiumon Antennas and Propagation Society, pp. 2451-2454, 2007 [8]X.Chen,S.Safavi-Naeini,Y.Liu,ADown-SizedPrintedHilbertAntennaforUHF Band,IEEEAntennasandPropagationSocietyInternationalSymposium,Vol.2, pp.581-584, 2003 [9]J. Zhu and A. Hoorfar, Bandwidth, Cross-Polarization, and Feed-Point CharacteristicsofMatchedHilbertAntennas,IEEEAntennasandWireless Propagation Letters, Vol.2, 2003 [10]J.M.Gozalez-Arbesu,S.Blanch,andJ.Romeu,Arespace-fillingcurvesefficient small antennas?, IEEE Antennas Wireless Propagat. Lett., vol. 2, pp. 147150, 2003 [11]J. Zhu and A. Hoorfar, Peano Antennas, IEEE Antennas and Wireless Propagation Letters, Vol.3, 2004 [12]X. Chen, Y. Liu, S. Safavi-Naeini,Printed Plane-FillingFractal Antennas for UHF Band, IEEE International Symposium on Antennas and Propagation Society, vol. 4, pp. 3425-3428, 2004 [13]J. McVayand A. Hoorfar, A Miniaturized Planar Space-filling Curve Antenna with WidebandMonopole-likeRadiationCharacteristics,IEEEAntennasand Propagation Society International Symposium, pp.3723-3726, 2006 [14]E.El-Khouly,H.Ghali,S.A.Khamis,HighDirectivityAntennaUsingaModified PeanoSpace-FillingCurve,IEEEAntennasandWirelessPropagationLetters, Vol.6, 2007 [15]J.McVayandA.Hoorfar,Miniaturizationoftop-loadedmonopoleantennasusing Peano-curves, Radio and Wireless Symposium, IEEE, pp. 253-256, 2007 [16]T. Terada, K. Ide, K. Iwata, T. Fukusako, Radiation characteristics of small and low profileprintantennausingpeanoline,AsiaPacificMicrowaveConference,pp.1-4, 2008 Chapter 6 RFID Tag Antenna Design Using Peano Curves RFID Tag Antenna Design Using Peano Curves 31 Chapter 6RFID Tag Antenna Design Using Peano Curves 6.1Outline of the chapter Inthepreviouschapters,therelevanttheoryandtheconceptsregardingPeanoline antennasarediscussedindetail.Inthischapter,thefocusisshiftedtowardsaparticular designproblemusingmicrostripPeanolineantenna.Asdiscussedearlier,Peanoline antennasinmicrostripconfigurationfindimmenseapplicationsinRFIDchips.Designof such achip antenna is taken into consideration and the necessarydesignsteps are discussed indetail.Moreover,thedifficultiesfacedindifferentdesignapproachesarestatedanda possiblemodificationishighlighted.Thischaptermainlyemphasizesonthepractical workableantennadesignandthedifficultiesthatneedtobeaddressedforfuture implementation. 6.2RFID frequency bands InChapter2,theRFIDbandsarediscussedbriefly.TheRFIDbandfrom26.957 27.283MHzismainlyusedforspecialapplicationsuchasbiomedicalapplications.For biomedical purposes, the distance required for signal transmission is very less. Therefore, the gainofthoseantennasneednotbeveryhigh.Moreover,humanbodycannotbeirradiated with very high power signals. Hence, a relatively lower antenna gain suffices our cause. The next higher RFID band is the less frequently used 433 MHz band. For this reason, a design problem relating to the design of microstrip Peano line antenna for 26 MHz application is considered. 6.3Design Goal Our design goal is to design a microstrip Peano line antenna, corresponding to a 26 MHz frequencyofoperation,tobeusedforbio-medicalapplicationsmeetingallspecifications. The design needs to be incorporated on an RFID chip, typically not exceeding 20 mm X 20 mm area dimensions. In addition, design for 433 MHz RFID band is also considered. RFID Tag Antenna Design Using Peano Curves 32 6.4Design Procedure The basic idea behind the design of such an antenna at very low frequency,yet keeping its dimensions small, is to fill the space over thesubstrate with a patch in the most efficient manner. This can be achieved if the patch or the microstrip line traces the shape of a space-filling curve, in our case, the Peano curve. As we are constrained in size, the best alternative is to incorporate a 3rd order Peano curve and to try out the design. But to realize the 3rd order Peano curve in reality is a tough task, especially as the fabrication difficulty creeps in. Hence, itiswisertosticktothemoreeasilyrealizable2ndorderPeanocurve.But,asthesurface currenttraversesapathoflessdistanceoveramicrostriplinefollowinga2ndorderPeano curvethanthatfollowinga3rdorderPeanocurve,somealternativedesignmethodmustbe thought of. The alternative method is to follow the repetitive pattern of a 2nd order Peano curve and to go on extending it keeping the symmetry of the curve intact, as long as the dimensions of the antenna are not exceeded. Thus, the work of Fukusako et al [1] can be taken as the basic guideline or prototype in this regard. Thedesignin[1]hasaPeanolineantennadesignedforacentralfrequencyof1GHz. Extending the length of the microstrip line by following a 2nd order Peano curvess repetitive pattern,weeffectivelyincreasethepathoverwhichthesurfacecurrenttraverses.Hence,it resultsinanadditionofinductiveeffectandalsoaddedcapacitiveeffectduetomutual couplingbetweenadjacentlinesegments.Inthisway,wereducetheresonantfrequencyof the antenna to a great extent. 6.5Design prototype The antenna design as shown by Fukusako et al. in [1] is shown in Fig. 6.1. The substrate used is a polymide substrate with a relative permittivity (r) of 3.5. The height of the substrate h is 50 m as shown in Fig. 6.2. The width of the microstrip line w is 0.1 mm. The RFID chipareais20mmX20mm,whiletheantennafootprintareais3.2mmX6.1mm.The simulation is performed using Method of Moment basedIE3D fromZeland SoftwareInc. [2]. RFID Tag Antenna Design Using Peano Curves 33

FromFig.6.1itisclearthatthepatchorthe microstriplinedoesnottraceanormal2ndorder Peano curve. Rather, a repetitive pattern is followed, whichisanextensiontothe2ndorderPeanocurve, truncatedaftercertaindistance.Thissectionforms theradiator.TheabovedesignofFig.6.1canbe usedasthebasicguidelineorprototypetoour design,tofillthespaceabovethesubstrateinthe most efficient manner The total path length ( l ) that the strip of the antenna traverses is 90.75 mm. Theresonanceoftheantennaasinferredfromthesimulatedresultsin[1]occursat1.02 GHz. This corresponds to a free space wavelength (0) of 294.1 mm. The effective permittivity (eff) can be found out from the expression [3] whr reff12 112121+++= (6.1)Thus, for r = 3.5, we geteff= 2.722 (a) (b) Fig. 6.1 (a) Antenna Structure [1]. (b) Detailed View Fig. 6.2 Height of the antenna substrate from the CPW feed end RFID Tag Antenna Design Using Peano Curves 34 Sotheeffectivewavelengthofthesignalthatispropagatingthroughtheantennacanbe obtained from the expression effeff0=(6.2) Thus, the effective wavelength in this case is 178.2 mm. If we desire to find out, the factor by which the effective wavelength is related to the antenna path length ( l ), we can do so by finding the factor x from the equationx eff = l (6.3) For this structure, x = 0.509, thus the antenna resonates almost for a length l = eff /2. 6.6Design approaches Thissectionhighlightsseveraldesignapproachesandrelevantexplanations,thedesign being based on the guideline stated in the last section. Study of the design guideline/prototype: Beforeproceeding furtherwiththedesign, itisessentialtogo throughtheimpedance characteristicsofthe designguidelineon whichthedesignis based.Fig.6.3shows theS11andthe impedanceversus frequency curves for the antennadescribedinFig.6.1overafrequencyrangeconfinedaroundthefirstresonant frequency.Ontheotherhand,Fig.6.4showsthesamecharacteristicsover0-20GHz frequency range for the same antenna. The simulation is performed using IE3D from Zeland Software Inc. [2]. (a) (b) Fig. 6.3 (a) S11 in dB vs. Frequency (b) Input impedance vs. frequency RFID Tag Antenna Design Using Peano Curves 35

Fig. 6.4 (a) S11 vs. frequency (b) Input impedance vs. frequency over 0-20 GHz frequency range DiscussionTheabovephenomenacanbeattributedtothedistributednatureoftheantenna.The microstripline,whichformstheantenna,isbasicallyatransmissionline,andaswithall transmission lines, the distributed effects cause the impedance characteristics to repeat itself with frequency. : From the above curves, it is obvious that, as the frequency range is increased the patternrepeatsitself.TheS11matchingisnotasgoodasdesired,buttheimpedance characteristicrevealsthattheinputresistanceandreactancerepeatsitself,thusexciting higher order modes at higher frequencies. 6.6.1Approach 1: Increase of path length of the antenna As discussed earlier, the method to reduce the resonant frequency of the antenna is to go on increasing the path length l that the microstrip line of the antenna traces.In the subsequent approaches, the basic prototype of [1] is adhered to, and the symmetric periodicrepetitionofthe2ndorderPeanocurveisfollowed.Maintainingsymmetryof repetition, we consider a certain yardstick such that, in each step of antenna length extension, 19.85mmpathlengthistraced.Also,theouterdimensionalongthepathofthecurve, increases by 1.2 mm. This process is carried out till the dimensional constraint along the path (a) (b) RFID Tag Antenna Design Using Peano Curves 36 length is exceeded.Thesubstrate is kept the same, i.e. r = 3.5. Other dimensions such as w and h are also kept similar to that of the antenna described in the design guideline Feed: The antenna is fed by a 50-ohm coplanar waveguide, with dimensions as given in Fig. 6.1.ThesimulationisdoneusingIE3Dsoftware,takingadvancedextensionasthede-embedding scheme for port definition. The signal line of the CPW is provided with a positive voltage level, and a negative polarity to the two ground planes on the side. The total antenna structure along-with the feed is conductor-backed. a) Extension 1: Incrementing a path length of 19.85 mm to the previous design, the antenna issimulated.Therefore,thetotalpathlengthlnowbecomes110.6mm.Hence,thenew antennafootprintdimensionis3.2mmX7.3mm,sinceanincrementof1.2mmoccurs along one dimension. The structure is shown in Fig. 6.5, while the S11 characteristic is shown in Fig. 6.6. Extensions of path length The first resonance of the antenna occurs at 837.807 MHz, with an S11 match of -15.2036 dB. The corresponding free space wavelength (0) for this frequency is 358.07 mm.Thus,using(6.2)wecanevaluateeffectivewavelength(eff)whichcomesouttobe217.03 mm. Fig. 6.5 Antenna structureFig. 6.6S11 characteristics for antenna in Fig. 6.5 For extension 1 RFID Tag Antenna Design Using Peano Curves 37 Finally, using (6.3) we can find out the factor x as 0.5096. Asthefirstresonanceoftheantennaoccursat837.807MHz,thereforeinordertoachieve our design goal, we require many such path length extensions.The above process is repeated in all the next extensions, keeping the basic parameters of the antenna unaltered. b) Extension 2: Antennafootprintarea:3.2mmX8.5 mm Path length l = 110.6 mm + 19.85 mm = 130.45 mm. Firstresonantfrequency,fr=718.985 MHz, with S11 = -9.18319 dB Free space wavelength, 0 = 417.25 mm. Effective wavelength, eff = 252.9 mm. Factor x = 0.5158. Asevidentfromthedataabove,thefirst resonantfrequencydoesnotprovidea substantial S11 match, i.e. it does not adhere to the 2:1 VSWR acceptable limits. Thesecondresonanceoccursat1.45303 GHz,withS11=-15.1831dB,thus providing good matching characteristics. In thiscase,wecanthereforeusethehigher ordermodeforoperation,butnotthe fundamental mode. Fig.6.7depictstheS11characteristicsand the impedance characteristics of the antenna.

(a) (b) Fig. 6.7(a) S11 vs. Frequency (b) Input impedance vs. Frequency for antenna in extension 2 RFID Tag Antenna Design Using Peano Curves 38 c) Extension 3: Antenna footprint area: 3.2 mm X 9.7 mmPath length l = 130.45 mm + 19.85 mm = 150.3 mm. First resonant frequency, fr = 632.242 MHz, with S11 = -5.85262 dB. Free space wavelength, 0 = 474.55 mm. Effective wavelength, eff = 287.6 mm. Factor x = 0.5226. Again, we have a poor match at the first resonant frequency. The second resonance occurs at 1.27GHz,withS11of-33.5dB.ThishigherordermodepossessesgoodVSWR characteristics, and hence can be excited for operation. Fig. 6.8 shows the S11 characteristics and the impedance characteristics of the antenna.

Discussion:Fig.6.8(b)highlightsaveryimportantaspectofthedesign.Itshowsthatthe first resonance actually occurs around 1.27 GHz. and not at 632.242 MHz as mentioned in the above data. (a) (b)

Fig. 6.8(a) S11 vs. Frequency (b) Input impedance vs. Frequency for antenna in extension 3

RFID Tag Antenna Design Using Peano Curves 39 This anomaly can be clarified by the following logic. The periodicity and the symmetry oftheimpedancecharacteristicpatternsuggeststhat,eventhoughthefirstresonant frequency,orthefirstzeroreactancecrossingfrequencyis1.27GHz,yettheoriginalfirst resonanceoftheantennashouldhaveoccurredatamuchlowerfrequency,i.e.at632.242 MHz.Itisonlyduetosomestraycapacitance,whichaddssomenegativereactanceonthe curvenearitsoriginalfirstresonance,andcausesthecurvetoshiftawayfromthezero reactance crossing line. The cause of this stray capacitive effect shall be investigated later. If the stray capacitancesplaya predominant role, the impedance pattern cannot provide anyinformationaboutthefirstresonance,sincethereactancecurvedoesnotcrossthezero reactancelinenearit.Therefore,fromnowonwards,asweincreasethepathlengthofthe antennainthesubsequentextensions,weshallonlyfocusonthefirstdipoftheS11 characteristics to find out the first resonant frequency. d) Extension 4: Antenna footprint area: 3.2 mm X 10.9 mmPathlengthl=150.3mm+19.85mm= 170.15 mm. First resonant frequency, fr = 563.6 MHz S11 at first resonance = -4.1565 dB Free space wavelength, 0 = 532.29 mm. Effective wavelength, eff = 322.631 mm. Factor x = 0.527 e) Extension 5: Antenna footprint area: 3.2 mm X 12.1 mmPathlengthl=170.15mm+19.85mm=190 mm. First resonant frequency, fr = 508.32 MHz Fig. 6.9 S11 vs. frequency for antenna of ext.4 Fig. 6.10 S11 vs. frequency for antenna of ext.5

RFID Tag Antenna Design Using Peano Curves 40 S11 at first resonance = -3.07537 dB Free space wavelength, 0 = 590.179 mm. Effective wavelength, eff = 357.719 mm. Factor x = 0.531. f) Extension 6: Antenna footprint area: 3.2 mm X 13.3 mmPathlengthl=190mm+19.85mm=209.85 mm. First resonant frequency, fr = 462.848 MHz S11 at first resonance = -2.34511 dB Free space wavelength, 0 = 648.1 mm. Effective wavelength, eff = 392.8 mm. Factor x = 0.534. g) Extension 7: Antenna footprint area: 3.2 mm X 14.5 mmPathlengthl=209.85mm+19.85mm= 229.7 mm. First resonant frequency, fr = 425.041 MHz S11 at first resonance = -1.8317 dB Free space wavelength, 0 = 705.8 mm. Effective wavelength, eff = 427.79 mm. Factor x = 0.5369. Fig. 6.11 S11 vs. frequency for antenna of ext.6 Fig. 6.12 S11 vs. frequency for antenna of ext.7 RFID Tag Antenna Design Using Peano Curves 41 h) Extension 8: Antenna footprint area: 3.2 mm X 15.7 mmPath length l = 229.7 mm + 19.85 mm = 249.55 mm. First resonant frequency, fr = 392.962 MHz S11 at first resonance = -1.45881 dB Free space wavelength, 0 = 763.43 mm. Effective wavelength, eff = 462.72 mm. Factor x = 0.539. i) Extension 9: Antenna footprint area: 3.2 mm X 16.9 mmPathlengthl=249.55mm+19.85mm=269.4 mm. First resonant frequency, fr = 365.303MHz S11 at first resonance = -1.18201 dB Free space wavelength, 0 = 821.2 mm. Effective wavelength, eff = 497.7 mm. Factor x = 0.541. j) Extension 10: Antenna footprint area: 3.2 mm X 18.1 mmPath length l = 269.4 mm + 19.85 mm = 289.25 mm. First resonant frequency, fr = 341.408 MHz S11 at first resonance = -0.971126 dB Free space wavelength, 0 = 878.7 mm. Effective wavelength, eff = 532.5 mm. Fig. 6.14 S11 vs. frequency for antenna of ext.9 Fig. 6.15 S11 vs. frequency for antenna of ext. 10 Fig. 6.13 S11 vs. frequency for antenna of ext.8 RFID Tag Antenna Design Using Peano Curves 42 Factor x = 0.543. k) Extension 11: Antenna footprint area: 3.2 mm X 19.3 mmPath length l = 289.25mm + 19.85 mm = 309.1 mm. First resonant frequency, fr = 320.131 MHz S11 at first resonance = -0.808384 dB Free space wavelength, 0 = 937.1 mm. Effective wavelength, eff = 567.99 mm. Factor x = 0.544. 1. The first resonant frequency is still deviant from our design goal. Further reduction of the resonant frequency is required. However, we cannot go on increasing the antenna path length for further extensions, as the size limit of the RFID chip is fixed and prescribed.Inferences from the extension of antenna path lengths 2.TheS11 inputimpedancematchingcharacteristicfortheantennaatthefirstresonant frequency is very poor. Thus, the issue of impedance matching must be taken care of. 6.6.2Approach 2: Higher permittivity substrate Theearlierapproachrevealsthatthechipsizeistoosmalltofacilitateafrequency reductiontoafrequencystatedinourdesigngoal.Hence,anotheralternativeneedstobe employed.Inthisapproach,wesimulatetheantenna,usingaluminaasthedielectric substrate, instead of polymide. Alumina has a dielectric constant of 9.8. We know from (6.2), effeff0=

Fig. 6.16 S11 vs. frequency for antenna of ext. 11 RFID Tag Antenna Design Using Peano Curves 43 Therefore,asweincreaser, thereisanincreaseineff. Sotokeeptheeffectivewavelength effasconstant,anincreaseineff mustbeaccompaniedbyanincreaseinfreespace wavelength 0. Thus, using a higher dielectric medium aids in frequency reduction. DisadvantageInthisapproach,thesimulationresultsareperformedbyconsideringaluminaasthe substrate,andthenfollowingthelengthextensionprocedureofapproach1.Forthesakeof clarity,theextensionsarerepresentedinatabularform,andtheS11curvesarenotshown. Table 1 illustrates the relevant results obtained in this regard. For, r = 9.8, we get from (6.1), eff = 7.063: The disadvantage in this method is, as we increase the dielectric constant, the gainoftheantennaisboundtoreduce.Itisbecause;usinghigherpermittivitysubstrate confinesmostoftheelectricfieldlinesbeneaththeantennastrip,leavingonlyafewfield lines, as loosely bound for effective radiation. TABLE 6.1 LENGTH EXTENSIONS FOLLOWING APPROACH 2 Extension number Antenna footprint (mm2) Path length l (mm) First resonant freq. (MHz.) S11 at first resonance (dB) Free space wavelength (0) in mm Effective wavelength (eff) in mmFactor x 0 (design guideline) 3.2 X 6.190.75614.894-40.9954487.8183.50.494 13.2 X 7.3110.6513.800-11.8655583.8219.60.503 23.2 X 8.5130.45440.098-7.44185681.66256.490.508 33.2 X 9.7150.3385.106-5.13764779.0293.10.512 43.2X10.9170.15342.553-3.73499875.7329.50.516 53.2X12.1 190.0308.6-2.81363972.0365.70.519 63.2X13.3209.85280.8-2.17791068.0401.00.523 73.2X14.5229.7257.6-1.723671164.5438.10.524 83.2X15.7249.55238.0-1.3891260.5474.20.526 93.2X16.9269.4219.722-1.131365.36513.70.524 RFID Tag Antenna Design Using Peano Curves 44 Extension number Antenna footprint (mm2) Path length l (mm) First resonant freq. (MHz.) S11 at first resonance (dB) Free space wavelength (0) in mm Effective wavelength (eff) in mm Factorx 103.2X18.1289.25207.938-0.941442.7542.80.532 113.2X19.3309.1193.863-0.791547.4582.20.531 Inferences from Approaches 1 & 21. From the above approaches of length extension, it follows that it is quite difficult to achieve a resonance at such a low frequency, keeping the dimensions within the prescribed limits.: 2. Moreover, in most of the cases, the S11 matching characteristics at the first resonant frequency is poor. 6.6.3Approach 3: Input impedance match using quarter wave transformer Having discussed the concept of length extension, we now turn our attention towards the next approach, which mainly deals with theconcept of impedance matching. As revealed in theearliersections,thedesignneedstoachievetherequired2:1VSWRlimit.Forthis purpose, we can start with a quarter-wave transformer impedance matching scheme. The basic idea in this approach is highlighted below: 1.Firstandforemost,findouttheimpedanceattheendoftheantenna.Thatimpedanceis treated as the load impedance. 2. Designa quarter-wave transformer of lengtheff/4, whereeff is the effective wavelength, for the design frequency of interest. 3.Thequarter-wavesectionwillhaveacharacteristicimpedancewhichisthegeometric mean of the magnitude of the load impedance (in our case, it is the edge or end impedance of the antenna) and the characteristic impedance of the section that is connected at its input. As thequarter-wavetransformerisconnectedtoacoaxialcableatitsinputforinitialfeed,the characteristicimpedanceofthatsectionistakenas50ohms.Usingthesedata,the characteristic impedance of the transformer is calculated. RFID Tag Antenna Design Using Peano Curves 45 4.Thequarter-wavesectioncannowbeimplementedusing,eitheramicrostriplineora coplanar waveguide (CPW). Difficulties and bottlenecksForourdesignfrequencyofinterest,i.e.26MHzwecancalculatethelengthofthe transformer for both the substrates used above. : The main difficultyin this design is the length of the quarter-wave transformer, which exceeds our dimensional constraints. For 26 MHz, 0 = 11.538 m. a) For polymide substrate: r = 3.5Therefore, using (6.1), we get eff = 2.722. Effective wavelength, eff using (6.2) amounts to 6.993 m Thus, the length of the quarter-wave transformer, eff/4 = 1.748 m = 1748 mm. b) Similarly, for Alumina substrate: r = 9.8 eff = 7.063. Effective wavelength, eff = 4.341 m Hence, the length of the quarter-wave transformer, eff/4 = 1.085 m = 1085 mm. DesigngoalrevisitedHowever,thedifficultypersists.Afrequencyof433MHzcorrespondstoafreespace wavelength of 692.8 mm. The effective wavelength considering polymidesubstrate is 419.9 mm,whilethatconsideringaluminasubstrateis260.68mm.Therefore,theimplementation of the quarter-wave transformer on polymide substrate requires a length of 104.97 mm, while thelengthofthesameforaluminasubstrateis65.17mm,bothofwhichexceedour dimensionalconstraint.Thismodificationthereforecannotovercomethedimensional difficulties as faced earlier.:Duetoseveraldifficultiesfaced,asdocumentedabove,wealterour design goal to the next higher RFID frequency of 433 MHz. Extension number 2 from Table 6.1 specifies that, there is a first resonance at 440.098 MHz that is quite close to our revisited design goal. For this reason, we try our design around this frequency. RFID Tag Antenna Design Using Peano Curves 46 InferencefromApproach3:Thelengthofthequarter-wavetransformeritself(without antenna) exceeds our prescribed dimensional constraints for an RFID chip by a good margin. 6.6.4Approach 4: Use of different dielectric materials for feed and antenna Theproblemstatedabovecanbeaddressedbytakingtwodifferentdielectricmedium side by side, and gluing them together, so that the quarter-wave transformer feed is placed on thematerialwithahigherdielectricconstant,andtheantennaonthelowerpermittivity substrate. Theantenna being placed on the low permittivity substrate ensures that its gain is notreduced,whileusinghigherpermittivitysubstrateforthetransformerascertainsa miniaturized length for it. An increase in the dielectric constant brings about a decrease in the effectivewavelengthatthedesignfrequencyofinterest,therebyreducingthelengthofthe quarter-wave transformer required.DrawbackofthedesignInthisapproach,analternativedesigntoaddresstheaboveproblemisproposed.The schematicsideviewofthedesignis presented in Fig. 6.17. :Theprimarydrawbackofthisdesignisthediscontinuityarising from the dielectric-dielectric interface. Due to this discontinuity, however small it may be, a gap arises in the structure at the interface, thereby adding an extra amount of stray capacitive reactance,thusdeviatingtheantennafurtherawayfromresonance.Theremedyforthis problemistodesignthestructureontwodifferentdielectricmediaasstatedabove,but avoidingthegapduetodiscontinuityasfaraspracticable.Thismethodisillustratedinthe next approach. 6.6.5Approach 5: Use of stacked dielectric layersThestructureismadeupoftwo-stackeddielectriclayerwithr2 >r1. Onthehigherpermittivitysubstrate2, thequarter-wavefeedisplaced,while theantennaisplacedonthelower permittivitysubstrate1.Theantenna Fig. 6.17 Schematic side view of the design

RFID Tag Antenna Design Using Peano Curves 47 inputend,i.e.theedgeoftheantenna,formstheloadtothetransformer.Theloadis connected to the matching section by a shorting post or via. The via or the shorting post is very small in length, as compared to the effective wavelength, since we are operating at a very low design frequency. Therefore, it can safely be considered as a lumped connector, due to absence of any distributed effect. DifficultyThemodifiedschemeasdepictedisalmostsimilartotheschemediscussedintheprevious attempt.WenowshiftourdesigngoaltothenexthigherRFIDfrequencyof433MHz. Consideringthisfrequencyasthedesign frequency,wehaveacloserlookatthis design approach. :Thisdesigncanbetriedout,butitcallsforabitofmodification.Thequarter wavetransformerisactuallyimmersedinbetweentwodifferentdielectricmedia,noneof whichisair.Asthequarter-wavetransformerisimplementedusingamicrostripline, standard closeform relations are available assuming one of the dielectricmedium as air. So to avoid any loss of generality, we slightly modify the structure in the next approach. 6.6.6Approach 6: Modification of the structure described in approach 5 For modification, we just invert the layer denoted by substrate 2 along with the quarter-wavetransformeronit.Therefore,thegroundplanecomesinbetweenthetwomedia,and thus separates them. Both the transformer and the antenna, have a dielectric medium on one sidewithacommongroundplane,andairontheotherside.Also,theshortingpostisan elongatedone,drillingaholeonthegroundplanefortransformertoantennaconnectivity. Fig. 6.18 depicts the modified scheme. As we observed from extension number 2ofTable6.1,thereisaresonanceat 440.098 MHz, which happens to be the first resonanceoftheantenna.Henceforth,our design is mainly centered at this frequency. Wetakethatstructureforfurther analysis,inordertoinvestigatethe suitabilityofquarterwavematching Fig. 6.18 Modified schematic side view of the design RFID Tag Antenna Design Using Peano Curves 48 techniqueonit.ThefirststepistoremovetheCPWfeedfromtheantenna,andkeepthe antenna isolated. Then, the edge impedance of the antenna is measured using Extension for wavesde-embeddingschemeinIE3Dsimulator.Thisde-embeddingschemeservesasa wave-portfortheantenna.Boththecasesaresimulated,andtheS11andtheimpedance curvesareobservedforcomparativestudy,whichrevealssomeimportantfacts.Fig.6.19 showstheSparametersandtheinputimpedancecharacteristicsoftheantennadescribedin extension2ofTable6.1.Fig.6.20showsthesameantennastructureanditsimpedance characteristics, with the CPW feed removed, in order to measure its edge or end impedance. As seen from the figure above, the first dip of the S11 curve occurs near 440.098 MHz, when theCPWfeedisconnected(antennaofext.2,table1).Theimpedancecurvesontheother hand,cannotconclusivelyascertainitasthefirstresonantfrequency,sincethereactance curvedoesnotcrossthezero-reactanceline.Therefore,consideringthefirstdipoftheS11 curve, we assume 440.098 GHz as the first resonant frequency. Fig. 6.19 (a) S11 vs. frequency(b) Input impedance vs. frequency for antenna of ext.2, table1 (a) (b) RFID Tag Antenna Design Using Peano Curves 49 Fig. 6.20 (a) Antenna described in ext.2 of Table 1, with CPW feed removed (b) Input impedance characteristics for the same antenna Thesameantenna,withCPWfeedremoved,lookslikethatinFig.6.20(a).Here,wehave appliedawave-portforcalculatingitsinputedgeimpedance.Thecharacteristiccurveis shown in Fig. 6.20 (b).Discussion : If we have a closer look at the curves in Fig. 6.19 (b) and Fig. 6.20 (b), we arrive ataveryimportantconclusion.WhentheCPWisusedforfeedingtheantenna,astray capacitance as discussed earlier, shifts the input reactance curve away from resonance near its first resonant frequency. However, when the CPW feed is removed, the reactance curve near thefirstresonantfrequencyrises,andresonanceoccurs,sincethestraycapacitiveeffectis removed.Wecanthusinferfromtheobservationthat,theCPWstructureaddsthestray capacitance. AnalysisandresultsFrom Fig. 6.20 (b), we find the impedance at the input edge of the antenna at 440.098 MHz. The input resistance Rin =96.3777 ohms. :Inthissection,weverifythesuitabilityofthisdesignfor implementing quarter wave matching technique on it. (a)

(b) RFID Tag Antenna Design Using Peano Curves 50 The input reactance Xin = 97.5295 ohms. Therefore, the magnitude of input impedance is|Zin| = { (Rin)2 + (Xin)2 }1/2=137.11 ohms at 440.098 MHz. This |Zin| acts as the load to the quarter-wave matching section. Let us denote it by ZL. The input to the matching section is a standard 50 ohms coaxial cable, with |Z0| = 50 ohms. Let the characteristic impedance of the matching section be Z1. Therefore, Z1 can be calculated from the relation [4] |Z1| = { |Z0| |Zin| }1/2(6.4)Putting the values of |Zin| and |Z0| in (6.4), we get |Z1| = 82.79 ohms.Therefore, the quarter-wave matching section has a characteristic impedance of 82.79 ohms. We can implement it using a microstrip line.Standardclosedformsynthesisformulaeformicrostripdesignareavailableintheliterature [5]. They are stated below: 1' exp 418' exp||.|

\| =HHhwFor narrow strips ( i.e. when Z0 > {44 2 r} ohms ) (6.5) where,||.|

\|+||.|

\|+++= 4ln12ln11219 . 119) 1 ( 2'0r rrrZH ( ) ( ) { } ( ))` + + =rerre ed d dhw 517 . 0293 . 0 1 ln11 2 ln 12For wide strips ( i.e. when Z0 < {44 2 r} ohms ) (6.6) where, rZd0295 . 59=Case 1: Taking the substrate as polymide ( r = 3.5 ) and Z0 = 82.79 ohms Using (6.5), the value of microstrip width w = 0.044 mm. Case 2: Taking the substrate as alumina ( r = 9.8 ) and Z0 = 82.79 ohmsRFID Tag Antenna Design Using Peano Curves 51 Using the same formula, the width of the microstrip w = 0.013 mm. Therefore,theimplementationofaquarter-wavetransformerforthisdesignusinga microstriplinerequiresthemicrostripwidthtobeofthedimensionsasstatedabove.The antennaitselfisplacedonanaluminasubstrate,andasdiscussedinprevioussections,it cannotprovideaminiaturizedlengthforthequarter-wavesection.So,thequarter-wave transformer must be placed on a still higher permittivity substrate. However, as evident from the formulae(6.5) and (6.6) above,and from the two case studies, the more is the dielectric constantofthemedium,thesmalleristhemicrostripwidth.Foralumina,itisassmallas 0.013mm.Forotherhigherpermittivitysubstrates,itisevensmaller.Hence,fabrication difficulty comes in, and micro-fabrication techniques must be employed. Difficulties from the design: 1. As discussed above, if the dielectric constant of the substrate is kept very low, the width of themicrostriplinerequiredmaybewithinnormalfabricationlimits,andthequarter-wave sectioncanbeimplemented.Nevertheless,thelengthofthequarter-wavesectionatour design frequency of interest becomes very large. 2. Conversely, if the permittivity of the substrate used is high, it is advantageous as far as the lengthofthequarter-wavesectionisconcerned.However,thewidthofthemicrostripline becomes very small, and fabrication problems appear. 6.6.7Approach 7: Single stub matching We arrive at the last ofour design approaches, i.e. impedance match using single shunt stub.Inmicrostripconfiguration,itisdifficulttorealizeaseriesstub.Thebasicconcept behind single shunt stub matching is very briefly presented in the next section. Single-stubtuning:Thistechniqueusesasingleopen-circuitedorshort-circuitedlengthof transmission line (stub), connected in parallel with the feed line at a certain distance from the load. The circuit is shown in Fig. 6.21. RFID Tag Antenna Design Using Peano Curves 52 The task is to find out the distance of thestubdfromtheloadend,and thelengthoftheopenorshorted stub,l.Byselectingpropervalues ofdandl,aperfectmatch betweenthefeed-lineof characteristicimpedanceZ0andthe load impedance ZL is accomplished. Thestubmatchingtechnique canbeimplementedonthe samestructureshowninFig. 6.18.Thequarter-wave matching section in the figure isreplacedbyasingleshunt stubsection.Therestofthe structureremainsthesame. Thetransmissionfeedlineas wellasthestubis implementedusingmicrostrip lines.Asinearliercase,the input edge of the antenna acts as the load. The characteristic impedance of the microstrip transmission feed line is taken as 50ohms.Fig.6.22showsthesameschematicstructureofFig.6.18inbottomview,with quarter-wave matching transformer replaced bya stub matching section.The antenna which servesastheload,andconnectedtothematchingsectionbyashortingpostorvia,isnot shown in the figure, as it is placed below the bottom layer. Analysis [4]Let the load be denoted as ZL = RL + j XL. :The impedance Z, down a length d of the line from the load as shown in Fig. 6.21 is given by Fig. 6.21 Single shunt stub tuning circuit Fig. 6.22 Implementation of Shunt stub in structure of Fig. 6.18 (bottom view) Y = 1/Z RFID Tag Antenna Design Using Peano Curves 53 t jX R j Zt jZ jX RZ ZL LL L) () (000+ ++ += , where t = tan d. (6.7) The admittance at this point isY = G + j B = 1/Z, where 2022) () 1 (t Z X Rt RGL LL+ ++=(6.8a) ] ) ( [) )( (20200 02t Z X R Zt Z X t X Z RBL LL L L+ ++ =(6.8b) Now,d(whichimpliest)ischosensothatG=Y0=1/Z0.From(6.8a),thisresultsina quadratic equation for t. Solving for t gives002 20/ ] ) [(Z RZ X R Z R XtLL L L L+ = , for RL Z0(6.9) Thus, the two principal solutions for d are)`+=) tan (21tan2111ttd (6.10) The length of the stub can be found from the formulae below: For an open-circuit stub, ||.|

\| =01 0tan21YB l (6.11a) For a short-circuited stub, |.|

\|=BY ls 0 1tan21 (6.11b) If the length given by (6.11a) or (6.11b) is negative, /2 can be added to give a positive result. ResultsFor our design as we found earlier, the input end of the antenna has a resistance of 96.3777 ohms and a reactance of 97.5295 ohms. :fort 0 for t < 0 RFID Tag Antenna Design Using Peano Curves 54 For ease of calculation, we take Rin 96 ohms, and Xin 97 ohms. This impedance serves as the load impedance ZL for the matching section. Therefore, ZL = RL + j XL 96 + j 97, where RL 96 ohms and XL 97 ohms. We consider a 50-ohm microstrip line for transmission feed, hence, Z0 = 50 ohms. Putting these data in (6.9), we evaluate the value of t. We get, t = 5.34, -1.125 as two solutions for t. Now we have two cases, one when t = 5.34, and another when t = -1.125.Case 1: t = 5.34 From (6.10), we get d = 0.22 . Using (6.8b), B = 0.03098. Putting B in (6.11a), we getlo = -0.1587 This length being negative, we add a length of /2 to it.Therefore, lo = 0.3413 Putting B in (6.11b), we get ls = 0.091 Case 2: t = -1.125 Following the similar steps as above, we obtain, d = 0.365 . lo = 0.1587 ls = -0.091 => -0.091 + 0.5 = 0.409 Optimum solution: From the two cases discussed, the optimum solution for minimum dimension is for t = 5.34. The distance between the load and the stub, d = 0.22 The length of the stub is least when it is a short-circuited one. The length of the stub, ls = 0.091 RFID Tag Antenna Design Using Peano Curves 55 Dimensions: The wavelength , withrespect to whichall theabove dimensions are provided, is basically theeffectivewavelengtheffforthisdesign.Wenowevaluatethedimensionsintwocases, onewhenthesubstrateispolymide,andagainwhenthesubstrateisalumina.The transmission feed line in both the cases is 50-ohm microstrip line. Z0 = 50 ohms for microstrip feed line. a) Polymide substrate (r = 3.5) To implement this microstrip line, let the width required for the same is w. Usin