ANALYSIS AND DESIGN OF A CIRCULARLY POLARIZED MICROSTRIP ANTENNA

ANALYSIS AND DESIGN OF A CIRCULARLY POLARIZED MICROSTRIP ANTENNA A THESIS SUBMITTED TO THE GRADUATE SCHOOL OF NATURAL AND APPLIED SCIENCES OF MIDDLE EAST TECHNICAL UNIVERSITY BY MEHMET TAŞTAN IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE IN ELECTRICAL AND ELECTRONICS ENGINEERING DECEMBER 6

Approval of the Graduate School of Natural ad Applied Scieces Prof. Dr. Caa ÖZGEN Director I certify that this thesis satisfies all the requiremets as a thesis for the degree of Master of Sciece. Prof. Dr. İsmet ERKMEN Head of Departmet This is to certify that we have read this thesis ad that i our opiio it is fully adequate, i scope ad quality, as a thesis for the degree of Master of Sciece. Assoc. Prof. Dr. Secer KOÇ Supervisor Examiig Committee Members Prof. Dr. Altua HIZAL (METU, EE Assoc. Prof. Dr. Secer KOÇ (METU, EE Prof. Dr. Gülbi DURAL (METU, EE Assoc. Prof. Dr. Özlem ÇİVİ (METU, EE Dr. Özlem ŞEN (TÜBİTAK, Uzay Te.Est.

I hereby declare that all iformatio i this documet has bee obtaied ad preseted i accordace with academic rules ad ethical coduct. I also declare that, as required by these rules ad coduct, I have fully cited ad refereced all material ad results that are ot origial to this wor. Name, Last ame : Mehmet TAŞTAN Sigature : iii

ABSTRACT ANALYSIS AND DESIGN OF A CIRCULARLY POLARIZED MICROSTRIP ANTENNA TAŞTAN, Mehmet M.S., Departmet of Electrical ad Electroics Egieerig Supervisor: Assoc. Prof. Dr. Secer KOÇ December 6, 99 pages I this study we tried to desig a microstrip atea, to get a suitable radiatio patter for a LEO satellite. Our aim is to get a radiatio patter that has a maximum power which is ot i the broadside directio to the atea surface; istead broadside radiatio has a relatively lower power desity. Maximum power radiatio is desired to be at about 3 5 degrees agle beyod the ormal to the atea surface. We desire circularly polarized radiatio. We used two cocetric ateas; oe is a circular patch at the ceter ad the other is a aular rig which is used at the outer regio. By usig Asoft Esemble 8. software, we desig a atea which has a resoace frequecy at 8. GHz. Usig the result of the program we desig the real atea. The measuremet results are compared with the simulatio results. Key words: circular patch, aular rig, edge port model, method of momet, microstrip ateas, circularly polarized microstrip atea. iv

ÖZ DAİRESEL POLARİZASYONLU MİKROŞERİT ANTEN ANALİZ VE TASARIMI TAŞTAN, Mehmet Yüse Lisas, Eletri ve Eletroi Mühedisliği Bölümü Tez Yöeticisi: Doç. Dr. Secer KOÇ Aralı 6, 99 Sayfa Bu çalışmada alça yörüge uyduları içi ullaılabilece, uygu bir ışıma diyagramıa sahip miroşerit ate tasarımı yapılmıştır. Bu çalışmaı amacı; masimum radyasyou ate düzlemie di istiamette değil de, ate düzlemi ile 3 5 derece açı yapaca şeilde yayı yapa bir miroşerit ate tasarlamatır. Bu çalışmada dairesel polarizasyolu bir radyasyo elde edilmiştir. İç içe geçmiş; biri dis, diğeri de buu çevreleye hala şelide ii ate ullaılmıştır. Asoft Esemble 8. yazılım programı ullaılara 8. GHz. Freasıda, istee radyasyoa sahip bir ate simule edilmiştir. Bu programda elde edile verilere göre gerçe bir ate tasarlamıştır. Souçta deeysel verilerle programda elde edile veriler muayese edilmiştir. Aahtar Kelimeler: Dairesel dis, hala ate, Kear bağlatı otası modeli, Mometler Yötemi, Miroşerit ateler, Dairesel polarizasyolu miroşerit ateler. v

To My Wife vi

ACKNOWLEDGMENTS I wish to express my sicere gratitude to my advisor Prof. Dr. Secer KOÇ without whose support, this thesis would ot have bee possible. He carefully guided me throughout of my Master s degree. His ideas ad suggestios have bee ivaluable to this thesis. I would lie to tha him for beig my advisor at METU. I would lie to express my sicere thas to my commader Col.Mehmet ERKUT who always supported me i all my studies. I would lie to also express my sicere appreciatio to Fatih ÜSTÜNER, Mustafa SEÇMEN, Öder Halu TEKBAŞ, Megüç ÖNER, Emre ÇAKIR, Semih KAYA, Arda BALKIŞ, Taju Hasa GÜN, Fevzi ŞİMŞEK, Hasa Basri ERKUZU, Ayha Ali BALABAN ad Col.Rame ASLAN for their valuable friedship, help ad support. I am also grateful to Military Sigal School for the completio of this thesis. Last i the list but first i my heart, I am grateful to my wife, Özlem, because she always supported emotioally ad ecouraged me whe I eeded. vii

TABLE OF CONTENTS PLAGIARISM... iii TUABSTRACTUT... iv TUÖZUT... v TUACKNOWLEDGMENTSUT... vii TUTABLE OF CONTENTSUT... viii TULIST OF FIGURESUT... x TULIST OF TABLESUT... xiiit CHAPTERS 1. UINTRODUCTIONU... 1. UMICROSTRIP ANTENNASU... 6 U.1 Why we use microstrip atea; advatages ad disadvatages.u... 6 U. Radiatio fields from a microstrip ateau... 7 U.3 Feedig Techiques of Microstrip AteasU... 8 3. UCIRCULAR DISK AND ANNULAR RING MICROSTRIP ANTENNASU 11 U3.1 Circular Dis Microstrip AteasU... 11 U3.. Aular Rig Microstrip AteasU... 19 4. UCIRCULAR DISK ANNULAR RING MICROSTRIP ANTENNAU... 7 viii

5. URESULTS AND DISCUSSIONSU... 3 U5.1 Simulatio with Asoft Esemble 8.U... 3 U5.. Experimetal Results:U... 59 U5.3 Compariso ad DiscussiosU... 64 6. UCONCLUSIONU... 66 REFERENCES 68 UAPPENDICESU... 7 A - UGENERAL DESCRIPTIONS OF MICROSTRIP ANTENNASU... 7 B - UCIRCULAR DISK MICROSTRIP ANTENNASU... 77 ix

mode LIST OF FIGURES UFigure 1 1 Ideal radiatio patter of the LEO satellite atea.u... UFigure 1 Satellite geometrical shapeu... UFigure 1 3 Secat-squared graphics.u... 4 UFigure 1 Typical microstrip ateau... 6 UFigure Electric field distributios i the microstrip cavityu... 8 UFigure 3 Coaxial feedig of microstrip ateau... 9 UFigure -4 Microstrip lie feedig of a patchu... 1 UFigure 3 1 Circular dis microstrip ateau... 11 UFigure 3 Four probe feed phase relatio for TMUBU11UBU to get circular polarizatiou... 18 UFigure 3 3 Magitude of re field (db, Normalized vs. θ at 8. GHz. (Asoft Esemble 8.U... 19 UFigure 3 4 Geometry of a aular rig microstrip ateau... UFigure 3 5 Frigig field cosideratiou... UFigure 4 1 CDAR Atea 3 dimesioal view.u... 7 UFigure 4 CDAR Atea dimesioal view.u... 8 UFigure 5 1 CDAR atea top view; a=7.3, b=8.9, c=.5 mm.u... 31 UFigure 5 CDAR atea 3 dimesioal view; a=7.3, b=8.9, c=.5 mm.u... 3 UFigure 5 3 CDAR atea side viewu... 3 UFigure 5 4 CDAR atea scatterig parameters versus frequecy graph.u... 33 UFigure 5 5 Radiatio patter at 7.8 GHz.U... 34 UFigure 5 6 Radiatio patter at 8.5 GHz. (Efficiecy is 74 %U... 35 UFigure 5 7 Radiatio patter at 8.5 GHz. (db scaleu... 36 UFigure 5 8 Frequecy versus scatterig parameter graph. (Liear scaleu... 36 UFigure 5 9 Frequecy versus scatterig parameter graph.u... 37 UFigure 5 1 Frequecy versus scatterig parameter graph. (Logarithmic scale.. 37U UFigure 5 11 Far field radiatio patter i db scale.u... 38 UFigure 5 1 3 Dimesioal view of the ateau... 39 x

UFigure 5 13 Aular rig feedig sectiou... 4 UFigure 5 14 Circular dis feedig sectiou... 4 UFigure 5 15 Frequecy versus scatterig parameter graph.u... 41 UFigure 5 16 Far field radiatio patter of the ateau... 41 UFigure 5 17 3 Dimesioal view of the atea (feedig from portsu... 43 UFigure 5 18 Frequecy versus scatterig parameter (db scaleu... 43 UFigure 5 19 at 8.1 GHz Far field radiatio patter.u... 44 UFigure 5 Far field radiatio patter at 8. GHz.U... 44 UFigure 5 1 Far field radiatio patter at 8.3 GHz.U... 45 UFigure 5 3 Dimesioal view of the atea.u... 46 UFigure 5 3 Circular atea feedig sectio.u... 47 UFigure 5 4 Aular rig atea feedig sectio.u... 47 UFigure 5 5 Scatterig parameter versus frequecy graph of the project that has oly oe feed poit.u... 48 UFigure 5 6 Far field radiatio patter at 8 GHzU... 48 UFigure 5 7 Far field radiatio patter at 8.1 GHzU... 49 UFigure 5 8 Far field radiatio patter at 8. GHzU... 49 UFigure 5 9 Scatterig parameter graph of CDAR ateau... 5 UFigure 5 3 Far field radiatio patter at 8 GHz.U... 5 UFigure 5 31 Far field radiatio patter at 8.1 GHz.U... 53 UFigure 5 3 Far field radiatio patter at 8. GHz.U... 53 UFigure 5 33 Scatterig parameter graphu... 54 UFigure 5 34 Far field radiatio patter at 8. GHz.U... 55 UFigure 5 35 Atea 3 dimesioal viewu... 56 UFigure 5 36 Scatterig parameter graphu... 56 Figure 5 37 Far field radiatio patter at 8.1 GHz 57 Figure 5 38 Far field radiatio patter at 8. GHz 57 Figure 5 39 Far field radiatio patter at 8.3 GHz 58 UFigure 5 4 Far field radiatio patter at 8.35 GHz.U... 58 UFigure 5 41 Drawig of the project with AutoCAD for productio to measure the atea with experimetallyu... 6 xi

Figure 5 4 Compariso betwee experimetal ad simulatio results 61 UFigure 5 43 Far field radiatio patteru... 6 UFigure 5 44 Far field radiatio patteru... 6 UFigure 5 45 Far field Radiatio patter at 7.4 GHz.U... 63 UFigure 5 46 Far field Radiatio patter at 7.4 GHz.U... 63 UFigure 5 47 Far field Radiatio patter at 8.6 GHz.U... 64 UFigure A 1 Electric field distributios i the microstrip cavityu... 7 UFigure A Source of curret sheetu... 7 UFigure B 1 Coaxial feed of a microstrip ateau... 8 xii

LIST OF TABLES UTable 3 1 The roots of JUBUUBU (au... 13 UTable 3 The roots of the fuctio UJ ( χ Y ( χ J ( χ Y (χ =. 4 m m m m UTable 3 3 Roots of the fuctio UJ (.5χ Y ( χ J ( χ Y (.5χ = 5 m m m m UTable 3 4 The roots of the fuctio UJ ( 3χ Y ( χ J ( χ Y (3χ =.5 m m m m Table 5 1 The efficiecy of the atea at some frequecies 55 xiii

CHAPTER 1 INTRODUCTION Low Earth Orbit (LEO satellites are beig used widely for various applicatios i the world. Some of the mai features of LEO satellites are that they are ot geostatioary which meas that they are cotiuously i motio with respect to a statioary poit o the Earth ad that their velocity is related to the height of their orbit from the groud level. I commuicatio area, there occur some problems if we try to use a classical beam shaped atea o a LEO satellite because of the fact that a commoly used atea, such as a microstrip patch operatig i the domiat mode, has a radiatio patter with a maximum i the broadside directio. To overcome this problem a special type of atea whose beam shape is give i Fig.1 1 is proposed. If the atea beam shape is of this type the sigal level will always be the same i a statioary earth statio (e.g. for a Global Positioig System GPS user. I other words, the motio of the satellite will ot cause ay problem sice the earth statio gets always the same level of sigal from the satellite. As for the geometry ad statemet of the problem metioed above, cosiderig the parameters show i Fig.1 where the satellite boresight is show to be aimed at the Earth, we ca defie: r + h + ah cosθ = (1.1 r ( a + h where h is the height of the satellite from the earth level ad θ is the agle of the earth statio with respect to the satellite atea. 1

Ideal Radiatio patter of the atea Directio of Movemet EARTH Satellite Figure 1 1 Ideal Radiatio Patter of a LEO Satellite Atea. α β r θ a a+h Figure 1 The Geometry of the problem The power received by the user is

GBeB is GBsB is PBsB is is λ = GeGsPs (1. ( 4πr Pr where λ is the wavelegth, the earth statio atea gai, the satellite atea gai, the satellite trasmitter power. The aim is to get a costat power whe satellite moves or, i other words, r chages. Because earth statio atea is poited towards the satellite at all times, the oly chagig parameters are the distace r ad the agle θ. So it is required that: G s C cost. = = (1.3 r For a LEO satellite, it ca be assumed that h<<a ad i that coditio, the satellite atea has a secatp P power patter: G s ( θ = G( sec θ for <θ<θbmb (1.4 where θ is the elevatio agle ad θbmb the agular limit up to which the beam is requested to follow a secat squared shape. Beyod that agle, radiatio patter should drop to zero as fast as possible for a LEO satellite atea. A approximate power patter is give i Fig.1 3 where G( is assumed to be 1. 3

SecatP P(θ θ (radia Figure 1 3 Secat-squared power patter. Sice the locatio of the satellite is arbitrary with respect to the user statio, it would be better to have a circularly polarized atea. If satellite does t use circularly polarized radiatio patter, the user statio must be rotated for polarizatio match. I the literature, oe ca fid umerous studies realized o the subject described above. Some of them are summarized below: I [1] a circularly polarized coical beam atea has bee desiged to commuicate betwee a mobile statio ad a statioary satellite. The radiatio towards a desired directio was accomplished by usig moopole ateas with simple structures at low cost. Similar coical beam patter obtaied by usig a microstrip structure was discussed i []. The pea of the coical patter could be varied withi a wide agular rage by excitig the patch at differet higher order modes ad/or by loadig the substrate with materials of differet dielectric substrate. 4

Uipolar coical beam ateas usig microstrip patch radiators i a rig formulatio was studied i [3] for the same applicatio. A dual polarized coical beam microstrip atea was preseted ad realized as a array of three square patches whose corers meet at a cetral feed poit. The desig ad performace of two low gai shaped beam quadrifilar helix ateas QHA s o a large complex spacecraft were preseted i [4]. Cosiusoidal or coical shaped beams were desiged usig QHA s. I this thesis, the same radiatio patter which was ivestigated i [4] is used. The mai differece is that we tried to desig the atea by usig a microstrip structure because of its low profile ad suitability for space ad mobile applicatio. The mai reaso of this study is to get a suitable radiatio patter for a LEO satellite atea by usig a microstrip structure. This thesis is composed of six mai chapters ad two appedices: The first chapter is the itroductio. The secod chapter gives a detailed explaatio of microstrip structure ad its use. The third chapter explais the circular ad aular microstrip structures i detail. The fourth chapter describes the circular dis aular rig microstrip CDAR structure ad the formulas eeded to uderstad the desig of our project. The fifth chapter presets the simulatio ad experimetal results together with some discussios. The last chapter cocludes this thesis. 5

CHAPTER MICROSTRIP ANTENNAS Microstrip ateas have bee used extesively i the past 3 years, because of their light weight, suitability for space ad mobile applicatios. Microstrip ateas are composed of maily three sectios: the groud plae, a isulatig substrate material ad the atea sectio as give i Fig. 1. h Radiatig atea sectio Isulatig dielectric material with relative permittivity εbr Coductig Groud Plae Figure 1 Typical microstrip atea.1 Why we use microstrip atea; advatages ad disadvatages. Microstrip ateas have bee used i the frequecy rage from 1 MHz. to 1 GHz. Microstrip ateas, discussed i [5], have the followig advatages: a. Light weight, low volume ad coformal to surfaces of some vehicles, b. Low fabricatio cost, so these ateas ca be maufactured i large quatities, 6

c. These ateas ca be polarized both, liear as well as circular, d. Microstrip ateas ca be easily itegrated with microwave itegrated circuits (MICs. e. Microstrip ateas are capable of dual ad triple frequecy operatios. f. They ca be maufactured mechaically robust whe mouted o rigid surfaces. Beyod these advatages, microstrip ateas have a umber of disadvatages as compared to covetioal ateas. The major disadvatages, discussed i [5], are give below: a. Narrow badwidth (this ca be icreased by usig thicer substrate, b. Lower trasmitter power, up to about 1 W. c. Most of them radiate ito the half space, d. Surface wave excitatio decrease the efficiecy, e. Cross polarizatio is high, ad some other disadvatages are give i [5]. I our study we used a circular ad aular microstrip atea to get our idealized radiatio patter.. Radiatio fields from a microstrip atea I microstrip trasmissio lies it is preferred to use a thi dielectric substrate with a high dielectric costat to decrease radiatio. O the other had, thic ad lower dielectric costat substrates are preferred to icrease efficiecy of the microstrip atea. Radiatio from a rectagular patch ca be explaied with the fields that occur betwee the patch metallizatio ad the groud plae. 7

h W L Figure Electric field distributios i the microstrip cavity Related formulas about the radiatio field calculatios are give i Appedix A. Some feedig techiques of microstrip structure will be preseted i the followig subsectio..3 Feedig Techiques of Microstrip Ateas Some feedig techiques are microstrip feed, coaxial feed, proximity coupled microstrip feed, aperture coupled microstrip feed ad coplaar waveguide feed. For this study probe feed ad microstrip feed techiques will be discussed i detail to explai our studies..3.1 Coaxial Probe Feed Coaxial probe feedig techique is show i Fig. 3 below. 8

is to Cotactig poit of ier copper wire with radiatig patch h Dielectric, εbr d p Figure 3 Coaxial feedig of microstrip atea (p is the radius of the ier copper wire, d is the radius of the outer copper of the coaxial cable Probe positio is adjusted to get the best matchig coditio. The couplig betwee the probe ad the patch is obtaied from the curret JBzB EBzB. Couplig for a rectagular patch is give by; the patch field Couplig E J dv Cos( πx / L (.1 v z z where xbb the offset positio from the patch edge, ad L is the resoat legth of the patch. [5] Coaxial feedig techique is simple to adjust the positio of probe. But if thicer substrate ad may probe feedig is eeded, this creates some problems. For example fabricatio will be difficult ad also reliability decreases i this coditio. This icreases spurious radiatio from probe. 9

.3.. Microstrip Lie Feedig I this feedig techique, patch ad feedig lie both lie o the same surface; this results i the simple fabricatio show i Fig. 4 below. Microstrip lie Radiatig Patch Figure 4 Microstrip lie feedig of a patch Modelig of equivalet circuit, Edge coupled feedig desig techique ad Fiite Differece Time Domai FDTD techique based approaches of edge coupled feedig are give i [5]. Leavig the details of the formulatios to the refereces, let s study a little more about circular ad aular rig ateas i the ext chapter. 1

CHAPTER 3 CIRCULAR DISK AND ANNULAR RING MICROSTRIP ANTENNAS Circular ateas ad rig ateas ca be used i the same structure to get the atea radiatio patter desired i this wor. These two ateas must resoate i differet modes. I this chapter circular ad aular rig ateas are discussed i details. 3.1 Circular Dis Microstrip Ateas Circular microstrip ateas ca be aalyzed usig cavity model. A circular dis atea is show i Fig.3 1. z a x φ y h εbr Figure 3 1 Circular dis microstrip atea 11

abeb is P zero The wave equatio for the electric fields ca be writte as; ( + E = = π ε / λ (3.1 r I the cylidrical coordiate system, the wave equatio has the solutio, E z = E J ( cos φ (3. where JBB( are the Bessel fuctios of order. The details are give i Appedix B. UResoat frequecy: Resoat frequecy of a circular dis atea ca be calculated for the TMBmB mode from the basic relatio χbmb=a. Usig this relatioship, the resoat frequecy ca be obtaied by; f m χ m = (3.3 πa e c ε r where; χbmb is the mp th of JBPB P(a, c is the velocity of light i free space, the effective radius of the circular dis atea. Some values of the roots of the χbmb are give i the Table 3.1 below. 1

Table 3 1 The roots of JBB (a m 1 3 4 1 1.84118 3.544 4.119 5.317 3.38171 5.331 For TMB11B mode of the circular dis atea, the followig formula has bee suggested i [11] to determie the effective radius with a error of less tha,5 % for a/h >> 1; a e h πa = a 1 + l + 1.776 πaε r h 1/ (3.4 For a edge fed atea, measured iput resistace is always maximum. O the other had, we must use a feedig poit that match the impedace of the feedig lie (this geerally equals to 5Ω, uless otherwise determied to get a miimum reflectio. If we use a probe feedig, the circular dis atea is divided ito two regios accordig to the probe positio. [11] I the first regio (i.e. < BB; E z = AJ = ( cos φ, (3.5a 1 H = AJ ( si φ jwµ, (3.5b = 13

EBzB ad HBφB is IBsB is are ad is; ad ad are as H = A J( cos φ φ jwµ, (3.5c = I the secod regio (i.e. > BB; E z = = [ B J ( + C Y ( ]cos φ (3.6a 1 H = [ BJ( + CY ( ]si φ jwµ, (3.6b = H = [ ( + φ BJ CY ( ]cos φ, (3.6c jwµ = I Eqs.3-5 through 3-6 costat coefficiets ABB, BBB usig mode matchig techique at = BB CBB determied by HBB cotiuous at = B, Bwhich yields: A J( + = B J ( C J ( (3.7 discotiuous at the same poit, that is; jw µ [ BJ ( + CY AJ ( ( = ]cos φ = I s (3.8 the z-directed feed curret at = BB. For a thi probe with costat curret IBpB located at (BB,φ, the the IBsB I s = I p δ ( φ / The we ca write the uow parameters for ABB, BBB 14 CBB follows;

A jwµ Ip 1 = { J ( [ Y ( a + jη1y sy ( a] DY ( } (3.9a (1 + ε D B jwµ I p 1 = J( [ Y ( a + jη1y sy ( a] (3.9b (1 + ε D C jwµ I p = J( (3.9c (1 + ε where; D = J ( a + jη1y J ( a (3.9d s η 1π 1 = ε r For a circular dis atea of radius a, radiated field compoets of the domiat mode TMB11B are give below; E θ = jv a e r jr cosθj ( 1 a siθ (3.1a E φ jr a e J1( a siθ = jv cosθ siφ (3.1b r a siθ The radiatio patter of the TMB11B mode has a maximum ad that of TMB1B mode has a ull i the broadside directio. The radiated fields are liearly polarized for oly oe probe feedig. Neither of these modes has desired characteristics; however these structures are quite simple to fabricate ad operate. Either mode ca be used as the satellite atea if simplicity is preferred over performace. 15

Let s simply explai other parameters; lie radiated power, polarizatio ad so o. Radiated Power; Radiated power ca be calculated usig the formula give below; P r 1 ππ / = ( Eθ Eφ r siθdθdφ (3.11 η + By usig umerical techique give i [] we ca get; P r 3 ( Eh π a 4 8 11 4 = ( a + ( a... λ η 3 15 15 Polarizatio of a Circular Dis Microstrip Atea Normally for a oe poit probe feedig of a circular dis microstrip atea, we get liear polarizatio. However, circularly polarized radiatio is also possible by usig oe probe feedig but a little differet shaped atea must be used i that case. Aother method for circular polarizatio is to use two or four probe feedig with equal amplitude but 9 phase differece betwee each probe. The advatage of usig four probe feed is to suppress uwated modes. To preserve beam symmetry ad eep cross polarizatio low, especially for relatively thic substrate radiators, the uwated modes eed to be suppressed. As a geeral case the two eighborig modes of a resoat mode have the highest magitudes. Oe way to suppress these adjacet modes is to employ four feed probes located at geometrically symmetrical positios. These four feeds should have a phase arragemet of, 9,, 9 for the eve order modes ad, 9, 18, 7 16

for the odd order modes so that the fields of the uwated modes from the two opposig feeds cacel. The detailed explaatios about these ideas are give i []. Assumig that oly TMB11B mode is excited from these four feeds, electrical fields ca be writte as; E s θ θ θ θ θ + ( θ, φ = E ( θ, φ + je ( θ, φ + π / E ( θ, φ + π je ( θ, φ 3π / (3.1a E s φ φ φ φ φ + ( θ, φ = E ( θ, φ + je ( θ, φ + π / E ( θ, φ + π je ( θ, φ 3π / (3.1b Where E θ ( a θ, φ = [ J ( a siθ J ( siθ ] cosφ (3.13a E θ, φ = [ J ( a siθ + J ( siθ ]cosθ siφ (3.13b φ ( a ad BB=πf/c is the free space wave umber. The equatios are the E s θ ( φ θ, φ = [ J ( a siθ J ( a siθ ](cosφ j si (3.14a E s φ ( φ θ, φ = j[ J ( a siθ + J ( a siθ ]cosθ(cosφ j si (3.14b ad if θ depedet terms are approximately equal for θ ad φ compoets of the fields, the patter will be circularly polarized. I that case we have 11a χ11 1.84118 a = = = (3.15 ε ε ε r r r ad if the substrate is ow the patters ca be easily calculated. The patters simulated by Asoft Esemble 8. software are show i Fig.3 4. 17

BB I our project we also desig the circular ad aular sectio for circularly polarized radiatio. Phase differeces must be adjusted for each probe appropriately. The probe feedig magitude ad phases are show i the Fig.3 3 below; Probe 4, Phase 7 Probe 1, Phase Probe 3, Phase 18 Probe, Phase 9 Figure 3 Four probe feed phase relatio for TMB11B mode to get circular polarizatio Ivestigatig Fig.3 3, we see that the maximum radiatio is i the broadside directio ad also cross polarizatio is low (about db i the related regio 18

Magitude of re field (db V Norm vs. Theta at 8. GHz Figure 3 3 Magitude of re field (db, Normalized vs. θ at 8. GHz. (Asoft Esemble 8. 3.. Aular Rig Microstrip Ateas Aular rig ateas have some useful features; resoat modes ca be adjusted by cotrollig the ratio of the outer radius to the ier radius. It is possible to operate i two differet frequecies by usig two cocetric ateas; oe is circular dis at the ier side ad the other is a aular rig at the outer sectio of the atea. I this thesis we also used two cocetric ateas operatig at the same resoat frequecy, but at differet modes. A Aular rig microstrip atea is show i Fig.3 4 below. It comprises a rig shaped coductor o oe side of a dielectric substrate with a groud plae o the other side. The structure resoates at discrete frequecies give i [8] 19

εbrb h b a y z x Figure 3 4 Geometry of a aular rig microstrip atea Radiatio field compoets are calculated usig the formula below; [11] E z = E [ J ( Y ( a J ( a Y ( ] cos φ (3.16a j Ez H =, (3.16b wµ φ j Ez H φ = (3.16c wµ Iside the cavity; the other field compoets are zero. The surface curret o the lower surface of the rig is;

ad J s = zˆ H = ˆ φh + ˆ H φ (3.17 ad writig it i the other form we get; J φ jηe = [ J( Y ( a J( a Y ( ] si φ wµ (3.18a J je = [ J ( Y ( a J ( a Y ( ] cos φ wµ (3.18b At = a ad = b radial compoet of the surface curret must vaish to satisfy the magetic wall boudary coditios so that; JBB(=b=HBφB(=b (3.19 J ( ( ( b Y a J a Y ( b = (3. If a, b, εbrb are ow, the roots of the above formula ca be foud. For a approximate calculatio; B1Ba = a/(a+b for 5 (b-a/(b+a <,35 Resoat frequecy; The resoat frequecy is obtaied by settig; = χbmb/a or m m = (3.1 f χ πa c ε r 1

abeb = bbeb = wbeb ad for is I the above formula o frigig field is tae ito accout. I order to iclude the effect of frigig field effective dielectric costat εbreb ca be used istead of εbrb. So we get a approximate expressio for the resoace frequecy as; f m χ m = (3. πa c ε re Frigig fields ca be tae ito accout by cosiderig a atea that is wider tha the physical width of the atea. This is show i the Fig.3 5 where w is the physical width of the atea ad wbeb the effective width of the atea. w Figure 3 5 Frigig field cosideratio as; Modified values of ier ad outer radii of the aular rig atea are give a (wbeb w/ (3.3a b + (wbeb w/ (3.3b Empirical formulas for abeb bbeb aular rig atea are give as; [8] the ier ad outer effective radii of the

abeb = bbeb = usig a 3h/4 (3.4a b + 3h/4 (3.4b where h is the thicess of the substrate material. If thicess is very small the we ca use as abeb a ad bbeb b. ad bbeb As a computatio guidelie; give a ad b, first of all oe ca calculate abeb the formula (3.4a, 3.4b, the fid the χbmb usig the formula (3., ad the calculate the resoat frequecy of the aular rig atea. Radiatio Fields: Radiatio fields of a aular rig microstrip atea ca be calculated from; The surface electric curret distributio of the aular rig or, The magetic curret formulatio, We ca use equivalet magetic curret formulatio due to its simplicity. Radiatio fields are calculated idepedetly at = a ad = b from the magetic currets ad these two fields added vectorially to get the radiatio fields of the microstrip rig atea. [11] E θ = j j e h r r [ aez( a J ( a siθ bez( b J ( b siθ cos φ (3.5a E φ = j j e h r r J ( a siθ J ( b siθ [ ae z( a be z( b cosθ siφ a siθ b siθ (3.5b 3

where; E z E ( a = E[ J( ma Y ( ma J ( ma Y ( ma ] = (3.5c π a m E z a E J ( ( b = E[ J ( b Y m ( ma J ( ma Y ( mb ] = b π a J ( m m m a b (3.5d E θ = j E π m j e h r r J J ( a siθ J ( ( m m a J ( b siθ cos φ (3.6a b E φ = j E π m j e h r r J( a siθ J ( a siθ J ( m m a J( b siθ cosθ si φ b b siθ (3.6b where BmBa = χbmb For the ratio of b/a = some values of χbmb are give i Table 3. below. χb1 Bis show i bold character because this value will be used for our aular atea sectio desig. Table 3 The roots of the fuctio J ( χ Y ( χ J ( χ Y (χ = m m m m m 1 3 4 5 3.1966 5.613 9.4445 1.581 1.6773 3.85 5.653 9.4713 1.61 1.346 3.5313 6.4747 9.5516 1.661 4

For the ratio of b/a =.5 some values of χbmb are give i Table 3.3 below. Table 3 3 Roots of the fuctio J (.5χ Y ( χ J ( χ Y (.5χ = m m m m m 1 3 4 5 1.5847.635 4.73 6.339. 1.1369.5665 4.45 6.4365. For the ratio of b/a = 3 some values of χbmb are give i Table 3.4 below. Table 3 4 The roots of the fuctio J ( 3χ Y ( χ J ( χ Y (3χ = m m m m m 1 3 4 5 1.5136 1.7578 3.361...9775.91 3.465. For m odd, TMB1mB modes ier ad outer frigig fields are of opposite polarity, givig rise to less radiatio because of destructive iterferece, For m eve, TMB1mB modes ier ad outer frigig fields are of same polarity, givig rise to good radiatio modes. If the ratio of b/a icreases, the directivity of the atea will icrease. 5

Aular rig ateas for circular polarizatio have bee studied i [6] through [1]. Most of them used oly oe feedig poit with a ear o the aular rig. I our thesis we used 4 feedig poits i aular sectio for circular polarizatio to suppress the other modes defied i []. The patter of a sigle aular rig atea caot be made to have local miima i the broadside directio by adjustig its parameters. However, a combiatio of a circular rig ad a circular dis ca be used to obtai the desired patter. I this chapter we derive the formulas for circular dis ateas ad aular rig ateas as separate ateas. I the ext chapter we derive the formulas for a cocetric atea; circular dis aular rig atea which is composed of a circular dis at the ceter ad a aular rig at the outer sectio. 6

CHAPTER 4 CIRCULAR DISK ANNULAR RING MICROSTRIP ANTENNA I chapter 3 we aalyzed circular dis microstrip atea ad aular rig microstrip atea separately. I this chapter we aalyze the circular dis aular rig CDAR microstrip atea with uited costructio o a sigle groud plae; i other words; circular dis is the ier part ad aular rig is the outer part of the atea. CDAR atea structure is show i the Fig.4 1 ad 4. Figure 4 1 CDAR Atea 3 dimesioal view. CDAR ateas ca be used for differet purposes; for example to get dual frequecy operatios. I this coditio ier part operates at oe frequecy, outer part operates at aother frequecy. 7

8 Figure 4 CDAR Atea dimesioal view. I our project we also used CDAR atea to obtai the desired radiatio patter for Low Earth Orbit LEO satellite atea. But to get such a radiatio patter ier ad outer parts of the CDAR atea must operate at differet modes. If ier part operates i TMB11B mode with amplitude A, outer part operates i TMB1B mode with amplitude B; the total radiatio fields ca be writte as; = si ( ( ( si ( si ( cos, ( 1 θ θ θ φ φ θ θ c J c J b J b J B a AJ E m m (4.1a = θ θ θ θ θ θ θ φ φ θ φ si si ( ( ( si si ( si si ( cos si, ( 1 c c J c J b J b b J B a a J A E m m (4.1b x y a b c z

I this study, we wat to get a radiatio patter; which has a maximum field stregth that is ot perpedicular to the atea surface. By chagig A ad B; we ca obtai a maximum field stregth with a icliatio agle α from the atea surface which is the coverage area of the satellite atea. This ideal radiatio patter is show i the Fig.1 i the first chapter. To get the radiatio patter for idealized atea; ier circular dis must be i TMB11B mode ad outer aular rig sectio must be i TMB1B mode, but each sectio must resoate at the same frequecy which is chose as 8. GHz. I this study to simplify mathematical calculatio we ca use superpositio priciple, i other words, first of all calculate the radiatio fields that comes from ier circular sectio, the calculate the radiatio fields that comes from aular sectio of the atea ad the add these two fields to fid the total fields. But to use this priciple we must choose optimum values of parameters a, b ad c. Ivestigatig Tables 3. through 3.4 we ca chose a c/b ratio of.5 to get a ideal ad simple calculatio. It is see from Table 3.4 that c/b ca ot be chose as 3. Because i that coditio aular rig sectio will be smaller tha that of circular radius, this ca ot be physically costructed. O the other had, if we choose a c/b ratio of, aular rig sectio will be larger which is ot desirable. So i this study we have chose a c/b ratio betwee ad 3. I the ext chapter we discuss the solutios we got by usig Asoft Esemble 8. software ad the experimetal results ad compariso of experimetal ad simulatio results. 9

= CHAPTER 5 RESULTS AND DISCUSSIONS I this chapter, the CDAR atea with the desired characteristics has bee desiged. First, the atea geometry is calculated usig the results from chapter 3. The the resultig desig has bee aalyzed with the simulatio program Asoft Esemble 8. software. Subsequetly, the atea geometry is refied usig the simulatio results, util the desired radiatio patter is reached. Fially, the resultig atea desig is implemeted ad the simulatio results are compared with the experimetal measuremets. 5.1 Simulatio with Asoft Esemble 8. Equatios (4.1a ad (4.1b give the electric field of a CDAR atea. Our aim is to desig a atea which has a resoace at 8. GHz. To get the ideal atea patter we choose c/b =.5 ad a duroid substrate with a dielectric costat εbrb. ad a thicess of.17 mm. The relatively low thicess of the substrate leads to a egligible frigig field effect, so abeb a, bbeb b ad cbeb c. Circular rig sectio is i TMB11B mode ad the aular rig sectio is i TMB1B mode. Usig (3.3 ad (3. the atea geometry ca be calculated as; 8 1.84118 3 1 a = = 7.3 mm 9 π 8. 1. 8.635 3 1 b = = 8.9 mm 9 π 8. 1. c =.5 x 8.9 =.5 mm. 3

P probes P ad P probes. P Iitially the atea is fed with 8 differet probes. The Circular sectio is fed with a amplitude of oe at each probe but with a 9 phase differece betwee each probe, similarly, the aular rig sectio is fed with a amplitude of. at each probe ad the same phase differece betwee each probe. The atea geometry, the frequecy respose ad the radiatio patter are show i Figs.5 1 through 5 5. The simulatio results displayed i Fig.5 4 idicate that the port 1 displayed i Fig.5 1 has a resoace frequecy of 7.8 GHz, istead of the desired resoace frequecy of 8. GHz. Similarly it is see that the port 5 resoates at 8.5 GHz. Furthermore, the simulatio results show that there is a couplig betwee the 1P ad 3P rd ad also betwee the 5P th 7P has to be refied to reach the desired atea characteristics. th Thus the atea geometry st Figure 5 1 CDAR atea top view; a=7.3, b=8.9, c=.5 mm. 31

Figure5 CDAR atea 3 dimesioal view; a=7.3, b=8.9, c=.5 mm. Atea sectio At. dielectric sectio with a thicess of.17 mm Upper dielectric sectio with a thicess of.51 mm Feedig sectio Lower dielectric sectio with a thicess of.51 mm Groud plaes (upper ad lower sectios Figure 5 3 CDAR atea side view 3

Figure 5 4 CDAR atea scatterig parameters versus frequecy graph. Simulatio of the atea structure show i Fig.5-1 ad 5- usig Asoft Esemble 8. results i the far field radiatio patter displayed i Figs.5-5 to 5-7. (The circular sectio is fed with amplitude 1 at each probe ad the aular sectio is fed with. at each probe at 7.8 GHz. The simulatio results show a discrepacy compared to the desired ad the theoretically calculated atea characteristics. The radiatio patter ad the resoat frequecy differ cosiderably. However, at 8.5 GHz, the simulatio result approaches the desired radiatio patter. 33

Magitude of re Field (V vs. Theta at 7.8 GHz Magitude of re Field (db V Norm vs. Theta at 7.8 GHz (a (b Figure 5 5 Radiatio patter at 7.8 GHz. (Exactly ice circular polarizatio, but ot the idealized patter. Also atea efficiecy, as explaied i Appedix B, is good eough, 98,5 % Fig.5-5(a displays the ormalized patter ad 5-5(b displays the patter i db. The atea patter at 8.5 GHz is also displayed i Fig.5-6, which shows a patter very similar to the desired oe, however, the atea efficiecy decreases to 74% from 98.5%. Thus the atea geometry has to be modified to reach the desired atea characteristics. The ew values for a, b ad c ca be calculated by proportioal calculatio; if 7.3 mm gives us 7.8 GHz, what must be the value of a to get 8. GHz. resoace. By a simple calculatio oe gets, a = 6.9, b = 8.7 ad c = 1.8 mm. Usig these values i the Asoft Esemble 8. simulatio software results i the atea characteristics displayed i Figs.5-7 ad 5-8. 34

Magitude of re Field (V Norm vs. Theta at 8.5 GHz Figure 5 6 Radiatio patter at 8.5 GHz. (Efficiecy is 74 % It is uderstood from Fig.5 8 that SB11B does ot have a miimum at 8. GHz as desired. To overcome this problem the circular sectio dimesio must be modified a little more to achieve the ideal resoace coditio. After some calculatios we choose the value of a to be 6.84 mm. I that coditio the circular ad the aular sectios come to resoace at 8. GHz. For these values of a, b ad c (a = 6.84, b = 8.7 ad c = 1.8 mm. we get the scatterig versus frequecy as displayed i Figs.5 9 ad 5.1 ad also the radiatio patter i Fig.5 11. 35

Magitude of re Field (db V Norm vs. Theta at 8.5 GHz Figure 5 7 Radiatio patter at 8.5 GHz. (db scale Figure 5 8 Frequecy versus scatterig parameter graph. (Liear scale 36

Figure 5 9 Frequecy versus scatterig parameter graph. (Liear scale - a = 6.84 mm., b = 8.7 mm ad c = 1.8 mm Figure 5 1 Frequecy versus scatterig parameter graph. (Logarithmic scale 37

Magitude of re Field (db V Norm vs. Theta at 8. GHz Figure 5 11 Far Field Radiatio patter i db scale (a=6.84, b=8.7, c=1.8 mm. ad circular sectios are fed at B1B= 4 mm. ad aular sectios are fed at BB=1.5 mm. It is see from Fig.5 9 that both the circular ad the aular sectios resoate at 8. GHz. If we excite the circular sectios with a amplitude of 1, ad the aular sectios with amplitude., we get a Far Field radiatio patter as show i Fig.5 11. This is the idealized radiatio patter for the LEO satellite atea. The cross polarizatio is also low eough i the target regio. Efficiecy of the atea is 99% at 8. GHz. I the previous simulatios, we fed all 8 ports separately. Our aim is to feed all 8 ports from oe poit. First we try to combie two ports to oe port, leadig to a total of 4 ports istead of 8 ports. To get a circular polarizatio, the lie legth must be adjusted to get 9 phase differece. Furthermore, the total port impedace is required to be 5 Ω. To this ed, we use two parallel lies with 1 Ω impedace each, resultig i 5 Ω whe combied. λ/4 legth sectios are used 38

for impedace trasformatio; that trasforms the impedace from 5 Ω to 1Ω. We used two separate feedig sectios; oe for circular sectio ad the other for aular sectio. Feedig sectios are show i Fig.5 13 ad 5 14 separately. All substrates are duroid, (εbrb=. with a thicess of.17mm for the atea sectio, ad.51mm for the feedig sectio. duroid substrate thicess.51 mm duroid substrate thicess.51 mm duroid substrate thicess.51 mm duroid substrate thicess.51 mm Figure 5 1 3 dimesioal view of the atea Atea frequecy versus scatterig parameter graph is show i Fig.5 15. 39

Figure 5 13 Aular rig feedig sectio Figure 5 14 Circular dis feedig sectio 4

Figure 5 15 Frequecy versus scatterig parameter graph. Figure 5 16 Far field radiatio patter of the atea 41

It is see From the Fig.5 16 that the radiatio patter is very similar to the desig specificatio, but the cross polarizatio is much higher tha expected. This may be the result of the iteractio betwee the edge port feedig of the ports 1 ad from the same edge. Aother iterestig result is the efficiecy of the atea which is 78 % at 8. GHz. We see a decrease i the efficiecy because of the mergig of the two ports. Subsequetly; we combie the upper ad lower ports i oe port, resultig i a total of two feedig ports, istead of 4. Upper ad lower sectios are ot of equal impedaces; they are chose to be differet selected to get the desired radiatio patter. The circular sectio is trasformed from 5 Ω to 6 Ω, the aular sectio is trasformed from 5 Ω to 3 Ω. Parallel coectios of these two impedaces is equal to 5 Ω. The other parameters for that atea are as follows; dimesios of the atea; a=6.84 mm., b=8.7 mm. ad c=1.8 mm. feedig radius ; for circular sectio B1B=4 mm. ad aular sectio BB=1.5 mm to get the best matchig coditio. The 3 Dimesioal view of the atea, the scatterig parameter graph ad the radiatio patter of the atea are show i Figs.5 17 to 5 1. 4

Figure 5 17 The 3 dimesioal view of the atea (feedig from ports Figure 5 18 Frequecy versus scatterig parameter (db scale 43

f=8.1 GHz. PBiB=98 W. PBradB=85 W. ebrb=87% Figure 5 19 Far field radiatio patter at 8.1 GHz. f=8. GHz. PBiB=98 W. PBradB=78 W. ebrb=8% Figure 5 Far field radiatio patter at 8. GHz. 44

f=8.3g Hz. PBiB=98 W. PBradB=9 W. ebrb=9% Figure 5 1 Far field radiatio patter at 8.3 GHz. By aalyzig Figs.5 18 to 5-1 we see that the radiatio patters are similar to the desired patter, however, the cross polarizatio is much larger tha expected. Also, we uderstad that mergig of ports results i decreased atea efficiecy. To reach the desired 1 port atea, we use the same atea geometry as i the previous case, ad merge the two remaiig ports as show i Fig.5. (i.e. a = 6.84 mm., b = 8.7 mm. ad c = 1.8 mm. Circular feedig sectios are all B1B = 4 mm. ad aular sectios BB = 1.5 mm.. Circular ports are coverted from 5 Ω to 6 Ω ad aular sectios are coverted from 5 Ω to 3 Ω ad the resultig impedace is 5 Ω. The 3 dimesioal view of the atea, the feedig sectios, the scatterig patter ad the radiatio patter are show i Figs.5 to 5 8. 45

Figure 5 The 3 dimesioal view of the atea (All ports were merged to feed the atea from oly o poit.. The Upper feed sectio feeds aular atea, the dowward feed sectio feeds the circular atea. Impedace trasformers are used to get the total port impedace to 5 Ω. 46

Figure 5 3 Circular atea feedig sectio. Figure 5 4 Aular rig atea feedig sectio. 47

Figure 5 5 Scatterig parameter versus frequecy graph of the project that has oly oe feed poit. Figure 5 6 Far field radiatio patter at 8 GHz 48

Figure 5 7 Far field radiatio patter at 8.1 GHz Figure 5 8 Far field radiatio patter at 8. GHz 49

= We get similar radiatio patters for oe port feedig ad two port feedig. The optimal operatig frequecy is see from the scatterig parameter graph as 8 GHz. At this frequecy the efficiecy was calculated as 98%. But the radiatio patter at this frequecy is ot the desired oe. At 8.1 GHz. the radiatio patter is suitable for the desired LEO atea specificatios, however at this frequecy the efficiecy of the atea decreases to 96% ad also cross polarizatio is greater tha ormal polarizatio. The efficiecy cotiues to decrease at 8. GHz., operatig frequecy of our atea, to 8%, at that frequecy the cross polarizatio is also greater tha the ormal polarizatio. These effects occur as a result of the mergig of 8 ports to oe sigle port. I the previous examples the atea substrate thicess was.17 mm. This is extremely thi substrate to fabricate without a error. By ivestigatig laboratory equipmet it has bee decided to simulate the atea with the RO43 substrate material with a atea layer thicess of.51 mm. Circular feed ad aular feed sectios use two differet layers of the same substrate material, ad thicesses are 4 layers of 1.5 mm each. The relative permittivity of RO43 is 3.38 ad the tagetial loss factor is.7 (εbrb 3.38 ad a loss factor taδ =.7. Usig these parameters, we simulated the atea as correctly as possible before the fabricatio. The substrate thicesses adjusted so that the feedig lies ca be produced practically. To get ideal atea patter we agai choose coditio c/b =.5 ad a RO43 substrate material. For that c/b ratio, ξb1b =.635. Substrate thicess is.51 mm. which is comparable to the wavelegth at this operatig frequecy. This is a thicess that must be tae ito accout for frigig fields. For that coditio we must fid a, b ad c values; a = 1.84118 3 1 π 8. 1 9 8 3.38 m = 5.83 mm. 5

bbeb = cbeb = 8.635 3 1 b = m. = 7.17 mm. 9 π 8. 1 3.38 c =.5 x 7.17 = 17.95 mm. The above values are effective values, so exact physical values must be foud usig the formulas i [8], a e h πa = a 1 + l + 1.776 πaε r h 1/ b 3h/4 c + 3h/4 Usig these formulas, oe calculates the physical dimesios as; a = 5.61 mm., b = 7.55 mm., ad c = 17.54 mm. Usig a similar methodology as i the previous case, the theoretical atea dimesios are adjusted by usig simulatios. At the begiig, for the adjustmet of the atea dimesios, 8 differet port feedig techique is used. The circular sectio is fed with amplitude equal to 1, ad aular sectio with amplitude equal to.. The atea, frequecy respose ad the radiatio patter for 8, 8.1, 8. GHz are show i Figs.5 9 through 5 3. 51

Figure 5 9 Scatterig parameter graph of CDAR atea (a=5,61 mm., b=7,55 mm. ad 17,54 mm. B1B=3,5 mm., BB =11 mm. Magitude of re Field (db V Norm vs. Theta at 8 GHz Figure 5 3 Far field radiatio patter at 8 GHz. 5

Magitude of re Field (db V Norm vs. Theta at 8.1 GHz Figure 5 31 Far field radiatio patter at 8.1 GHz. Magitude of re Field (db V Norm vs. Theta at 8. GHz Figure 5 3 Far field radiatio patter at 8. GHz. 53

Ivestigatig the above graphs, we uderstad that the circular sectio ad aular sectio resoace frequecy is ot 8. GHz., istead they have differet frequecies, but the radiatio patter is similar to the desired patter especially at 8.1 GHz. At that frequecy the efficiecy of the atea is 84%. The radiatio patter decreases more at the top sectio of the atea at 8. GHz with a greater efficiecy of 86%. Similar is the patter, however, the efficiecy decreases to 8% at 8. GHz. At other frequecies radiatio patters differ largely from our desired patter. By maig some adjustmet we attempted to get a resoace frequecy at 8. GHz. For a=6,1 mm, b=7,5 mm, c=17,4 mm, B1B=3,5 mm ad BB =11 mm, the scatterig parameter ad far field radiatio patters are show i the Fig.5 33 ad 5 34 respectively. Figure 5 33 Scatterig parameter graph 54

Magitude of re Field (db V Norm vs. Theta at 8. GHz Figure 5 34 Far field radiatio patter at 8. GHz. Accordig to the above simulatio results we followed a similar methodology as i the previous case to feed the atea from oly oe port. We get atea shape, scatterig parameter ad far field radiatio patters at differet frequecies as show i Figs.5 35 through 5 4. At some frequecies the efficiecy of the atea is give i Table 5 1 below. Table 5 1 The efficiecy of the atea at some frequecies f (GHz PBiB (W PBoutB (W e (Efficiecy 8.1 49.44 48.71.98 8.15 49.44 48.75.99 8. 49.44 48.39.98 8.5 49.44 48.45.98 8.3 49.44 47.89.97 8.35 49.44 47.3.96 55

Figure 5 35 Atea 3 dimesioal view Figure 5 36 Scatterig parameter versus frequecy graph 56

Magitude of re Field (db V Norm vs. Theta at 8.1 GHz Figure 5 37 Far field radiatio patter at 8.1 GHz Magitude of re Field (db V Norm vs. Theta at 8. GHz Figure 5 38 Far field radiatio patter at 8. GHz Cotrary to the assumptio that superpositio priciple is applicable, simulatio program shows that there is a couplig betwee dis ad aular sectio. This result ca be see i Figs.5 37 through 5 39. 57

Magitude of re Field (db V Norm vs. Theta at 8.3 GHz Figure 5 39 Far field radiatio patter at 8.3 GHz Magitude of re Field (db V Norm vs. Theta at 8.35 GHz Figure 5 4 Far field radiatio patter at 8.35 GHz. The atea patter i Fig.5 4 ca be cosidered as a sufficietly accurate approximatio to the desired atea patter. (There is oly a small discrepacy at the broadside directio. The cross polarizatio is about 1 db below from the ormal polarizatio at the regio of iterest. Dimesios for that atea are 58

a=5.8 mm, b=7.7 mm, c=17.9 mm, B1B=3.5 mm ad BB =1 mm. The efficiecy of the atea at 8.35 GHz. is 96%, so it is a acceptable percetage. The above values ca be used to fabricate the atea. The ext sectio gives the experimetal results. 5.. Experimetal Results: We desig the atea as; a=5.8 mm, b=7.7 mm, c=17.9 mm, B1B=3.5 mm ad BB =1 mm. These are the same parameters as the last simulatio results with Asoft Esemble 8. software. The desiged atea, feedig lies ad groud plaes are draw by usig AutoCAD drawig program, as show i Fig.5 41. 59

Atea sectio Upper feed sectio Groud plae betwee atea ad upper feed sectio Lover feed sectio Dowward Groud plae Groud plae betwee dow feed ad upper feed sectio Figure 5 41 The Drawig of the atea desig used i the experimetal aalysis. (All dimesios ca be foud i the disette attached to this thesis. 6

Frequecy S11 (db Figure 5 4 Compariso betwee experimetal ad simulatio results (Scatterig parameter, experimetal, simulatio with Asoft Esemble 8. 61

Magitude of re Field (db V Norm vs. Theta at 8.35 GHz Experimetal result at 8.3 GHz. Vertical patter Simulatio results at 8.35 GHz Figure 5 43 Far field radiatio patter Magitude of re Field (db V Norm vs. Theta at 8.35 GHz Experimetal result at 8.3 GHz. horizotal patter Simulatio results at 8.35 GHz Figure 5 44 Far field radiatio patter 6

Magitude of re Field (db V Norm vs. Theta at 7.4 GHz. Experimetal result at 7.4 GHz. vertical patter Simulatio results at 7.4 GHz Figure 5 45 Far field radiatio patter at 7.4 GHz. Magitude of re Field (db V Norm vs. Theta at 7.4 GHz. Experimetal result at 7.4 GHz. horizotal patter Simulatio results at 7.4 GHz Figure 5 46 Far field radiatio patter at 7.4 GHz. 63

Magitude of re Field (db V Norm vs. Theta at 8.6 GHz. Experimetal result at 8.6 GHz. vertical patter Simulatio results at 8.6 GHz Figure 5 47 Far field radiatio patter at 8.6 GHz. 5.3 Compariso ad Discussios Ivestigatig the simulatio ad the experimetal results; we see from the scatterig parameter graph that these are roughly similar, but there are some discrepacies. Especially at 7.4 GHz the experimetal atea has a resoace, but that resoace ca ot be see i the simulatio. At 8.4 GHz. which is the best resoace of the overall atea system, the experimet results show better matchig coditios tha that of the simulatio. The best match betwee the simulatio ad experimetal results occur at 8.6 GHz. Ivestigatig the far field radiatio graphs; the experimetal results at 7.4 GHz vertical patter is suitable for the LEO satellite atea, but the horizotal patter is ot adequate. Simulatio results at that frequecy show that the amout of eergy radiated i the broadside directio is much smaller. At 8.3 GHz. the far field radiatio graphs show us little similarity betwee experimetal ad simulatio results that is very close to the specified frequecy of 8. GHz. At 8.6 64

GHz. best similarity at far field radiatio graphs betwee experimet ad simulatio results is obtaied. The reaso for the discrepacies betwee the experimet ad simulatio may possibly be due to the formulatio characteristics of the simulatio program. Aother importat factor may be the effect of the couplig betwee feedig probes i the fialized desig. Ad the other factor may be the cause of implemetatio problems durig fabricatio period. It ca be see that the chose parameters are ot suitable for proper operatio. Feedig from oe port, istead of feedig from eight differet ports, may have caused this result. Studies have to cotiue i this matter. The ext sectio presets the coclusio of the thesis. 65

CHAPTER 6 CONCLUSION The aim of this study is to desig a atea at 8. GHz for a LEO satellite. The desired atea patter is show i Fig.1 1. We have chose a microstrip structure for this desig. The atea is cosidered to compose of two mai parts; a circular dis at the ceter ad a aular rig at the outer sectio. By meas of a theoretical aalysis, it has bee cocluded that the circular ad aular diss must operate at TMB11B ad TMB1B modes respectively. S I this study, a 8 port feedig structure is, first, simulated usig Asoft Esemble 8. software program. I this structure, all ports are assumed to be fed separately ad the desired atea patter is achieved by adjustig the magitudes of ier ad outer sectio feedigs. By doig so,s Swe could get differet radiatio patters which are all suitable for the LEO satellite atea. S But, 8 ports feedig is difficult to implemet for users ad requires that all probes have differet phases ad magitudes. I order to simplify the feedig of the atea, we tried to combie all 8 ports to a sigle feedig poit. While combiig the ports we adjusted their phases ad magitudes for the desired radiatio coditio by usig microstrip lie sectios. The combiatio of ports to a sigle feedig poit, however, resulted i some problems: Although simulatio results yielded appropriate (or at least acceptable radiatio shapes as log as LEO satellite atea specificatios are cosidered, experimetal results failed. The deviatio from the desired atea patter i experimetal results ca be related to followig factors: I the simulatio program, the groud plae is assumed to be ifiite whereas it is fiite i the experimets. I 66

additio, the thicess of the feedig probes is assumed to be zero i simulatios; but, i reality, they have some thicess. If we mae a assessmet that a sigle probe yields a cotributio of 5% deviatio from the desired atea patter, the total deviatio for a 8 port feedig structure would certaily be much higher. A possible solutio to the problem stated above would be the implemetatio of a electroic circuit at the bottom of the atea sectio to feed the atea emulatios o 8 probe feedig. Aother solutio might be the use of a hybrid circuit. The ivestigatio of these suggestios is left as future wors. 67

REFERENCES [1] H.Kawaami, G.Sato ad R.Waabayashi, Research o Circularly Polarized Coical Beam Ateas, IEEE Ateas ad Propagatio Magazie, Vol.39, No.3, pp.7-37, Jue 1997. [] J.Huag, Circularly Polarized Coical Patter from Circular Microstrip Ateas, IEEE Trasactios o Ateas ad Propagatio, Vol.AP-3, No.9, pp.991-994, September 1984. [3] N.J.McEva, R.A.Abd-Alhameed, E.M.Ibrahim, P.C.Excell ad J.G.Gardier, A New Desig of Horizotally Polarized ad Dual Polarized Uipolar Coical Beam Ateas for HIPERLAN, IEEE Trasactios o Ateas ad Propagatio, Vol.51, No., pp.9-37, February 3. [4] R.Cahill, I.Cartmell, G.Va Doore, K.Clibbo ad C.Sillece, Performace of Shaped Beam Quadrifilar Ateas o the METOP Spacecraft, IEE Proc.-Microw. Ateas Propag., Vol.145, No.1, pp.19-4, February 1998. [5] P. Bhartia, I. Bahl, R. Garg, A. Ittipiboo, Microstrip Atea Desig Hadboo, Artech House Ateas ad Propagatio Library, pp.-43, 1. [6] H.M.Che ad K.L.Wog, O the Circular Polarizatio Operatio of Aular-rig Microstrip Ateas, IEEE Trasactios o Ateas ad Propagatio, Vol.47, No.8, pp.189-19, August 1999. 68

[7] A.K.Bhattacharyya ad R.Grag, Iput Impedace of Aular Rig Microstrip Atea Usig Circuit Theory Approach, IEEE Trasactios o Ateas ad Propagatio, Vol.AP-33, No.4, pp.369-374, April 1985. [8] M.Taaa ad N.Taahashi, Suppressig Udesired Modes i a Higher Order Mode Microstrip Rig Patch Atea, Electroics ad Commuicatios i Japa, Part 1, Vol.85, No.3, pp.9-18,. [9] A.K.Bhattacharyya ad L.Shafai, A Wider Bad Microstrip Atea for Circular Polarizatio, IEEE Trasactios o Ateas ad Propagatio, Vol.36, No., pp.157-163, February 1988. [1] K.Tamauma ad H.Iwasai, A Small Size Circularly Polarized Aular Microstrip Atea, IEEE -783-7846-6/3/$17., pp.716-719, 3. [11] P. Bhartia, I. Bahl, R. Garg, A. Ittipiboo, Microstrip Atea Desig Hadboo, Artech House Ateas ad Propagatio Library, pp.317-386, 1. 69

B B APPENDIX A GENERAL DESCRIPTIONS OF MICROSTRIP ANTENNAS Radiatio from a rectagular patch ca be explaied with the fields that occur betwee the patch metallizatio ad the groud plae. [5] h L W Figure A 1 Electric field distributios i the microstrip cavity Practical microstrip ateas have small h/w ratio. To simply explai the field distributio, let s assume that o fields variatio alog h. (assume h << λ As a result the patch ca be modeled as a cavity. The electric field lies of TMB1B modes are plotted i Fig.. Equivalet currets are; J = ˆ B(A.1.a s H a M = ˆ B(A.1.b s E a 7

Groud plae effect ca be tae ito accout by image theory, this will double the magetic curret desity i (.1.b, while the image of the electric curret desity will be i opposite directio ad cacel. Thus the curret desity will be; M = ˆ (A. s E a The electric field for the domiat mode, as show i Fig.., is give by: E = zˆ a E o (A.3 for the slots of height h ad legth W. Similarly for the other slot the electric field ca be writte as; E a = ze ˆ si( πx / L (A.4 From Fig. ; the radiatio from slots that laid alog x axis is almost zero, because the same amplitude but opposite currets. The oly fields that radiate from the slots that laid alog y axis. Electric ad magetic fields at ay poit outside the microstrip atea regio ca be writte as: E m 1 ( r = F (A.5 ε H m 1 ( r = ( F jωf (A.6 jωµε F ε 4π = S j r r e M ( r r r ds (A.7 71

BB is rb where; ε is the permittivity of the medium, µ is the permeability of the medium, the free space wave umber, M (r is the surface magetic curret desity at a poit r o the surface of the patch as show i Fig. 3 below. z P field poit rb x a φ θ φ ddφ y Figure A Source of curret sheet Similar methods ca be used to write the fields due to a electric curret, 1 ( r = ( A jωa (A.8 jωµε E e 1 ( r = A (A.9 µ H e 7

is where; A = µ 4π j r r e r r J( r ds S (A.1 Total fields ca be writte as; E = E e + E m = 1 ( A jωµε 1 jωa F ε (A.1 H = H e + H m = 1 ( F jωµε 1 jωf + A µ (A.11 The importat field compoets i the far field regio are the θ ad φ compoets, that are trasverse to the directio of propagatio. For magetic curret aloe; Hθ = jωf θ ad Hφ = jωfφ, i free space; E = η rˆ H = η ( ˆ ˆ ( ˆ φhθ θhφ = jωη φf ˆ θf θ φ (A.1 Where ηbb the free space impedace = 1π, For electric curret aloe; Eθ = jωa θ, Eφ = jωaφ 73

E H = rˆ η I the far field, the phase term is approximated by; r r = r r cosφ i the umerator, while r r r i the deomiator, this gives us; F ε e 4π r j r jr cosφ M( r e ds S (A.13 A e 4π r jr µ cos jr φ J( r e ds S (A.14 I our studies we mae a circular ad aular atea, so let s formulate for a circular atea that show i the Fig.A. Far field vector magetic potetial is [5]; A = jr π a µ e 4π r ] J(, φ exp[ j θ φ φ φ si cos( d d (A.15 Surface curret desity i polar coordiates is; J (, φ = J (, φ ˆ + J (, φ ˆ φ φ A = j r π a { J (, φ ˆ + J (, φ ˆ φ } µ e 4π r ] φ exp[ j si θ cos( φ φ ddφ (A.16 A θ = µ 4π π { jr a e cosθ J (, φ cos( φ φ r 74

ad J (, φ si( φ φ } exp[ j θ φ si cos( φ] ddφ (A.17a φ A φ = µ 4π π { jr a e J (, φ si( φ φ r J (, φ cos( φ φ } exp[ j θ φ si cos( φ] ddφ (A.17b φ Similar expressios ca be derived for the vector electric potetial FBθB FBφB jr π e Fθ = cosθ φ φ φ φ θ φ φ φ π M (, si( exp[ j si cos( ] d d 4 r (A.18a e 4π r jr π φ = Mφ F (, φ cos( φ φexp[ j siθ cos( φ φ] ddφ (A.18b E θ = jωη F φ E φ = jωη F θ Usig (A.18a ad (A.18b, we ca write, jr π j e Eθ = φ φ φ φ θ φ φ φ π ( M (, cos( exp[ j si cos( ] d d 4 r (A.19a jr π j e Eφ = cosθ φ φ φ φ θ φ φ φ π ( M (, si( exp[ j si cos( ] d d 4 r (A.19b Radiated power from a microstrip atea ca be calculated by itegratig the Poytig vector over a closed surface as; 75

RBsB is 1 P r = Re ( E H ds η aperture ad i the microstrip atea regio electric field is ormal to the patch ad groud plae, magetic field is parallel to strip so above formula ca be writte as; P r 1 = ( Eθ Eφ r siθdθdφ (A. η + Dissipated power i a microstrip atea ca be calculated by the sum of coductor loss ad the dielectric loss. Coductor loss is P c = Rs ( J J S ds the real part of the surface resistace of the patch the other comes from the groud plae total ca be calculated from the above formula. The dielectric loss ca be calculated usig the formula below; P d ωε = V E dv ωε = h S E ds for thi substrate. Where ω is the radia frequecy, h is the substrate thicess ad ε is the imagiary part of the complex permittivity of the substrate. 76

APPENDIX B CIRCULAR DISK MICROSTRIP ANTENNAS Circular microstrip ateas ca be aalyzed usig cavity model. [11] The wave equatio for the electric fields ca be writte as; ( + E = = π ε / λ (B.1 r I side the cylidrical coordiate system, the wave equatio, E z = E J ( cos φ (B. JBB( are the Bessel fuctios of order. Because the electric field compoet has oly a z compoet ad / z =, the magetic field compoets becomes; H j E z j = = EJ( siφ (B.3 ωµ φ ωµ H φ j Ez j = E J( cos φ ωµ = ωµ (B.4 π jr j e Eφ = cosθ φ φ φ φ θ φ φ φ π ( M (, si( exp[ j si cos( ] d d 4 r (B.5 77

the We ca use resoace approximatio that oly oe mode cotributes at a give frequecy. To get a expressio for the radiatio fields we obtai the followig; jr π a+ h j e Eθ = E χ φ φ φ θ φ φ φ π J( m / acos cos( exp[ j si cos( ] d d 4 r a (B.6 Usig the approximate itegratio accordig to, we get the followig expressio; jr π j e Eθ = ahe J χ φ φ φ θ φ φ φ ( m π cos cos( exp[ ja si cos( ] d 4 r (B.7 π + 1 cos φ cos( φ φexp[ ja siθ cos( φ φ] dφ = π ( j cos φj ( a siθ (B.8 By usig this expressio we get; E θ = j e r jr ahe J ( χ cos φj m ( a siθ (B.9 E θ = j Va e r jr cos φj ( a siθ V = he J ( χ m is ow as the edge voltage at φ= To compute EBφ,B followig useful itegratio ca be used similarly; 78

π + 1 cosφ si( φ φexp[ jasiθ cos( φ φ] dφ = π ( j a J( asiθ siφ cosθ siθ (B.1 ad we get; E φ jr Va e J( a siθ = j si φ cosθ (B.11 r a siθ The effect of substrate material ad the groud plae are ot icluded i the above formulas. Some suitable correctio factors must be tae ito accout for these effects. Followig expressios are obtaied; E θ = j Va e r jr cos φj ( a siθ F ( θ 1 (B.1a E φ = j Va e r jr J( a siθ siφ cosθ F ( θ a siθ (B.1b Where FB1B(θ ad FBB(θ are give below; cosθ ε r si θ F 1( θ = (B.13a ε si θ jε cosθ cot( h ε si θ r r r cosθ F ( θ = (B.13b cosθ j ε si θ cot( h ε si θ r r UField Excited by the Feed Source: The feedig techique of a microstrip atea by a coaxial feed is show i Fig.B 1 below, 79

BB J zj ˆ = z ( ( φ φ y I, π φ π + J z ( φ =, elsewhere x Figure B 1 Coaxial feed of a microstrip atea If there is a curret source J, The wave equatio will be give by the followig formulatio; ( J E + E = jwµ J, where ε = ε ε r (B.14 jwε Let s assume J ad E has oly z compoet ad o z variatio. Accordig to that assumptio; J = J z z = Usig this assumptio we get; ˆ µ J Ez + Ez = jwµ Jz = jw z (B.15 8

The solutio of this equatio i a circular circumstace; E ψ (, φ (B.16a = z A m m m ( + ψ = (B.16b m m ψ m =a = (B.16c Solutios of the above equatios are; ψ m = J ( cos φ =, 1,,, m=1,, 3,. (B.17 m A m = ( ψ _ m m ( jwµ J ds ψ z m ψ m ds (B.18 A 1 = jwµ I =, m=1, (B.19a πa A m = J( m jwµ I m, =, (B.19b πa J ( a( m m A m = ( 1 4 si( J( m m jwµ I 1 (B.19c π( ( a J ( a m m m E z = + J( jwµ I πa m = πa J ( m m J a( ( m m + ( 1 4 si( J ( π ( J( m a J ( m m = 1 m= 1 m ( m m cos φ a (B. 81

8 The iput impedace ca be calculated as ZBiB=VBi B/ IB VBiB=-EBavBh, + = π π φ φ d E E z av, ( 1, (B.1 + = m m m m av d J A E φ π φ π φ φ cos ( 1 ZBiB is calculated as the followig expressio i [11] + = = ] (1 [ ( ( (1 1 m m m m i j a J a J j a h jw Z δ π δ π µ + = = ]( (1 [ cos ( ( si ( 1 1 a j a J J m m eff m m m m δ φ π (B. Iput Impedace; The iput impedace is calculated from the formula; ( 1 m e T i W jw W P V V Z + = (B.3 Where; = h E z dz V

PBTB=PBrB+PBcB+PBdB If we assume =1 mode is the domiat mode the voltage ca be obtaied as; V = A1hJ1( (B.4 1 P r = π ah B1 J 1( a + C1Y 1( a g s 1 (B.5 where; g 1 1 = ( I + I 1 siθdθ s ahη (B.6 π a si( h cosθ I 1 = J 1( a siθ (B.7a cosφ si( h cosθ I = J1( a siθ (B.7b siθ wwm Pc = (B.8 h fµ σ π P = ww taδ (B.9 d e W e πε ε r h ] a = { A 1 [ x ( J1 JJ ] + B1 [ x ( J1 JJ (B.3a 8 a 1 a + C1 [ x ( Y1 YY ] + ( B1C 1 + B1 C1[ x (Y 1J1 JY JY ] } 83

84 1 1 1 1 1 1 ] ( [ ] ( [ { 8 ε πε a r m J J J x B J J J x A h W + + + = (B.3b 1 1 1 ] ( [ a Y Y Y x C + + } ] 1 1 ( [ ( 1 1 3 3 1 1 1 1 1 1 1 a Y J J Y Y J J Y J Y x C B C B + + + + Radiatio Resistace First of all we must calculate the radiated power, dielectric loss ad copper loss, the we ca calculate the radiatio resistace for resoace coditio. Edv E w P v d = taδ ε (B.31 = e e b a m e m e m m d d Y a J a Y J h E w P π δ ε ] ( ( ( ( [ ta = 1 1 ( ( ta e m e m e m e m m d a b b J a J E w P π δ ε Similarly for copper loss calculatio; ( φ π φ d d J J R P b a s c + = (B.3 = 1 1 ( ( a b b J a J w E R P m m m m s c µ π

85 1 I E wh P m r = η (B.33 Where IB1B is; / 1 si ( ( ( si ( si cos = b b J b J a J a a J I m m θ θ θ θ π (B.34 θ θ θ θ d b J b J a J a J m m + si ( ( ( si ( si We ca use the above formulas to calculate the radiatio resistace at resoace frequecy as; T r P V R =, (B.35 PBTB = PBrB+PBcB+PBdB, VBB is the voltage at = b ad φ =. Usig the formulas oe ca derive the radiatio resistace. Directivity ad Gai of a Circular Microstrip Dis Atea; Directivity D is calculated; π η π θ φ θ θ θ φ φ θ 4 ( 4 Re( 1 r P r E E r r P H E H E D = = + = = (B.36 The gai of a atea is calculated as; G = ebrb D

is < Where ebr B calculated by the formula; the radiatio efficiecy of the atea which is < ebrb 1 ad e P P r r r = = (B.37 Pi Pr + Pc + Pd + Psur. 86