Ultrawideband Low-Profile Arrays of Tightly Coupled Antenna Elements

Ultrawideband Low-Proﬁle Arrays of Tightly Coupled Antenna Elements: Excitation, Termination and Feeding Methods

Dissertation

Presented in Partial Fulﬁllment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University

By Ioannis Tzanidis, B.S., M.S.

Graduate Program in Electrical and Computer Engineering

The Ohio State University

2011

Dissertation Committee:

John. L. Volakis, Advisor Kubilay Sertel, Co-advisor Joel T. Johnson Fernando Teixeira Robert Garbacz c Copyright by

Ioannis Tzanidis

2011 Abstract

The need for high resolution imaging radars and high data rate telecommunications has direct implications for the employed antennas. Speciﬁcally, modern RF front-ends require ultra-wideband (UWB) performance using low proﬁle antennas for inconspicuous installation. Other functionalities such as beam steering and multiple input multiple output

(MIMO) are highly desired in an eﬀort to create diverse, multi-functioning antenna systems.

To this end, antenna arrays have been successfully used for beam steering and MIMO applications. However, a key limitation is narrow bandwidth and often bulky size (i.e. non-conformal). Also, in the past, arrays were designed to have minimum mutual coupling.

This itself limited their bandwidth to that of their individual antenna elements.

More recently, a novel class of antennas referred to as “tightly coupled phased arrays”

(TCPAs) were shown to exhibit UWB performance while residing on a thin substrate.

In contrast to traditional arrays, TCPAs utilize the mutual capacitance between array elements to counteract the ground plane inductance. Typically, TCPAs provide very large bandwidths (up to 5 : 1) while maintaining small thickness (λ/10 at the lowest operational frequency). It has been shown that TCPAs are a class of metamaterial antennas, and thus inherently provide signiﬁcant wave slow-down that can be harnessed for miniaturization.

This miniaturization can be exploited for bandwidth increase. Speciﬁcally, utilization of the wave slow-down resulted in a novel UWB interwoven spiral array (ISPA) that achieved

10 : 1 bandwidth using λ/23 thickness.

ii Although the design of tightly coupled arrays is well understood, for a successful implementation several key challenges remain to be addressed. Firstly, finite size arrays suffer from reduced bandwidth due to non-uniform excitation and insufficient mutual coupling.

To alleviate this issue, in this dissertation we propose a novel excitation technique based on the characteristic modes (CM) of the mutual impedance matrix of the array. Unlike uniform excitation, the proposed feeding scheme provides for very low active VSWRs for all array elements, even the ones at the array’s edges. To further improve the finite array bandwidth we considered termination techniques for the edge elements, including resistive and short-/open-circuit terminations. Comparisons between these techniques are provided in terms of the array’s active VSWR, efficiency, realized gain and radiation patterns. We found that simple short-circuit terminations of the edge elements was the most effective.

A second challenge relates to the feeding of the UWB TCPAs. Speciﬁcally, designing an UWB balun/impedance transformer while conforming to stringent space, weight, cost, and power constraints is not trivial. To address these issues, we designed a novel UWB feed with ∼ 4 : 1 bandwidth having an impedance transformation ratio of 50Ω − 200Ω (or 4 : 1) as well.

The above contributions led to the development of a 7 × 7 tightly coupled dipole array.

Measurements showed that the dipole array can achieve very low VSWRwith a measured realized gain of approximately 3dBi at 200MHz and 7dBi at 600MHz.Theaperture eﬃciency of the array was numerically estimated at about 90% throughout the 200MHz−

600MHz band.

iii This is dedicated to my parents Iakovos-Maria, to my brother Anestis, and to my love

Aspasia

iv Acknowledgments

I would like to thank the following friends who have supported me and through our discussions broadened my perspective on antennas and electromagnetics: Stylianos Dosopou- los, George Trichopoulos, Erdinc Irci, Tao Peng, Will Moulder, Jon Doane, Faruk Erkmen,

Nathan Smith, Jae Young, Haksu Moon, Jing Zhao, Gil young, Jeﬀ Challas, Ugur Olgun,

Nil Apaydin, and Elias Alwan. And of course the older fellows: Gokhan Mumcu, Salih

Yarga, Yijun Zhou, Brad Kramer and Lanlin Zhang.

I would like to thank separately, researchers Dr. Dimitris Psychoudakis and Dr. Stavros

Koulouridis for our discussions on various antenna topics, and for their guidance in conducting antenna measurements. Their support and friendship is very much appreciated.

I would like to thank professors Prof. Robert Garbacz, Prof. Joel Johnson and Prof.

Fernando Teixeira for being my dissertation reading committee and for kindly sharing with me their perspectives on this work. Also, I would like to thank professors Prof. Jin-Fa Lee, and Prof. Roberto Rojas for serving in my candidacy exam committee, and Prof. Jin-Fa

Lee, Prof. Roberto Rojas, Dr. Chi-Chih Chen, and Prof. Ed Overman for serving in my qualiﬁer exam.

I would like to extend my respect and appreciation to Dr. Chi-Chih Chen, who co- advised me during the ﬁrst two years at ElectroScience Laboratory. Dr. Chen initiated me into the mysteries of spiral antennas, antenna miniaturization, and into conducting antenna measurements. Thank you Chi-Chih.

v I would like to express my gratitude, respect and admiration for my co-advisor Dr.

Kubilay Sertel. Throughout my course at ElectroScience Lab., Kubi has been one of the most inﬂuential people and a role model for me. His mentorship and guidance in conducting research are invaluable. I wish every student had an advisor like Kubi. Thank you so much for everything you have done for me Kubi.

I would like to express my gratitude for having Prof. John Volakis as my mentor.

Few people in the world will ever have a chance to study and learn from such a charismatic professor. I would like to thank him for giving me the opportunity to study at ElectroScience

Laboratory and for his continuous support throughout my 5 years at ElectroScience. Thank you very much Prof. Volakis.

Last but not least, I would like to express my respect to the staﬀ of the ElectroScience

Laboratory because with their hard work and dedication they made my life easier.

vi Vita

August 6, 1983 ...... Born - Volos, Greece

2006 ...... B.S. Electrical and Computer Engineer- ing, Democritus University of Thrace, Xanthi, Greece 2010 ...... M.S.ElectricalEngineering, The Ohio State University, Columbus, Ohio, USA 2006-present ...... GraduateResearchAssociate, The Ohio State University, Columbus, Ohio, USA

Publications

Journal Publications

I. Tzanidis, K. Sertel, J. L. Volakis, “Characteristic excitation taper for ultra-wideband tightly coupled antenna arrays”, accepted for publication in IEEE Transactions Antennas and Propagation.

N. K. Nahar, J. Y. Chung, I. Tzanidis, K. Sertel, J. L. Volakis, “Optically Transparent RF-EO Aperture With 20:1 Bandwidth”, Microwave and Optical Technology Letters,Vol. 53, No. 8, 2011.

I. Tzanidis, K. Sertel, J. L. Volakis, “Interweaved Spiral Array (ISPA) With a 10:1 Band- width on a Ground Plane”, IEEE Antennas and Wireless Propagation Letters,Vol.10, 2011.

I. Tzanidis, C-C. Chen, J. L. Volakis, “Low Proﬁle Spiral on a Thin Ferrite Ground Plane for 220-500 MHz Operation”, IEEE Transactions on Antennas and Propagation,Vol.58, No. 11, 2010.

vii Conference Publications

Nahar, N.K., Tzanidis, I.I., Sertel, K., Volakis, J.L., “Ultra Wideband Transparent RF Aperture for Electro-Optical Integration”, Antennas and Propagation Symposium,Jul. 2010.

I. Tzanidis, K. Sertel, J. L. Volakis, “An Interweaved Spiral Array (ISPA) Providing a 10:1 Bandwidth Over a Ground plane”, Antennas and Propagation Symposium, Jul. 2010.

J. L. Volakis, K. Sertel, I. Tzanidis, “Small Wideband Antennas Based On Photonic Crys- tals”, European Conference on Antennas and Propagation, 2010.

J. L. Volakis, J. A. Kasemodel, C.C. Chen, K. Sertel, I. Tzanidis, “Wideband Conformal Metamaterial Apertures”, International Workshop on Antenna Technology, 2010.

I. Tzanidis, C.-C. Chen, J.L. Volakis, “Low Proﬁle, Cavity Backed Spiral on Thin Fer- rite Ground Plane for High Power Operation above 200MHz”, Antennas and Propagation Symposium, Jun. 2009.

I. Tzanidis, C.-C. Chen, J.L. Volakis, “Smaller UWB Conformal Antennas for VHF/UHF Applications with Ferrodielectric Loadings”, Antennas and Propagation Symposium,Jul. 2008.

I. Tzanidis, S. Koulouridis, K. Sertel, D. Hansford, J.L. Volakis, “Characterization of Low- Loss Magnetodielectric Composites for Antenna Size Reduction”, Antennas and Propaga- tion Symposium, Jul. 2008.

I. Tzanidis, C.-C. Chen, J.L. Volakis, “Antenna Miniaturization Using Impedance Matched Ferrites”, Antenna Measurement Techniques Association, Nov. 2007.

Student Awards

1st place in Student Paper Competition in Antennas and Propagation Symposium, Toronto, Canada, 2010. Paper title: An Interweaved Spiral Array (ISPA) Providing a 10 : 1 Band- width Over a Ground plane.

viii Honorable mention in Student Paper Competition in Antennas and Propagation Sympo- sium, Charleston, SC, USA, 2009. Paper title: Low Proﬁle, Cavity Backed Spiral on Thin Ferrite Ground Plane for High Power Operation above 200MHz.

Fields of Study

Major Field: Electrical and Computer Engineering

Studies in: Electromagnetics Antennas RF Circuits Mathematics

ix Table of Contents

Page

Abstract...... ii

Dedication...... iv

Acknowledgments...... v

Vita...... vii

ListofTables...... xiii

ListofFigures...... xiv

1. Introduction to Ultra-wideband (UWB) Low-proﬁle Phased Array Design . . . 1

1.1State-of-the-ArtinUWBTightlyCoupledPhasedArrays...... 4 1.1.1 CurrentSheetArray...... 5 1.1.2 LongSlotArray...... 5 1.1.3 TaperedSlotorVivaldiArrays...... 7 1.1.4 SpiralArrays...... 8 1.2FeedingTechniquesforWidebandArrays...... 8 1.2.1 DipoleArrayFeedingTechniques...... 9 1.2.2 TaperedSlotArrayFeedingTechniques...... 14 1.3RemainingChallengesforWidebandArrays...... 14 1.4ContributionsandDissertationOutline...... 15

2. Operation Principles of Inﬁnite Tightly Coupled Phased Arrays (TCPA) . . . . 19

2.1Weaklyvs.TightlyCoupledPhasedArrays...... 19 2.2EvolutionofWidebandTightlyCoupledArrays...... 22 2.2.1 “Inﬁnite-Bandwidth” Connected Arrays in Free Space ...... 23 2.2.2 BandwidthDegradationAboveaGroundPlane...... 25

x 2.2.3 UWB Tightly Coupled Phased Arrays Above a Ground Plane . . 27 2.3TCPAsfroma“Metamaterials”Perspective...... 31 2.4Conclusions...... 33

3. ANovelUWBInterwovenSpiralArray(ISPA)...... 34

3.1DevelopmentofISPAUnitCell...... 34 3.2TheISPAfromanImpedanceMatchingPerspective...... 42 3.3 Validation of a 5 × 5ISPAArray...... 45 3.4Conclusions...... 47

4. DesignofFiniteSizeTCPAs...... 48

4.1OverlappingDipoleArrayElementDesign...... 48 4.2 7 × 7ArrayofOverlappingDipoles...... 51 4.2.1 Active Impedance and Bandwidth with Uniform Current Excitation 54 4.2.2 Active Impedance and Bandwidth with Uniform Power Excitation 57 4.3FiniteArrayEdgeEﬀects...... 59 4.4Conclusions...... 59

5. ExcitationofFiniteSizeTCPAsforBroadbandMatching...... 61

5.1CharacteristicModesofFiniteArrayStructures...... 62 5.1.1 CharacteristicExcitationofFiniteArrays...... 63 5.2 Example: 7 × 7 Array of Overlapping Dipoles Over a Ground Plane . . . 69 5.3CharacteristicExcitationforImprovedBandwidth...... 73 5.4PerformanceValidationUsingFull-waveSimulations...... 78 5.5Conclusions...... 81

6. Edge Element Termination Techniques for Uniformly Excited UWB TCPAs . . 82

6.1TechniquesforCalculatingEdgeElementTerminations...... 83 6.1.1 Array Termination Method Based on Mutual Impedance Matrix . 83 6.1.2 AlternativeMethodBasedonScatteringMatrix...... 86 6.2ResistiveTerminationofEdgeElements...... 87 6.3Short-/Open-CircuitTerminationsofEdgeElements...... 92 6.4 A Simpliﬁed 7 × 7 Overlapping Dipole Array with Short-circuited Edge Elements...... 99 6.5Conclusions...... 99

7. WidebandBalun/TransformersforTCPAFeeding...... 103

7.1BalancedandUnbalancedTransmissionLines...... 105

xi 7.2CommonModeandDiﬀerentialMode...... 106 7.3SuitableBalunsTypesforTCPAs...... 107 7.4ANovelUWBPrintedBalunforTCPAFeeding...... 109 7.4.1 Initial Feed Design With Coiled Transformer Balun ...... 110 7.4.2 Development of Planar Ultra-wideband Balun/Trans-former . . . 114 7.5DiscussiononBalunDesign...... 124 7.6Conclusions...... 124

8. Measurements of 7 × 7OverlappingDipoleArrayPrototype...... 126

8.1DesignofCorporateFeedNetwork...... 128 8.2 7 × 7ArrayMeasurementsforBroadsideScan...... 129 8.2.1 VSWRMeasurements...... 129 8.2.2 RealizedGainandPatternMeasurements...... 130 8.3 7 × 7 Array Measurements for 30◦ H-planeScan...... 140 8.3.1 ElementPhasingviaTimeDelay...... 140 8.3.2 VSWRMeasurements...... 142 8.3.3 RealizedGainandPatternMeasurements...... 143 8.3.4 BeamSquintvs.FrequencyPhenomenon...... 150 8.4Conclusions...... 150

9. ConclusionsandFutureWork...... 153

9.1 Summary and Conclusions ...... 153 9.2FutureWork...... 156

Appendices 158

A. Electrical Speciﬁcations of Power Dividers Used in 7 × 7 Array Measurements . 158

Bibliography...... 160

xii List of Tables

Table Page

1.1 Summary table of state-of-the-art in wideband tightly coupled arrays. . . . 9

7.1ElectricalspeciﬁcationsofthebalunshowninFig.7.5(a)...... 111

7.2CurrentamplitudeandphaseonthetwostripsoftheCPSline...... 116

7.3CurrentamplitudeandphaseonthetwostripsoftheCPSline...... 120

8.1 Phase diﬀerence between consecutive elements within each array column for scanning the beam to θ =30◦ intheH-plane...... 142

xiii List of Figures

Figure Page

1.1 (a) 3 × 6 CSA array for VHF/UHF bands designed to be ﬂush-mounted into a cavity [35]. (b) A prototype UHF test array (1.12m × 2.24m)with4× 8 elements was constructed for 150−600MHz experiment [42]. (c) 144 element Vivaldi array [59]. (d) 8 × 8 dual-polarized planar array of ﬂared-notches [39]. 6

1.2 (a) A “bunny-ear” ﬂared dipole array [44] is a reduced-height version of the Vivaldi or Tapered Slot arrays. (b) 5 × 10 balanced antipodal vivaldi array (BAVA)[13]...... 7

1.3 (a) Feed organizer [11] for feeding the CSA antenna [35, 52]. (b) Feeding of thePUMAarray[30]...... 11

1.4 (a) A balun proposed for operation at 8 − 12GHz [36, 37]. (b) A balanced transformer for common mode rejection and operation at 6 − 12GHz [6]. . 13

1.5TypicalVivaldiarrayfeed...... 14

2.1 A weakly coupled array. The elements patterns have low side-lobes to ensure minimummutualcoupling...... 20

2.2 A tightly coupled phased array (TCPA) above a ground plane. The elements areplacedveryclosetoachievestrong,yetcontrolledcoupling...... 21

2.3 An 8 × 8overlappingdipolearrayanditsunitcell...... 22

2.4 (top left) Wheller’s inﬁnite uniform current sheet and (top right) its practical implementation with an array of connected dipoles. (bottom left) A frequency independent implementation of Wheeler’s current sheet with self- complementary bowties. (bottom right) Input impedance of connected, inﬁ- nitedipoleandbowtiearraysinfreespace...... 24

xiv 2.5 (top left) An array of connected dipoles over a ground plane. (top right) Radiation resistance and (bottom left) reactance of the array in free space and at distance d = λ/2 above a ground plane. (bottom right) VSWR of inﬁnite, connected dipole array in free space and over a ground plane. . . . 26

2.6 (top left) Equivalent circuit of connected dipole array in free space. (top right) Equivalent circuit of connected dipole array at height h above a ground plane. (bottom) An array of capacitively coupled dipoles at height h above a ground plane and its equivalent circuit. These circuits model the input impedance of one element within an inﬁnite array...... 28

2.7 (left) Input impedance of one element of an inﬁnite dipole array above a ground plane. The eﬀect of the mutual capacitance is demonstrated. (right) The capacitively coupled dipole array achieves almost double bandwidth as comparedtoaconnecteddipolearray...... 30

2.8Equivalentcircuitofmetamaterialarrayunitcell[18]...... 32

3.1 ISPA unit cell and its dimensions in mm. The element is fed at the center. 35

3.2 (a) Interconnected (i.e. continuous) spiral array unit cell without interwoven arms. (b) Simulated VSWR in free space and above a PEC ground plane (7mm and 8.2mm height). Reference impedance was chosen 188Ω...... 37

3.3 (a) Unit cell of interconnected bowtie array. (b) unit cell of the CSA dipole array. (c) Comparison of real and (d) imaginary impedance of the conformal bowtie, CSA dipole and interconnected spiral (not interwoven) arrays (see Fig.3.2(a)forunitcelloflatter)...... 38

3.4 (a) Unit cell of disconnected spiral array. (b) Simulated VSWR...... 40

3.5 (a) VSWR of ISPA array using HFSS ver. 10 and FEKO suite ver. 5.5. Reference impedance was chosen 200Ω and 250Ω respectively. (b) Total, RHCP and LHCP directivity calculated with HFSS ver. 10 as compared to the directivity of a uniformly excited aperture of area A=8.2mm × 8.2mm.41

3.6 ISPA equivalent circuit with multi-stage network for increasing the bandwidth. 43

xv 3.7 Geometry of interwoven spiral array (ground plane is not shown). The multistage matching network shown in Fig. 3.6 is implemented by the spiral shaped transmission line. Mutual coupling is controlled by weaving the arms ofadjacentspiralsintoeachother...... 44

3.8 (a) Fabricated 5 × 5 ISPA array prototype. The central element is fed while the rest are terminated in 200Ω resistors. (b) Measured and simulated VSWR.46

4.1 Unit cell of inﬁnite overlapping dipole array above ground plane. The lateral dimensions of the unit cell were 2/7 × 2/7 and the distance from the ground . plane to the feed point of the dipole was 6 . The dielectric board had r =38, tanδ =0.007 and was 20mils thick...... 50

4.2 Real and imaginary active input impedance of an element of an inﬁnite array. ThearrayunitcellisshowninFig.4.1...... 51

4.3 Active VSWR of an element of the inﬁnite overlapping dipole array of Fig. 4.1.Thereferenceimpedancewaschosen200Ω...... 52

4.4 7×7 overlapping dipole array on a ground plane. Element numbering denotes the (row,column) of each element in the array...... 53

4.5 Self-impedances of center row elements. Each line segment shows the variation of the self-impedance along the center row of elements shown in Fig. 4.4. The impedances are plotted at four frequencies: 200(×), 300(+), 400(2), and 600MHz(•)...... 54

4.6 Active-impedances of center row elements with uniform current excitation. Each line segment shows the variation of the active-impedance along the center row of elements shown in Fig. 4.4. The impedances are plotted at four frequencies: 200(×), 300(+), 400(2), and 600MHz(•). The corresponding active impedance of the inﬁnite array element for the same frequencies is annotatedwiththickermarkers...... 56

4.7 Active VSWR for all 49 elements. We assumed uniform current excitation andequalreferenceimpedances(200Ω)forallelements...... 57

4.8 Active VSWR for all 49 elements. We assumed uniform power excitation and equal reference impedances (200Ω) for all elements...... 58

xvi 5.1 (a) Tightly coupled dipole array over a ground plane and associated mode current distributions at their resonance frequency. (b) Typical modal significance plots for the array in Fig. 5.1(a); modes resonate approximately at the frequencies where aperture size D is multiples of half-wavelength. (c) Radiation patterns corresponding to modes 1 − 5atφ =0◦, 90◦ and θ =90◦ cuts...... 66

5.2 Coprorate network VSWRvs. element feed line VSWRs...... 70

5.3 7 × 7 overlapping dipole array on a ground plane. The array size was size 2 × 2 and height 6. The ground plane size is 4 × 4...... 71

5.4ModesigniﬁcanceplotforthearrayofFig.5.3...... 72

5.5 (a) Current distribution of mode 1 at 472MHz. Element numbering and array orientation are shown in Fig. 5.3. (b) Mode 1 radiation pattern at φ =0◦, 90◦ and θ =90◦ planes...... 73

5.6 Active-impedances of center row elements under mode 1 excitation. Each line segment shows the variation of the active-impedance along the center row of elements shown in Fig. 4.4. The impedances are plotted at four frequencies: 200(×), 320(+), mode 1 resonance at 472(2), and 600MHz(•)...... 74

5.7 (left to right) Active VSWR for all array elements, line impedances Z0i, excitation coeﬃcients |ai|, and mismatch eﬃciency. (a) Excitation based on current distribution of mode 1 at 472MHz. (b) Uniform power excitation. Element numbering is shown in Fig. 5.3. Overlap section length was s =2mm.75

5.8 Mode signiﬁcance plot for the array of Fig. 5.3 with longer overlapping section (s =20mm)...... 76

5.9 (left to right) Active VSWR for all array elements, line impedances Z0i, excitation coeﬃcients |ai|, and array mismatch eﬃciency. Element numbering is shown in Fig. 5.3. Overlap section length was s =20mm. (a) Excitation based on mode 1 at 320MHz.(b)Uniformexcitation...... 77

5.10 (a) Co-pol. and (b) cross-pol. realized gain of array shown in Fig. 5.3 with overlapping section length s =20mm. For comparison the array was excited withCMexcitationanduniformexcitation...... 79

xvii 5.11 Simulated realized gain radiation patterns (dB scale) of the array shown in Fig. 5.3 with the characteristic mode excitation shown in Fig. 5.9(a) and the uniform excitation shown in Fig. 5.9(b). (a) 200MHz,co-pol,φ =0◦ plane. (b) 400MHz,co-pol,φ =0◦ plane. (c) 600MHz,co-pol,φ =0◦ plane. (d) 200MHz, cross-pol, φ =0◦ plane. (e) 400MHz, cross-pol, φ =0◦ plane. (f) 600MHz, cross-pol, φ =0◦ plane.(g) 200MHz,co-pol,φ =90◦ plane. (h) 400MHz,co-pol,φ =90◦ plane. (i) 600MHz,co-pol,φ =90◦ plane. (j) 200MHz, cross-pol, φ =90◦ plane.(k) 400MHz, cross-pol, φ =90◦ plane. (l) 600MHz, cross-pol, φ =90◦ plane...... 80

6.1 (a) A 2-element array used to demonstrate the collapse of a 2-port to 1-port. (b)Theveninequivalentofaloadedarrayelement...... 84

6.2 7 × 7 array of overlapping dipoles. The array size was 2 × 2 and thickness 6 from the ground plane. The ground plane size was 4 × 4. Overlapping section length was s =20mm...... 88

6.3 Active VSWRs of elements of the array depicted in Fig. 6.2. Terminated rows and/or columns are given on top of the ﬁgures. Uniform excitation of the active elements was assumed. Termination impedances and feed-line impedances all assumed 200Ω. Dashed line corresponds to corporate network VSWR...... 89

6.4 (left) Mismatch eﬃciency. (middle) total eﬃciency. (right) Estimated and calculated realized gain of array shown in Fig. 6.2 with the 1st,2nd,6th,and 7th columns terminated in 200Ω resistors...... 91

6.5 Computed realized gain radiation patterns (dB scale) of the array shown in Fig. 6.2 with the 1st,2nd,6th,and7th columns terminated in 200Ω resistors and the rest of the elements excited uniformly. (a) co-pol, φ =0◦ plane. (b) cross-pol, φ =0◦ plane. (c) co-pol, φ =90◦ plane. (d) cross-pol, φ =90◦ plane. 93

6.6 (a) Active VSWR, (b) total array eﬃciency and (c) realized gain assuming short-circuit (left), open-circuit (middle) and short-/open-circuit termination (right) of the two edge columns on each side of the array. In the active VSWR plots, the red solid lines correspond to the 21 active elements and the blue dashed line to the corporate network VSWR...... 94

xviii 6.7 Computed realized gain radiation patterns (dB scale) of the array shown in Fig. 6.2 with the 1st,2nd,6th,and7th columns terminated in short-circuits and the rest of the elements excited uniformly. (a) co-pol, φ =0◦ plane. (b) cross-pol, φ =0◦ plane. (c) co-pol, φ =90◦ plane. (d) cross-pol, φ =90◦ plane. 96

6.8 Computed realized gain radiation patterns (dB scale) of the array shown in Fig. 6.2 with the 1st,2nd,6th,and7th columns terminated in open-circuits and the rest of the elements excited uniformly. (a) co-pol, φ =0◦ plane. (b) cross-pol, φ =0◦ plane. (c) co-pol, φ =90◦ plane. (d) cross-pol, φ =90◦ plane. 97

6.9 Computed realized gain radiation patterns (dB scale) of the array shown in Fig. 6.2 with the 1st,2nd,6th,and7th columns terminated in short-/open- circuits and the rest of the elements excited uniformly. (a) co-pol, φ =0◦ plane. (b) cross-pol, φ =0◦ plane. (c) co-pol, φ =90◦ plane. (d) cross-pol, φ =90◦ plane...... 98

6.10 7×7 array of overlapping dipoles with short-circuited edge elements replaced with long strips. The array size was 2 × 2 and thickness 6 from the ground plane. The ground plane size was 4 × 4...... 100

6.11 Comparison between fully excited array, array with short-circuit terminations and resistive terminations at the edges. (a) Active VSWR. (b) Co-pol and cross-pol realized gain. (c) Total eﬃciency. The array is shown in Fig. 6.2 and in the terminated array the 1st,2nd,6th,and7th columns were terminated in short-circuit. All active elements excited equally with 200Ω feed lines. . . 102

7.1 Schematic of feed conﬁguration for tightly coupled dipole arrays. A balun performs the transition between an unbalanced 50Ω coaxial line to a balanced 200Ω line required for feeding the array...... 104

7.2(a)Unbalancedtransmissionline.(b)Balancedtransmissionline...... 106

7.3 (a) Generic balun circuit. (b) Coil based transformer. (c) Transmission line transformer...... 108

7.4 (a) Microstrip (MS) to coplanar strip (CPS) transition. The MS line is fed by a SMA connector attached to the ground plane on the back side. (b) Comparisonbetweenmeasuredandsimulateddata...... 112

xix 7.5 (a) Commercial balun bridging a 50Ω coplanar waveguide line with a 200Ω coplanar strip line. (b) Schematic representation of CPW fed by a coaxial cable...... 113

7.6 CPW to CPS transition for 50Ω − 100Ω transformation. (a) Feed model and (b) simulated S−parameters...... 115

7.7 CPW to CPS transition for 100Ω − 200Ω transformation. (a) Feed model and (b) simulated S−parameters...... 117

7.8 (a) Combination in parallel of two feeds for 50Ω − 200Ω transformation. (b) S-parameters...... 118

7.9MeanderedUWBbalunfor50Ωto200Ωtransformation...... 119

7.10(a)Singleand(b)back-to-backfabricatedmeanderedbaluns...... 122

7.11 (a) Simulated and (b) measured data for the single and back-to-back mean- deredbaluns...... 123

8.1 (a) 7 × 7 array of overlapping dipoles with 21 active and 28 short-circuited elements. Part of the element feeds (CPW and CPS) are incorporated in the model. A gap is left for the commercial balun to ﬁt in. (b) Active VSWR of 21 active elements. Blue dashed line is the corporate network VSWR..127

8.2 Feeding network of the 7 × 7 overlapping dipole array with 21 active and 28 short-circuited elements. This network was used for broadside scanning (no phasingoftheelements)...... 128

8.3 (a) 7 × 7 tightly coupled dipole array breadboard in the ElectroScience Lab. compactrangefortesting.(b)Close-upofthearray...... 130

8.4 Measurement set up in ElectroScience Laboratory compact range...... 132

8.5 Simulated and measured (a) corporate network VSWRand (b) realized gain for broadside scan of the 7 × 7 array of dipoles shown in Fig. 8.3(b). . . . . 133

8.6 Simulated cross-pol realized gain at broadside (θ =0◦) and at two directions slightly oﬀ broadside: (θ =1◦, φ =1◦)and(θ =1◦, φ =2◦)...... 134

xx 8.7 (a) Simulated and (b) measured realized gain radiation patterns of the 7 × 7 array of dipoles shown in Fig. 8.3(b) at 200MHz...... 135

8.8 (a) Simulated and (b) measured realized gain radiation patterns of the 7 × 7 array of dipoles shown in Fig. 8.3(b) at 300MHz...... 136

8.9 (a) Simulated and (b) measured realized gain radiation patterns of the 7 × 7 array of dipoles shown in Fig. 8.3(b) at 400MHz...... 137

8.10 (a) Simulated and (b) measured realized gain radiation patterns of the 7 × 7 array of dipoles shown in Fig. 8.3(b) at 500MHz...... 138

8.11 (a) Simulated and (b) measured realized gain radiation patterns of the 7 × 7 array of dipoles shown in Fig. 8.3(b) at 600MHz...... 139

8.12 Beam steering via time delay phasing. Extra cable sections with variable lengths (a, 2a, ...) were added to create the necessary phase diﬀerence between the elements and tilt the array beam maximum to 30◦ at the H-plane. 141

8.13 Simulated and measured (a) corporate network VSWRand (b) realized gain of the 7 × 7 array shown in Fig. 8.3(b). These plots correspond to scanning at θ =30◦ intheH-plane...... 144

8.14 (a) Simulated and (b) measured realized gain radiation patterns of the 7 × 7 array shown in Fig. 8.3(b) at 200MHz. These plots correspond to scanning at θ =30◦ intheH-plane...... 145

8.15 (a) Simulated and (b) measured realized gain radiation patterns of the 7 × 7 array shown in Fig. 8.3(b) at 300MHz. These plots correspond to scanning at θ =30◦ intheH-plane...... 146

8.16 (a) Simulated and (b) measured realized gain radiation patterns of the 7 × 7 array shown in Fig. 8.3(b) at 400MHz. These plots correspond to scanning at θ =30◦ intheH-plane...... 147

8.17 (a) Simulated and (b) measured realized gain radiation patterns of the 7 × 7 array shown in Fig. 8.3(b) at 500MHz. These plots correspond to scanning at θ =30◦ intheH-plane...... 148

xxi 8.18 (a) Simulated and (b) measured realized gain radiation patterns of the 7 × 7 array shown in Fig. 8.3(b) at 600MHz. These plots correspond to scanning at θ =30◦ intheH-plane...... 149

8.19 (a) Normalized element pattern, array factor and total pattern for a 7−element linear dipole array above a ground plane. The element spacing was 2/7, exactly like our 7×7 array. (b) Measured, simulated and estimated beam squint vs.frequency...... 152

A.1 Electrical speciﬁcation of 1 : 8 power dividers...... 158

A.2 Electrical speciﬁcation of 1 : 3 power dividers...... 159

xxii Chapter 1: Introduction to Ultra-wideband (UWB) Low-proﬁle Phased Array Design

Someday, someone will build a multifunction radar antenna that scans a 90o cone electronically, is only eight inches thick, rejects rain clutter, weighs 1600lbs,searches 360o

Raytheon advertisement, 1967

The most vital component of a radar or telecommunication system is its antenna. The role and importance of the antenna is easy to understand once we realize that it performs a role very similar to the human eye: it receives information from the surrounding environment and transfers it through a cable (much like the optical nerve) to a detector, which, like our brains, interprets the received information. Without doubt, the quality and accuracy of the interpretation of any signal is highly related to the features of the employed antenna such as its bandwidth, radiation pattern, gain and polarization.

In order to acquire images from high altitudes and long ranges (> 40Km)newgeneration

synthetic aperture radars (SAR) need to operate at lower frequencies than typical SAR,

going as low as 100MHz. This is due to the fact that wave attenuation in free space

is proportional to the square of the frequency, implying that low frequencies propagate

at longer distances. Low frequency operation is also useful for penetration of common

1 target obscuration techniques. Moreover, for obtaining high resolution images (even a few millimeters in resolution!) modern SARs operate in ultra-wide frequency bands (UWB), typically extending up to 1GHz. This is because UWB SAR allows use of short pulse widths and wideband chirping, leading to improved range resolution and signal to noise ratio (SNR) [64]. Operation over UWB (100MHz − 1GHz) also implies more spectral information of target reﬂectivity and therefore better recognition of the target’s features.

Besides radars, new generation of communication networks will be based on multi- functional multiple input multiple output (MIMO) antennas that setup a wireless grid through which nodes exchange information at high data rates. To accommodate that, the wireless channels need to be UWB, utilizing the whole currently available bandwidth between 698MHz − 2.7GHz.

To this end, antennas with bandwidths approaching 5 : 1 or 10 : 1 are required. While the antenna bandwidth requirements are increasing, the desired antenna size is continu- ously shrinking. In fact, very thin or low-proﬁle antennas (<λ/20 at lowest operational frequency) are necessary for inconspicuous installation and minimum disturbance of the platform aesthetics or the vehicular aerodynamics. Ideally, antennas that can conform to the shape of the platform are desired.

In addition to the bandwidth and thickness requirements, antennas need to allow for other vital functions, such as beam and null steering. This is very crucial both for radar and telecommunication applications. In the former case, it is useful for tracking multiple targets and minimizing interference from unwanted sources (jamming), whereas in the latter case it is necessary for versatile point-to-point communication and also for reducing noise coming from designated locations. Besides beam steering, other antenna features such as polarization diversity and high power operation are much desired. However, the aforementioned

2 stringent antenna requirements mandated by the emerging RF technologies, seem to be in conﬂict with traditional wideband antenna design principles.

In particular, creating a single aperture that combines wideband operation and sub- wavelength thickness is a perennial challenge. It is now well known that ultra-wideband

(UWB) antennas lose their bandwidth when placed above a ground plane. This happens because as the frequency gets lower the electrical distance from the ground plane becomes smaller and eventually the antenna gets short-circuited (i.e. radiation resistance becomes zero). Another bandwidth limiting factor associated with conformal antenna installation, is the inductance introduced by the ground plane1. One solution to deal with bandwidth

degradation of conformal UWB antennas was proposed in [71]. The authors used a thin,

low-loss ferrite layer on the ground plane to enhance the bandwidth of an UWB spiral

antenna at low frequencies (around 220MHz). Although attractive, ferrites are known to

increase the antenna weight signiﬁcantly and this is a drawback.

Apart from the known bandwidth vs. thickness trade-oﬀs, beam steering or MIMO

applications require the existence of several excitation ports on the aperture to allow for

proper phase control or multiple input/output conﬁguration. In addition, a multi-port an-

tenna would be useful for distributing high input power on the aperture. A well known class

of multi-port antennas are the phased arrays. However, traditional phased antenna arrays

are narrowband and bulky. Their bandwidth is limited due to inter-element (or mutual)

coupling at low frequencies. To minimize coupling and increase bandwidth, elements with

high directivity are used such as horn antennas, but this comes at the expense of a very

bulky array.

1Detailed explanations are provided in Chapter 2.

3 Recently, a novel class of antennas referred to as tightly coupled phased arrays (TCPAs)

has been shown to uniquely accommodate UWB performance and low thickness proﬁle. In

using TCPAs, the basic idea is to bring very small (λ/10) elements very close to each other.

The strong capacitive coupling between them is utilized to counteract the ground plane

inductance. Although this counteraction occurs at a single frequency, that alone yields a

2× increase in the array bandwidth, reaching 5 : 1. Of course, at higher frequencies the array is limited by grating lobes as well as the λ/2 reﬂection from the ground plane. At the same time, the array height from the ground plane is maintained at around λ/10 at the

lowest operational frequency. Another feature that makes tightly coupled arrays attractive

is their multiple excitation ports. Feeding of the array elements in groups could either allow

for beam steering (by phasing the diﬀerent groups), or MIMO applications (some groups

receive and others transmit).

The above features render tightly coupled phased arrays unique. Recently, several UWB

TCPA prototypes were developed and tested. In the following section, we review the current

state-of-the-art in modern ultra-wideband tightly coupled phased arrays.

1.1 State-of-the-Art in UWB Tightly Coupled Phased Ar- rays

The basic types of elements used currently in UWB tightly coupled phased arrays are

dipoles, long slots, tapered slots, and spirals. Here, we review the performance of these

arrays based on prototypes published in the literature. We compare them in terms of

bandwidth and electrical thickness from the ground plane.

4 1.1.1 Current Sheet Array

By manipulating one of the previously most dreaded phenomena occurring in phased arrays, namely the mutual coupling, Munk initiated a new class of arrays, referred to as tightly coupled phased arrays [35, 52]. These arrays were comprised of electrically small

(λ/10) dipoles connected via interdigital capacitors and placed above a metallic ground plane at height λ/10, at the lowest operational frequency. Most notably, the strong mutual coupling between dipoles enabled the unprecedented 4.5 : 1 impedance bandwidth.

The ﬁst antenna demonstrating that concept was the current sheet array (CSA). A

3 × 6 version of the CSA is shown in Fig. 1.1(a) [35, 52]. Munk suggested several ways for further increasing the bandwidth of the CSA array. Among them were the use of dielectric superstrates, magnetic substrates, or lossy absorber layers placed on the ground plane. The use of low-loss dielectric superstrates2 enhances the CSA bandwidth signiﬁcantly (up to

10 : 1), but at the expense of signiﬁcantly increasing its height.

Having the CSA as a benchmark, various tightly coupled dipole arrays have been recently

proposed. These arrays feature novelties mainly in the feeding of dipole elements and scan

performance [30, 37, 38]. Besides dipole arrays, tightly coupled bowtie arrays, such as the

four square array [75] have been proposed.

1.1.2 Long Slot Array

Instigated by Munk’s concept, an array comprised of log slots (shown in Fig. 1.1(b))

above a ground plane was presented in [42]. The long slots were excited by an array

of connected dipoles spaced at λ/2 (at highest operational frequency) and placed closely

2Dielectric superstrates of tapered thickness and dielectric constant act like impedance matching sections that match the array impedance to free space impedance. From that perspective the array acts like the tapered slot array, which achieves UWB performance due to its long tapered slot.

5 (a) (b)

Figure 1.1: (a) 3 × 6 CSA array for VHF/UHF bands designed to be ﬂush-mounted into a cavity [35]. (b) A prototype UHF test array (1.12m×2.24m)with4×8elements was constructed for 150 − 600MHz experiment [42]. (c) 144 element Vivaldi array [59]. (d) 8 × 8 dual-polarized planar array of ﬂared-notches [39].

beneath the slots. Due to the feeding method, the long slot array can be viewed as a connected dipole array placed under a slotted frequency selective surface (FSS). This design

6 (a) (b)

Figure 1.2: (a) A “bunny-ear” ﬂared dipole array [44] is a reduced-height version of the Vivaldi or Tapered Slot arrays. (b) 5 × 10 balanced antipodal vivaldi array (BAVA) [13].

was also low-proﬁle, about λ/8 at the lowest operation frequency. The bandwidth of the long slot array was 4 : 1. A prototype of the long slot array is shown in Fig. 1.1(b) [42].

1.1.3 Tapered Slot or Vivaldi Arrays

Tapered slot or Vivaldi elements have also been used in UWB arrays, referred to as

Tapered Slot Arrays or Vivaldi arrays [59] (see Fig. 1.1(c)). By making the elements tall enough (2 ∼ 3λ at the highest operational frequency) the array can sustain as much as

10 : 1 bandwidth. Another implementation of a tapered slot arrays was presented in [39]

(see Fig. 1.1(d)). However, for certain applications arrays of that thickness can not be considered low-profile. Efforts to reduce the array profile were conducted in [44] resulting in a much thinner array. The reduced height “bunny-ear” array (see Fig. 1.2(a)) features a

4 : 1 bandwidth with a thickness of λ/8 at the lowest operational frequency.

Due to their unbalanced feeding, Vivaldi arrays exhibit high cross-polarization [40]. A solution to this problem was given by the balanced antipodal Vivaldi Array (BAVA) ﬁrst

7 presented in [40]. A recent implementation of a BAVA achieved 3 : 1 bandwidth with thickness λ/7 at the lowest operation frequency [13] (see Fig. 1.2(b)). Clearly, as the height of Vivaldi-type arrays is reduced, their bandwidth is greatly degraded.

1.1.4 Spiral Arrays

Arrays of spiral elements have also been investigated. In [20] a dual polarization spiral array was constructed by using single polarization spirals. This was achieved by interleaving spirals with opposite polarizations (right hand and left hand) and optimizing their position within the array via genetic algorithms. Distributed resistive loading of the spiral arm ends was used to improve axial ratio and bandwidth. The reported bandwidth was almost 2 : 1 for VSWR<2, AR < 3dB and SLL < −10dB simultaneously and for angles up to ±30o.

The VSWR bandwidth alone was about 3.5 : 1 for an 80-element array. However, in that work no ground plane was used. In [65] an inﬁnite array of rectangular thin wire spirals was analyzed. The array achieved approximately 2 : 1 bandwidth with thickness λ/8at the lowest operational frequency. In this latter work, although the spirals were arranged tightly into a rectangular grid, no emphasis was put on controlling the mutual coupling for bandwidth enhancement.

In Table 1.1, we compare the bandwidth and thickness (at the lowest operation frequency) of the state-of-the-art in tightly coupled phased arrays over a ground plane.

1.2 Feeding Techniques for Wideband Arrays

One of the greatest challenges and a key contribution of this dissertation pertains to the feed design for tightly coupled phased arrays. The reason array feeding is such a challenging task is simple: because it can not be done directly with a standard 50Ω coaxial cable. Connecting a coaxial cable directly to a dipole antenna, for example, is known to

8 Array type Bandwidth Thickness CSA 4:1 λ/10 Dipole arrays PUMA 3:1 λ/9 Long slot 4:1 λ/8 Vivaldi 10 : 1 λ/3 Tapered slot Bunny-ear 4:1 λ/8 BAVA 3:1 λ/7 Spiral 2:1 λ/8

Table 1.1: Summary table of state-of-the-art in wideband tightly coupled arrays.

cause unbalanced currents ﬂowing on the outer coaxial conductor, resulting in unwanted monopole-type radiation. Radiation from the feeding network occurs generally when a balanced antenna is connected directly to an unbalanced feed (such as a coax). This concept is more clearly explained in Chapter 7. To avoid or suppress these common mode currents, a structure that makes a smooth transition from the bal anced to the unbalanced side, i.e. a balun, must be used. Besides balanced to unbalanced transformation, the balun has to also perform impedance transformation, from 50Ω (coaxial cable) to 200Ω, typically required for feeding tightly coupled phased array elements. On top of that, the balun needs to sustain

UWB performance, be of small size and weight and handle high power levels (> 10W ). All these requirements make the array feed design a tedious process.

The existing feeding techniques used in the above UWB phased arrays are summarized below. Although feeding is such a critical issue, it is important to note that not many details are published in the literature regarding that topic.

1.2.1 Dipole Array Feeding Techniques

Dipole arrays are probably the most popular amongst tightly coupled phased arrays.

This is because they are easy to fabricate, provide polarization versatility and are very low

9 proﬁle. Probably the earliest feeding technique for tightly coupled dipole arrays was used in the CSA array and is shown in Fig. 1.3(a) [11]. This “feed organizer” was intended for feeding a dual-polarized array (see Fig. 1.1(a)) and is nothing else but a grouping of four coaxial cables into a single component. With respect to Fig. 1.3(a) left, two pairs of coaxial cables are driven through the four holes, annotated in Fig. 1.3(a) as 61. The outer conductors of the cables are soldered to the main body of the feed organizer, which is ﬁxed on the ground plane using the holes numbered as 68. Upon reaching the array level, the coaxial outer conductors are cut out and their center conductors are soldered to the dipoles as usual. At the bottom side, each pair of cables is connected to a 0◦ − 180◦ hybrid.

Although compact, this feed organizer is not a balun. In fact the balun is provided by the 0◦ − 180◦ hybrid used under the array. This hybrid creates the 180◦ phase diﬀerence

between the two coaxial cables driving each dipole, as shown in Fig. 1.3(a) right. Any

common mode on the cables would be driven to the sum port or (Σ port) of the hybrid

and get suppressed. For a dual-polarized array two hybrids would be needed. Also the

impedance transformation ratio provided by this conﬁguration is only 2 : 1.

This feeding technique is generally compact, easy to implement and can handle large

input powers. However, the use of hybrids can be very costly considering that a typical

commercially available UWB hybrid (30MHz − 3GHz) costs around $500. The additional

weight might also be a serious problem.

A method for feeding dipole arrays that circumvents the use of external hybrids was

presented in [30]. This method is depicted in Fig. 1.3(b). As seen, the dipoles are directly

fed by a coaxial cable. Its outer conductor is soldered to the ground plane and the center

pin to a printed strip that is driven up to one dipole arm. The other arm is connected to

the ground plane with a similar printed strip. The connection of the unbalanced coaxial

10 (a)

(b)

Figure 1.3: (a) Feed organizer [11] for feeding the CSA antenna [35,52]. (b) Feeding of the PUMA array [30].

11 line to the balanced coplanar strips (CPS) will yield a net current on the CPS line that is non-zero and therefore radiates as a common mode (monopole mode).

The authors claimed that the resonance frequency of the common mode is related to the array unit cell size and and can be pushed out of the operational 3 : 1 bandwidth by introducing shorting posts at speciﬁc locations.

This technique is compact and low cost as it is comprised of only printed circuit boards

(PCBs). However, the intended bandwidth is relatively small (3 : 1) and the eﬀect of the common mode on the inﬁnite array VSWR can be pushed out of the band. In arrays were the bandwidth reaches 10 : 1 this practice is not that simple. More importantly, the characteristics of this balun in isolation (without the array present), such as the phase balance, the bandwidth and the impedance transformation ratio are not provided, making this design useful only for the particular application. Also, to lower the array impedance to

50Ω a dielectric superstrate was used which doubled the array thickness.

A diﬀerent, balanced, yet less broadband feeding solution (2 : 1) was provided in [36,37].

As seen in Fig. 1.4(a) the balun is based on the coupled ring hybrid concept [47]. This feed

is planar but requires precisely engineered vertical twin lead wires to connect to the dipoles.

Therefore it is not very practical. The impedance transformation ratio was 50Ω − 100Ω (or

2:1).

Lastly, a more comprehensive study of baluns and common mode rejection techniques

for dipole arrays was presented in [6]. One of the proposed feeds is shown in Fig. 1.4(b).

This feed is based on the principle of coupling a microstrip line (MS), fed by a 50Ω coax, to

a coplanar strip line (CPS) through a slot. As seen, this design requires printing on three

layers which makes it a little more costly. Nevertheless, it provides for 2 : 1 bandwidth.

12 (a)

(b)

Figure 1.4: (a) A balun proposed for operation at 8 − 12GHz [36,37]. (b) A balanced transformer for common mode rejection and operation at 6 − 12GHz [6].

The impedance transformation ratio is 2 : 1 but a method to combine two of these baluns in parallel was shown to achieve a 4 : 1 impedance transformation ratio.

13 1.2.2 Tapered Slot Array Feeding Techniques

When compared to dipole array feeding, tapered slot array feeding seems trivial. The reason is that tapered slot or Vivaldi elements extend all the way down to the ground plane and connect to it. The metalization of the element itself (see Fig. 1.5) can be used to print a simple microstrip line feed on it with no serious bandwidth limitations.

Ground plane Copper (bottom side)

Microstrip line (top side)

Figure 1.5: Typical Vivaldi array feed.

1.3 Remaining Challenges for Wideband Arrays

The current state-of-the-art in UWB low-proﬁle arrays is ∼ 5 : 1 bandwidth and λ/10 thickness at the lowest operational frequency. Although the operation mechanism and the potential of TCPAs are well understood, several key challenges remain to be addressed for their successful implementation.

Contrary to infinite arrays, when designing a finite size array the elements near the array edges experience reduced mutual coupling than those at the array center. As a result, edge elements exhibit significantly different active impedances and are typically mismatched.

This causes a further reduction in the ﬁnite array’s impedance bandwidth, as compared to

14 the infinite array. This phenomenon is known as finite array edge (or truncation) effects.

Dealing with edge eﬀects is a big challenge in ﬁnite TCPAs.

Another challenge has to do with their feeding network. As the array bandwidth and

number of elements increases, feeding with commercially available components becomes very

costly. Typical array feeding includes the individual element feeds, as well as a network of

transmit/receive (T/R) modules comprised of power dividers/combiners, phase shifters,

ampliﬁers and circulators. Oﬀ the shelf solutions exist to some extent for most of the

components listed above, except for the individual element feeds. Typically, the element

feed is the circuit that drives power from the ground plane level up to the array level. As

such, this circuit has to perform UWB unbalanced to balanced transformation (unbalanced

coaxial cable to balanced element) and also impedance transformation (50Ω to typically

around 200Ω or 4 : 1). Performing these functions while conforming to the stringent space,

weight, cost, and power constraints is a major hurdle.

Besides the aforementioned practical issues, there still remains the open ended challenge

of obtaining wider bandwidth. The state-of-the-art in tightly coupled phase arrays is 5 : 1

bandwidth with thickness λ/10 at the lowest operational frequency. By scaling the height to

λ/3 like in the Vivaldi array case the bandwidth can reach to 10 : 1. But the real challenge

is to obtain more bandwidth without increasing the array height. Of course, the problem of

scanning the array beam over large scan volumes while maintaining UWB is the ultimate

challenge for UWB phased arrays.

1.4 Contributions and Dissertation Outline

In this dissertation, we introduced novel techniques for exciting and feeding ﬁnite tightly coupled arrays, leading to remarkable bandwidth improvements. Speciﬁcally:

15 • We designed a novel, UWB (10 : 1), low-proﬁle (λ/23) interwoven spiral array (ISPA).

The ISPA is the ﬁrst array in the literature to demonstrate a 10 : 1 VSWRbandwidth

without superstrates or lossy substrates. Most notably, the array height was only

λ/23 at the lowest operational frequency. This performance seems to approach the

bandwidth limits for planar arrays without superstrates above a ground plane. A

5 × 5 ISPA prototype was fabricated and measured for validation.

• We proposed and demonstrated a novel, general technique for exciting ﬁnite tightly

coupled arrays. This technique accounts for the ﬁniteness of the arrays and utilizes the

associated array resonance modes to calculate an optimum, tapered array excitation.

As a result all array elements can be excited (even the ones on the edges) with very

low VSWRsandhigharrayeﬃciency.

• We studied and proposed three practical techniques for terminating the edge elements

in ﬁnite, wideband tightly coupled arrays. Our goal here was to increase the ﬁnite

array bandwidth by terminating some of the edge elements while uniformly exciting

the central ones. To achieve this goal, we investigated resistive termination vs. short-

/open-circuit termination and demonstrated that short-circuit case provides for the

highest array eﬃciency.

• We designed and fabricated a simple, novel, planar UWB balun/ impedance trans-

former featuring a 4 : 1 bandwidth and 4 : 1 impedance transformation ratio. This

new balun was used for feeding the proposed tightly coupled dipole arrays.

This dissertation is organized as follows:

16 In Chapter 2, we revisit the operation principles of inﬁnite tightly coupled arrays. We illustrate why connected arrays lose their bandwidth when placed above a ground plane and also one remedy to resolve that issue.

In Chapter 3, we propose a novel UWB interwoven spiral array (ISPA). In an inﬁnite array environment, the ISPA array is the only array to achieve 10 : 1 bandwidth above a ground plane with only λ/23 thickness at the lowest operational frequency. This is 2×

improvement in bandwidth and thickness compared to the state-of-the-art in UWB tightly

coupled arrays. The array design is presented in detail and compared to known arrays.

Measurements are conducted for validation purposes.

In Chapter 4, we switch from inﬁnite to ﬁnite array design. Using full-wave numerical

simulations, we demonstrate the bandwidth degradation that occurs in ﬁnite size arrays

due to truncation eﬀects. We also show that the widely used uniform array excitation is

not optimal in terms of array eﬃciency and impedance matching.

In Chapter 5, we present a novel excitation technique for ﬁnite size UWB tightly coupled

arrays. The proposed technique is based on the characteristic mode theory and provides an

array excitation taper that yields extremely low VSWRs for all array elements, including

the ones on the array edges. This is very useful in high power applications where matching

of all elements simultaneously is very crucial. Simulations of a 7 × 7 dipole array show that

our proposed technique results in almost optimum VSWRs for all active elements, when

compared to uniform excitation. This feeding technique can be applied to any array type

and setup.

The ﬁnite array edge eﬀects can be suppressed by loading, rather than exciting the edge

elements. In that case simple uniform excitation of the central elements provides adequate

impedance bandwidth and no tapered excitation is required. In Chapter 6, we study and

17 evaluate different techniques for terminating edge elements in finite arrays. Specifically, we use a 7 × 7 dipole array and compare resistive termination and short-/open-circuit

terminations of the array edge elements. We compare the diﬀerent terminations with respect

to the array VSWR, eﬃciency, realized gain and radiation patterns.

In Chapter 7, we elaborate on the array feeding. We explain in detail the operation

and types of balun that can be used in feeding TCPAs. We propose a novel array feed-

ing technique based on a combination of printed transmission lines and a commercially

available lumped transformer/balun. We also propose a novel fully printed, low cost trans-

former/balun with 4 : 1 bandwidth and impedance transformation ratio 4 : 1.

In Chapter 8, we present measured data for the 7 × 7 dipole array, with 21 active and

28 short-circuited elements on the edges. The array was measured in broadside and 30◦ scan angle and measurements were collected regarding the active VSWR, realized gain and

radiation pattern, validating our simulated data.

Finally, in Chapter 9 we summarize this work and provide some insight towards future

research.

18 Chapter 2: Operation Principles of Inﬁnite Tightly Coupled Phased Arrays (TCPA)

To create a single aperture that is ultra-wideband and thin is a very challenging task.

This challenge was recently addressed by a new class of antennas, referred to as tightly coupled phase arrays (TCPAs) [35, 52]. TCPAs are to be distinguished from traditional antenna phased arrays (or weakly coupled phased arrays) because of a fundamental diﬀer- ence in their operation principles: the role of mutual coupling. In short, mutual coupling is a limiting factor in weakly coupled arrays, but a performance boosting factor in tightly coupled arrays. In this chapter we explain this diﬀerence and demonstrate how the mutual coupling was harnessed to improve the bandwidth of phased arrays.

2.1 Weakly vs. Tightly Coupled Phased Arrays

In traditional or weakly coupled phased arrays, the mutual coupling between the elements is considered detrimental. To minimize coupling, elements such as horns are prefer- able because they have narrow beams and low side lobe levels (SLLs) and thus don’t “see” each other (see Fig. 2.1). The spacing, d, between the array elements typically ranges between λ>d>λ/4 depending on the application. In a weakly coupled array, each ele-

ment radiates almost as if it was in isolation and contributes to the total array far-ﬁeld via

superposition (array factor).

19 broadside scan

Total far-field array pattern

end-fire scan

elements with low side lobes for weak mutual coupling

Weakly coupled array

Figure 2.1: A weakly coupled array. The elements patterns have low side-lobes to ensure minimum mutual coupling.

The bandwidth of weakly coupled arrays is limited at high frequencies by the occurrence of grating lobes. This happens when the element spacing d is one wavelength for broadside

scan, or half-wavelength for end-ﬁre scan. To avoid grating lobes for any scan angle, ele-

ments should be spaced less than half-wavelength apart. However, close spacing increases

mutual coupling, especially at lower frequencies. The optimum element spacing is chosen to

satisfy the bandwidth requirements of the particular application. To further isolate the ele-

ments and suppress mutual coupling, several narrowband electromagnetic bandgap (EBG)

structures have been proposed [82]. Interleaving EBG structures with the array elements is

shown to mitigate mutual coupling.

On the contrary, a tightly coupled phased array (TCPA) operates in a strongly coupled,

yet controlled environment. Because of the strong near-ﬁeld interactions between the ele-

ments, a TCPA can be viewed as a single antenna (see Fig. 2.2). By feeding the antenna

20 broadside scan

Total far-field array pattern end-fire scan

strong mutual coupling between elements

h ground plane

Tightly coupled array

Figure 2.2: A tightly coupled phased array (TCPA) above a ground plane. The elements are placed very close to achieve strong, yet controlled coupling.

at multiple locations, the current on the aperture can be controlled to either increase the bandwidth, or steer the array beam at diﬀerent angles. A typical spacing d between the elements of a TCPA is λ/10 at the lowest frequency of operation. The bandwidth of tightly coupled arrays is limited at low frequencies mainly by the electrical thickness h from the

ground plane. As the electrical distance becomes smaller, the array gets short-circuited by

the ground plane.

The presence of the ground plane in a TCPA is necessary for back-side radiation reduc-

tion. However, the array can not be placed very close to the ground plane because it will get

shorted. Placing the array far from the ground plane is not a good idea either, because the

array image will cause detrimental cancellations (i.e. beam splitting), when the separation

h, between array and ground plane is λ/2. In other words, the bandwidth limitations of a

21 8 x 8 overlapping dipole array array unit cell

feed gap

ground plane

Figure 2.3: An 8 × 8 overlapping dipole array and its unit cell.

TCPA above a ground plane are generally set by the electrical separation between the two.

An example of a tightly coupled array is the array of overlapping dipoles, depicted in Fig.

2.3.

Tightly coupled phased arrays established new frontiers in antenna design and introduced great challenges, which called for innovative solutions. This dissertation proposes novel techniques for increasing the bandwidth of thin, ﬁnite, tightly coupled antenna arrays. Below we present the evolution of TCPAs from our perspective.

2.2 Evolution of Wideband Tightly Coupled Arrays

A tightly coupled phased array (TCPA) is an array of very closely spaced elements

(see Fig. 2.3). The elements can be connected to each other (connected array), or more frequently separated by a small gap (capacitively coupled array). This gap serves as a natural capacitor between neighboring elements and can be adjusted to provide a wide

22 range of capacitance values (coupling capacitance). To control the capacitance3, standard capacitor geometries, such as overlapping sections or interdigital ﬁngers are usually formed in that gap.

As a result of the strong mutual coupling, the array behaves like a continuous current distribution. To understand the potential of the coupled array concept, we will go back approximately 6 decades and trace its evolution from the conception of the uniform current sheet by Wheeler [79, 80].

2.2.1 “Inﬁnite-Bandwidth” Connected Arrays in Free Space

The uniform current sheet was ﬁrst proposed and studied by Wheeler back in 1948

[79,80]. His premise was that an inﬁnite, planar sheet of uniform current J (or M), radiates identically at all frequencies. In particular, a real current distribution on the xy-plane generates two plane waves: one propagating towards the +ˆz and the other towards the −zˆ direction (see Fig. 2.4). If a linear phase variation of the current is assumed along each dimension of the sheet, radiation could be steered oﬀ the z-axis.

Wheeler visualized the uniform current sheet as the limiting case of a planar, linear array of extremely small, closely spaced dipole elements. To study this problem, Wheeler considered all dipoles to be laying within inﬁnite parallel plate PEC waveguides, with the waveguide walls (PEC and PMC) deﬁning the array lattice. The impedance of the waveguide is proportional to the intrinsic impedance of free space (377Ω) times the ratio of the height over the width of the waveguide cross-section [80]. This is the reason that square lattice dipole arrays in free space exhibit constant impedance (at least at low frequencies), independent of element shape. However, Wheeler’s studies were more focused on studying

3We will see later, that this capacitance plays an instrumental role in increasing the bandwidth of TCPAs above a ground plane.

23 Wheeler’s infinite uniform Practical realization with infinite current sheet array of connected dipoles

J J d

x y d y x

Frequency independent realization with infinite array of connected bowties 800 600 dipole array 400 bowtie array ) real J Ω 200

0 imaginary Impedance ( Impedance -200

-400 d x d y -600 0 c/4d c/2d Frequency

Figure 2.4: (top left) Wheller’s inﬁnite uniform current sheet and (top right) its practical implementation with an array of connected dipoles. (bottom left) A frequency independent implementation of Wheeler’s current sheet with self-complementary bowties. (bottom right) Input impedance of connected, inﬁnite dipole and bowtie arrays in free space.

the scan impedance of this hypothetical array, rather than its bandwidth. Undoubtedly, the current sheet as envisioned by Wheeler, was an ideal radiator which could not be implemented in practice.

Although the uniform current sheet concept was known, it took another 20 years until its was implemented. From a practical point of view, a connected dipole array is the simplest

24 way to implement Wheeler’s current sheet. Hansen coins Baum [23] for recognizing ﬁrst that connected, planar dipole arrays in free space exhibited unlimited low frequency performance.

Indeed, an inﬁnite, planar array of connected strip dipoles (see Fig. 2.4) can achieve unlimited low frequency bandwidth in free space. As seen in Fig. 2.4, the input impedance of each dipole at low frequencies is ∼ 188Ω. This shows that the connected dipole array couples eﬃciently to the two free space plane waves (each with impedance 377Ω). Of course, as the dipoles approach their λ/2 resonance, the impedance increases and the bandwidth is limited.

To resolve this issue, one could use self-complementary elements, like bowtie antennas.

In that case, one could obtain a purely resistive input impedance of 188Ω, throughout a theoretically infinite bandwidth. This is depicted in Fig. 2.4. Although connected dipole or bowtie arrays could practically implement the current sheet, they suffered from two fundamental issues: they had to be of infinite extent and also had to lie in free space.

2.2.2 Bandwidth Degradation Above a Ground Plane

An inﬁnite connected dipole (or bowtie) array approached the performance of the theoretical uniform current sheet. However, as mentioned above, it was still impractical for two reasons: 1) the connected dipole array lied in free space, and 2) it was of inﬁnite size.

Even if we could circumvent the second issue by making the array very large (e.g. size∼ 10λ), still, an antenna lying in free space is impractical for most applications. Most real-world applications would require the antenna to be backed by a metallic surface. This is necessary for shielding the array feeding network and also for conﬁning radiation to only half-space. The problem is that when an UWB antenna is placed above a ground plane, its input impedance changes dramatically. Fig. 2.5 demonstrates this phenomenon for a

25 Connected dipole array over a ground plane 1000

750 J free space

d )

Ω over ground plane

500 h

d Resistance (

y 250 x ground plane effect 0 ground plane 0 c/4d c/2d Frequency

500 10

over ground plane 9 free space 8 250 7 ) Ω 6 0 over ground plane ground plane

VSWR 5 effect

Reactance ( Reactance 4 free space -250 3

-500 1 0 c/4d c/2d 0 c/4d c/2d Frequency Frequency

Figure 2.5: (top left) An array of connected dipoles over a ground plane. (top right) Radiation resistance and (bottom left) reactance of the array in free space and at distance d = λ/2 above a ground plane. (bottom right) VSWRof inﬁnite, connected dipole array in free space and over a ground plane.

TCPA. As seen in Fig. 2.5, when the TCA is placed above a perfectly conducting ground

plane, its input impedance is aﬀected in two ways: 1) the radiation resistance drops to zero

at low frequencies (the array gets short-circuited), and 2) its reactance becomes strongly

inductive. Both of these factors hinder the impedance matching at low frequencies and thus

limit the array bandwidth.

Here, the array bandwidth measures the frequency band in which the array is very well

matched to a reference (or system) impedance. The reference impedance is usually chosen

between 50 − 400Ω. The bandwidth is then deﬁned as the ratio of the highest over the

26 lowest frequency of the band for which VSWR<2 (or sometimes even 3). For example, as shown in Fig. 2.5, the connected dipole array achieves unlimited bandwidth in free space, but a limited 2.5 : 1 bandwidth over a ground plane.

The short-circuiting of the array by the ground plane at low frequencies, could be addressed by placing a ferrite layer on the ground plane, similarly to [71]. By doing so the low frequency bandwidth could be improved, at the cost of increasing the weight of the antenna. On the other hand, the bandwidth degradation related to the increased inductance at low frequencies, can be substantially improved at almost no cost. At this point, and about

50 years after Wheeler, Munk introduced a concept that completely changed the philosophy of phased array design.

2.2.3 UWB Tightly Coupled Phased Arrays Above a Ground Plane

A solution to the low frequency matching problem of tightly coupled dipole arrays over a ground plane was ﬁrst proposed by Munk [52]. His concept introduced two breakthroughs.

The ﬁrst, was the use of a simple equivalent circuit to model the array input impedance, using lumped elements. The second, was the control of mutual coupling between the array elements to compensate for the ground plane inductance. These two very important concepts are discussed below.

Although array equivalent circuits were previously devised by Wheeler [80], Munk’s version [52] provided more physical insight. Essentially, Munk’s circuits clariﬁed the operation principle of tightly coupled phased arrays. Also, the use of equivalent circuits helped identify and solve the matching problem, caused by the presence of the ground plane. As stated in [52], the circuits are only valid under the assumption of an inﬁnite array with electrically short elements, no grating lobes, and only when scanning principal planes. The

27 Equivalent Circuit of Connected Equivalent Circuit of Connected dipole array in free space dipole array over a ground plane

Z0 = 377ȍ Z0 = 377ȍ

Lself Lmutual Lself Lmutual

Zin

Cself Cself h Z0 = 377ȍ Z1

ground plane

Capacitively coupled dipole array over a ground plane and equivalent circuit J Z0 = 377ȍ d

Lself Lmutual d h Cmutual y Cself x h Z1 ground plane ground plane

Figure 2.6: (top left) Equivalent circuit of connected dipole array in free space. (top right) Equivalent circuit of connected dipole array at height h above a ground plane. (bottom) An array of capacitively coupled dipoles at height h above a ground plane and its equivalent circuit. These circuits model the input impedance of one element within an inﬁnite array.

equivalent circuits are an extremely powerful tool that help with studying, understanding and improving the performance of TCPAs. This is probably one of the biggest contributions of late Prof. Benedict Munk.

Fig. 2.6 shows the equivalent circuit of one of the elements of an inﬁnite, connected dipole array in free space and also at height h above a ground plane. These circuits are slightly modiﬁed as compared to Munk’s [52]. As seen, the radiation of a connected dipole

28 array in free space is modeled by parallel connection of two semi-inﬁnite transmission lines

(TL) with characteristic impedance 377Ω. The self and mutual inductances of each dipole are represented by lumped inductors Lself and Lmutual, and the self capacitance by Cself .

As seen, at low frequencies, the input impedance of the array is 188Ω.

To account for the addition of a ground plane at distance h behind the array, the bottom

TL is shorted at distance h (see top right circuit in Fig. 2.6). The presence of the ground

plane aﬀects the characteristic impedance of the bottom transmission line, which now is

assigned some impedance Z1, instead of Z0 = 377Ω. Then, the input impedance Zin of the shorted section is given by Zin = jZ1tan(2πh/λ). At low frequencies (h<λ/4), the shorted

section dominates the array impedance. The radiation resistance of the array becomes very

small, almost zero, and the reactance becomes proportional to jZ1tan(2πh/λ). This is in agreement with the impedance plots shown in Fig. 2.5. As a result, the impedance bandwidth of a connected dipole array over a ground plane is limited to about 2.5:1.

The ideal way to solve this problem would be to introduce a negative inductance [23] in series with the ground plane inductance. For example, if the mutual inductance Lmutual shown in Fig. 2.6 was negative, it could be used to cancel the ground plane inductance and extend the low frequency bandwidth. A negative inductance is not readily available but could be obtained using active elements. However, active elements imply signiﬁcantly more complexity in the feeding and also suﬀer from poor stability, narrow bandwidth and power handling issues.

As a partial solution, Munk introduced a mutual capacitance Cmutual between the ad-

jacent elements (see Fig. 2.6). This was done simply by disconnecting the dipoles, and

leaving a small gap between their tips. Moreover, in that gap, Munk formed interdigital

capacitors to enhance and control the capacitance. As a result, the mutual capacitance

29 1000 10

connected 8

500 7 )

Ω real 6 connected

VSWR 5

Impedance ( Impedance 0 4 with capacitors effect of imaginary 3 capacitors 2 with capacitors -500 1 0 c/4d c/2d 0 c/4d c/2d Frequency Frequency

Figure 2.7: (left) Input impedance of one element of an inﬁnite dipole array above a ground plane. The eﬀect of the mutual capacitance is demonstrated. (right) The capacitively coupled dipole array achieves almost double bandwidth as compared to a connected dipole array.

introduced between adjacent dipoles, cancels out the inductance coming from the ground plane at a single frequency. At the same time, the radiation resistance does not change very much. This is shown in Fig. 2.7. As seen, this simple technique was enough the double the array bandwidth from 2.5:1to4.5:1(VSWR<2).

By controlling the mutual capacitance between the dipoles’ tips, Munk was able to partially cancel out the inductance presented by the ground plane. As a result, capacitively coupled dipole arrays could now reach larger bandwidths (> 5 : 1 bandwidth4), even when installed very close (λ/10 at lowest frequency) to a perfectly conducting ground plane. This approach opened up a whole new class of conformal phased arrays, collectively termed as tightly coupled phased arrays. The ﬁrst practical implementation of such an array was the current sheet array, presented in [35].

4By using dielectric superstrates, Munk showed that even larger bandwidths were possible [52].

30 It was Munk [52] who demonstrated for the ﬁrst time that increasing coupling between array elements could lead to very wideband and thin apertures. This revolutionary concept was in contrast to the philosophy of traditional antenna array design, where coupling was resented.

Having the current sheet array as a benchmark [35], a lot of eﬀort has been directed towards improving the performance of this new class of arrays. One of the goals of this dissertation is to understand and extend the bandwidth of TCPAs. In Chapter 3, we present a novel interwoven spiral array (ISPA) with 10 : 1 bandwidth and λ/23 thickness at the lowest operational frequency.

2.3 TCPAs from a “Metamaterials” Perspective

Tightly coupled phased arrays (TCPAs) can also be classiﬁed as metamaterial5 arrays

[18]. There are several indications that can lead us to this conclusion. Firstly, TCPAs are

engineered, periodic structures with physical features (e.g. interdigital capacitors, see Fig.

1.1(a)) which are tens of times smaller than the wavelength. For example, the unit cell of

the CSA array is only λ/10 in size, at the lowest operational frequency, with features as

small as λ/100. Remarkably, it is these small features that lead to the necessary wave slow down and allow the CSA to operate at twice as low frequency than a connected dipole array

(see Fig. 2.7).

Secondly, the properties of the CSA are not readily available in nature. The CSA is an implementation of Wheeler’s uniform current sheet [79, 80]. Wheeler’s current sheet was practically implemented with an array of connected dipoles and was shown to lose its

5Definition: Metamaterials are artificial materials engineered to provide properties which may not be readily available in nature. These materials usually gain their properties from structure rather than composition, using the inclusion of small inhomogeneities to enact effective macroscopic behavior.

31 R C1 L1

L C2 2

Figure 2.8: Equivalent circuit of metamaterial array unit cell [18].

broadband characteristics when placed above a ground plane (see Fig. 2.5). By incorporat- ing small size, periodic, structural inhomogeneities, such as interdigital capacitors, into the connected array its bandwidth was increased by two times.

Lastly, the classiﬁcation of TCPAs as metamaterial arrays is based on the correspondence between the equivalent circuit models of the inﬁnite TCPA unit cell and that of a metamaterial transmission line (TL) [18, 76]. Fig. 2.8 shows the circuit model of a metamaterial TL unit cell [4]. If the line is lossless, the series resistor R should be ignored.

In this basic metamaterial TL circuit, we can easily identify all the electrical features of

a TCPA. Namely, the series inductance L1 accounts for the self-inductance of each element

and also the mutual inductance due to coupling from adjacent elements. Also, the shunt

capacitance C2 represents the capacitance due to the image of each element, as a result of the

PEC ground plane. In metamaterials terminology, L1 and C2 correspond to the right hand inductance and capacitance, LR and CR, shown in [4]. In addition, the series capacitance C1 represents the capacitive mutual coupling between adjacent elements, which is a key feature of UWB TCPAs. Further, the other key feature, the ground plane inductance is modeled

32 by the shunt inductance L2. Clearly, L2 and C1 correspond to the left hand inductance

and capacitance, LH and CH , seen in the metamaterial TL circuit model in [4]). Finally,

to account for radiation a series resistor R has been added. This correspondence justiﬁes the classiﬁcation of TCPAs as metamaterial arrays.

At this point, we would like to disambiguate the diﬀerence between metamaterials and negative refraction index (NRI) materials. In fact, due to their allegedly supernatural focusing properties, NRI materials belong to the wider metamaterial family, but are not the only type of metamaterials. According to its deﬁnition the metamaterials family is much broader than just NRI materials. Hence, we clearly state that we have not observed any

NRI properties related to TCPAs.

2.4 Conclusions

In this chapter we presented the operation principles of inﬁnite tightly coupled phased arrays (TCPA). As noted, the importance of TCPAs relates to the fact that they emulate

Wheeler’s uniform current sheet, an ideal radiator with unlimited bandwidth and scanning capabilities. However, the presence of a ground plane limits the TCPA bandwidth to only

2.5 : 1. A matching technique introduced by Munk and based on mutual coupling control, provided for an almost 2× increase of TCPA bandwidth (4.5 : 1) and reduction of their thickness to λ/10 at the lowest operational frequency. This unique feature of TCPAs clas- siﬁes them as metamaterial arrays. At the same time, this technique paved the way for the introduction of one of the most broadband and low-proﬁle antennas in the literature, the interwoven spiral array (ISPA), presented next in Chapter 3.

33 Chapter 3: A Novel UWB Interwoven Spiral Array (ISPA)

In Chapter 2, we presented the theory of tightly coupled phased arrays (TCPA). We showed how the mutual coupling can be utilized to increase the array bandwidth to 4.5:1 while maintaining a low-proﬁle λ/10 at the lowest frequency of operation. In this chapter, we describe a novel, planar, interwoven spiral array (ISPA) with 10 : 1 bandwidth and thickness λ/23. The array is comprised of rectangular, quasi- self-complementary spirals.

However, unlike typical spiral arrays the elements have their arms “interwoven” to enhance coupling. This coupling serves to mitigate the inductive eﬀects contributed by the PEC ground plane. The ISPA array performance is presented in comparison to that of the CSA array and other broadband arrays, such as bowtie arrays.

3.1 Development of ISPA Unit Cell

The array unit cell is shown in Fig. 3.1. It is comprised of a rectangular, almost self-complementary, two-arm Archimedean spiral covering the entire unit cell, except for the small region close to the unit cell edges, where it also incorporates arm sections from adjacent cells on the right and left. These interwoven arms extend for about 3/8ofaturn.

The unit cell is repeated in two dimensions to form a 2D inﬁnite array.

The dimensions of the spiral are given in detail in Fig. 3.1 (all in mm). Also, the overall unit cell size is 8.2mm×8.2mm with the array placed at 8.2mm from the PEC ground plane.

34 d

d d d d f mm i d a a 0.04 b k c b 0.14 d j d c 0.21

d d 0.25 d e 0.24 d g f 0.2 d d g 0.23 d i 0.18 d d j 0.09

d k 0.08 e f

i e g d Arms from adjacent spiral c d d forming the interweaved d d nature of ISPA

Figure 3.1: ISPA unit cell and its dimensions in mm. The element is fed at the center.

We note that the spiral arm width varies within the unit cell. In particular, it is chosen to be 0.25mm at the central region of the spiral but becomes thinner (0.15mm)towardthe spiral arm ends. This particular design layout (and associated dimensions) was generated via a trial-and-error process with the objective of maximizing the VSWR bandwidth. At this point, no formal optimization was adopted, therefore, the presented design is one of many possibilities within the ISPA concept. Below, we present some intermediate steps that led us to the development of the ISPA.

35 As mentioned earlier, interconnected, planar dipole arrays (where adjacent elements are connected) exhibit adequate low frequency performance in free space [23]. The same also holds for self-complementary structures such as interconnected bowtie and spiral arrays. To observe their performance and therefore assess the improvement achieved by the proposed

ISPA, we refer to Figs. 3.2 and 3.3. Fig. 3.2(a) shows the unit cell (8.2mm × 8.2mm)and calculated VSWRof a self-complementary, interconnected (i.e. continuous) spiral array in

free space. The arm width and gap dimensions are indicated. The calculated VSWRof 2D

inﬁnite arrays in free space and above a PEC ground plane (7mm and 8.2mm height) are shown in Fig. 3.2(b). The array’s impressive low frequency performance in free space can be attributed to Wheeler’s current sheet [79] concept and the self-complementary nature of the geometry (as in the bowtie array of Fig. 2.4).

However, when placed above a ground plane the low frequency performance is lost due to the highly inductive impedance due to the ground plane [52] (see also Fig. 2.5). Speciﬁcally, the spiral array of Fig. 3.2(a) while exhibiting an over 20 : 1 bandwidth (VSWR<2) in

free space, it only achieves a 4 : 1 or 4.5 : 1 bandwidth when placed at 8.2mm or 7mm, respectively, above a PEC ground plane (note that λ/2 grating lobes occur at 18.3GHz).

Of interest is also the performance of the interconnected bowtie array and the CSA [35] shown in Figs. 3.3(a) and 3.3(b). Again, for those arrays, the unit cell was 8.2mm×8.2mm in aperture and placed 7mm above the ground plane. As seen, the interconnected spiral array exhibits much less variation in the real and imaginary impedance across the bandwidth where VSWR < 2. The spiral array is also associated with a more highly oscillatory behavior even though the maximum value of the oscillations is much lower and within

25% of the average real impedance value. We also found, that the ripples in the spiral’s impedance performance are associated with the spiral arm tightness (in other words with

36 0.25 0.25

0.12

0.14

0.22 0.14

0.12 Connected to the next spiral element

(a)

4 free space 7 mm above gp 8.2 mm above gp

3 VSWR

1 0 2 4 6 8 10 12 14 16 18 20 Frequency (GHz)

(b)

Figure 3.2: (a) Interconnected (i.e. continuous) spiral array unit cell without interwoven arms. (b) Simulated VSWRin free space and above a PEC ground plane (7mm and 8.2mm height). Reference impedance was chosen 188Ω.

37 0.35 0.2 0.75 0.2 1 0.8

1.5 feed 0.1 feed 0.1

0.1

(a) (b)

700 400

spiral 600 300 bowtie spiral

CSA dipoles ) bowtie

Ω 200 ) 500 CSA dipoles Ω 100 400 0 300 −100

Real impedance ( 200 −200 Imaginary impedance (

100 −300

0 −400 0 2 4 6 8 10 12 14 16 18 0 2 4 6 8 10 12 14 16 18 Frequency (GHz) Frequency (GHz) (c) (d)

Figure 3.3: (a) Unit cell of interconnected bowtie array. (b) unit cell of the CSA dipole array. (c) Comparison of real and (d) imaginary impedance of the conformal bowtie, CSA dipole and interconnected spiral (not interwoven) arrays (see Fig. 3.2(a) for unit cell of latter).

the number of turns within a given unit cell size). From Figs. 3.3(c) and 3.3(d), the interconnected spiral array has more broadband impedance behavior.

Concurrently, it was found that substantial improvement in the VSWR performance

at lower frequencies could be achieved by increasing the coupling capacitance between the

38 spiral elements to counter the increased inductance from the ground plane. A way to increase mutual capacitance is to disconnect the arms of adjacent elements and leave a small gap. This was done in Fig. 3.4, where the performance is shown for the same spiral array (7mm above the ground plane) but with a gap of 0.04mm. This separation was

produced by shrinking the spiral of Fig. 3.2(a) to 99% of its size. As seen (see Fig. 3.4(b))

the bandwidth (for VSWR < 2) is dramatically increased to 7 : 1 (2.5GHz − 17.5GHz) from 4.5:1(4GHz − 18GHz) shown in Fig. 3.2(b). We remark that the largest bandwidth was found when the gap was 0.04mm (2 × 0.02mm).

To further increase the bandwidth, we increased inter-element coupling by extending the arm lengths. We initially did so by planar meandering the arms into the next spiral, to form a conﬁguration similar to interdigital capacitors. However, this approach did not appreciably increase the bandwidth. After attempting several interweaving approaches to increase the coupling, we found that the design in Fig. 3.1 was best in terms of improving the spiral array’s low frequency performance. Because of its geometry, we named this design the ISPA. The corresponding VSWRand directivity are shown respectively in Figs.

3.5(a) and 3.5(b). As seen, both FEKO ver. 5.5 and HFSS ver. 10 provide close results giving conﬁdence on the performance. We note that the array gives a 10 : 1 bandwidth

(1.6GHz − 16GHz)withVSWR < 2 with thickness 8.2mm above a PEC ground plane.

In that range, the array achieves a ∼ 7dB isolation between co- and cross-pol gains (see

Fig. 3.5(b)). The RHCP and LHCP directivity of the ISPA array were calculated based on one unit cell as part of an inﬁnite array. The two gains are compared to the directivity of a uniformly excited aperture A,withA being equal to the unit cell size [1].

39 0.02

Disconnected arms forming a gap of 0.04 mm between the adjacent element arm

(a)

3 VSWR

1 0 2 4 6 8 10 12 14 16 18 20 Frequency (GHz)

(b)

Figure 3.4: (a) Unit cell of disconnected spiral array. (b) Simulated VSWR.

40 5

4 HFSS FEKO

3 VSWR

1 0 5 10 15 20 Frequency (GHz)

(a)

−5

−10 4πA/λ2 Total RHCP Directivity (dBi) −15 LHCP

−20

−25 0 5 10 15 20 Frequency (GHz)

(b)

Figure 3.5: (a) VSWRof ISPA array using HFSS ver. 10 and FEKO suite ver. 5.5. Reference impedance was chosen 200Ω and 250Ω respectively. (b) Total, RHCP and LHCP directivity calculated with HFSS ver. 10 as compared to the directivity of a uniformly excited aperture of area A=8.2mm × 8.2mm.

41 3.2 The ISPA from an Impedance Matching Perspective

The impedance matching technique Munk proposed to increase the bandwidth of dipole arrays was based on canceling the ground plane inductance with the capacitance coming from mutual coupling. By looking at the VSWR plot shown in Fig. 2.7, we can make an interesting observation. Let us think of the array as a two port network. The input of this network is the power pumped into the antenna and the output is the radiated power into free space. Then, the VSWR of the antenna can be seen as the transfer function between

the input and the output, in the sense that it shows how eﬃciently power is transfered from

the input to the output. Indeed, when VSWR= 1 all of the input power is transfered to

the output (assuming no material or copper losses).

In complex analysis terms, all that Munk’s technique did was to insert one more pole (or

another impedance matching stage) into the transfer function (the VSWR) of the network

(the array). This pole occurs at the frequency where the imaginary impedance of the

array crosses zero (around frequency c/8d). At that frequency the array is almost perfectly

matched, indicated by the low VSWR = 1. In plain words, Munk incorporated a single-

stage matching into the array geometry. This matching “trick” doubled the bandwidth of

tightly coupled dipole arrays, from 2.5:1infreespaceto4.5:1(VSWR < 2) above a

ground plane. In the same context, we can view the ISPA as a matching technique that

doubles the bandwidth of arrays on a ground plane from 4.5:1to10:1(VSWR < 2).

To explain that concept we will build upon the equivalent circuit introduced by Munk, as

shown in Fig. 2.6.

The standard way of designing a network with broadband response is to insert more

pole/zero pairs (or matching stages) into its transfer function. Munk had already very

elegantly incorporated the ﬁrst matching stage into the array geometry. This matching

42 stage was comprised, as usual, by an parallel inductor (the ground plane) and a series capacitor (mutual coupling). Of course the inductance and capacitance values were not chosen randomly but rather they were tuned, by adjusting the array height and the gap between the dipoles tips, respectively.

Based on this elegant concept we inserted more matching stages (more tuned inductor- capacitor pairs) in order to extend the bandwidth. This is illustrated with the ISPA equivalent circuit shown in Fig. 3.6 [18].

Z0 = 377ȍ Lmutual Lself

Cmutual

Cself Z 1 LN

h C Z L N 1 2 … ground plane L1 C2

C1 Multi-stage matching network

Figure 3.6: ISPA equivalent circuit with multi-stage network for increasing the bandwidth.

Looking closer at Fig. 3.6, we can readily identify that the multi-stage network is nothing else but a transmission line, made up of diﬀerent sections each with diﬀerent characteristic impedance equal to Z0N = LN /CN .

43 Connection points with adjacent cell gap

Figure 3.7: Geometry of interwoven spiral array (ground plane is not shown). The multistage matching network shown in Fig. 3.6 is implemented by the spiral shaped transmission line. Mutual coupling is controlled by weaving the arms of adjacent spirals into each other.

The ISPA shown in Fig. 3.7 is actually an implementation of the equivalent circuit shown in Fig. 3.6. The ISPA incorporates two matching techniques: 1) The mutual coupling technique proposed by Munk; This is achieved by weaving the arms of one spiral into the arms of the two adjacent spiral (to the right and left). 2) The multi-stage matching technique implemented by the spiral shaped transmission line; The width of each sections of the transmission line was numerically tuned to achieve maximum VSWR bandwidth.

Tuning the width of each section is equivalent to tuning the parameters LN ,andCN .

44 3.3 Validation of a 5 × 5 ISPA Array

In order to obtain a 10 : 1 bandwidth, the ISPA array should be made, in theory, infinitely large. However, in practice the infinite extent was emulated [35] using a finite number of fed elements within a larger array of resistively terminated elements. Considering our design being still in early stages of development, at this point, we did not pursue the full 10 : 1 bandwidth. Instead, we tested the concept of the ISPA in terms of fabrication and also validated the performance of a 5 × 5 array (see Fig. 3.8).

The unit cell of Fig. 3.1 was scaled by 3.6 times (i.e. 29.52mm × 29.52mm) to allow for in-house fabrication using a readily available printed circuit board (PCB) milling machine.

The latter is capable of milling 6mil traces (slots) with a precision of ±1mil. The array was

mil . ,tan . printedona20 RO5880LZ board ( r =196 δ =0002). Only the central element

was fed while the other 24 elements were terminated in 200Ω resistors (this was the value of

the system impedance in the inﬁnite array analysis in Fig. 3.5(a)), as seen in the detail in

Fig. 3.8(a). The array was placed above a circular, 22 diameter aluminum ground plane,

with foam separators providing the appropriate height (= 29.52mm).

To cover the intended 444MHz−4.44GHz bandwidth the active element was fed with a

broadband microstrip-to-coplanar strip (CPS) balun [66], which provides a 4 : 1 impedance

transformation (i.e. 50Ω coax.− 200Ω CPS). More details on the balun design can be found

in Chapter 7, Section 7.4.2. The balun was placed vertically under the ground plane and

the CPS was driven through a small hole to the antenna terminals (see Fig. 3.8(a)). The

measured VSWR is shown in Fig. 3.8(b) in comparison with the simulated performance.

The numerical analysis was carried out using FEKO suite ver. 5.5. An inﬁnite ground

plane and dielectric layer were used to make the analysis feasible. As seen, the measured

and numerical data are in good agreement with VSWR < 2.5above2GHz. This initial

45 prototype gives us conﬁdence that the proposed ISPA can achieve a 10 : 1 bandwidth via excitation of multiple elements and the use of a larger (ex. 10 × 10 element) aperture.

(a)

6 measured

VSWR 5 simulated

1 0 1 2 3 4 5 6 Frequency (GHz)

(b)

Figure 3.8: (a) Fabricated 5 × 5 ISPA array prototype. The central element is fed while the rest are terminated in 200Ω resistors. (b) Measured and simulated VSWR.

46 3.4 Conclusions

A novel, conformal, interwoven spiral array was presented. The array can theoretically achieve a 10 : 1 bandwidth (VSWR< 2) on a ground plane, i.e. a performance nearly a factor of 2 better than other published arrays, such as the CSA dipoles. The unit cell size was 8.2mm×8.2mm×8.2mm. Electrically, this size corresponds to λ/2.28×λ/2.28×λ/2.28 at the highest frequency (16GHz)andλ/23 × λ/23 × λ/23 at the lowest (1.6GHz). The reported performance is based on an inﬁnitely periodic, planar array and all elements were fedwith0◦ phase (broadside radiation). In this operating mode, grating lobes will not occur

until the frequency reaches ∼ 36GHz (λ = d,whered the element spacing). For scanning

at low grazing angles the frequency should be kept to less than ∼ 18GHz (d = λ/2, for

end-ﬁre radiation). Nevertheless, Fig. 3.5(a) indicates that the performance will degrade

before 18GHz, due to poor VSWR above 16GHz. Assessing the array scanning behavior is a future task. We remark that our design is based on simulations, where feeding was done by simple ports. In practice, a broadband transformer/balun will be required to suppress the common mode resonances [6].

47 Chapter 4: Design of Finite Size TCPAs

For convenience, a tightly coupled phased array (TCPA) is initially designed as inﬁnite.

Using numerical techniques (like FEM or MoM) and Floquet’s theory for periodic structures, the design of an inﬁnite array boils down to the design of its unit cell. In this chapter, we

first design the unit cell of an infinite array of overlapping dipoles and optimize it for maximum impedance bandwidth. Using that unit cell we compose a finite, 7 × 7 array of overlapping dipoles and evaluate the bandwidth of each element with uniform excitation

(i.e. all elements fed with the same amplitude).

4.1 Overlapping Dipole Array Element Design

An inﬁnite array of overlapping dipoles was numerically simulated in HFSS ver.12. The unit cell is shown in Fig. 4.1. For more practical fabrication, the dipoles were arranged on vertical boards. For numerical modeling, the array unit cell was surrounded by a box.

This box deﬁnes the space occupied by a unit cell. The top face of the box was assigned radiation boundary condition, emulating radiation into free space. The bottom face was assigned PEC boundary condition, modeling the ground plane. All 4 side faces of the box were assigned periodic boundary conditions, implying repetition of this unit cell in a 2D inﬁnitely periodic fashion. The phase delay between the opposite sides of the box was set to zero, implying that all array elements are fed in phase (no scanning) and thus radiation

48 maximum will occur towards broadside (θ =0◦). Finally, a lumped port was used to feed the dipole at the aperture plane as indicated in Fig. 4.1.

The lateral dimensions of the unit cell were 2/7×2/7 and the distance from the ground

plane to the feed point of the dipole was 6. These dimensions were chosen so that we could later synthesize a ﬁnite 7 × 7 array of overall size 2 × 2 and thickness 6 from the ground

. tan . mils plane. The dielectric board had r =38, δ =0007 and was 20 thick.

The overlapping section provided for the capacitive coupling needed to cancel out the inductance from the ground plane. The length, s, of that section was tuned to achieve maximum VSWR bandwidth6. We note that the periodicity assumed above, implies that

all elements are fed with the same amplitude and phase as the unit cell. Hence the input

impedance obtained for the unit cell is equal to the active impedance of an element of a

uniformly excited inﬁnite array.

Fig. 4.2 shows the real and imaginary active impedance of the input impedance of the

unit cell for diﬀerent overlapping section lengths. The corresponding active VSWR with

reference to 200Ω is shown in Fig. 4.3.

As depicted in Fig. 4.3 the bandwidth of the array can be controlled by tuning the length

of the overlap section. Particularly, we see that for s =2mm we obtain VSWR<2from

175 − 700MHz. At these frequencies the array height (6) corresponds to ∼ λ/11 − λ/2.8.

This frequency range corresponds to active VSWRbandwidth of 4 : 1. As indicated by our parametric study, this bandwidth is almost optimum for the chosen height from the ground plane.

6In this dissertation, we refer to VSWR bandwidth as the ratio of the highest to the lowest frequencies of the band for which VSWR<2.

49 feeding with lumped port

overlapping section

d d

Figure 4.1: Unit cell of inﬁnite overlapping dipole array above ground plane. The lateral dimensions of the unit cell were 2/7 × 2/7 and the distance from the ground . plane to the feed point of the dipole was 6 . The dielectric board had r =38, tanδ =0.007 and was 20mils thick.

In the following section, we will use the unit cell with overlapping length s =2mm

to create a 7 × 7 array. Our goal is to excite all 49 elements and study their impedance,

bandwidth and how they compare to the inﬁnite array.

50 500 0.5mm 400 2mm 7mm 14mm 300 20mm ) Ω 200

100

Impedance ( real

imaginary −100

−200 100 200 300 400 500 600 700 800 Frequency (MHz)

Figure 4.2: Real and imaginary active input impedance of an element of an inﬁnite array. The array unit cell is shown in Fig. 4.1.

4.2 7 × 7 Array of Overlapping Dipoles

The 7×7 overlapping dipole array is shown in Fig. 4.4. The array size was 2 ×2 and the height 6.A4 ×4 ground plane was used. All 49 elements were fed with lumped ports. The

array was analyzed in HFSS ver.12 using a discrete frequency sweep from 200 − 600MHz.

In inﬁnite array analysis, we only need to analyze one element (i.e the unit cell) because

all the rest were identical. In that case, the array bandwidth was deﬁned as the bandwidth

of its unit cell. However, the elements of a 7 × 7 ﬁnite array, although geometrically

identical, are electrically different. Due to finite size, each element experiences different

mutual coupling and therefore exhibits diﬀerent input impedance and bandwidth. Hence,

we have to examine all 49 input impedances separately.

51 10

8 0.5mm 2mm 7 7mm 14mm 6 20mm

VSWR 5

1 100 200 300 400 500 600 700 800 Frequency (MHz)

Figure 4.3: Active VSWR of an element of the inﬁnite overlapping dipole array of Fig. 4.1. The reference impedance was chosen 200Ω.

An N−element ﬁnite array is generally characterized by its N × N mutual impedance

matrix [Z]. The elements of [Z] are given by the standard formula V Z i . ij = I (4.1) j Ik=0, i,j,k=1...N, k= j

The 49×49 [Z]matrixofthe7×7 dipole array was obtained from the numerical simulation.

Let us examine the self-impedances Zii of the middle row of elements (see Fig. 4.4) as a function of frequency. These are plotted in Fig. 4.5. We note that the rest of the rows exhibit very similar impedances.

As seen, at lower frequencies the element impedances are mostly reactive (∼ 0Ω radiation resistance). This is expected because at 200MHz each element is about λ/18 in size and

the height from the ground plane is λ/10. At higher frequencies the impedances become

52 (1,1) 7x7 overlapping dipole array

ϮĞ ĚŐĞ ϱ ĞůĞ ĐĞŶ ŵĞ ƚĞƌ ŶƚƐ ĞůĞ ŵĞ ŶƚƐ (1,7)

(7,7) detail ground plane

feed

overlapping sections

Figure 4.4: 7 × 7 overlapping dipole array on a ground plane. Element numbering denotes the (row,column) of each element in the array.

less reactive and the radiation resistance is substantially higher (∼ 30Ω). We note that at

600MHz the element size is λ/5.7 and the height from the ground plane λ/3.3. Also, the overall array size at 200 and 600MHz is λ/2.5and1.2λ respectively.

Obviously, if we were to measure the impedance bandwidth of the array elements in the passive case (i.e one element fed and the rest left open-circuited) that would have been very small, due to the dominating reactive impedance. Next, we will demonstrate how the element impedances change when all array elements are excited simultaneously. When

53 100

0 5 center −100 elements 2 edge −200 elements 600MHz −300 ) Ω −400 400MHz

−500

Imaginary ( 300MHz −600

−700

−800 200MHz −900

−1000 −10 0 10 20 30 40 50 Real (Ω)

Figure 4.5: Self-impedances of center row elements. Each line segment shows the variation of the self-impedance along the center row of elements shown in Fig. 4.4. The impedances are plotted at four frequencies: 200(×), 300(+), 400(2), and 600MHz(•).

more than one array elements are excited, their input impedance is referred to as active impedance.

4.2.1 Active Impedance and Bandwidth with Uniform Cur- rent Excitation

The mutual impedance matrix [Z] is a very powerful tool as it allows us to calculate the active impedance of any element with an arbitrary current excitation. Suppose the array is excited with current {I}, imposed at the feed terminals of each dipole. The excitation

54 currents of the dipoles can be arranged in a vector as ⎛ ⎞ I1,1 ⎜ ⎟ ⎜I2,1⎟ {I} = ⎜ . ⎟ . (4.2) ⎝ . ⎠ I7,7 Then, the voltages at the terminals of each dipole are given by

{V } =[Z]{I}, (4.3)

and the active impedance of each dipole {Za} by

{Za} = {V }./{I} (4.4)

where ./ denotes vector division by element.

The active impedances of the center row of elements (see Fig. 4.4) with uniform current

excitation ({I} = {1}) is shown in Fig. 4.6. Along with that, we plot the active impedance

of the inﬁnite array element.

As seen, the 2 edge elements exhibit a high capacitance, ranging from 250 − 600Ω, and

low radiation resistance, ranging from 20 − 180Ω at all frequencies. These elements would

be extremely diﬃcult to match. The 5 center elements exhibit higher radiation resistances

but also signiﬁcant reactance. For good impedance matching the ratio of the radiation

resistance to the reactance has to be as small as possible (< 1). For comparison the active

impedance of the inﬁnite array element is shown (in blue) at the same frequencies.

To obtain precisely the bandwidth of each element we calculated their active VSWR.

Since uniform current excitation was used (as in the inﬁnite array), we decided to also use

the same system impedance for all elements, namely 200Ω (as in the inﬁnite array). In Fig.

4.7, we present the active VSWRsfor all array elements (not only those of the central row).

As seen, the 14 edge elements (7 on the ﬁrst column and 7 on the last column) are

severely mismatched when uniform current excitation is used. The remaining central 35

55 400

200

0 400MHz ) 300MHz Ω

−200

600MHz 5 center Imaginary ( 2 edge elements −400 elements 200MHz

−600

−800 −100 0 100 200 300 400 500 Real (Ω)

Figure 4.6: Active-impedances of center row elements with uniform current excitation. Each line segment shows the variation of the active-impedance along the center row of elements shown in Fig. 4.4. The impedances are plotted at four frequencies: 200(×), 300(+), 400(2), and 600MHz(•). The corresponding active impedance of the inﬁnite array element for the same frequencies is annotated with thicker markers.

elements exhibit VSWR<3 for most part of the frequency band. However, when compared to the infinite array VSWR the finite array performance is still inferior, especially at low frequencies. In fact, not even the central elements are close to the infinite array VSWR.

We conclude that using uniform current excitation in a ﬁnite array does not provide good bandwidth for the elements on the array edges.

56 10

9 14 edge elements 8

VSWR 5

4 infinite array 3

1 200 250 300 350 400 450 500 550 600 Frequency (MHz)

Figure 4.7: Active VSWRfor all 49 elements. We assumed uniform current excitation and equal reference impedances (200Ω) for all elements.

4.2.2 Active Impedance and Bandwidth with Uniform Power Excitation

Antenna excitation with current sources is not practical at microwave frequencies. At these frequencies excitation is imposed in terms of incident power waves. In that way the S− parameters of any network can be directly extracted ([S] matrix) using a network analyzer.

Without going into details7 for a ﬁnite size array, uniform current excitation is diﬀerent

from uniform power excitation. Assuming uniform power excitation i.e. all elements fed

7A detailed calculation of array active VSWRsfor any power excitation is given in Chapter 5.

57 10

7 infinite array 6

VSWR 5 14 edge elements 4

1 200 250 300 350 400 450 500 550 600 Frequency (MHz)

Figure 4.8: Active VSWRfor all 49 elements. We assumed uniform power excitation and equal reference impedances (200Ω) for all elements.

with the same power (a =1)theactiveVSWRsfor all elements of the 7 × 7 array shown in Fig. 4.4 are plotted in Fig. 4.8.

The diﬀerence between the two excitation types is clearly illustrated by the diﬀerent

VSWRsshown in Figs. 4.7 and 4.8. As seen, both excitation schemes lead to mismatched edge elements. In general, the performance of the 7 × 7 array is inferior to that of the inﬁnite array.

58 4.3 Finite Array Edge Eﬀects

The comparison between the active element VSWRsin a uniformly excited inﬁnite vs.

ﬁnite array is illustrated in Fig. 4.8. This clearly demonstrates the bandwidth degradation

in finite arrays due to finite array edge effects. As seen, although the infinite array was

designed for 4 : 1 bandwidth (for VSWR<2, see Fig. 4.3), the bandwidth of the individual

elements of a 7 × 7 finite array is only 2 : 1 for VSWR<3, and only a few central elements had VSWR<2 for a small bandwidth. This phenomenon is due to the following reason: the infinite array is a uniformly excited array and is optimized under that assumption for maximum VSWR bandwidth. However, a finite array is not a uniformly excited array even when we impose a uniform excitation (current or power). Because of the finiteness of the aperture the elements residing close to the array edges experience reduced mutual coupling and their active impedances differ significantly from those of the central elements.

Therefore, imposing a uniform excitation in a finite array in an attempt to create the same excitation conditions as in the infinite array, results in narrowband matching. We note that the edge effects are more prominent in relatively small size arrays, like the 7×7 array under consideration. As the array size grows i.e. > 10 × 10, the central elements will begin to approach the infinite array bandwidth more and more.

4.4 Conclusions

In this chapter, we studied the effects of size truncation on the bandwidth of tightly coupled phased arrays (TCPAs). We found that the concept of a uniformly excited aperture, is violated in finite size arrays. The size truncation of TCPAs leads to non-uniform aperture excitation and thus bandwidth degradation. We studied that phenomenon using a 7 × 7 tightly coupled dipole array. The array was first designed as infinite and tuned for maximum

59 VSWRbandwidth. We found that the impedance bandwidth of the 14 elements laying on the two array edges parallel to the array H-plane gets degraded the most. This is because those edge elements are the most electrically isolated and therefore experience the least mutual coupling of all. Therefore exciting a ﬁnite array uniformly, just like an inﬁnite array, does not necessarily yield maximum VSWR bandwidth. A remedy to this problem is presented in Chapters 5 and 6.

60 Chapter 5: Excitation of Finite Size TCPAs for Broadband Matching

In Chapter 4, we demonstrated that uniform array excitation should not be applied by default, especially when dealing with small to medium size arrays. We demonstrated that uniform array excitation results in high VSWRs, particularly for the edge elements.

In this chapter, we propose a novel technique to calculate a quasi-optimal aperture excitation for ﬁnite size, ultra wide band phased arrays. The approach is based on using the characteristic modes of the array’s mutual impedance matrix. Unlike standard excitation tapers, primarily used for beam shaping, the proposed characteristic mode taper provides for wideband matching of all array elements, including those at the edges of the ﬁnite array.

As such, it maximizes aperture eﬃciency and is particularly attractive for ﬁnite size, tightly coupled antenna arrays. Our method solely relies on the N × N mutual impedance matrix of the array which is pre-computed (or measured). We demonstrate this novel excitation method for an 7 × 7 array of tightly coupled dipole elements. When compared to a uniform excitation, the characteristic mode excitation achieves very low VSWRs for all elements

over a large bandwidth. Improvements in realized gain are also demonstrated. Due to its

simplicity, this new method can be incorporated into the design process to optimize element

and array geometries, leading to further performance improvements.

61 5.1 Characteristic Modes of Finite Array Structures

The theory of characteristic modes was ﬁrst introduced by Garbacz [15,16] at Ohio State and further expanded by Harrington [25–27,29,48] and the reader is referred to any one of these papers for its basic principles. One of the important features of the CM technique as related to array excitation is that it can incorporate the eﬀects of the platform on which the array is mounted on.

For perfect electrically conducting (PEC) bodies the CMs correspond to ﬁelds associated with the the N eigenvectors (or eigencurrents) {I} of the generalized eigenvalue problem

[X]{I} = λ[R]{I}, (5.1) where

[Z]=[R]+j[X](5.2) is the N × N moment method impedance matrix of the structure at frequency f and λ are the usual eigenvalues. The eigenproblem of equation (5.1) can be seen as a generalization of the simpler problems [X]{I} = 0 or [X]{I} = λ{I}, which only have the trivial solution

{I} = 0 because of the symmetry of [X]. We remark, that throughout the paper, vector

quantities are denoted by {·}, and matrices by [·].

Obviously, from equation (5.2), [R]and[X] correspond to the real and imaginary parts

of the impedance matrix, respectively. As the impedance matrix [Z] is a symmetric matrix,

both [R]and[X] are symmetric and real matrices. As a consequence, the eigenvalues and eigenvectors of equation (5.1) are all real. Also, [R] is positive deﬁnite for open-surfaces.

When an eigenvalue λk is near zero at a certain frequency f,theCM{Ik} is said to

be at resonance, implying [X]{Ik}≈0. The fact that [X]{Ik}≈0foraCMcloseto

resonance is key to the proposed CM aperture excitation. However, before we go into

62 details, the following property of CMs is noteworthy; namely, the eigencurrents {I} obey the generalized orthogonality relationship

I˜∗ R I δ . m[ ] n = mn (5.3)

In the above, the asterisk denotes complex conjugate, the tilde denotes transpose, and δmn is the Kronecker’s delta.

As mentioned in [50], characteristic modes can also be deﬁned for N-port networks using the N × N mutual network impedance matrix [ZS].TheCMsofthenetworkcanbealso

found from equation (5.1) by replacing [Z]with[ZS]. For our antenna study, the N-port network is simply the N-element tightly coupled array. Below, we illustrate how the CM theory is applied to calculate the excitation taper for ﬁnite size wideband arrays, resulting in a minimum reﬂection at all ports.

5.1.1 Characteristic Excitation of Finite Arrays

As noted above, the CMs for a general N−port network are related to the eigenvectors of the mutual impedance matrix. For a ﬁnite array of N elements, such as the one shown in Fig. 5.1(a), the N−port impedance matrix [ZS] can be used in equation (5.1) to extract

{Ik}.Since[ZS] is symmetric, with [RS] being positive deﬁnite the CMs {Ik} are real.

Further, when the eigenmode {Ik} corresponding to λk ≈ 0 is used to excite the array, the induced port voltages {Vk} are all real and in phase with the excitation. That is

{Vk} =[ZS]{Ik}

=[RS]{Ik} + j[XS]{Ik}

=[RS]{Ik} + jλk[RS]{Ik}

≈ [RS]{Ik}. (5.4)

63 The active impedance {Za} for each array element then be found as

{Za} = {Vk}./{Ik}→[RS]{Ik}./{Ik}, (5.5) where ./ denotes element-wise division between the two vectors. We also note that since both {Vk} and {Ik} are real valued, the resulting active port impedances are also real.

Consequently, all array ports can now be matched simultaneously, provided each port is fed by a transmission line with characteristic impedance equal to the active port impedance.

Although the above procedure leads to optimal current excitation, it is more appropriate to calculate the incident power excitation taper as the S−parameters can then be employed in evaluating matching. Before we proceed to do that, we need to address the following subtleties.

Speciﬁcally, so far, CMs have been calculated and used at a single frequency. However, for arrays, we are interested in wideband matching. Clearly, the eigenvalues are frequency dependent, indicating that purely resistive active impedance (as suggested by equation

(5.5)) may not be achieved over a wide bandwidth. Thus, the frequency behavior of the

CMs will need be assessed prior to using the CM method as guidance for feed excitations.

With the above concerns in mind, we can proceed to introduce the mode signiﬁcance parameter 1 α = . (5.6) 1+|λ|

This simple expression maps the range of CM eigenvalues λ ∈ (0, +∞) to the interval (0, 1),

making it convenient for plotting. It will be shown later that the range of frequencies

for which 1 ≥ α ≥ 0.7 can empirically deﬁne operational array bandwidth under modal

excitation. Let us illustrate the concept of CM and the modal signiﬁcance parameter α.

64 Consider a coupled dipole array of size D × D above a ground plane (see Fig. 5.1(a)).

A typical plot of the mode signiﬁcance α vs. frequency for such an array is given in Fig.

5.1(b), for the ﬁrst 5 dominant modes. As seen, each CM either resonates around D ≈ λ/2 or D ≈ λ or both. Indeed, ordinary resonances occur when the aperture size D is a multiple of half-wavelength. The corresponding current distributions on the array at resonance are also illustrated in Fig. 5.1(a) using the same color and line “coding”.

We observe that among the 5 CMs shown in Fig. 5.1(b), mode 1 (solid curve) is observed to exhibits the largest frequency span where α>0.6. Hence, the eigencurrent corresponding to mode 1 is a good choice for guiding aperture excitation. From Fig. 5.1(a)), we see that mode 1 has sinusoidal current along the dipole lines and almost uniform in the transverse direction.

The corresponding radiation patterns of modes 1−5 are simply found by the 2D Fourier transform of the mode currents [1]. As the finite ground plane would affect radiation, the actual pattern must be computed after the final excitation is calculated. Nonetheless, the computation of radiation patterns from the CM currents (see Fig. 5.1(c)), is an excellent means of evaluating the different CMs.

From Fig. 5.1(c), we observe another advantage of mode 1 over modes 3 − 5. The radiation pattern of mode 1 is broadside whereas modes 3 − 5 yield endﬁre patterns. Note that mode 2 gives a more directive broadside pattern than mode 1. Thus, it terms of bandwidth and pattern mode 1 is the best choice to guide the array excitation.

The next step in the procedure is to calculate the excitation coeﬃcients ai for incident power waves, and the input line impedances Z0i, for each array element. As summarized below, ai can be readily found using the standard deﬁnitions of the S−parameters [83].

65 Characteristic modes on a tightly coupled dipole array

1 0.9 0.8 0.7 mode 1 mode 2 0.6 mode 3 ɲ 0.5 mode 4 mode 5 0.4 Ground plane z 0.3 ș 0.2 D D 0.1 x ĳ y 0 c/2D c/D Frequency

(a) (b)

o o φ = 0 mode 1 φ = 90 mode 2 0° mode 3 0° -30° 30° mode 4 -30° 30° mode 5

-60° 60° -60° 60°

-90° 90° -90° 90°

-40 -40 ° ° -120° 120 -120° 120 -20 -20 o = 90 ș 150° -150° 150° -150° 0dB 0dB ±180° 0° ±180° -30° 30°

-60° 60°

-90° 90°

-40

-20 ° -120° 120 0dB

-150° 150° ±180°

(c)

Figure 5.1: (a) Tightly coupled dipole array over a ground plane and associated mode current distributions at their resonance frequency. (b) Typical modal signiﬁcance plots for the array in Fig. 5.1(a); modes resonate approximately at the frequencies where aperture size D is multiples of half-wavelength. (c) Radiation patterns corresponding to modes 1 − 5atφ =0◦, 90◦ and θ =90◦ cuts.

Namely we have

−0.5 [Z0] {V1} = {a} + {b}, (5.7)

66 and

0.5 [Z0] {I1} = {a}−{b}, (5.8)

where {a} and {b} contain the coeﬃcients ai and bi for the incident and reﬂected waves,

th respectively, at the i element. Also, [Z0] is a diagonal matrix containing the characteristic

impedances of the feeding lines, {I1} is the current associated with mode 1 at the port

location, and {V1} is calculated from equation (5.4). By adding equations (5.7) and (5.8)

we get the CM excitation coeﬃcients, viz.

−0.5 0.5 {a} =0.5[Z0] {V1} +0.5[Z0] {I1}. (5.9)

In addition, the entries of the diagonal matrix [Z0] are found by

[Z0]=|{V1}./{I1}| , (5.10)

where, as before, ./ denotes element-wise division between the two vector arguments. These coeﬃcients and line impedances form the excitation taper to be used for feeding the array elements.

Of course, the above distribution is computed at a single frequency (CM resonance frequency) within the operational bandwidth. We will see later that the optimal choice of that frequency depends on the ﬁnal performance of the array when the computed excitation taper is applied.

In general, the computed wave excitations ai are complex. In our realization though,

we choose |{a}|. This choice does not aﬀect matching signiﬁcantly since {a} and [Z0]are

computed for CMs close to resonance. As was shown in (5.4), at resonant frequency {V }

and {I} are real, as well as [Z0] and hence {a}. The computed coeﬃcients |{a}| and line impedances [Z0] are constant for all frequencies.

67 The reﬂected wave coeﬃcients {b} can be computed using the N−port S−parameter matrix [SS] of the array found from

−0.5 −1 0.5 [SS]=[Z0] ([ZS] − [Z0])([ZS]+[Z0] )[Z0] . (5.11)

Subsequently, the magnitude of the active reﬂection coeﬃcient Γ, and the active VSWRat

each port can readily be computed via

{b} =[SS]|{a}|, (5.12)

|{Γ}| = |{b}./|{a}||, (5.13)

{VSWR} =(1+|{Γ}|)./(1 −|{Γ}|). (5.14)

Given {a} and {b}, we can also evaluate the mismatch eﬃciency of the system, emis,

from

|a |2 − |b |2 e i i . mis = 2 100% (5.15) |ai|

Before we demonstrate the proposed CM technique, we would like to add the following: most times TCPAs are comprised of some tens to hundreds of elements. In these cases, it is impractical to feed each element with its own source. To circumvent that diﬃculty power splitters are used. Typically, a single coaxial input (blue dash-dot line in Fig. 5.2) is divided (equally or unequally) into many outputs that are driven to the array elements

(red solid lines in Fig. 5.2). The array VSWR can be measured at the single input of the

array. This is referred to as corporate network VSWR. In order to calculate the corporate

network VSWR, we need to know the S-parameters of the power dividers. In practice,

these can be obtained from measurements. For our convenience, here we will assume that

our 1 : N dividers/combiners are lossless, perfectly matched at all ports, with perfect phase balance and inﬁnite isolation between the output ports. In that case, the [S]matrixofthe

68 power divider with the common input being the first port, would look like ⎡ ⎤ 0 a1 a2 ··· aN ⎢ ⎥ ⎢ a1 ⎥ ⎢ ⎥ S 1 ⎢ a ⎥ , [ ]= ⎢ 2 0 ⎥ (5.16) a2 + a2 + ...+ a2 ⎢ . ⎥ 1 1 N ⎣ . ⎦ aN where a1,...,aN are the excitation taper coefficients (= 1 for uniform excitation) equal to the magnitudes of (5.9). To find the corporate network VSWR we need to find first the total reflected wave bt, which will be the combination of the reflected waves bi (i =1...N)

from each element (given by (5.12)) and weighed by the above S−parameters. Hence

1 bt = (a1b1 + a2b2 + ...+ aN bN ). (5.17) a2 a2 ... a2 1 + 2 + + N

The magnitude of the corporate network reﬂection coeﬃcient Γt can be found from

|Γt| = |bt|/|at|, (5.18)

a a2 a2 ... a2 VSWR where t = 1 + 2 + + N . Finally the corporate network can be calculated

from

VSWRt =(1+|Γt|)./(1 −|Γt|). (5.19)

Below, we present an example of the procedure outlined above for a 7 × 7 element array of

coupled dipoles situated 6 above a ground plane and operating in 200-600MHz band.

5.2 Example: 7 × 7 Array of Overlapping Dipoles Over a Ground Plane

To illustrate the CM excitation method for UWB arrays, the 7 × 7 array of overlapping

dipoles shown in Fig. 5.3 was considered (see [73] for an 8 × 8 array). The overall size of

the array was 2 × 2, while the array was placed 6 above a 4 × 4 ground plane. The unit

cell of this array was designed in Section 4.1.

69 array

feed line VSWRs power divider

corporate network VSWR

Figure 5.2: Coprorate network VSWRvs. element feed line VSWRs.

As the ﬁrst step, the entire array was analyzed in HFSS ver.12 and the 49 × 49 mutual impedance matrix [ZS] was obtained at a discrete set of frequencies within the 200-600MHz band. Subsequently, the eigenvalue problem (5.1) was solved to obtain the modal signiﬁ- cance parameter α, which is plotted in Fig. 5.4 as a function of frequency.

As highlighted in Fig. 5.4, mode 1 resonates at 472MHz. The current distribution and

radiation patterns corresponding to this mode at resonance are shown in Fig. 5.5.

Fig. 5.6 illustrates the eﬀect of CM 1 excitation on the array active impedance. Notice

that by using the modal current excitation, the array impedances are all real at the resonance

frequency of the mode (472MHz). This chart should be compared to the active impedance

under uniform current excitation, {I} = 1, shown in Fig.4.6.

Applying the CM excitation process described above, one can calculate the excitation coeﬃcients |a|, characteristic impedances Z0 of feed lines, active VSWR, and mismatch

70 (1,1) 7x7 overlapping dipole array

(1,7)

(7,7) detail ground plane

feed gap z ș 2ǆs xy ĳ

overlapping sections

Figure 5.3: 7 × 7 overlapping dipole array on a ground plane. The array size was size 2 × 2 and height 6. The ground plane size is 4 × 4.

eﬃciency for each individual element. Of particular importance is the active VSWR of

each array element, as depicted in leftmost column of Fig. 5.7(a). When the CM current

of mode 1 at resonance is used to calculate the array’s excitation, all array elements are

matched at that frequency. The corresponding distribution of feed line impedances and

mismatch eﬃciency are also shown in Fig. 5.7(a).

For comparison, the array performance using uniform power excitation with {a} = {1},

and Z0 = 200Ω is also given in Fig. 5.7(b). As seen, all array elements exhibit signiﬁcant

71 1

0.9

0.8 mode 1 0.7

0.6

α 0.5

0.4

0.3

0.2

0.1

0 200 250 300 350 400 450 500 550 600 Frequency (MHz)

Figure 5.4: Mode signiﬁcance plot for the array of Fig. 5.3.

mismatches across the intended operation band. This performance should be contrasted with the original inﬁnite array VSWR performance. The severe mismatch as a result of

ﬁnite array size is clearly demonstrated in that plot. Because of that mismatch, uniform excitation might be prohibitive if high power needs be used for transmission.

As clearly seen from Fig. 5.7(b), for a ﬁnite array uniform power excitation does not necessarily provide an optimal impedance matching for all array elements, as in the inﬁnite array case. On the contrary, the proposed CM excitation (Fig. 5.7(a)) results in simultaneous impedance matching for all array elements at the CM resonance frequency of 472MHz.

Nonetheless, the overall impedance bandwidth for active VSWR< 3 is not large enough

72 y ° 1 1 0 φ o −30° 30° =0 φ o x 0.9 =90 2 θ=90o 0.8 −60° 60°

3 0.7

0.6 4 −90° 90°

0.5

5 −40 0.4 −120° 120° 6 0.3 −20

0.2 −150° 150° 0dB 7 ± ° 1 2 3 4 5 6 7 180

(a) (b)

Figure 5.5: (a) Current distribution of mode 1 at 472MHz. Element numbering and array orientation are shown in Fig. 5.3. (b) Mode 1 radiation pattern at φ =0◦, 90◦ and θ =90◦ planes.

to accommodate UWB operation. The bandwidth can be slightly increased if the CM resonance condition (α = 1) is relaxed, allowing for a small amount of port mismatches for the beneﬁt of greatly improved bandwidth. This concept is demonstrated in the following section.

5.3 Characteristic Excitation for Improved Bandwidth

By looking at Figs. 5.4 and Fig. 5.7(a), we can see that there exists a correlation between the modal significance parameter α of mode 1 and the array bandwidth when excited with that mode. In particular the range of frequencies for which 1 ≥ α ≥ 0.7 seems to be approximately equal to the band for which active VSWR<2 for all elements. We also notice that mode 1 becomes significant at around 415MHz. We found that a way to increase the array bandwidth would be to shift the cutoff of mode 1 to lower frequencies.

We found that this is possible by increasing the mutual capacitance between the elements.

73 600

320MHz 400 200MHz

200 ) Ω 472MHz 0 5 center 2 edge

Imaginary ( elements elements −200

−400 600MHz

−600 −100 0 100 200 300 400 500 600 700 800 Real (Ω)

Figure 5.6: Active-impedances of center row elements under mode 1 excitation. Each line segment shows the variation of the active-impedance along the center row of elements shown in Fig. 4.4. The impedances are plotted at four frequencies: 200(×), 320(+), mode 1 resonance at 472(2), and 600MHz(•).

In practice this was implemented by increasing the length s, of the overlapping section (see

Fig. 4.1) from 2mm to 20mm. The new the modal signiﬁcance plot is shown in Fig. 5.8.

As seen, by simply increasing the capacitance between the dipoles changes the resonance frequency of the array’s characteristic modes. Speciﬁcally, mode 1 became more broadband.

Also, mode 1 now resonates at a higher frequency (511MHz) and becomes signiﬁcant at

250MHz, which is signiﬁcantly lower than before (compare with 400MHz in Fig. 5.4).

Also, the low frequency modes have shifted below 250MHz leaving mode 1 to be the only

74 signiﬁcant mode within the 250 − 400MHz range. However, choosing to excite the array with mode 1 at its new resonance frequency 511MHz yields very good, yet still narrowband matching, similar to what was reported in Fig. 5.7(a).

Nevertheless, the bandwidth broadening of mode 1 allows us to do the following: instead of exciting the array with mode 1 at its resonance frequency, which yields narrow bandwidth, we can increase the bandwidth by exciting it below resonance at 320MHz,whereα ∼ 0.6.

Thus, by allowing for a small mismatch we can achieve signiﬁcant bandwidth improvement.

With this in mind, the array excitation was calculated based on the CM current of mode 1

√ Z (Ω) normalized |α|( W ) 0 10 1 1 1 100

90 9 700 0.9 2 2 80 8 0.8 600 70 7 3 3 0.7 60 6 500 4 4 0.6 50

VSWR 5 400 0.5 40 4 5 5 30 0.4 300 Mismatch efficiency (%) 3 20 6 6 0.3 2 10 200

1 7 7 0.2 0 200 300 400 500 600 1 2 3 4 5 6 7 1 2 3 4 5 6 7 200 300 400 500 600 Frequency (MHz) Frequency (MHz) (a) √ Z (Ω) 0 normalized |α|( W ) 10 1 201 1 2 100

9 200.8 1.8 90 infinite array 2 2 8 200.6 1.6 80

200.4 1.4 70 7 3 3 200.2 1.2 60 6 4 200 4 1 50

VSWR 5 199.8 0.8 40 4 5 5 199.6 0.6 30

3 Mismatch efficiency (%) 199.4 0.4 20 6 6 2 199.2 0.2 10

1 7 199 7 0 0 200 300 400 500 600 1 2 3 4 5 6 7 1 2 3 4 5 6 7 200 300 400 500 600 Frequency (MHz) Frequency (MHz) (b)

Figure 5.7: (left to right) Active VSWR for all array elements, line impedances Z0i, excitation coeﬃcients |ai|, and mismatch eﬃciency. (a) Excitation based on current distribution of mode 1 at 472MHz. (b) Uniform power excitation. Element numbering is shown in Fig. 5.3. Overlap section length was s =2mm.

75 1

0.9

0.8 mode 1 0.7

0.6

α 0.5

0.4

0.3

0.2

0.1

0 200 250 300 350 400 450 500 550 600 Frequency (MHz)

Figure 5.8: Mode signiﬁcance plot for the array of Fig. 5.3 with longer overlapping section (s =20mm).

at f = 320MHz. Indeed, a much better VSWR performance was achieved as depicted in

Fig. 5.9(a). The overall active impedance bandwidth (for VSWR<3) can now cover the entire 300 - 600MHz for almost all elements. Reference port impedances (i.e. characteristic impedances of feed lines), excitation coeﬃcients and array mismatch eﬃciency are also shown in Fig. 5.9(a). For comparison, the array performance using uniform power excitation a =1andZ0 = 200Ω is also given in Fig. 5.9(b).

As indicated, the overall mismatch eﬃciency is approximately the same for modal and uniform excitations. In addition, the corporate network VSWRappears to be better when the array is uniformly excited. Thus, it might seem that the beneﬁt of using the proposed

76 CM taper is inconsequential. However, the reason this happens is the following: in the uniformly excited array the reflected waves from the mismatched individual feed lines add up destructively in the power combiner, and therefore appear as a small overall reflection at the common input. Therefore the corporate network VSWRappears to be small. This phenomenon is not as pronounced with the CM excitation. This observation accentuates the fact that a high system efficiency, even as much as 75% in the uniform excitation case, can still hide the fact that a significant number of elements are mismatched.

√ Z (Ω) normalized |α|( W ) 0 10 1 450 1 1 100

9 90 2 400 2 0.9 80 8

350 0.8 70 7 3 3 60 6 300 0.7 4 4 50

VSWR 5 250 0.6 40 4 5 5 30

200 0.5 Mismatch efficiency (%) 3 20 6 6 2 10 150 0.4

1 7 7 0 200 300 400 500 600 1 2 3 4 5 6 7 1 2 3 4 5 6 7 200 300 400 500 600 Frequency (MHz) Frequency (MHz) (a) √ Z (Ω) normalized |α|( W ) 0 10 1 201 1 2 100

9 200.8 1.8 90 2 2 8 200.6 1.6 80

200.4 1.4 70 7 3 3 200.2 1.2 60 6 4 200 4 1 50

VSWR 5 199.8 0.8 40 4 5 5 199.6 0.6 30

3 Mismatch efficiency (%) 199.4 0.4 20 6 6 2 199.2 0.2 10

1 7 199 7 0 0 200 300 400 500 600 1 2 3 4 5 6 7 1 2 3 4 5 6 7 200 300 400 500 600 Frequency (MHz) Frequency (MHz) (b)

Figure 5.9: (left to right) Active VSWR for all array elements, line impedances Z0i, excitation coeﬃcients |ai|, and array mismatch eﬃciency. Element numbering is shown in Fig. 5.3. Overlap section length was s =20mm. (a) Excitation based on mode 1 at 320MHz. (b) Uniform excitation.

77 The above procedure illustrates our new approach based on the CM theory using only the mutual impedance matrix of the array. The simplicity and eﬃcacy of this approach is demonstrated using simple matrix operations. Below, we present the performance of the method using full-wave simulations of a full-scale array excited with the CM taper.

5.4 Performance Validation Using Full-wave Simulations

To further demonstrate the validity of the proposed approach, here we present full-wave simulation data for the simple array shown in Fig. 5.3. The element geometry was designed for optimal performance within an infinite array. Subsequently, an 7 × 7 finite array was considered. The finite array was excited using the CM taper and the feed-line impedances found in Section 5.2 (see Fig. 5.7(a)). For comparison, the same array was also excited uniformly using 200Ω feed lines, as given in Fig. 5.7(b).

The realized array gain at broadside (θ =0◦) is shown in Fig. 5.10 for both CM and uniform excitation. Also for reference, the directivity of a uniformly excited rectangular aperture of area A =2 × 2 on an inﬁnite PEC ground plane is shown [1]. As can be

observed, the CM taper provides an additional 1dB of gain over the uniform excitation.

This improvement is obviously due to the improved impedance match at all array elements.

Finally, we should also note that the co-/cross-polarized gain isolation for both excitations

was ∼ 50dB throughout the whole band.

The radiation patterns for both excitations at 200, 400 and 600MHz are shown Fig.

5.11 for the φ =0◦, 90◦ principle planes. As seen, similar radiation patterns were obtained

for both excitations.

78 13

9 mode 1 @ 320 MHz unifom 8

Realized gain (dBi) 7

4 200 250 300 350 400 450 500 550 600 Frequency (MHz)

(a)

−34

−36 mode 1 @ 320MHz uniform −38

−40

−42

−44

−46 Realized gain (dBi) −48

−50

−52

−54 200 250 300 350 400 450 500 550 600 Frequency (MHz)

(b)

Figure 5.10: (a) Co-pol. and (b) cross-pol. realized gain of array shown in Fig. 5.3 with overlapping section length s =20mm. For comparison the array was excited with CM excitation and uniform excitation.

79 Co−pol 0° Co−pol 0° Co−pol 0° o o 200MHz, φ=0o 400MHz, φ=0 600MHz, φ=0 −45° 45° −45° 45° −45° 45°

−90° 90° −90° 90° −90° 90°

−20 −20 −20 mode 1 @ 320MHz mode 1 @ 320MHz −10 mode 1 @ 320MHz −10 −10 uniform uniform 0 uniform 0 0 −135° 135° −135° 10 135° −135° 10 135° 10 20 20 ±180° ±180° ±180°

(a) (b) (c)

Cross−pol 0° Cross−pol 0° Cross−pol 0° o o 200MHz, φ=0o 400MHz, φ=0 600MHz, φ=0 −45° 45° −45° 45° −45° 45°

−90° 90° −90° 90° −90° 90°

−70 −70 −70 mode 1 @ 320MHz mode 1 @ 320MHz mode 1 @ 320MHz −60 −60 −60 uniform uniform uniform −50 −50 −50 −135° 135° −135° −40 135° −135° −40 135° −40 −30 −30 ±180° ±180° ±180°

(d) (e) (f)

Co−pol 0° Co−pol 0° Co−pol 0° o o 200MHz, φ=90o 400MHz, φ=90 600MHz, φ=90 −45° 45° −45° 45° −45° 45°

−90° 90° −90° 90° −90° 90°

−20 −20 −20 mode 1 @ 320MHz mode 1 @ 320MHz −10 −10 mode 1 @ 320MHz −10 uniform uniform uniform 0 0 0 −135° 135° −135° 10 135° −135° 10 135° 10 20 20 ±180° ±180° ±180°

(g) (h) (i)

Cross−pol 0° Cross−pol 0° Cross−pol 0° o 200MHz, φ=90o 400MHz, φ=90 600MHz, φ=90o −45° 45° −45° 45° −45° 45°

−90° 90° −90° 90° −90° 90°

−70 −70 −70 −60 mode 1 @ 320MHz −60 mode 1 @ 320MHz mode 1 @ 320MHz −60 uniform uniform uniform −50 −50 −50 −135° 135° −135° −40 135° −135° −40 135° −40 −30 −30 ±180° ±180° ±180°

(j) (k) (l)

Figure 5.11: Simulated realized gain radiation patterns (dB scale) of the array shown in Fig. 5.3 with the characteristic mode excitation shown in Fig. 5.9(a) and the uniform excitation shown in Fig. 5.9(b). (a) 200MHz,co-pol,φ =0◦ plane. (b) 400MHz,co-pol,φ =0◦ plane. (c) 600MHz,co-pol,φ =0◦ plane. (d) 200MHz, cross-pol, φ =0◦ plane. (e) 400MHz, cross-pol, φ =0◦ plane. (f) 600MHz, cross- pol, φ =0◦ plane.(g) 200MHz,co-pol,φ =90◦ plane. (h) 400MHz,co-pol,φ =90◦ plane. (i) 600MHz,co-pol,φ =90◦ plane. (j) 200MHz, cross-pol, φ =90◦ plane.(k) 400MHz, cross-pol, φ =90◦ plane. (l) 600MHz, cross-pol, φ =90◦ plane.

80 The simulated active VSWRsobtained from HFSS, were found to be precisely equal to

those given in Figs. 5.9(b) and 5.9(a) for all elements and for both excitation tapers (CM

and uniform). Therefore these plots are omitted.

5.5 Conclusions

We proposed a simple, yet eﬀective, array excitation technique for ﬁnite size UWB antenna arrays. To achieve improved active impedance matching at all N array elements, we considered the CMs of the N × N mutual coupling matrix. Using the CM current distributions, we computed the optimal array excitation and feed-line impedances. As compared with the standard uniform excitation, the CM excitation technique provides superior impedance matching, simultaneously for all array elements over a broad range of frequencies.

We demonstrated that this novel technique also improves realized array gain. Speciﬁcally, a

0.5 − 1dB additional gain was obtained for a simple 7 × 7 coupled dipole array. Continuous

300 − 600MHz bandwidth coverage was also demonstrated for the VSWR.

Our approach revealed a very interesting fact. The impedance bandwidth of a ﬁnite array is proportional to the bandwidth of its characteristic modes. To obtain large bandwidth the array geometry and particularly the edge elements must be engineered such that the dominant CMs are wideband. The modal signiﬁcance plot could be used to guide that process. In addition, this simple approach can also be implemented into existing array structures using the measured mutual impedance matrix. Particularly for high power arrays, the simultaneous matching of all array elements is of utmost importance. Next, in

Chapter 6 we present a more practical technique for suppressing edge eﬀects in ﬁnite arrays and extending their bandwidth.

81 Chapter 6: Edge Element Termination Techniques for Uniformly Excited UWB TCPAs

In the previous chapter, we demonstrated that the bandwidth of finite arrays is limited when the array aperture is truncated. To alleviate this problem, we proposed and demonstrated a novel array excitation technique based on the finite array’s characteristic modes. Specifically, the excitation coefficient of each element is weighed proportionally to the intensity of the array’s characteristic currents at its feed location. We showed that the characteristic mode excitation can provide almost perfect matching for all array elements, including those at the edges, resulting in very high efficiency. This method can be extremely useful in high power applications, where exceptionally low VSWRsare required.

The main drawback of the characteristic mode excitation technique is that it requires a custom made feeding network. To implement the required tapered excitation, an unequal power dividing network is needed. However, in applications where eﬃciency is not a critical system requirement, simple uniform array excitation can yield very low VSWRs, provided that some of the array’s edge elements are terminated.

In this chapter, we study diﬀerent termination techniques for edge elements of ﬁnite tightly coupled dipole arrays. Namely, we consider resistive termination and short/open circuit terminations. We evaluate each technique based on the active element VSWRsand

the array eﬃciency and gain.

82 6.1 Techniques for Calculating Edge Element Terminations

For a given ﬁnite array with N−ports, we would like to know the active VSWR for a subset of M

6.1.1 Array Termination Method Based on Mutual Impedance Matrix

The ﬁrst method is based on collapsing an N−port network to an (N −1)−port network

while applying a speciﬁed load condition to one port. This process of loading can be repeated

until the desired number of active and loaded (or terminated) ports has been reached. Below,

we demonstrate how the method works for a simple 2−port network, where port 2 is loaded

in a load impedance ZL.

Suppose we have a 2−port network and particularly a 2−element antenna array as

shown in Fig. 6.1(a). Suppose both elements are excited with total currents at their feed

locations I1 and I2 respectively. Then, the active impedance Za1 of element 1 (similarly for element 2) can be calculated by ﬁrst ﬁnding the total induced voltage V1 given by

V1 = z11I1 + z12I2, (6.1)

83 I1 I2 V1 V2

(a)

- +

(b)

Figure 6.1: (a) A 2-element array used to demonstrate the collapse of a 2-port to 1-port. (b) Thevenin equivalent of a loaded array element.

and then dividing that voltage with the total current I1.So

z12I2 Za1 = z11 + . (6.2) I1

Now, we want to ﬁnd the active impedance of element 1 when the port of element 2 is

terminated in load ZL. When element 2 is loaded with ZL, the current I2 is no longer imposed at its terminals. Thus, we need to ﬁnd that current in terms of the load ZL.Once we know I2, we just have to substitute it back in equation (6.2) which still holds true for

port 1. To ﬁnd I2, we use Thevenin’s equivalent circuit of element 2, shown in Fig. 6.1(b).

Applying Kirchoﬀ’s voltage law for the depicted closed loop we have

V2 + I2ZL =0. (6.3)

84 But V2 is given from

V2 = z21I1 + z22I2, (6.4) and so substituting back (6.4) into (6.3) we get

z21I1 + z22I2 + I2ZL =0. (6.5)

From (6.5) we can ﬁnd I2 in terms of I1 as

z21I1 I2 = − , (6.6) z22 + ZL and then substitute (6.6) back into (6.2) and obtain the active impedance of element 1 when element 2 is loaded with ZL as

z12z21 Za1 = z11 − . (6.7) z22 + ZL

The above method for applying port terminations can be generalized to an array of

N + M ports of which N-ports are active and M-ports are terminated in loads ZLk, k =

1 ...M. In such a case the active impedance of the ith element (i =1...N) will be given

M zikzki Zai = zii − . (6.8) zkk + ZLk k=1 With the active impedance known, we can calculate the active VSWR at the feeding

lines of each element. Assuming element i is fed via a line with characteristic impedance

Z0i (i =1...N), the active reﬂection coeﬃcient Γi is given via

Zai − Z0i Γi = , (6.9) Zai − Z0i and the active VSWRi by

1+|Γi| VSWRi = . (6.10) 1 −|Γi|

85 6.1.2 Alternative Method Based on Scattering Matrix

Instead of the active impedance, we can directly calculate the active reﬂection coeﬃcient at the N-ports when M-ports are terminated in given loads ZLk, k =1...M.Thiscan

be done using the S-parameters. Assume that the N active ports are fed with lines of

characteristic impedance Z0i, i =1...N. The line impedances of the active ports and load

impedances of the terminated ports are placed in the diagonal matrix [Z0]as

⎡ ⎤ Z01 ⎢ ⎥ ⎢ .. ⎥ ⎢ . ⎥ ⎢ 0 ⎥ ⎢ Z0N ⎥ [Z0]=⎢ ⎥ . (6.11) ⎢ Z ⎥ ⎢ L1 ⎥ . ⎣ 0 .. ⎦ ZLM

Here, [Z0] is used in converting the mutual impedance matrix [Z]intotheS-matrix [S] via equation (5.11). For the excited elements we set the incident waves ai =1(i =1...N)

while for the terminated elements we set ak =0(k =1...M). Then the reﬂected waves b

are calculated at all N + M ports by

b =[S]a. (6.12)

The active reﬂection coeﬃcient can be found from

Γi = bi/ai (6.13)

for i =1...N and the active VSWR can be calculated from equation (6.10). The two

methods described above for calculating array terminations are identical. In this dissertation

we will be using the second method.

86 6.2 Resistive Termination of Edge Elements

Probably the most effective and popular edge element termination technique is resistive termination. The concept relies on dissipating the power traveling towards the array edges thus preventing it from reflecting back towards the active elements. Usually the active elements are located at the array center and surrounded by a ring of terminated elements acting as power absorbers. This setup closely emulates the infinite array concept. The resistive termination technique provides low VSWRsat the active elements for wide band-

width, but at the expense of power loss at the resistors, which eventually reduces the array

eﬃciency. Below, we present a typical implementation of resistive terminations in a ﬁnite

7 × 7 dipole array on a ground plane.

The array is depicted in Fig. 6.2. This is the same array we presented in Chapter 5 with

overlapping sections length s =20mm. As seen, it is comprised of 7 rows and 7 columns of

tightly coupled dipoles. The dipoles lines form the array rows. In Fig. 6.3, we present the

active VSWR of the active elements under diﬀerent termination schemes. The red, solid

lines correspond to the VSWR at the feeds of the active elements. The blue, dashed line

corresponds to the VSWRat the common input line, if all element feeds were combined to

a single input via a lossless equal-way power combiner.

In Fig. 6.3 top-left, all 49 elements are equally excited with 200Ω feed lines. As seen,

most of the array elements are mismatched (high VSWR), except for only a small number

at the center of the array which exhibits low VSWR<2. However, the corporate network

VSWR is relatively low. This happens because when the element feed lines are combined

together, the large reﬂections which cause the high VSWRinterfere destructively yielding

a small overall reﬂection at the common input of the array. This demonstrates that the

corporate network VSWRcan hide the fact that elements are mismatched.

87 1st col. 2nd col. 1st row …

2nd row 7th col.

… …

7th row

ground plane z ș y x ĳ

Figure 6.2: 7×7 array of overlapping dipoles. The array size was 2 ×2 and thickness 6 from the ground plane. The ground plane size was 4 × 4. Overlapping section length was s =20mm.

In Fig. 6.3 top-right, we terminated the 1st and 7th columns in 200Ω resistors and

excited all other elements equally with 200Ω feed lines. As seen, the VSWR at the feed

lines of each element are lower than in the fully excited array. This shows that the resistive

termination of the edge elements lowers the VSWRoftheactiveelements.Thecorporate

network VSWRalso remained low after imposing the terminations.

In Fig. 6.3 middle-left, we terminated the 1st and 7th rows in 200Ω resistors and excited

all other elements uniformly with 200Ω feed lines. As seen, the VSWR at the active

elements remained at about the same levels as in the fully excited array, indicating that

row terminations have no eﬀect on the array performance.

88 st th No terminations 1 and 7 cols 10 10

8 8

6 6 VSWR VSWR 4 4

2 2

200 300 400 500 600 200 300 400 500 600 Frequency (MHz) Frequency (MHz)

st nd th th 1st and 7th rows 1 , 2 , 6 and 7 cols 10 10

8 8

6 6 VSWR VSWR 4 4

2 2

200 300 400 500 600 200 300 400 500 600 Frequency (MHz) Frequency (MHz)

1st, 2nd, 6th and 7th cols, st nd th th 1 , 2 , 6 and 7 rows and 1st and 2nd rows 10 10

8 8

6 6 VSWR VSWR 4 4

2 2

200 300 400 500 600 200 300 400 500 600 Frequency (MHz) Frequency (MHz)

Figure 6.3: Active VSWRsof elements of the array depicted in Fig. 6.2. Terminated rows and/or columns are given on top of the ﬁgures. Uniform excitation of the active elements was assumed. Termination impedances and feed-line impedances all assumed 200Ω. Dashed line corresponds to corporate network VSWR.

89 In Fig. 6.3 middle-right, we terminated the 1st,2nd,6th,and7th columns in 200Ω resistors and excited all other elements uniformly with 200Ω feed lines. In this case, we notice a remarkable change: the VSWR at all active elements is lower than 2.5forthe

wholefrequencyband.AtthesametimethecorporatenetworkVSWR is lower than 2.

This illustrates that terminating array columns signiﬁcantly improves the array bandwidth.

As a sanity check, in Fig. 6.3 bottom-left we terminated the 1st,2nd,6th,and7th rows in

200Ω resistors and excited all other elements uniformly with 200Ω feed lines. As expected,

the VSWRs of the active elements exhibit no improvements as compared to the those of

the fully excited array.

Finally in Fig. 6.3 bottom-right, we demonstrate that terminating the 1st,and7th rows

in addition to the 1st,2nd,6th,and7th columns yields no further improvements in the

VSWRsat the active elements.

As a conclusion, we demonstrated that resistive termination of the edge elements can

signiﬁcantly lower the VSWR at the active element feed lines. However, with respect to

the linear dipole array of Fig. 6.3, resistive terminations of the edge rows (rows 1 and 7)

has no eﬀect on the active element VSWRs. On the contrary resistive termination of the

edge columns (columns 1 and 7) lowers eﬀectively the VSWR of the active elements. We

showed that when the two columns on each array edge need to be terminated for optimum

performance. More aggressive terminations will eventually degrade, rather than improve,

the array bandwidth, because broadband performance requires a certain portion of the array

to be active (usually > 40%). From Fig. 6.3, the best termination scheme is the one shown

in the middle-right.

The array mismatch eﬃciency can be calculated from equation (5.15), where the sum-

mations are taken over the active elements only. Note that the denominator represents the

90 100 100 10 90 90

80 80 0 π λ2 × 70 70 4 A/ (total efficiency) −10 co−pol realized gain, HFSS 60 60 cross−pol realized gain, HFSS −20 50 50

40 40 −30 Total efficiency (%) 30 30 Realized Gain (dBi) −40 Mismatch efficiency (%) 20 20 −50 10 10

0 0 −60 200 300 400 500 600 200 300 400 500 600 200 300 400 500 600 Frequency (MHz) Frequency (MHz) Frequency (MHz)

Figure 6.4: (left) Mismatch eﬃciency. (middle) total eﬃciency. (right) Estimated and calculated realized gain of array shown in Fig. 6.2 with the 1st,2nd,6th,and7th columns terminated in 200Ω resistors.

total input power in the array. Similarly, the array total eﬃciency can be found by summing over all elements (active and terminated). The two eﬃciencies are plotted in Fig. 6.4 on the left and middle.

Once the total efficiency is known, we can estimate the realized gain of the array based on the array size. The maximum gain (normal gain) of an array of known effective aperture area A is given by 4πA/λ2. In a phased array, the effective aperture area is a function of

frequency and can not be calculated analytically. For our purposes, we will assume that the

eﬀective aperture area is equal to the physical area of the array, namely A =2 × 2.With

this in mind, we calculated an estimate of the array gain in Fig. 6.4 on the right. For more

accuracy, we calculated the directivity with HFSS and multiplied it with our computed

total eﬃciency to obtain the realized gain8. The result is overlaid with the estimated gain.

As seen in Fig. 6.4 on the right, the calculated realized gain with HFSS, exceeds the

theoretical normal gain that can be achieved by the given size aperture array. This is

8The radiation eﬃciency from HFSS was > 100% and so we did not trust the realized gain calculation straight from HFSS.

91 typical in tightly coupled phased arrays, because the eﬀective array aperture especially at low frequencies, extends well beyond the physical aperture size of the array. In our gain estimation, we assumed an eﬀective aperture area equal to the physical aperture area and that was obviously an underestimation.

Next, we calculated the radiation patterns in the two principal planes φ =0o, 90o and

at frequencies 200, 400, 600MHz. The patterns are shown in Fig. 6.5. As seen, the array maintains a smooth broadside pattern at all frequencies on both principal planes except for one case. The pattern at 600Mhz on the φ =90o plane (E-plane) splits slightly oﬀ broadside. This results in a 1.6dB lower gain and justiﬁes the gain drop observed in the computed realized gain curve of Fig. 6.4. This pattern split did not occur when the array was fully excited (see Fig. 5.11(i)). We also note that the pattern split does not occur either if we terminate the 1st,and7th columns only. Clearly, as the array active region is shrunk the current distribution on the aperture no longer supports a uniform, broadside pattern.

6.3 Short-/Open-Circuit Terminations of Edge Elements

Mismatch eﬃciency plot given Fig. 6.4 shows that resistive termination of the four edge array columns (4 × 7 = 28 elements) yields signiﬁcant improvements in the active

VSWR of the 3 × 7 = 21 active elements, as indicated by the high mismatch eﬃciency

(see Fig. 6.4 on the left). However, the high mismatch eﬃciency comes at the expense

of power dissipation of the resistors, which results in low total eﬃciency (see Fig. 6.4 in

the middle) and therefore degraded realized gain. To alleviate this problem, we propose

short- and open-circuit termination of the edge elements. as in the resistive termination

case, the short-/open-circuit termination calculations were performed using the S-matrix

method described above.

92 φ o φ o Co−pol, =0 0° Cross−pol, =0 0° 200MHz 200MHz 400MHz 400MHz −45° 45° 600MHz −45° 45° 600MHz

−90° 90° −90° 90°

−20 −70 −60 −10 −50 0 −135° 135° −135° −40 135° 10 −30 ±180° ±180°

(a) (b)

φ o φ o Co−pol, =90 0° Cross−pol, =90 0° 200MHz 200MHz 400MHz 400MHz −45° 45° 600MHz −45° 45° 600MHz

−90° 90° −90° 90°

−20 −70 −60 −10 −50 0 −135° 135° −135° −40 135° 10 −30 ±180° ±180°

Figure 6.5: Computed realized gain radiation patterns (dB scale) of the array shown in Fig. 6.2 with the 1st,2nd,6th,and7th columns terminated in 200Ω resistors and the rest of the elements excited uniformly. (a) co-pol, φ =0◦ plane. (b) cross-pol, φ =0◦ plane. (c) co-pol, φ =90◦ plane. (d) cross-pol, φ =90◦ plane.

Fig. 6.6(a) shows the active VSWRsof all excited elements under short- (left) and open-

circuit (middle) terminations respectively. Also, the combination of short-/open-circuit

termination was tested (right). In particular the 1st and 7th columns were left open and

the 2nd and 6th were shorted. Figs. 6.6(b) and 6.6(c) show the total array eﬃciency and

realized gain respectively, of the array under short (left side of ﬁgure) and open (middle)

terminations.

93 Short−circuit terminations Open−circuit terminations Short−/open−circuit terminations 10 10 10

9 9 9

8 8 8

7 7 7

6 6 6 VSWR VSWR VSWR 5 5 5

4 4 4

3 3 3

2 2 2

1 1 1 200 300 400 500 600 200 300 400 500 600 200 300 400 500 600 Frequency (MHz) Frequency (MHz) Frequency (MHz) (a)

Short−circuit terminations Open−circuit terminations Short−/open−circuit terminations 100 100 100

90 90 90

80 80 80

70 70 70

60 60 60

50 50 50

40 40 40

Total efficiency (%) 30 Total efficiency (%) 30 Total efficiency (%) 30

20 20 20

10 10 10

0 0 0 200 300 400 500 600 200 300 400 500 600 200 300 400 500 600 Frequency (MHz) Frequency (MHz) Frequency (MHz) (b)

Short−circuit terminations Open−circuit terminations Short−/open−circuit terminations 20 20 20

10 10 10

0 0 0

2 2 −10 4πA/λ × (total efficiency) −10 4πA/λ × (total efficiency) −10 4πA/λ2 × (total efficiency) co−pol realized gain, HFSS co−pol realized gain, HFSS co−pol realized gain, HFSS cross−pol realized gain, HFSS cross−pol realized gain, HFSS −20 −20 −20 cross−pol realized gain, HFSS

−30 −30 −30 Realized gain (dBi) Realized gain (dBi) Realized gain (dBi) −40 −40 −40

−50 −50 −50

−60 −60 −60 200 300 400 500 600 200 300 400 500 600 200 300 400 500 600 Frequency (MHz) Frequency (MHz) Frequency (MHz) (c)

Figure 6.6: (a) Active VSWR, (b) total array eﬃciency and (c) realized gain assuming short-circuit (left), open-circuit (middle) and short-/open-circuit termination (right) of the two edge columns on each side of the array. In the active VSWR plots, the red solid lines correspond to the 21 active elements and the blue dashed line to the corporate network VSWR.

94 We observe that in terms of array eﬃciency the open-circuit terminations yield much poorer performance when compared to the short-circuit terminations. This is more prominent at low frequencies where in the open-circuit case the array eﬃciency is only 10% vs.

50% in the short-circuit case. This difference is reflected in the realized gain of the arrays shown in Fig. 6.6(c). However, at high frequencies the open-circuit terminations seem to be more effective. In terms of active VSWRthe open-circuit terminations appear to be again

the least eﬀective, while the short-circuit terminations provide for better matching of the

active elements. The array performance when using combined short-/open-circuit termina-

tions lays between the two cases. We note that the short-circuit terminated array achieves

best performance: 6.6dBi of gain, 70% eﬃciency for nealry the whole 200 − 600MHz band,

and VSWR<2 from 300 − 600MHz. The diﬀerence between co- and cross-polarized gains

is also 50dB.

In Figs. 6.7, 6.8, and 6.9 below, we present the simulated realized gain patterns for the

7x7 dipole array using short-circuit, open-circuit, and combination of short-/open-circuit terminations respectively. Again terminations were applied to the 1st,2nd,6th,and7th columns of the array with respect to Fig. 6.2.

As seen, the 2dB gain drop of the co-polarized gain at the E-plane (φ =90o) at 600MHz

and towards broadside direction observed in the resistively loaded array (see Fig. 6.5(c))

is alleviated signiﬁcantly. Besides that fact, the array patterns are well-behaved with low

backlobes (< −10dB).

95 φ o φ o Co−pol, =0 0° Cross−pol, =0 0° 200MHz 200MHz 400MHz 400MHz −45° 45° 600MHz −45° 45° 600MHz

−90° 90° −90° 90° −20 −70 −10 −60 0 −50 −135° 10 135° −135° −40 135° 20 −30 ±180° ±180°

(a) (b)

φ o φ o Co−pol, =90 0° Cross−pol, =90 0° 200MHz 200MHz 400MHz 400MHz −45° 45° 600MHz −45° 45° 600MHz

−90° 90° −90° 90° −20 −70 −10 −60 0 −50 −135° 10 135° −135° −40 135° 20 −30 ±180° ±180°

Figure 6.7: Computed realized gain radiation patterns (dB scale) of the array shown in Fig. 6.2 with the 1st,2nd,6th,and7th columns terminated in short-circuits and the rest of the elements excited uniformly. (a) co-pol, φ =0◦ plane. (b) cross-pol, φ =0◦ plane. (c) co-pol, φ =90◦ plane. (d) cross-pol, φ =90◦ plane.

96 φ o φ o Co−pol, =0 0° Cross−pol, =0 0° 200MHz 200MHz 400MHz 400MHz −45° 45° 600MHz −45° 45° 600MHz

−90° 90° −90° 90° −20 −70 −10 −60 0 −50 −135° 10 135° −135° −40 135° 20 −30 ±180° ±180°

(a) (b)

φ o φ o Co−pol, =90 0° Cross−pol, =90 0° 200MHz 200MHz 400MHz 400MHz −45° 45° 600MHz −45° 45° 600MHz

−90° 90° −90° 90° −20 −70 −10 −60 0 −50 −135° 10 135° −135° −40 135° 20 −30 ±180° ±180°

Figure 6.8: Computed realized gain radiation patterns (dB scale) of the array shown in Fig. 6.2 with the 1st,2nd,6th,and7th columns terminated in open-circuits and the rest of the elements excited uniformly. (a) co-pol, φ =0◦ plane. (b) cross-pol, φ =0◦ plane. (c) co-pol, φ =90◦ plane. (d) cross-pol, φ =90◦ plane.

97 o o Co−pol, φ=0 0° Cross−pol, φ=0 0° 200MHz 200MHz 400MHz 400MHz −45° 45° 600MHz −45° 45° 600MHz

−90° 90° −90° 90° −20 −70 −10 −60 0 −50 −135° 10 135° −135° −40 135° 20 −30 ±180° ±180°

(a) (b)

o o Co−pol, φ=90 0° Cross−pol, φ=90 0° 200MHz 200MHz 400MHz 400MHz −45° 45° 600MHz −45° 45° 600MHz

−90° 90° −90° 90° −20 −70 −10 −60 0 −50 −135° 10 135° −135° −40 135° 20 −30 ±180° ±180°

Figure 6.9: Computed realized gain radiation patterns (dB scale) of the array shown in Fig. 6.2 with the 1st,2nd,6th,and7th columns terminated in short-/open-circuits and the rest of the elements excited uniformly. (a) co-pol, φ =0◦ plane. (b) cross-pol, φ =0◦ plane. (c) co-pol, φ =90◦ plane. (d) cross-pol, φ =90◦ plane.

98 6.4 A Simpliﬁed 7 × 7 Overlapping Dipole Array with Short- circuited Edge Elements

Our studies on edge element terminations showed that with respect to the 7 × 7over- lapping dipole array, short-circuit terminations are the most eﬀective in terms of array eﬃciency, realized gain, pattern and active VSWR. Short-circuit terminations are also far

more easy to implement than resistive terminations, which require extra cost for the resis-

tors and labor for soldering. In this section, we further simplify the array layout. First of

all, the short-circuited edge elements are replaced with a long continuous strip. In addition,

the overlapping sections of these elements were also shorted out (see Fig. 6.10). Lastly, the

dielectric boards were also trimmed from the top resulting in a slightly lower proﬁle design.

As expected, these minor changes had as no eﬀect on the array VSWR, gain or radiation

patterns, which remained unaltered. The array depicted in Fig. 6.10 was fabricated and

tested as discussed in Chapter 8.

6.5 Conclusions

In this chapter, we studied edge element termination techniques for improving the band-

width of wideband tightly couple dipole arrays. Speciﬁcally, we used a 7×7linear2Darray

(single-pol) of tightly coupled dipoles and evaluated the following terminations techniques:

1) resistive termination, 2) short-circuit termination, 3) open-circuit termination, and 4)

combination of short- and open-circuit termination. The above techniques were compared

in terms of array bandwidth, eﬃciency, realized gain and radiation pattern on the E- and

H-planes of the array.

99 We demonstrated that termination of the edge elements can significantly increase the overall array bandwidth and improve the VSWRof each active element individually. How- ever, if the terminations are not applied with caution they can actually hurt the array performance in terms of bandwidth (see Fig. 6.3 middle-left and bottom-left), efficiency, realized gain and radiation pattern (see Figs. 6.4 middle and right, and 6.5(c)). For the edge terminations to be effective we found that out of the four total array edges, only the elements on the two edges parallel to the H-plane of the array (designated as 1st and 7th columns, see Fig. 6.2) need be terminated. The elements along the E-plane edges (designated as 1st and 7th rows, see Fig. 6.2) should be excited to maintain wideband performance.

Moreover, we found that terminating the elements just on the outermost array edge is not effective enough. It is beneficial to also terminate the parallel column right inside the edge; but no more than that. Any further terminations seem to hurt the array efficiency

long strips 3x7=21 active elements ground plane z ș y x ĳ

Figure 6.10: 7 × 7 array of overlapping dipoles with short-circuited edge elements replaced with long strips. The array size was 2 × 2 and thickness 6 from the ground plane. The ground plane size was 4 × 4.

100 and bandwidth. Regarding the different types of termination we found that resistive termination, is the more effective in terms of VSWR bandwidth but results in low efficiency

(30%) at low frequencies. More importantly, it results in a pattern split at the E-plane at

600MHz.

Among the non-resistive terminations, we found that short-circuit termination is the

most eﬀective with respect to all array parameters. The resulting eﬃciency is 70% for

almost the whole band resulting in a realized gain greater than 6.6dBi. Most notably,

the pattern split is much improved (only 0.5dB gain drop) as compared to the resistively terminated array (1.6dB drop). In Fig. 6.11, we present a comparison in terms of VSWR, eﬃciency and realized gain between the fully excited array, and the array terminated in short-circuits and resistive loads.

The 7 × 7 array shown in Fig. 6.2 with the 1st,2nd,6th,and7th columns short- circuited was fabricated and measured in Chapter 8. However, before we elaborate on the measurements, we need to discuss the array feed. This is done next in Chapter 7.

101 Fully excited Short−circuit terminations Resistive terminations 10 10 10

9 9 9

8 8 8

7 7 7

6 6 6

VSWR 5 VSWR 5 VSWR 5

4 4 4

3 3 3

2 2 2

1 1 1 200 300 400 500 600 200 300 400 500 600 200 300 400 500 600 Frequency (MHz) Frequency (MHz) Frequency (MHz)

(a)

14 −34

−36 12 −38

−40 10 −42

8 −44

−46 pol realized gain (dBi)

6 − pol realized gain (dBi) −48 − fully excited Co −50 short−circuit terminations Cross fully excited 4 resistive terminations short−circuit terminations −52 resistive terminations

2 −54 200 300 400 500 600 200 300 400 500 600 Frequency (MHz) Frequency (MHz)

(b)

100

50 fully excited 40 short−circuit terminations resistive terminations

Total efficiency (%) 30

0 200 300 400 500 600 Frequency (MHz)

(c)

Figure 6.11: Comparison between fully excited array, array with short-circuit terminations and resistive terminations at the edges. (a) Active VSWR. (b) Co-pol and cross-pol realized gain. (c) Total eﬃciency. The array is shown in Fig. 6.2 and in the terminated array the 1st,2nd,6th,and7th columns were terminated in short-circuit. All active elements excited equally with 200Ω feed lines.

102 Chapter 7: Wideband Balun/Transformers for TCPA Feeding

So far, we have used simple ports (lumped ports) to feed our arrays. These ports emulate infinite length transmission lines with a specified characteristic impedance (we have been using 200Ω). Each array element was fed by such a line carrying a differential signal.

Although convenient for numerical analysis, this feeding approach is not practical.

In real life, power generators usually provide 50Ω coaxial outputs, which are known to be unbalanced lines. However, when feeding dipoles, which are balanced antennas, balanced feed lines are needed. Besides that, as we demonstrated in Chapter 6, for maximum bandwidth, a tightly coupled dipole array needs to be fed by 200Ω lines. This implies that an impedance transformer from 50Ω to 200Ω is also required between the coaxial line and the array feed (see Fig. 7.1). This transition from the unbalanced 50Ω coaxial line to the

200Ω balanced line can be performed by a circuit called balun (bal anced-to-unbalanced).

The design of a balun for low-proﬁle tightly coupled phased arrays (TCPAs) turns out to be a great challenge for several reasons.

First of all, the balun/impedance transformer has to ﬁt within the limited real estate of the array unit cell (since every active element will have to have one). In addition, the balun should not cause a substantial increase in the array thickness and weight. Further, the physical presence of the balun should not degrade the array performance (pattern,

103 Dipole array

200ȍ balanced

balun/ transformer

Ground plane

50ȍ unbalanced

Figure 7.1: Schematic of feed conﬁguration for tightly coupled dipole arrays. A balun performs the transition between an unbalanced 50Ω coaxial line to a balanced 200Ω line required for feeding the array.

bandwidth, cross-pol., etc). Most importantly, the balun should be able to sustain the same bandwidth as the array (at least 4 : 1) with low VSWR(< 2) and low insertion loss

(< 1dB). Another desirable balun feature is handling relatively large amounts of input power (> 10W ).

The size, bandwidth and impedance transformation ratio requirements make the design of balun one of the greatest challenges of the feed network design for TCPAs. Oﬀ the shelf baluns exist, in various sizes, operational frequencies, impedance transformation ratios,

104 and power handling capabilities. However, these commercially available components are relatively expensive ($50 − $500 a piece), considering that typical TCPAs consists of tens of active array elements. Furthermore, baluns that sustain large powers (> 10W )tendto be bulky, heavy and narrowband, which makes their integration with the planar TCPAs problematic.

In this chapter, we propose two novel, inexpensive printed circuit board (PCB) balun impedance transformers that we developed for feeding our 7×7 tightly coupled dipole array shown in Fig. 6.10. However, first we would like to review the definitions of balanced and an unbalanced transmission lines (TLs), and those of common and differential modes.

7.1 Balanced and Unbalanced Transmission Lines

A common definition of a balanced line is the following: A balanced line is a transmission line (TL) consisting of at least three conductors: the two of them, which are usually of the same type, are balanced with respect to the third (called the reference or ground plane) in the sense that they have equal impedances along their lengths to ground and to other circuits. The chief advantage of a balanced line is rejection of external noise. External noise affects both conductors in the same way, and therefore appears as a common mode which can be easily removed by the differential receiver. Balanced lines are to be contrasted to unbalanced lines, such as coaxial cable, which is designed to have its return conductor connected to ground.

A schematic representation of an unbalanced and a balanced line are given in Fig. 7.2.

Clearly, in an unbalanced transmission line (Fig. 7.2(a)), the potential diﬀerence V , between the two conductors is deﬁned with respect to the ground plane, which is connected directly to one of the lines. However, in a balanced transmission line (Fig. 7.2(b)), the

105 + V -

ground

(a)

V+ 2 - + virtual ground ground V V+ - 2 - VV§· V =−−¨¸ 22©¹

(b)

Figure 7.2: (a) Unbalanced transmission line. (b) Balanced transmission line.

V potential difference between each conductor and the ground plane is 2 .Ifthesetwopo- tentials are phased with a 180o phase difference there will be a net voltage between the two conductors equal to V . In that way the transmission line operates in a differential (or symmetric) mode i.e. equal and opposite currents flow on the two conductors and therefore no radiation occurs from the transmission line, reducing interference to other circuits.

Balanced and unbalanced circuits can be interconnected using a transformer called a balun.

7.2 Common Mode and Diﬀerential Mode

Most explanations of balanced lines assume diﬀerential (symmetric) signals but this is a confusion; signal symmetry and balanced lines are quite independent of each other.

106 Essential in a balanced line is matched source impedances of the “hot” and “cold” signals.

This condition implies that any external signal will affect each leg of the balanced line equally and will thus appear as a common mode signal, which will be removed by the differential receiver. In summary, symmetrical differential signals exist to prevent interference with other circuits; the electromagnetic fields are canceled out by the equal and opposite currents.

But they are not necessary for interference rejection from other circuits. That is what balanced lines are for.

Common mode propagation is unwanted in transmission lines. From an antenna stand- point, if the antenna feeding line supports common modes, it basically becomes a radiator, causing distortion of the antenna pattern, increasing the cross-polarized antenna gain, and even bandwidth degradation. Due to reciprocity, the same phenomena occur in the receiving mode of the antenna.

In conclusion, common modes occur in balanced lines but are completely suppressed by a differential receiver. However, if a differential receiver is not available, a balun is used to convert the differential signal to a single-ended signal. If the balun is designed properly common modes can be suppressed. Besides that, another function performed by the balun is matching the balanced antenna impedance to the unbalanced 50Ω coaxial line impedance.

Below we brieﬂy present the two main categories of baluns: the coiled transformer type and the transmission line transformer type.

7.3 Suitable Baluns Types for TCPAs

The function of a balun can be generally described by the circuit shown in Fig. 7.3 There are two main types of baluns: the classic coiled transformer type and the transmission line transformer type. Each type has diﬀerent advantages and disadvantages.

107 unbalanced balanced (wrt ground) + balun - ground

(a)

Np : Ns

(b) (c)

Figure 7.3: (a) Generic balun circuit. (b) Coil based transformer. (c) Transmission line transformer.

The classic coiled transformer balun is based on the magnetic ﬂux coupling between the primary and secondary circuits. This is depicted in Fig. 7.3(b). For low power applications this type of transformer is compact, and provides wide bandwidth and various impedance transformation ratios. An example of such balun/transformer is shown in Fig. 7.5. Its electrical speciﬁcations are given in Table 7.1. One problem with coiled transformer baluns is that they are relatively expensive. Also, small size baluns imply small power handling

108 capability (< 3W ). For handling larger powers, their size becomes prohibitively large and their bandwidth gets much smaller.

Another type of wideband balun for RF frequencies is the transmission line (TL) balun/transformer. These baluns are based solely on transmission lines and thus are generally more compact, less expensive and easier to fabricate than classic coiled balun/transformers.

Due to the nature of electromagnetic coupling, their balanced to unbalanced transformation is sometimes subtle compared to classic baluns. They usually incorporate several lines and operate based on a combination of mutual coupling, short-/open-circuited stubs, and delay lines [49]. Some well known examples are the Guanella balun/transformer [19], the

Marchand and the double-Y baluns [70].

7.4 A Novel UWB Printed Balun for TCPA Feeding

We present the development of an ultra-wideband (UWB) TL based balun/impedance transformer for feeding our tightly coupled dipole array. The desired operational bandwidth was from 200MHz − 600MHz (3 : 1) and the impedance transformation ratio was 50Ω −

200Ω (4 : 1). The balun had to also ﬁt within the space between the array and the ground

plane (6 ) and be printed on the same thin (20mil) dielectric substrate (r =3.8) as the array.

The balun design was based on the concept of microstrip (MS) to coplanar strip (CPS) transition, published in [62, 67]. For validation purposes we designed, fabricated and measured a balun of that type. Fig. 7.4(a) shows the fabricated balun on a 125mil thick

RO5880. As seen in Fig. 7.4(b), the balun achieves low return loss (< 10dB)formorethan a decade bandwidth (> 10 : 1) and low insertion loss (∼ 1dB). However, there existed some practical issues with using this design for TCPA feeding.

109 However, the ﬁrst practical issue was the overall length of the balun. The feed of Fig.

7.4(a) was 8.5, much longer than the available 6 space under the array. Scaling the feed

for operation down to 200MHz would imply an even longer design. The second issue was

the very thick substrate (120mil) required to design a 50Ω microstrip (MS) line. The third

issue was the presence of the ground plane conductor on the back side of the PCB. The

ground plane occupied almost the whole back side of the PCB and would most probably

interfere with the array radiation. To circumvent these issues instead of using a microstrip

line we used a coplanar waveguide [43, 74].

7.4.1 Initial Feed Design With Coiled Transformer Balun

The new feed design started with a short section of a 50Ω coplanar waveguide (CPW) line printed on the 20mil substrate. The CPW was designed using the standard equations found in [77] and then ﬁne tuned in HFSS. The next step was to design a short 200Ω balanced line of coplanar strips (CPS). Each dipole would be fed with a CPW/CPS pair.

The CPS was designed following the guidelines in [77] and ﬁne tuned in HFSS.

The missing link between the unbalanced CPW and the balanced CPS line was the balun. For testing purposes, we used a commercially available coiled transformer (50Ω −

200Ω) balun (for balun specs see Table 7.1) with its unbalanced side connected to the CPW and its balanced side to the CPS, as shown in Fig. 7.5(a). The two ground strips of the

CPW were soldered to the array ground plane. The CPW was excited by a 50Ω coaxial cable coming from under the ground plane through a hole. The coax outer conductor was split in two and soldered to the left and right onto the CPW ground, while its center conductor was soldered to the middle strip of the CPW (see Fig. 7.5(b)).

110 The feed shown in Fig. 7.5(a) was applied to each of the 21 active elements of the array designed in Fig. 6.10. Measurements of that array are reported in Chapter 8 and indicate a successful feed implementation.

Parameter Test conditions Frequency Units Min. Typ. Max. Input −50Ω Unbalanced − − − − − Impedance Output −200Ω Balanced − − − − − Insertion loss − 10 − 50MHz dB − − 0.6 − − MHz − − . VSWR 2 500 Ratio 1 4:1 500KHz − 1GHz Ratio − − 2.0:1 500KHz − 1MHz Watts − − 1.0 Input power − 1MHz − 5GHz Watts − − 1.5 5MHz − 1GHz Watts − − 3.0 Rise time 10 − 90% − nS − 0.18 − Droop (10%) − − nS − 160 −

Table 7.1: Electrical speciﬁcations of the balun shown in Fig. 7.5(a).

111 8.5’’

200ȍ front resistor

back

(a)

−5

−10

−15 (dB) −20

−25 |S11| measured |S11| simulated |S21| simulated −30

−35 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 Frequency (GHz)

(b)

Figure 7.4: (a) Microstrip (MS) to coplanar strip (CPS) transition. The MS line is fed by a SMA connector attached to the ground plane on the back side. (b) Comparison between measured and simulated data.

112 200ȍ coplanar strips (balanced)

balun/4:1 impedance transformer 6’’

50ȍ coplanar waveguide (unbalanced)

(a)

50ȍ CPW

Array ground plane 50ȍ coax

(b)

Figure 7.5: (a) Commercial balun bridging a 50Ω coplanar waveguide line with a 200Ω coplanar strip line. (b) Schematic representation of CPW fed by a coaxial cable.

113 7.4.2 Development of Planar Ultra-wideband Balun/Trans- former

The array feed shown in Fig. 7.5(a) was successfully tested in Chapter 8. The two main limitations of this feeding technique was the power restriction (max. power < 3W )ofthe

balun and its relatively high cost ($50 per piece). As we mentioned in Chapter 1, one of

the main requirements for long range radar and telecommunications is transmission of high

power (∼ 1KW). In a uniformly excited an array of 21 active elements, like our array for example, this number translates to about 50W per element. For these reasons, the use of the above balun is prohibited.

To solve this problem, we next designed a low cost, planar balun/transformer. Our main design limitation came from the small available space between the 50Ω CPW and the

200Ω CPS (see Fig. 7.5(a). In that limited space, performing the required 4 : 1 impedance transformation and also the transition from a CPW to a CPS line was very challenging.

Below, we describe the main stages of the balun/transformer development.

Our ﬁrst eﬀort to bridge the gap between the CPW and CPS lines is shown in Fig. 7.6.

The 50Ω CPW is printed on one side of the board. Its center conductor is tapered to a thinner strip, for matching to the 100Ω CPS line. Towards the end of the CPW, the two ground conductors are transfered to the back side of the board with vias. There, they are connected and tapered to transition smoothly into one of the CPS strips. The CPW line and ground plane were tuned for low |S11| and insertion loss between 200MHz− 600MHz.

The performance is shown in Fig. 7.6(b).

This design covers the 200MHz − 600MHz bandwidth with low return loss (< 10dB)

and low insertion loss (< 0.5dB). The current magnitude and phase on the balanced

CPS lines is shown in Table 7.2. As seen, the phase balance is approximately 180◦ for all

114 20mils

Port 2 (100ȍ) 100ȍ Paired Strips 6’’

via 50ȍ CPW

PCB Port 1 N4380 13RF İ = 3.8 (50ȍ) r

(a)

−2 |S | −4 11 |S | 21 −6

−8

(dB) −10

−12

−14

−16

−18 200 300 400 500 600 Frequency (MHz) (b)

Figure 7.6: CPW to CPS transition for 50Ω − 100Ω transformation. (a) Feed model and (b) simulated S−parameters.

115 Frequency (MHz) Strip 1 Strip 2 MHz Amplitude Phase Amplitude Phase 200 160 −53◦ 135 126◦ 400 165 −108.8◦ 139 69.3◦ 600 161 −167◦ 136 10.3◦

Table 7.2: Current amplitude and phase on the two strips of the CPS line.

frequencies, but the amplitude balance is not very satisfactory. Nevertheless, we were only able to obtain a 2 : 1 transformation ration (from 50Ω − 100Ω).

Our next step was to design the same type of feed for 100Ω − 200Ω transformation.

This feed is shown in Fig. 7.7(a). As seen, with a small modiﬁcation, a 2 : 1 impedance transformation is achievable. This design achieves very low return and insertion loss as indicated by Fig. 7.7(b). At this limited space matching from 50Ω−200Ω seemed impossible.

However, Fig. 7.8(a) we demonstrate a method to combine in parallel the two previous

2 : 1 designs and obtain a wideband 4 : 1 transformer. The performance for the two parallel connected feeds is shown in Fig. 7.8(b). As seen, both feeds are very well matched with a very low insertion loss (only 0.5dB below 3dB due to equal power split). However, the

isolation between the two output ports (ports 2 and 3) is not very good because of the

absence of a resistor, like in the Wilkinson power divider. This resistor however, is needed

for port isolation, which in our case might not be that crucial since we are designing tightly

coupled arrays. In other words, the elements are designed for increased coupling, thus a

high isolation might not be necessary. The biggest limitation of the parallel connected

feeds is that it restricts the phase control of each element individually, which is required for

scanning. Combination of parallel feeding has also been reported in [6, 57].

116 Front side Back side

200ȍ Port 2 paired (200ȍ) strips vias 6’’

100ȍ CPW Port 1 (100ȍ)

(a)

|S | −5 11 |S | 21

−10

(dB) −15

−20

−25

200 300 400 500 600 Frequency (MHz) (b)

Figure 7.7: CPW to CPS transition for 100Ω − 200Ω transformation. (a) Feed model and (b) simulated S−parameters.

117 Port 3 Port 3 Port 2 200ȍ each Port 2 200ȍ each parallel 100ȍ connection 100ȍ 6’’ each 6’’

Port 1 50ȍ

50ȍ Port 1

(a)

0 0

−2 −2

−4 −4 |S | −6 11 −6 |S | 21 −8 −8

(dB) (dB) |S | −10 −10 11 |S | 21 −12 −12 |S | 23 −14 −14

−16 −16

−18 −18 200 250 300 350 400 450 500 550 600 200 250 300 350 400 450 500 550 600 Frequency (MHz) Frequency (MHz) (b)

Figure 7.8: (a) Combination in parallel of two feeds for 50Ω − 200Ω transformation. (b) S-parameters.

118 Next, we present a novel feed that performs the so far seemingly unattainable 50Ω−200Ω

(4 : 1) impedance transformation from an unbalanced CPW to a balanced CPS line. That was achieved by meandering the ground plane strips of the CPW before they are transfered to the back side of the board with vias and merged together to form one of the CPS strips.

200ȍ Port 2

6’’ 1 Strip 2 Strip

50ȍ Port 1

Figure 7.9: Meandered UWB balun for 50Ω to 200Ω transformation.

119 In addition, the center CPW conductor was tapered to a thinner line for increasing its impedance and then meandered so as to achieve the same electrical length as the ground conductor and thus maintain the phase balance. Several simulations were carried out to tune the balun for more bandwidth and better matching. The new meandered balun is shown in Fig. 7.9.

The current amplitude and phase on the two strips of the CPS line are shown in Table

7.3. As seen, the balun has almost excellent amplitude and phase balance. The proposed

balun was fabricated and tested both as a single feed and in a back-to-back conﬁguration.

Photos of both designs are given in Fig. 7.10. The single feed was fed with a 50Ω coaxial

cable at the CPW side in the way shown in Fig. 7.5(b). The balanced CPS end was

terminated in a 200Ω chip resistor. On the other hand, the back-to-back design was fed

on both sides with 50Ω coaxial cables. Both designs were simulated and measured and the

results are shown in Fig. 7.11.

Measurements and simulations are in excellent agreement. The measured return loss

of the single balun indicates an UWB balun/impedance transformer. The bandwidth is

> 4:1for|S11| < −10dB and insertion loss < 1dB. Wewouldliketonotethatthe

measured transmission coeﬃcient (S21) of the single balun was not actually “measured”

Frequency (MHz) Strip 1 Strip 2 200 0.0983−62.7 0.0979117.2 300 0.105−100.7 0.10579.2 400 0.106−138 0.10641.9 500 0.104−175 0.1034.86 600 0.104151 0.101−28.7

Table 7.3: Current amplitude and phase on the two strips of the CPS line.

120 but deduced from the measured transmission coeﬃcient of the back-to-back conﬁguration.

This is possible as a consequence of the following: any type of loss in the single balun is exactly half of that in the back-to-back balun. The loss in the back-to-back balun can be found from

2 2 Lossb2b =1−|S11| −|S21| . (7.1)

So the loss in the single balun is then

Loss Loss = b2b , (7.2) s 2 which implies that |S21| of the single balun is

2 |S21| = 1 −|S11| − Losss. (7.3)

121 Single 200ȍ load

top view

bottom view

(a)

Back-to-back top view

bottom view

(b)

Figure 7.10: (a) Single and (b) back-to-back fabricated meandered baluns.

122 0

−5

−10

−15

−20 (dB)

−25 |S | single 11 |S | back−to−back −30 11 |S | single 21 −35 |S | back−to−back 21

−40 200 300 400 500 600 700 800 Frequency (MHz)

(a)

−5

−10

−15

−20 (dB)

−25 |S | single 11 −30 |S | back−to−back 11 |S | single −35 21 |S | back−to−back 21 −40 200 300 400 500 600 700 800 Frequency (MHz)

(b)

Figure 7.11: (a) Simulated and (b) measured data for the single and back-to-back meandered baluns.

123 7.5 Discussion on Balun Design

As mentioned above, the term “balance” describes the relative behavior of the two conductors of a transmission line (TL) with respect to a third conductor, which is usually the system reference or ground plane. The advantages of a balanced over an unbalanced line were discussed in Sections 7.1 and 7.2. A potential problem with baluns, is that their balance might be destroyed when other conductors are added close by. For example, the balun shown in Fig. 7.10(a) exhibits adequate balance when it is free standing. However, when the balun is placed vertically on the array ground plane, as shown in Fig. 7.5, it can become unbalanced. Re-balancing is then needed. In fact, all baluns that have their parts exposed like our meandered balun, can be potentially unbalanced. But if the balun is enclosed or shielded, with the shield being its ground reference, it will most probably sustain its balance no matter what environment it is used in. An example of a shielded balun is the coiled balun shown in Fig. 7.5(a). The unbalancing of a balun is a potential problem that occurs usually for a narrow band, which sometimes might be outside the operational band of the array. We remark, that the meandered balun shown in Fig. 7.10(a) was successfully used in feeding an 8 × 8 overlapping dipole array and no common mode radiation occurred.

The related measurements will be soon reported.

7.6 Conclusions

The goal of this chapter was to design a planar, low cost, UWB balun for feeding UWB tightly coupled phased arrays (TCPAs). Besides balanced to unbalanced transformation the balun should also perform impedance transformation from 50Ω − 200Ω. With this in mind, we reviewed the operation mechanism of the balun and its key role as a feed component

124 of TCPAs. We also presented the advantages and drawbacks of the basic existing types of baluns suitable for TCPA feeding.

Along these lines, we ﬁrst designed a simple UWB balun based on a commercially available, small size coiled transformer. This balun was successfully integrated and tested with the 7 × 7 overlapping dipole array designed in Chapter 6. Measured results are shown in Chapter 8.

Furthermore, we designed a novel, fully planar, PCB based UWB balun/impedance transformer. The measured and simulated data indicate UWB > 4 : 1 bandwidth and impedance transformation from 50Ω − 200Ω (4 : 1 ratio). The balun was designed on the same printed circuit board as the array, which simpliﬁes the fabrication process tremen- dously. Our proposed balun exhibits excellent balance in terms of current amplitude and phase. This balun was successfully used in feeding an 8 × 8 overlapping dipole array.

125 Chapter 8: Measurements of 7 × 7 Overlapping Dipole Array Prototype

In Chapter 6, we presented a 7×7 overlapping dipole array with 21 active and 28 short- circuited elements, (see Fig. 6.10). The element feeds for that speciﬁc array were designed separately in Chapter 7 (see Fig. 7.5(a)). Before conducting measurements we included the element feeds into the array model for validation via simulations. However, the balun component could not be included in the full wave simulation. Instead, we fed the array as shown in Fig. 8.1(a), by assigning 200Ω lumped ports at the bottom of the coplanar strip lines (CPS). The coplanar waveguide (CPW) lines were also included in the simulated model. The simulated active VSWRs are shown in Fig. 8.1(b). As seen, the presence of the CPW and CPS sections had practically no eﬀect on the array bandwidth (compare to

Fig. 6.11(a)).

In this chapter, we present measurements of the impedance bandwidth, realized gain and radiation patterns of the array depicted in Fig. 8.1(a). The measurements were conducted in the compact range of ElectroScience Laboratory at the Ohio State University. Measure- ments were collected for both broadside scan (all active elements fed with same phase) and for 30◦ scan in the H-plane of the array. Before we elaborate on the measurements we ﬁrst present the array corporate feeding network.

126 z ș xy e ĳ n la p d n u o r g

200ȍ CPS

200ȍ lumped ports Space for hole for SMA balun

50ȍ CPW

(a)

VSWR 5

1 200 250 300 350 400 450 500 550 600 Frequency (MHz)

(b)

Figure 8.1: (a) 7×7 array of overlapping dipoles with 21 active and 28 short-circuited elements. Part of the element feeds (CPW and CPS) are incorporated in the model. A gap is left for the commercial balun to ﬁt in. (b) Active VSWR of 21 active elements. Blue dashed line is the corporate network VSWR.

127 8.1 Design of Corporate Feed Network

The 7×7 dipole array was comprised of 21 = 3×7 active and 28 short-circuited elements.

To split the power among the 21 active elements we used three 1 : 8 power dividers and one 1 : 3. The feeding network is shown in Fig. 8.2. As seen, the elements were grouped in three groups of seven elements each. Each group was connected to one 1 : 8 power divider, the 8th port of which was terminated in a 50Ω load. The three input ports of the 1 : 8

dividers were connected to the three output ports of the 1 : 3 divider, the input of which

was the array’s input port (blue-dashed line). The speciﬁcations for the 8-way and 3-way

power dividers are given in Appendix A.

short- short- circuited circuited

time gating reference 200ȍ twin lead balun balun balun transformertransformer transformertransformer transformertransformer Individual element VSWRs 50ȍ CPW

50ȍ GP coax

… 5050?ȍ … 5050?ȍ … 5050?ȍ 7 elements

1:8 divider 1:8 divider 1:8 divider

1:3 divider Corporate network VSWR

Figure 8.2: Feeding network of the 7 × 7 overlapping dipole array with 21 active and 28 short-circuited elements. This network was used for broadside scanning (no phasing of the elements).

128 8.2 7 × 7 Array Measurements for Broadside Scan

The assembled array is shown in Fig. 8.3(b). The overall size of the array was 2 × 2,

and 6 thickness. The size of the ground plane was 4 × 4. Foam separators were used

to space the array PCBs appropriately. The measurement setup in the compact range is

shown in Figs. 8.3(a) and 8.4. The array was placed sideways on a foam column supporting

the array from the bottom (white foam column in Fig. 8.4). The foam column was placed

on an electric rotator for pattern measurements. A crane was also used (located on the

chamber ceiling) to support the array from the top. We carried out measurements of the

corporate network VSWR, realized gain, and radiation patterns for broadside scan (no

phase diﬀerence the elements).

8.2.1 VSWR Measurements

The measured and simulated VSWRare plotted in Fig. 8.5(a). The diﬀerence between

measurement and simulation owes to the fact that the feeding network is lossy. In average

the loss was estimated at 2.8dB, which came from: 1) ∼ 1dB from ∼ 1 : 8 dividers, 2)

∼ 0.7dB from the 1 : 3 divider, 3) 0.6dB from terminating one of the eight output ports of the 1 : 8 dividers, and 4) ∼ 0.5dB transformer insertion loss. These numbers can be veriﬁed by looking at Table 7.1 and Figs. A.1 and A.2 in Appendix A.

To factor out feed loss, we applied time gating. With respect to Fig. 8.2 and after transforming the corporate network input from frequency to time domain, we gated out the dividers and baluns, thus bringing the reference point up to the level of the dipole terminals.

In addition, we also added back the two-way loss (2 × 2.8dB =5.6dB) due to the feeding network. The time gated VSWR shown in Fig. 8.5(a) is much closer to the simulated curve.

129 (a)

balun transformer (4:1)

foam separators

(b)

Figure 8.3: (a) 7 × 7 tightly coupled dipole array breadboard in the ElectroScience Lab. compact range for testing. (b) Close-up of the array.

8.2.2 Realized Gain and Pattern Measurements

The measured and simulated realized gain of the 7 × 7 array for broadside scan are shown in Fig. 8.5(b). To account for the feed network loss, we also plotted the measured 130 gain augmented by a 2.8dB ﬂat loss. The compensated measured co-pol. gain is in generally

good agreement with the simulated one. However, more interesting is the diﬀerence between

the measured and simulated cross-pol. gains.

As seen, the measured cross-pol. gain is much higher than the simulated one. This

occurred due to the following reason: The array was hanging from the ceiling crane (see

Fig. 8.4). Because of the uneven distribution of its weight, the array was slightly leaning

forward (∼ 5◦). This means that in Fig. 8.5(b) where we show the measured realized gain

at broadside (θ =0◦), this gain corresponds in reality to the gain at that θ =2◦ − 5◦,

because the array was leaning forward. This phenomenon occurs as a beam tilting of the

radiation patterns shown in Figs. 8.7, 8.8, 8.9, 8.10, 8.11, at all frequencies. Also, it is very

likely that the array was misaligned a couple of degrees in the E-plane.

For example, to demonstrate the eﬀect of any misalignment we calculated the gain at

broadside (θ =0◦) and also at two directions slightly off broadside, namely (θ =1◦, φ =1◦) and (θ =1◦, φ =2◦). These gains are shown in Fig. 8.6. As seen, a few degrees off the broadside can substantially increase the cross-pol isolation. levels by 20 − 30dB.Further, the horn that was used as a feed could most likely have been slightly off its axis and therefore contributed as well to the high measured cross-pol. gain. It is well known that the cross-pol. gain of horns deteriorates about 20dB when the observation point is shifted as little as 2◦ off the broadside.

131 crane

reflector

feed

foam column

Figure 8.4: Measurement set up in ElectroScience Laboratory compact range.

132 10 measured 9 measured, gated simulated 8

VSWR 5

1 200 250 300 350 400 450 500 550 600 Frequency (MHz)

(a)

θ = 0o 20

−10

−20 co−pol, measured co−pol, measured, +2.8dB loss −30 co−pol, simulated

Realized gain (dBi) cross−pol, measured cross−pol, measured, +2.8dB loss −40 cross−pol, simulated

−50

−60 200 250 300 350 400 450 500 550 600 Frequency (MHz)

(b)

Figure 8.5: Simulated and measured (a) corporate network VSWRand (b) realized gain for broadside scan of the 7 × 7 array of dipoles shown in Fig. 8.3(b).

133 10

o 0 θ = 0 θ = 1o, φ = 1o θ o φ o −10 = 1 , = 2

−20

−30 pol realized gain (dBi) −

−40 Cross

−50

−60 200 250 300 350 400 450 500 550 600 Frequency (MHz)

Figure 8.6: Simulated cross-pol realized gain at broadside (θ =0◦) and at two directions slightly oﬀ broadside: (θ =1◦, φ =1◦)and(θ =1◦, φ =2◦).

134 10

−10

−20 co−pol, H−plane −30 cross−pol, H−plane co−pol, E−plane −40 cross−pol, E−plane

−50

Realized gain (dBi) −60

−70

−80

−90 −180 −150 −120 −90 −60 −30 0 30 60 90 120 150 180 θ (deg)

(a)

−10

−20

−30

−40

−50 co−pol, H−plane cross−pol, H−plane −60 co−pol, E−plane Realzized Gain (dBi) cross−pol, E−plane −70

−80

−90 −180 −150 −120 −90 −60 −30 0 30 60 90 120 150 180 θ (deg)

(b)

Figure 8.7: (a) Simulated and (b) measured realized gain radiation patterns of the 7 × 7 array of dipoles shown in Fig. 8.3(b) at 200MHz.

135 10

−10

−20 co−pol, H−plane −30 cross−pol, H−plane co−pol, E−plane −40 cross−pol, E−plane

−50 Realized gain (dBi)

−60

−70

−80 −180 −150 −120 −90 −60 −30 0 30 60 90 120 150 180 θ (deg)

(a)

−10

−20

−30

−40 co−pol, H−plane cross−pol, H−plane −50 co−pol, E−plane

Realized gain (dBi) cross−pol, E−plane −60

−70

−80 −180 −150 −120 −90 −60 −30 0 30 60 90 120 150 180 θ (deg)

(b)

Figure 8.8: (a) Simulated and (b) measured realized gain radiation patterns of the 7 × 7 array of dipoles shown in Fig. 8.3(b) at 300MHz.

136 10

−10

co−pol, H−plane −20 cross−pol, H−plane co−pol, E−plane −30 cross−pol, E−plane

−40

−50 Realized gain (dBi)

−60

−70

−80 −180 −150 −120 −90 −60 −30 0 30 60 90 120 150 180 θ (deg)

(a)

−10

−20

−30

−40

−50 co−pol, H−plane Realized gain (dBi) cross−pol, H−plane −60 co−pol, E−plane cross−pol, E−plane −70

−80 −180 −150 −120 −90 −60 −30 0 30 60 90 120 150 180 θ (deg)

(b)

Figure 8.9: (a) Simulated and (b) measured realized gain radiation patterns of the 7 × 7 array of dipoles shown in Fig. 8.3(b) at 400MHz.

137 10

−10

−20

−30

−40

−50 Realized gain (dBi)

−60 co−pol, H−plane cross−pol, H−plane −70 co−pol, E−plane cross−pol, E−plane −80 −180 −150 −120 −90 −60 −30 0 30 60 90 120 150 180 θ (deg)

(a)

−10

−20

−30

−40

−50 Realized gain (dBi)

−60 co−pol, H−plane cross−pol, H−plane −70 co−pol, E−plane cross−pol, E−plane −80 −180 −150 −120 −90 −60 −30 0 30 60 90 120 150 180 θ (deg)

(b)

Figure 8.10: (a) Simulated and (b) measured realized gain radiation patterns of the 7 × 7 array of dipoles shown in Fig. 8.3(b) at 500MHz.

138 10

−10 co−pol, H−plane cross−pol, H−plane −20 co−pol, E−plane cross−pol, E−plane

−30

Realized gain (dBi) −40

−50

−60 −180 −150 −120 −90 −60 −30 0 30 60 90 120 150 180 θ (deg)

(a)

−10

−20

−30

Realized gain (dBi) −40 co−pol, H−plane cross−pol, H−plane −50 co−pol, E−plane cross−pol, E−plane −60 −180 −150 −120 −90 −60 −30 0 30 60 90 120 150 180 θ (deg)

(b)

Figure 8.11: (a) Simulated and (b) measured realized gain radiation patterns of the 7 × 7 array of dipoles shown in Fig. 8.3(b) at 600MHz.

139 8.3 7 × 7 Array Measurements for 30◦ H-plane Scan

The 7 × 7 array shown in Fig. 8.3(b) was phased for steering the beam maximum oﬀ broadside to θ =30◦ at the H-plane (xz−plane with respect to Fig. 8.1(a)). To avoid costly phase shifters, we implemented a phase shifting network by simple coaxial cables.

The measured array VSWR, realized gain and radiation patterns are reported below.

8.3.1 Element Phasing via Time Delay

In phased arrays, feeding all elements in phase creates a beam maximum at the array broadside (θ =0◦ in our case). To steer the array beam maximum off broadside to a specified direction (θ, φ), a progressive phase difference β needs to be applied between its adjacent elements [1]. For our array, in order to scan at angle θ in the H-plane (i.e. φ =0deg), we needed to apply a progressive phase difference β among the 7 elements within each of the

3 columns given from

π β −2 dsin θ , = λ ( ) (8.1)

d 2 λ where is the distance between them (= 7 )and the free space wavenumber. Since we

were not scanning on the E-plane, the phase diﬀerence between the 3 columns needed to be

exactly zero.

To implement that phase diﬀerence we used simple 50Ω coaxial cables with diﬀerent

lengths. Namely, a cable of length a would insert a phase diﬀerence β given from

√ 2π 2π β = − a = − r a (8.2) λg λ

140 ș = 30Ƞ

21 excited dipoles

extra cable d sections

a 2a 3a 4a 5a 6a 1 7a 50 ȍ : 8 co mbine r time gating refe rence

Figure 8.12: Beam steering via time delay phasing. Extra cable sections with variable lengths (a, 2a, ...) were added to create the necessary phase diﬀerence between the elements and tilt the array beam maximum to 30◦ at the H-plane.

where λg is the guided wavelength in the coaxial cable and r is the dielectric constant of

the coax, which for our case was r =2.1. Equating the right parts of equations (8.1) and

(8.2) and substituting θ =30◦ we ﬁnd that a is given as

d a = √ . (8.3) 2 r

This method of beam steering is independent of frequency because it is based on time delay. However, for steering at a different angle we would need a different set of cables. The configuration is shown in Fig. 8.12. The red-dotted lines represent the extra cable sections

141 β(◦) Frequency(MHz) 10.45 200 15.67 300 20.9 400 26.12 500 31.35 600

Table 8.1: Phase diﬀerence between consecutive elements within each array column for scanning the beam to θ =30◦ in the H-plane.

added to each dipole. For clarity, we only show that for one column, but the same was done for the dipoles in the back. For reference, the inserted phase diﬀerence β between two adjacent elements within a column was

8.3.2 VSWR Measurements

The measured and simulated VSWR for scanning at 30◦ in the H-plane are shown in

Fig. 8.13(a). The difference between measurement and simulation is mainly due to the presence of the lossy feeding network. Again we tried to remove the effect of the feeding network by time gating the corporate network input. However, this time and due to the extra cable sections for the phase control we shifted the reference of the time gating lower in the network, right at the output of the 1 : 8 dividers. This is shown in Fig. 8.12. By doing that, the effect of the baluns on the network VSWR was not removed. Also, the average two-way estimated loss of the time gated network was now 2 × 2.3dB =4.6dB (1dB lower than before due to the remaining baluns). The time gated VSWRshown in Fig. 8.13(a) is much closer to the simulated curve, but still reflects the effect of the baluns.

142 8.3.3 Realized Gain and Pattern Measurements

The measured and simulated realized gain at θ =30◦ of the 7 × 7 array for 30◦ scan in the H-plane are shown in Fig. 8.13(b). To account for the feed network loss we also plotted the measured gain augmented by a 2.3dB ﬂat loss. The compensated measured co-pol. gain is in generally good agreement with the simulated one. The diﬀerence between the measured and simulated cross-pol. gains was explained in Fig. 8.6 and is due to minor misalignments.

The measured and simulated radiation patterns are shown in Figs. 8.14, 8.15, 8.16,

8.17, 8.18. A close observation of the measured and simulated radiated patterns, reveals a very interesting phenomenon: beam squint vs. frequency. In fact, in the measured data the beam maximum squints from 8◦ − 30◦ throughout the 200MHz − 600MHz band. We

investigated this phenomenon and found that it occurs due to the ﬁnite ground plane eﬀects

on the active element pattern. Below follows a more detailed explanation.

143 10

6 measured measured, gated

VSWR 5 simulated

1 200 250 300 350 400 450 500 550 600 Frequency (MHz)

(a)

H−plane, θ = 30o 20

−10

−20 co−pol, measured co−pol, measured, +2.3dB −30 co−pol, simulated

Realized gain (dBi) cross−pol, measured cross−pol, measured, +2.3dB −40 cross−pol

−50

−60 200 250 300 350 400 450 500 550 600 Frequency (MHz)

(b)

Figure 8.13: Simulated and measured (a) corporate network VSWRand (b) realized gain of the 7 × 7 array shown in Fig. 8.3(b). These plots correspond to scanning at θ =30◦ in the H-plane.

144 10

−10

−20

−30

−40

−50

−60 Realized gain (dBi) −70 co−pol, H−plane −80 cross−pol, H−plane −90 co−pol, E−plane cross−pol, E−plane −100 −180 −150 −120 −90 −60 −30 0 30 60 90 120 150 180 θ (deg)

(a)

−10

−20

−30

−40

−50

−60 co−pol, H−plane Realized gain (dBi) −70 cross−pol, H−plane co−pol, E−plane −80 cross−pol, E−plane −90

−100 −180 −150 −120 −90 −60 −30 0 30 60 90 120 150 180 θ (deg)

(b)

Figure 8.14: (a) Simulated and (b) measured realized gain radiation patterns of the 7 × 7 array shown in Fig. 8.3(b) at 200MHz. These plots correspond to scanning at θ =30◦ in the H-plane.

145 10

−10

−20

−30

Realized gain (dBi) −40 co−pol, H−plane cross−pol, H−plane co−pol, E−plane −50 cross−pol, E−plane

−60 −180 −150 −120 −90 −60 −30 0 30 60 90 120 150 180 θ (deg)

(a)

−10

−20

−30

Realized gain (dBi) −40 co−pol, H−plane cross−pol, H−plane co−pol, E−plane −50 cross−pol, E−plane

−60 −180 −150 −120 −90 −60 −30 0 30 60 90 120 150 180 θ (deg)

(b)

Figure 8.15: (a) Simulated and (b) measured realized gain radiation patterns of the 7 × 7 array shown in Fig. 8.3(b) at 300MHz. These plots correspond to scanning at θ =30◦ in the H-plane.

146 co−pol, H−plane 10 cross−pol, H−plane co−pol, E−plane 0 cross−pol, E−plane

−10

−20

−30 Realized gain (dBi) −40

−50

−60 −180 −150 −120 −90 −60 −30 0 30 60 90 120 150 180 θ (deg)

(a)

−10

−20

−30

Realized gain (dBi) −40 co−pol, H−plane cross−pol, H−plane −50 co−pol, E−plane cross−pol, E−plane

−60 −180 −150 −120 −90 −60 −30 0 30 60 90 120 150 180 θ (deg)

(b)

Figure 8.16: (a) Simulated and (b) measured realized gain radiation patterns of the 7 × 7 array shown in Fig. 8.3(b) at 400MHz. These plots correspond to scanning at θ =30◦ in the H-plane.

147 10

−10

−20

−30

−40

−50 Realized gain (dBi) co−pol, H−plane −60 cross−pol, H−plane co−pol, E−plane −70 cross−pol, E−plane

−80 −180 −150 −120 −90 −60 −30 0 30 60 90 120 150 180 θ (deg)

(a)

−10

−20

−30

Realized gain (dBi) −40 co−pol, H−plane cross−pol, H−plane −50 co−pol, E−plane cross−pol, E−plane −60 −180 −150 −120 −90 −60 −30 0 30 60 90 120 150 180 θ (deg)

(b)

Figure 8.17: (a) Simulated and (b) measured realized gain radiation patterns of the 7 × 7 array shown in Fig. 8.3(b) at 500MHz. These plots correspond to scanning at θ =30◦ in the H-plane.

148 10

−10

−20

−30

Realized gain (dBi) −40 co−pol, H−plane −50 cross−pol, H−plane co−pol, E−plane cross−pol, E−plane −60 −180 −150 −120 −90 −60 −30 0 30 60 90 120 150 180 θ (deg)

(a)

−10

−20

−30

Realized gain (dBi) −40 co−pol, H−plane cross−pol, H−plane −50 co−pol, E−plane cross−pol, E−plane

−60 −180 −150 −120 −90 −60 −30 0 30 60 90 120 150 180 θ (deg)

(b)

Figure 8.18: (a) Simulated and (b) measured realized gain radiation patterns of the 7 × 7 array shown in Fig. 8.3(b) at 600MHz. These plots correspond to scanning at θ =30◦ in the H-plane.

149 8.3.4 Beam Squint vs. Frequency Phenomenon

The purpose of this section is to study the pattern of a ﬁnite array above a ﬁnite ground plane. Let us assume a linear dipole array comprised of 7−elements above a ground plane.

The element spacing is 2/7, which is exactly the same as in our 7 × 7 overlapping dipole

array. A typical dipole pattern over a ﬁnite ground plane in the H-plane [1] is shown in Fig.

8.19(a). Due to the ﬁnite ground plane size the element pattern tapers oﬀ as we move from

the broadside (θ =0◦) and eventually “folds” around it. The array factor is also shown assuming the phase progression β shown in Table 8.1. Although the array factor maximum occurs at 30◦ for all frequencies, as expected, the total pattern squints because the element

pattern is non-uniform. Fig. 8.19(b) shows the measured, simulated and theoretically

estimated beam squint with frequency. Because of that beam squint, beam steering can not

be performed with simple time delay methods. Time delay methods insert a linear phase

diﬀerence with frequency; but to avoid the beam squint the phase diﬀerence needs to be

controlled diﬀerently.

8.4 Conclusions

We presented measurement results for a 7 × 7 array of overlapping dipoles. In broadside

scan, the array achieves more than 3 : 1 bandwidth (200MHz − 600MHz)withmeasured

realized gain > 3dBi. The cross-pol. realized gain was below −10dBi. The measured radiation patterns were generally in agreement with the simulated ones, besides a small beam tilt, which occurred due to an actual physical tilt of the array during the measurement setup. Further, we carried out scan measurements for the same array. The array beam was successfully steered 30◦ oﬀ broadside with only a small reduction of its gain (> 0dBi)over the whole bandwidth. Scanning was achieved by controlling the element phases with simple

150 time delay. This was implemented by adding cable sections with progressively increasing length to the element feeds. We report that due to ﬁnite ground plane eﬀects the array beam squints with frequency. Therefore, scanning can not be performed by just adding delay, but only with regular phase shifters.

151 total pattern 0o o o element pattern 30 330

o 60 300o

1 0.8 0.6 0.4 o 0.2 90 270o

o 120 240o

array factor

o 150 210o 180o

(a)

Location of pattern maximum −5

measured −10 simulated estimated

−15

−20 (deg) θ

−25

−30

−35 200 250 300 350 400 450 500 550 600 Frequency (MHz)

(b)

Figure 8.19: (a) Normalized element pattern, array factor and total pattern for a 7−element linear dipole array above a ground plane. The element spacing was 2/7, exactly like our 7 × 7 array. (b) Measured, simulated and estimated beam squint vs. frequency.

152 Chapter 9: Conclusions and Future Work

9.1 Summary and Conclusions

Tightly coupled phased arrays (TCPAs) are one of today’s most attractive antenna sys-

tems. This owes to the fact that they combine two key features: ultra-wide bandwidth,

> 5 : 1 and and very low thickness proﬁle, <λ/10 at the lowest operational frequency.

Most notably, due to their multiple excitation ports, TCPAs allow for precise control of the

current amplitude and phase on the array aperture. This feature endows them with unique

beam steering and also MIMO (multiple input-multiple output) capabilities. However, the

demands for more broadband (20 : 1 bandwidth), thinner, and wider scan angle antennas

render the current state-of-the-art in TCPAs outdated. One of the main bandwidth-limiting

factors in contemporary TCPAs is associated with their feeding. This includes: the indi-

vidual element feeds, the power distribution scheme among the active elements, and also

the termination of edge elements. With these issues in mind, we proposed several practical

and innovative solutions.

In Chapter 1, we reviewed the existing types of tightly coupled phased arrays and

compared their bandwidth and thickness characteristics. In addition, we reviewed and

evaluated the diﬀerent feeding techniques used in these arrays.

153 The operating principles of TCPAs were explained in detail in Chapter 2, where, we established the relation between TCPAs and Wheeler’s uniform current sheet, an ideal radiator with unlimited bandwidth and scanning capabilities. We demonstrated, via numerical simulations, the bandwidth degradation of TCPAs when placed above a ground plane, and also presented Munk’s technique to address that problem. In essence, Munk identiﬁed the ground plane inductance as one of the bandwidth-limiting factors of TCPAs and utilized the mutual capacitance between adjacent elements to counteract that inductance. This technique led to a ∼ 2× increase of TCPA bandwidth (4.5 : 1) and reduction of their thickness

to λ/10 at the lowest operational frequency.

At the same time, Munk’s technique paved the way for the introduction of a novel and one of the most broadband and low-proﬁle antennas currently found in the literature: the interwoven spiral array (ISPA). The operation and design of the ISPA are presented in detail in Chapter 3. The ISPA achieves 10 : 1 bandwidth with thickness λ/23 at the lowest operational frequency. This performance exceeds by a factor of 2 the current state-of-the-art in TCPAs.

In Chapter 4, we studied the effects of size truncation on the bandwidth of tightly coupled phased arrays (TCPAs). We found that the concept of a uniformly excited aperture, present in infinite TCPAs and responsible for their wide bandwidth, is violated in finite size arrays. The size truncation of TCPAs leads to non-uniform aperture excitation and subsequently to bandwidth degradation. We studied that phenomenon using a 7 × 7 linear

tightly coupled dipole array. This array was ﬁrst designed as inﬁnite and tuned for maximum

VSWRbandwidth. We found that the impedance bandwidth of the 14 elements laying on

the two array edges perpendicular to the dipole lines, gets degraded the most. This occurred

because was those edge elements are the most electrically isolated and therefore experience

154 the least mutual coupling of all. Therefore exciting a ﬁnite array uniformly, just like an inﬁnite array, does not necessarily yield maximum VSWRbandwidth.

Two remedies to this problem are presented in Chapters 5 and 6. In particular, in

Chapter 5 we proposed a simple, yet eﬀective, array excitation technique for ﬁnite size ultra-wideband (UWB) TCPAs. To achieve improved active impedance matching at all N array elements, we considered the CMs of the N ×N mutual coupling matrix. Using the CM

current distributions we computed the optimal array excitation and feed-line impedances.

As compared to the standard uniform excitation, the CM excitation technique provides

superior impedance matching, simultaneously for all array elements (even the ones on the

edges) over a broad range of frequencies. Our approach revealed a very interesting fact:

that the impedance bandwidth of a ﬁnite array is proportional to the bandwidth of its

characteristic modes.

An alternative solution to the bandwidth degradation of ﬁnite size TCPAs was pro-

posed in Chapter 6, where we studied various techniques for terminating edge elements

is uniformly excited TCPAs. We evaluated resistive termination and short-/open-circuit

terminations and compared them in terms of array bandwidth, eﬃciency, realized gain and

radiation pattern. We found that for our 7 × 7 overlapping dipole array simple short-circuit

termination of the edge elements was the most eﬀective technique.

In Chapter 7, we discussed the most crucial component in TCPAS: their feed. Cur-

rently, one of the biggest challenges associated with TCPA feeding is the design of UWB

balun/impedance transformer. After reviewing the role of balun and also the basic balun

types suitable for TCPA feeding, we proposed two novel UWB designs. The ﬁrst was a

hybridization of printed transmission lines (TLs) and a miniature, coiled balun/impedance

transformer. As an improvement to that, we designed and tested a novel, fully printed,

155 compact, low-cost TL balun providing > 4 : 1 bandwidth and 4 : 1 impedance transformation ratio (50Ω − 200Ω). The latter design was developed as part of the feed for an 8 × 8 overlapping dipole array.

Finally in Chapter 8, we carried out measurements on a 7 × 7 overlapping dipole array.

The overall size of the array was 2 × 2 and thickness 6. The array was placed above a

4 ×4 ground plane. Based on ﬁndings we excited 21 elements and short-circuited 28 on the

array edges. Also, the hybrid feed proposed in Chapter 7 was incorporated into the design.

The array was measured in broadside and also for 30◦ scan in the H-plane. We found that for a broadside scan, the array achieves > 3 : 1 bandwidth with measured realized gain

> 3dBi and cross-pol. gain below −10dBi. When scanning at 30◦ in the H-plane, the array

gain was maintained > 0dBi for the whole frequency band.

9.2 Future Work

TCPAs are currently used almost exclusively in radar imaging and tracking applications. However, due to their multi-functionality a lot of interest arises in other areas such as telecommunication networks. The idea is to use the multiple ports of a TCPA for MIMO applications. Further, miniaturization of electronic components such as operational ampli-

ﬁers, mixers, phase-shifters, baluns and power dividers along with improvements in liquid crystal polymer (LCP) printing and MMIC (monolithic microwave integrated circuit) technology [8, 32, 55] are expected to spread the use of TCPAs to a plethora of wireless sensor applications.

This dissertation studied and introduced novel concepts for addressing modern TCPA challenges. These novel concepts could be used as a starting point for guiding several future research topics including the following:

156 • Improving: (a) the polarization purity, and (b) scanning capabilities of the 10 : 1

interwoven spiral array (ISPA).

• Implement the characteristic mode excitation technique and use it for scanning the

array beam.

• Study the eﬀect of edge element terminations for improving scan impedance band-

width of TCPAs.

• Further miniaturize and improve the bandwidth of currently used baluns for TCPA

feeding.

• Perform thermal analysis on array and balun to ensure high power tolerance.

157 Appendix A: Electrical Speciﬁcations of Power Dividers Used in 7 × 7 Array Measurements

Figure A.1: Electrical speciﬁcation of 1 : 8 power dividers.

158 Figure A.2: Electrical speciﬁcation of 1 : 3 power dividers.

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