2011_59_04

APRIL 2011 VOLUME 59 NUMBER 4 IETPAK (ISSN 0018-926X)

PAPERS

AntennasReconfigurable Axial-Mode Helix Antennas Using Shape Memory Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S. Jalali Mazlouman, A. Mahanfar, C. Menon, and R. G. Vaughan 1070Electrical Separation and Fundamental Resonance of Differentially-Driven Microstrip Antennas . . . . . . . . . . . . . Y. P. Zhang 1078A Modal Approach to Tuning and Bandwidth Enhancement of an Electrically Small Antenna . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J. J. Adams and J. T. Bernhard 1085Multi-Beam Multi-Layer Leaky-Wave SIW Pillbox Antenna for Millimeter-Wave Applications . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . M. Ettorre, R. Sauleau, and L. Le Coq 1093A Modal-Based Iterative Circuit Model for the Analysis of CRLH Leaky-Wave Antennas Comprising Periodically Loaded

PPW .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J. S. Gomez-Diaz, A. lvarez-Melcon, and T. Bertuch 1101Evolved-Profile Dielectric Rod Antennas . . . . . . . . . .. . . . . . . . . . S. M. Hanham, T. S. Bird, A. D. Hellicar, and R. A. Minasian 1113A Compact UWB Antenna for On-Body Applications . . . . . . . . . . . . . . . . . . N. Chahat, M. Zhadobov, R. Sauleau, and K. Ito 1123Design of a Corner-Reflector Reactively Controlled Antenna for Maximum Directivity and Multiple Beam Forming at

2.4 GHz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T. D. Dimousios, S. A. Mitilineos, S. C. Panagiotou, and C. N. Capsalis 1132ArraysEnergy Patterns of UWB Antenna Arrays With Scan Capability . . . . . . . . . . . . . . . . . . . . C.-H. Liao, P. Hsu, and D.-C. Chang 1140Method of Moments Analysis of Slotted Substrate Integrated Waveguide Arrays . . . . . .. . . . . . E. Arnieri and G. Amendola 1148Substrate-Integrated Cavity-Backed Patch Arrays: A Low-Cost Approach for Bandwidth Enhancement . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . M. H. Awida, S. H. Suleiman, and A. E. Fathy 11553D Power Synthesis with Reduction of Near-Field and Dynamic Range Ratio for Conformal Antenna Arrays . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . M. Comisso and R. Vescovo 1164Adaptive Wideband Beamforming With Frequency Invariance Constraints . . . . . . . . . . . . Y. Zhao, W. Liu, and R. J. Langley 1175A 4-Element Balanced Retrodirective Array for Direct Conversion Transmitter . . . . . . . . L. Chiu, Q. Xue, and C. H. Chan 1185Dual Grid Array Antennas in a Thin-Profile Package for Flip-Chip Interconnection to Highly Integrated 60-GHz Radios . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Y. P. Zhang, M. Sun, D. Liu, and Y. L. Lu 1191Evaluation of a New Wideband Slot Array for MIMO Performance Enhancement in Indoor WLANs . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J. R. Costa, E. B. Lima, C. R. Medeiros, and C. A. Fernandes 1200Parameter Estimation of Damped Power-Law Phase Signals via a Recursive and Alternately Projected Matrix Pencil

Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . K. Chahine, V. Baltazart, and Y. Wang 1207Lenses for Circular Polarization Using Planar Arrays of Rotated Passive Elements . . . . R. H. Phillion and M. Okoniewski 1217

(Contents Continued on p. 1069)

(Contents Continued from Front Cover)

Electromagnetics and PropagationAutomated Analytic Continuation Method for the Analysis of Dispersive Materials . . . . . . . . . . . . . . K. Inan and R. E. Diaz 12283D-Aggregate Quantitative Imaging: Experimental Results and Polarization Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C. Eyraud, J.-M. Geffrin, and A. Litman 1237Characterization of Metamaterials Using a Strip Line Fixture . . . . . . . .. . . . . . . . L. Yousefi, M. S. Boybay, and O. M. Ramahi 1245LF Ground-Wave Propagation Over Irregular Terrain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . L. Zhou, X. Xi, J. Liu, and N. Yu 1254Ultrawideband Multi-Static Scattering Analysis of Human Movement Within Buildings for the Purpose of Stand-Off

Detection and Localization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . M. Thiel and K. Sarabandi 1261Analytical Propagation Modeling of BAN Channels Based on the Creeping-Wave Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T. Alves, B. Poussot, and J.-M. Laheurte 1269Numerical TechniquesFast Optimization of Electromagnetic Design Problems Using the Covariance Matrix Adaptation Evolutionary Strategy . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . M. D. Gregory, Z. Bayraktar, and D. H. Werner 1275Self-Adaptive Differential Evolution Applied to Real-Valued Antenna and Microwave Design Problems . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S. K. Goudos, K. Siakavara, T. Samaras, E. E. Vafiadis, and J. N. Sahalos 1286Improving the Accuracy of the Second-Kind Fredholm Integral Equations by Using the Buffa-Christiansen Functions . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S. Yan, J.-M. Jin, and Z. Nie 1299A Low-Dispersion Realization of Precise Integration Time-Domain Method Using a Fourth-Order Accurate Finite

Difference Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Z.-M. Bai, X.-K. Ma, and G. Sun 1311High-order Div- and Quasi Curl-Conforming Basis Functions for Caldern Multiplicative Preconditioning of the EFIE . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . F. Valds, F. P. Andriulli, K. Cools, and E. Michielssen 1321On the FDTD Formulations for Modeling Wideband Lorentzian Media . . . . . . .. . . . . . . Z. Lin, Y. Fang, J. Hu, and C. Zhang 1338An Analytical Expression for 3-D Dyadic FDTD-Compatible Greens Function in Infinite Free Space via z-Transform

and Partial Difference Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S.-K. Jeng 1347Pulsed Beams Expansion Algorithms for Time-Dependent Point-Source Radiation. A Basic Algorithm and a

Standard-Pulsed-Beams Algorithm .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Y. Gluk and E. Heyman 1356

COMMUNICATIONS

Compact UWB Antenna With Multiple Band-Notches for WiMAX and WLAN .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . M.-C. Tang, S. Xiao, T. Deng, D. Wang, J. Guan, B. Wang, and G.-D. Ge 1372

A Wideband Stacked Offset Microstrip Antenna With Improved Gain and Low Cross Polarization . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . V. P. Sarin, M. S. Nishamol, D. Tony, C. K. Aanandan, P. Mohanan, and K. Vasudevan 1376

Dual-Band Circularly-Polarized CPW-Fed Slot Antenna With a Small Frequency Ratio and Wide Bandwidths . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C.-H. Chen and E. K. N. Yung 1379

Rectangular Dielectric Resonator Antennas With Enhanced Gain . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . A. Petosa and S. Thirakoune 1385Design of a Microstrip Monopole Slot Antenna With Unidirectional Radiation Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C.-J. Wang and T.-L. Sun 1389Compact and Tunable Slot-Loop Antenna . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . P.-L. Chi, R. Waterhouse, and T. Itoh 1394Design of SIW Cavity-Backed Circular-Polarized Antennas Using Two Different Feeding Transitions . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D.-Y. Kim, J. W. Lee, T. K. Lee, and C. S. Cho 1398UWB Dielectric Resonator Antenna Having Consistent Omnidirectional Pattern and Low Cross-Polarization

Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . K. S. Ryu and A. A. Kishk 1403Analog Direction of Arrival Estimation Using an Electronically-Scanned CRLH Leaky-Wave Antenna . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . S. Abielmona, H. V. Nguyen, and C. Caloz 1408On the Mathematical Link Between the MUSIC Algorithm and Interferometric Imaging . . . . . . G. Hislop and C. Craeye 1412On the Nature of Oscillations in Discretizations of the Extended Integral Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . G. Fikioris, N. L. Tsitsas, and I. Psarros 1415Time Domain UTD-PO Solution for the Multiple Diffraction of Spherical Waves for UWB Signals . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . P. Liu, J. Tan, and Y. Long 1420Asymptotic Expansion of the Associated Legendre Function Over the Interval . . . . . . . . . . . . . . . . . . J. S. Gardner 1424Experimental Verification of Link Loss Analysis for Ultrawideband Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . K. Rambabu, A. E.-C. Tan, K. K.-M. Chan, and M. Y.-W. Chia 1428The Design of an Ultrawideband T-Pulse With a Linear Phase Fitting the FCC Mask . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Z. Mei, T. K. Sarkar, and M. Salazar-Palma 1432

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ADMINISTRATIVE COMMITTEEM. SALAZAR PALMA, President S. R. BEST, President Elect J. S. TYO, Secretary-Treasurer

2011 2012 2013 2014A. AKYURTLUW. A. DAVISH. LINGM. OKONIEWSKIC. M. RHOADS*

Y. M. M. ANTARJ. T. BERNHARD*S. MACIM. MARTINEZ-VZQUEZD. F. SIEVENPIPER

M. ANDO*D. B. DAVIDSONM. EL-SHENAWEES. K. RAOM. W. SHIELDS

R. D. NEVELS*

Honorary Life Members: R. C. HANSEN, W. R. STONE*Past President

Committee Chairs and RepresentativesAntenna Measurements (AMTA): S. SCHNEIDERAntennas & Wireless Propagation Letters Editor-in-Chief:

G. LAZZIApplied Computational EM Society (ACES): A. F. PETERSONAP-S/URSI Joint Meetings Committee: J. L. YOUNGAwards: C. G. CHRISTODOULOUAwards Coordinator: C. A. BALANISBest Paper Awards H. NAKANOChapter Activities: Z. SHENCCIR: P. MCKENNACommittee on Man and Radiation: K. ITOConstitution and Bylaws: O. KILICDigital Archive Editor-in-Chief: A. Q. MARTINDistinguished Lecturers: D. R. JACKSONEducation: D. F. KELLYEAB Continuing Education: S. R. RENGARAJANElectronic Design Automation Council: M. VOUVAKISElectronic Publications Editor-in-Chief: S. R. BESTEuCap Representative: J. L. VOLAKIS

EuRAAP Representative: W. ROSS STONEFellows Nominations Committee: L. C. KEMPELFinance: J. S. TYOGold Representative:Historian: K. D. STEPHANIEEE Press Liaison: R. J. MAILLOUXIEEE Public Relations Representative: W. R. STONEIEEE Social Implications of Technology: R. L. HAUPTInstitutional Listings: T. S. BIRDJoint Committee on High-Power Electromagnetics:Long-Range Planning: J. L. VOLAKISMagazine Editor-in-Chief: W. R. STONEMeetings Coordination: S. A. LONGMembership:Nano Technology Council: G. W. HANSON & A. AKYURTLUNew Technology Directions: S. C. HAGNESSNominations: R. D. NEVELSPACE: J. M. JOHNSON

Publications: T. S. BIRDRegion 8 Representative: B. ARBESSER-RASTBURGRegion 9 Representative: S. BARBINRegion 10 Representative: J. L-W. LISensor Council: A. I. ZAGHOUL, T. S. BIRD, M. W. SHIELDSStandards CommitteeAntennas: M. H. FRANCISStandards CommitteePropagation: D. V. THIELTABARC Correspondent: C. A. BALANISTAB Magazines Committee: W. R. STONETAB New Technology Directions Committee: S. C. HAGNESSTAB Transactions Committee: M. A. JENSENTransactions Editor-in-Chief: M. A. JENSENTransnational Committee:USAB Committee on Information Policy: S. WEINUSAB R&D Committee: A. C. SCHELLUSNC/URSI: J. T. BERNHARDWomen in Engineering Representative: P. F. WAHID

AP Transactions website: http://ieeeaps.org/aps_trans/ AP Transactions Manuscript Central website: http://tap-ieee.manuscriptcentral.comChapter Chairs

Albuquerque: HARALD J. WAGNONArgentina: GUSTAVO FANOAtlanta: KRISHNA NAISHADHAMAustralian Capital Territory: DAVID MURRAYBaltimore: MARK PACEKBangalore, India: KALARICKAPARAMBIL VINOYBenelux: GUY VANDENBOSCHBoston: GREGORY CHARVATBulgaria: KATYA ASPARUHOVACalcutta: DEBATOSH GUHACentral & South Italy: GUGLIELMO DINZEOCentral Texas: JEREMY PRUITTChicago: HOWARD LIUCleveland: MAX SCARDELLETTICollege Station: GREG HUFFColumbus: FERNANDO L. TEIXEIRAConnecticut: CHARLOTTE BLAIRCroatia: RADOVAN ZENTNERCzechoslovakia: MILAN POLIVKADallas: NARINDRA LAKHANPALDayton: ANDREW TERZUOLIDenver-Boulder: MICHAEL JANEZICEast Ukraine: OKSANA V. SHRAMKOVAEastern North Carolina: TODD NICHOLSEgypt: HADIA EL-HENNAWYFinland: ARTTU LUUKANEN

Florida West Coast: JING WANGFoothill Section: MAN-FAI WONGFort Worth: MINGYU LUFrance: MAN-FAI WONGFSU Georgia: GIORGI GHVEDASHVILIFukuoda: MASAHIKO NISHIMOTOGermany: KLAUS SOLBACHGujarat, India: RAJEEV JYOTI SHARMAHarbin, China: QUN WUHong Kong: QUAN XUEHouston: STUART A. LONGHungary: LAJOS NAGYHuntsville: ERIC R. GRIGORIANHyderabad, India: LAKSHMI MERUGUIndonesia: EKO RAHARDJOIsrael: SHAMUEL AUSTERJapan Council: HIROYUKI ARAIKansai: KOICHI OGAWAKharkov: NIKOLAY N. KOLCHIGINKitchner-Waterloo: RAAFAT R. MANSOURLong Island: BRYAN TROPPERLithuania: VYTAUTAS URBANAVICIUSLos Angeles: JOHN GIANVITTORIOMalaysia: MAZLINA ESAMelbourne, FL: RICK BOTSFORD

Milwaukee: SHRINIVAS G. JOSHIMontreal: KE WUMorocco: MOHAMED ESSAAIDIMoscow: DIMITRY M. SAZONOVNagoya, Japan: TOSHIKAZU HORINanjing: WEI HONGNew Jersey Coast: WEI SUNew South Wales: KARU ESSELLENizhny Novgorod: GEORGE L. PAKHOMOVNorth Italy: GIUSEPPE VECCHINorth Jersey Coast: HAR DAYALNorway: YNGVE THODESENOrlando: XUN GONGOttawa: QIUBO YEPhiladelphia: JACK NACHAMKINPhoenix: STEVE ROCKWELLPoland: WOJCIECH J. KRZYSZTOFIKPortugal: NUNO BORGES DE CARVALHOPrinceton-Central Jersey: ALLEN KATZQueensland: ASHLEY ROBINSONRio de Janeiro: JOSE RICARDO BERGMANNSanta Clara Valley - San Francisco: PAUL HARMSSaratov/Penza: NIKITA M. RYSKINSeattle: LIXIN CAISeoul: JAEHOON CHOI

SE Michigan: TAYFUN OZDEMIRSiberia Section Tomsk: ROMAN V. MESCHERIAKOVSingapore: LING CHUEN ONGSouth Africa: RIANA GESCHKESouth Australia: CHRISTOPHE FUMEAUXSouthern Alberta: ELISE FEARSpain: JOSE I. ALONSOSpokane DON MINFORDSpringfield: PAUL SIQUERIASt Louis: DAVID MACKESt Petersburg: SVETLANA P. ZUBKOSweden: ANDERS RYDBERGSwitzerland: MICHAEL MATTESSyracuse: HAKAN PARTALTainan: HUA-MING CHENTaipei: JEAN-FU KIANGThailand: PRAYOOT AKKARAEKTHALINToronto: GEORGE ELEFTHERIADESTurkey: BIRSEN SAKATuscon: HAO XINUK/RI: ALI REZAZADEHVancouver: ALON NEWTONVictoria: KAMRAN GHORBANIWashington DC: BRIAN RIELYWest Ukraine: DR. IRYNA IVASENKOWinnipeg: VLADIMIR OKHMATOVSKI

IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATIONIs the leading international engineering journal on the general topics of electromagnetics, antennas and wave propagation. The journal is devoted to antennas, including analysis, design, development, measure-ment, and testing; radiation, propagation, and the interaction of electromagnetic waves with discrete and continuous media; and applications and systems pertinent to antennas, propagation, and sensing, suchas applied optics, millimeter- and sub-millimeter-wave techniques, antenna signal processing and control, radio astronomy, and propagation and radiation aspects of terrestrial and space-based communication,including wireless, mobile, satellite, and telecommunications. Author contributions of relevant full length papers and shorter Communications are welcomed.See inside back cover for Editorial Board.

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Digital Object Identifier 10.1109/TAP.2011.2137012

1070 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 59, NO. 4, APRIL 2011

Reconfigurable Axial-Mode Helix AntennasUsing Shape Memory Alloys

Shahrzad Jalali Mazlouman, Member, IEEE, Alireza Mahanfar, Member, IEEE, Carlo Menon, Member, IEEE, andRodney G. Vaughan, Fellow, IEEE

AbstractReconfigurable structures based on smart materialsoffer a potential solution to realize adaptive antennas for emergingcommunication devices. In this paper, a reconfigurable axial modehelix antenna is studied. A shape memory alloy spring actuator isused to adjust the height of a helix antenna. With the total lengthof the helix wire fixed, the pitch spacing and pitch angle are variedas the height is varied. This in turn can alter the antenna pattern inorder to adjust to altered operating conditions. In order to under-take the design, the Kraus equations for the axial mode helix arecompared with simulation results, and their range of applicabilityis clarified. It is shown that based on these equations, antenna gainvariation is possible by varying the height of the antenna, whilekeeping its conductor length fixed. We then show that a pattern canbe reconfigured using a two-helix structure. Finally, a proof-of-con-cept helix antenna is implemented using a shape memory alloy ac-tuator. Measurement results confirm that the pattern can recon-figure while maintaining a reasonable impedance match.

Index TermsConical helix, helix antenna, reconfigurable an-tenna, shape memory alloy, smart antenna, steerable beam.

I. INTRODUCTION

H ELIX antennas have widely been used since the 1950s[1][3], including conical, and other shapes. Helix an-tennas have different modes of operation [3]. The helix is op-erating in the axial mode when the circumference is about onefreespace wavelength, although miniaturization is possible e.g.,[4][6].

Axial-mode helix antennas are surface wave antennas andso have medium gain, and wideband characteristics [1], [2],[6][8]. In particular, helices are for circular polarization(CP) [9], and this was Kraus motivation for his pioneeringdevelopments.

The helix antenna continues to appear in new designs and re-search papers. Several variations focus on optimizing the length,pitch angle or radius of the helix antenna for a certain appli-cation. For example, in [10], the pitch angle of an axial-mode

Manuscript received April 05, 2010; revised August 18, 2010; acceptedSeptember 20, 2010. Date of publication January 31, 2011; date of currentversion April 06, 2011. This work was supported by the Natural Science andEngineering Research Council of Canada (NSERC).

S. Jalali Mazlouman, C. Menon, and R. G. Vaughan are with the School ofEngineering Science, Simon Fraser University, Burnaby, BC V5A 1S6, Canada(e-mail: [email protected]; [email protected]).

A. Mahanfar is with the Mobile Device Strategy and Commercialization(MDSC) Division, Microsoft Corporation, Redmond, WA 98052 USA.

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


helix antenna is varied in a non-linear manner from a relativelysmall angle at the feed end to a large angle at the open end ofthe antenna, to optimally match the surface wave velocity tothat of the free space, and to provide multiple peak gains. In[11], exponential pitch spacing is proposed in order to increasethe CP bandwidth of the axial mode. A spring-tunable normalmode helix whip antenna is built in [12] for vehicular mounting.In addition, a tri-band normal mode helix antenna to cover theEGSM/GPS/PCS bands is designed in [13] using a dual pitchhelix. In [14], a dielectric tuning element is used to fine-tunethe normal-mode. In [15], a variable pitch design is given fora variable scanning-mode helix. There are several other exam-ples, too numerous to list here, but these are representative ofthe activity and interest. However, little attention has been paidto adaptively controlling the axial mode helix structure.

Emerging wireless communication devices call for antennasthat can dynamically adjust antenna characteristics such asthe far-field radiation pattern, centre frequency or main lobedirection (squint), in response to changing operating condi-tions. For example, reconfigurable antennas can dynamicallyalter their pattern in order to improve reception or transmission(c.f., switched diversity) by improving gain to the wanted orsuppressing interference, or a combination of these.

The adjustment of antenna characteristics can be realizedthrough electrical, mechanical or other means [16]. Conven-tional methods include solid-state switches such as PiN diodes,e.g., [17], [18], and RF-MEMS switches, e.g., [19]. Usually, thefocus of these methods is to alter the electric length of the an-tenna by activating and deactivating critically located switches,which in turn vary the operating (impedance match) frequency.Alternatively, the pattern can be varied by switching parasiticelements, which has the great advantage of not locating theswitch in the signal path. However, solid state switches cansuffer from non-linearity and low isolation [20]. In addition,their cost and reliability can be prohibitive, mostly in the case ofMEMS switches. Usually, only certain discrete configurationscan be attained using these methods. Continuous operation ispossible, in principle, from parasitic element continuous reac-tance loading (e.g., using a varactor, although these also havepractical problems such as small tuning range and affecting theinput impedance [16]).

Mechanical reconfiguration of antennas is slow but is alsoclaimed to deliver the most dramatic antenna parameter vari-ations [21]. In mechanical reconfiguration, actuators can besmart materials such as piezoelectric actuators [21], electro-ac-tive polymers (EAPs) [22] and shape memory alloys (SMAs)[23]. Unlike switches, electromechanical approaches do not

0018-926X/$26.00 2011 IEEE

JALALI MAZLOUMAN et al.: RECONFIGURABLE AXIAL-MODE HELIX ANTENNAS USING SHAPE MEMORY ALLOYS 1071

introduce non-linearity in the RF path. One feature is thatthese can provide continuous change and therefore a smoothtransition between antenna parameters (e.g., the pattern).

In this paper, a reconfigurable axial-mode helix antenna is im-plemented using an axially located SMA spring as an actuator.It is shown that by applying a direct current to the SMA spring,the height of the helix antenna and therefore its pitch spacing isvaried. The helix makes an excellent reconfigurable antenna be-cause, unlike other antenna types, the spring-like helix structureis deformable without imposing too much stress to the conduc-tors. Although the variation of the axial mode helix height doesnot tilt the beam, it is demonstrated how multiple reconfigurableaxial mode helices can be used to steer the main lobe.

The rest of the paper is as follows: the concept of reconfig-urable axial-mode helix antennas is discussed in Section II. Itis shown that axial-mode helix antenna pattern parameters suchas gain and half-power beamwidth (HPBW) can be varied byvarying the pitch spacing (height) of the antenna and keeping theconductor length fixed. These variations are studied for a regularand conical helix antenna, using Finite Integration Technique(FIT) numerical methods (CST) and empirical Kraus equations.We clarify the range of configurations for the axial mode helixthat is covered by the Kraus design equations. In addition, weshow that a two-element helix antenna configuration can be usedto attain significant pattern reconfigurability.

In Section III, proof-of-concept experimental results are pre-sented for an implemented reconfigurable helix actuated by anSMA spring-based on the idea proposed in Section II. Finally,Section IV concludes the paper.

II. THE RECONFIGURABLE AXIAL-MODE HELIX ANTENNAA. The Regular Reconfigurable Helix Antenna

The helix antenna is operating in the axial mode when thecircumference is about one free space wavelength, viz.,

[1].Let be the radius of the helix, the wavelength in free space,the spacing between turns (pitch spacing), the number of

turns, the total height of the helix and the pitch angle, wehave [1]

(1)The height refers to the length of the helix antenna, following

Kraus, and some authors use length to describe this. Wefollow Kraus terminology and use length for the lengthof the wire making up the helix. Empirical equations weredeveloped by Kraus [1] for the axial-mode helix which link thepitch spacing and the directivity of the antenna

(2)where is the spacing between turns in free space wave-lengths, so the height of the helix is wavelengths. Inaddition, the HPBW is related to the helix pitch spacing as [1]

(3)

Equations (2) and (3) are restricted to pitch angles of[1, pp. 281284], although Kraus original

results [2] indicate optimal contours, based on axial ratio(AR), impedance, and beam pattern, can be extended outsidethese pitch angles to about ([2]; [1, p. 308]).King and Wong [24] also built many helix antennas and de-veloped further empirical equations for gain and HPBW overpitch angles 11.5 to 14.5 .

In this section, numerical experiments are used to investigatepitch angles well outside of Kraus 12 14 limits. This is mo-tivated by the potential of reconfiguring the helix by varyingin the pitch angle (height), with a constant length helical wire.Strictly speaking the radius of the helix changes, but this is smallbecause we are dealing with small pitch angles.

FIT simulation results (CST) are shown in Fig. 1(a), (b) fora thin-wire (0.7 mm diameter) copper helix with ,

, and varying from 35 to 195 mm (about). A plastic hollow cylindrical base (, ), inside the helix, has a radius of

7.5 mm. This is to provide mechanical stability, and to reduceits bending as the height is varied. The effect of the actuator(SMA spring) is also modeled by including another helical wireof radius , wire thickness of ,

and Nitinol conductivity ofinside the plastic tube with the same height as the he-

lical antenna. More information on the mechanical structure andthe SMA is given in Section III. A square copperground plane is used. Fig. 1 depicts, for different heights, vari-ations of: (a) ; and (b) the 4.35 GHz ) pattern forthe plane.

In Fig. 1(a), a reasonable match is observed for heights 70mm or more over a wide bandwidth around 4.35 GHz. Thismatching is attained by tuning the feed angle (initial angle ofwire at ground plane) as explained in [25] in all the numericalsimulations (i.e., all configurations), as well as the experiments.As expected from the empirical equations in [1], the axial modepattern of the helix antenna generally becomes more directive asthe antenna pitch spacing (height) increases, i.e., the maximumgain/directivity increases and the HPBW decreases. It is evidentfrom the figures that the axial mode pattern can be changed byvarying the pitch spacing while maintaining the same operatingfrequency.

To further inspect variations of the helix antenna parame-ters outside of the specified pitch spacing range, the maximumgain and HPBW are determined numerically and results are pre-sented in Fig. 2. Also, the empirical curves [1], [2] for theseparameters are presented for comparison. The directivity curvefollows the mean form of the numerical experiments. The oscil-lating form of the experiments is expected from surface radia-tion principles (which were developed mainly after Kraus anal-ysis). Consequently, the directivity formula is not very accuratefor a given structure (with a given surface wave velocity) butis an excellent rule of thumb for the mean gain (over differentpitch angles or surface wave velocities) of a copper helix. TheHPBW curve holds for larger pitch angles, but not for smallerpitch angles. Both results confirm that different pitch spacings(or height for fixed wire length) of an axial mode helix will givedifferent gains. A reconfigurable axial mode helix antenna, with


Fig. 1. CST Simulation results for variations of a reconfigurable helix antenna for various heights: (a) the ; (b) the 4.35 GHz, pattern cut, .

Fig. 2. Simulated (CST) and empirical formula computations of maximum gain and HPBW of the axial-mode helix antenna versus. height (pitch angle). Krausformulas are only for a pitch angle of 12 to 14 , but it is clear that they apply over a much larger range.

pitch angles between 2 to 16 looks promising. For example,Figs. 1 and 2 show a gain variation between 7 to 13 dB, when theheight is varied between 40 to 110 mm. An associated HPBWof between 60 to 45 can be attained if the height is varied be-tween 55 and 80 mm.

B. The Conical Reconfigurable Helix AntennaThe conical axial-mode helix antenna can be used as a recon-

figurable helix antenna in a similar manner as the regular helixantenna. The conical helix offers axial radiation over a muchwider bandwidth [26]. The conical spiral helix is more mechan-ically stable when its height is varied. In principle, no plasticsupport is required.

Simulation results for the of a conical helix with a max-imum radius of 18 mm and a radius ratio of 0.55, with 6 turnsand its height varied between 50 to 90 mm confirm reasonablematching for a wideband around 3 GHz. Similar to the cylin-drical helix, the patterns of the conical helix at 3 GHz (notshown) demonstrate that by varying the height of the helix from40 to 95 mm, the gain ranges from 10 to 11.5 dB and the HPBWfrom 65 to 50 . The radiation mechanism, where the main axialradiation is from the region of a one wavelength circumference,tends to compensate for the height (and pitch) change.

C. The Axial-Mode Dual-Helix AntennaThe application of the variable helix is not limited to gain

variations. Various configurations of commonly fed multiple he-lices with variable heights provide more significant pattern re-configurability. The number of helices, their height, as well astheir relative location can be configured to attain desired pat-tern configurations. For example, the beam can be squinted, asin Fig. 4(a), discussed below.

One such configuration consists of two helix antennas, oneright handed with height , and the other left handed withheight , located at a distance of apart, as shown in Fig. 3. Thehelices are of the same radius and are otherwiseidentical. Note that since the two antenna elements are not iden-tical, the array equations do not apply. Each helix antenna heightcan be independently controlled, similar to the structures dis-cussed in the previous subsections. The two helix antennas arefed axially from a fixed corporate feed via a common striplinewith the same line length to each helix from the feed line split.No attempt was made to balance the powers in each helix ele-ment, although the single port match remained reasonable (seeFig. 6 below, at a frequency of 4.5 GHz). The separation of thehelices and the location of the feed point are configured to pro-vide a changing radiation pattern with reasonable impedancematching around the design centre frequency, respectively.


Fig. 3. The axial-mode counter-wound two-helix antenna structure.

Fig. 4 depicts the variations of the 4.5 GHz pattern by con-trolling the heights of the two helix antennas as described above,located at a distance of apart: (a) for

; (b) for , ; and (c), . The power pattern (both polarizations)

is no longer a beam in the axial direction, in general. The patterncan be reconfigured, spanning different polarizations and gaindirections. Some detail is depicted in the 4.5 GHz pattern cut at

, of Fig. 5. The gain is not array-enhanced, as expectedsince the elements are not identical. The polarized patterns arenot displayed here. The change of gain direction is evident par-ticularly for the configurations and (40,50).The directional gain is low, but the patterns from these configu-rations are essentially orthogonal, and therefore useful in diver-sity/MIMO applications.

Diversity correlation coefficients (inner products) [27] for thepatterns indicated in Fig. 5 are reported in Table I. As evidentfrom this table, low correlation coefficients show the near-or-thogonality of the patterns for the larger height differences.

Fig. 6. depicts the variations of the of the two helix an-tenna. As seen in these figures, while different patterns can beattained by varying the heights of the two helices, reasonableimpedance matching ( below about 10 dB) is maintainedfor all the configurations shown, at 4.5 GHz. The matchingbandwidth could probably be improved by further adjustmentof the feed.

III. EXPERIMENTAL RESULTS

A. Shape Memory Alloys (SMAs)SMAs are materials that can restore their original configura-

tion by heating after they are plastically deformed at low temper-ature. Previous applications of the SMA actuators for antennasinclude contour optimization of large space reflector antennas[28] and deployable space antennas and structures [29].

One of the most common shape memory alloys is Nitinol, analloy of Nickel and Titanium. The temperature variation can berealized by passing a DC current through it. The SMA used inthis work is the BMX-150 Biometal spring by Toki [30]. Theseactuators can be elongated at room temperature, typically byan external force, and contracted by applying the DC current.Quick cooling and appropriate design of the actuator can pro-vide subsecond return time to the original shape [30].

Variations of a load-free BMX-150 length by passing DC cur-rents through it, in a test at room temperature of 20 is shown

Fig. 4. Variations of the radiation pattern of an axial-mode counterwound two-helix antenna array with a constant distance of and: (a) for , (b) for , , and (c) , , around the 4.5 GHz frequency.

in Fig. 7. As can be seen in this figure, up to 40 mm of lengthvariation (42%) can be attained by applying up to 180 mA DCcurrent.

The disadvantages of SMA materials include their potentialsensitivity to ambient temperature, their low energy efficiency( 5%), and their non-linear characteristics such as hysteresisproperties [31]. Hysteresis problems can cause difficulties inthe length control of the SMAs, but can be resolved by use offeedback control systems [31]. SMAs should be isolated fromthe ambient temperature if dramatic changes are expected due


Fig. 5. Variations of the 4.5 GHz power pattern at plane for the twocounterwound, axial-mode helices with variable heights.

TABLE ICORRELATION COEFFICIENTS FOR PATTERNS OF FIG. 5

Fig. 6. Variations of the of an axial-mode two-helix structure with and various heights of the two helix independently-tunable-height an-tennas, fairly good impedance matching around 4.5 GHz.

to their sensitivity to the environment conditions. The effect ofminor changes in the ambient temperature is however minor.This can accounted for using a closed loop control circuitry inan adaptive antenna design. For example, the maximum temper-ature of the SMA used in this implementation is given 50 .

In this paper, SMA spring actuators are used to vary the heightof the helix. The reconfigurable helix antenna system using thisspring is explained in the following subsection.

B. Hardware PrototypeAs a proof-of-concept, a reconfigurable axial-mode helix

antenna was implemented as shown in Fig. 8, comprising an

Fig. 7. Variations of the total length of a load-free BMX-150 SMA springagainst the DC current passed through it. Up to 40 mm of length variation (42%)can be attained using a maximum DC current of 180 mA.

Fig. 8. The reconfigurable axial-mode helix antenna: (a) full model,(b) building blocks as an exploded diagram, (c) the prototype at original height,when no current is applied, and (d) the compressed helix prototype when DCcurrent is passed through the SMA. The SMA spring is connected from the topof the helix to below the groundplane by a thin wire which is between the helixand the SMA spring.

11-turn helix made of copper wire, a radius of 9.9 mm andwire thickness 0.7 mm. This antenna is wound loosely around acylindrical hollow plastic base (shown in Fig. 8(a), (b) and theprototype shown in Fig. 8(c), (d)) and fed from the center of a

square copper ground plane.Two SMA spring actuators in series (BMX-150 Biometal

Springs by Toki) are passed through the plastic tube with oneend connected to the open end of the helix and the other endpassed through a small hole and fixed under the ground plane,where it is connected to the DC circuitry. Note that the SMAis located inside the plastic cylinder and is only visible inFig. 8(b), which depicts an exploded diagram of the structure.

When sufficient DC current is applied to the SMA springs,they shrink, thereby decreasing the height and the spacing be-tween turns of the helix antenna. In this way, the heightof the antenna can be changed by changing the current passing


Fig. 9. Simulation and measurement results for the reconfigurable helix for some selected sweep points.

through the SMAs. When no current is applied, an external re-verse force spring is required to expand the SMA springs andreturn the helix antenna to its original height. The helix antennaitself acts as this external force spring to return the antenna toits original state.

Note that the SMA and the antenna are electrically isolated.The SMA spring actuators showed little hysteresis effect. Theyrequire a maximum DC current of 200 mA for full actuation,equivalent to shrinking (height variation) by 90 mm. Note thatthe variation is continuous and therefore smooth transitions be-tween various antenna pattern configurations are feasible. The

and patterns for different heights of the helix antenna arepresented in the following section.

C. Measurement ResultsThe reconfigurable helix system is measured using a 5071

Agilent VNA for measurements and a Satimo StarLab ane-choic chamber for pattern measurements. Measurements weredone under normal room temperature.

Fig. 9 depicts measurement results for some heights ofthe helix antenna (60, 70, 80 mm) as well as the simulationresults for the 80 mm, for comparison. It can be seen thatgood impedance matching is attained around 44.5 GHz forall sweep points (not all sweep points are shown, for brevity),as also expected from the simulation results. The match ispartly a result of manually adjusting the angle of the wire feed.The simulations below included the plastic base and the SMAspring. As expected, the prototype axial-mode helix is a fairlywideband structure and maintains its wide frequency band-width while mechanically reconfigured. Reasonable agreementis observed around the matching frequencies, i.e., 44.5 GHzbetween simulation and measurement results. The discrepan-cies are partly due to the uneven pitch spacing in the physicalhelix structure (c.f., Fig. 8(c) and (d)). A mechanical structureusing a more elastic wire for the antenna (or an actual springwith sufficiently low spring coefficient to be tunable using anSMA actuator), could improve the uniformity of pitch spacing.

Note that as stated before, the plastic is a thin cylinder forsupporting the helix conductors. It is not an essential part of the

antenna for radiation or actuation. It was chosen from readilyavailable material. It could be replaced by Styrofoam or anyother type of low loss material. The effect of the plastic is no-ticeable on the resonance frequency and is included in the sim-ulation. The SMA actuator does not have a significant impacton the antenna radiation pattern. This is because it has a muchsmaller radius than the helix and is centrally located. The pres-ence of a small center conductor in an axial mode helix is knownto not affect the patterns much. Many axial mode helices arein fact constructed this way. The radius of axial-mode helixis relatively large and the distance to the shape memory alloy(SMA) in the axis of the helix is substantial, given the radiusof SMA is sub-millimeter. Therefore the contribution of theSMA in overall radiation pattern is not significant. These ef-fects are modeled in numerical simulations and confirmed bymeasurements.

Fig. 10(a)(c) depict radiation pattern measurement resultsat 4.35 GHz for selected heights from 40 to 150 mm. Thesemeasurement results report the realized gain and thereforeinclude the effect of the plastic support and the SMA spring.As expected from simulation results, the pattern can be ad-justed by varying the helix height. Fig. 10(d) compares themaximum gain (empirical directivity), simulation (gain), andthe Fig. 10(a) measurement (realized gain) results for variousheights. (Impedance match is maintained over the band). Thegain of the helix can be adjusted from about 7.4 to 12.4 dB.However, this trend is not monotonic, as expected from surfacewave radiation principles. The speed of the axial mode surfacewave along the helical structure and the separation distanceof the feed and open end (the locations of radiation) are bothchanged. Comparing Figs. 10 and 2, it can be seen that simula-tion pattern results match the measurements reasonably well.

Fig. 11 depicts the experimental results for the axialratio of the helix antenna versus variations of its height. It canbe seen that the circular polarization is well maintained withinthe HPBW. The axial direction has a worst case axial ratio of 2,or a cross polar ratio of about 18 dB.

The dual helix structure has not been implemented physi-cally. However, the simulated patterns can be expected to bereliable and we have demonstrated the SMA actuation of asingle element. The dual helix structure is a subject of futuredevelopment.

IV. CONCLUSION AND SUMMARY

In this paper, a reconfigurable helix antenna is implementedusing shape memory alloy spring actuators. The height andtherefore pitch spacing of the helix is governed by the lengthof an SMA spring along the axis of the helix. Applying a directcurrent to the SMA spring causes it to shrink which decreasesthe pitch spacing and height of the helix antenna, while theradius is essentially constant owing to the small pitch angles.

Observations from both simulations and physical measure-ments confirm the Kraus empirical relations for the axial modehelix. The directivity equation is a good fit apart from the os-cillations expected from the surface wave radiation. The axialmode is dominant over a very wide range of pitch angles, and weuse this for a reconfigurable axial mode antenna. Experimentalresults demonstrate a reconfigurable axial-mode helix antennathat can maintain a reasonable impedance match and axial ratio


Fig. 10. Experimental results for variations of the implemented reconfigurable helix antenna parameters for some selected heights: the 4.35 GHz radiation pattern:(a) , (b) , (c) , and (d) the maximum gains at (measurements are from (a), for example), compared with simulation results.The gain from the simulations is compared to the realized gain of the measurements, (however, the impedance match is reasonable as seen in Fig. 9) and to theempirical directivity.

Fig. 11. Experimental results of AR of the prototype vs. height variations within HPBW. The AR increases drastically beyond the depicted range.

over a wide range of height variations. A dual helix structureallows beam squint through mutual reconfiguration.

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[27] R. G. Vaughan and J. B. Anderson, Antenna diversity in mobile com-munication, IEEE Trans. Veh. Technol., vol. VT-36, pp. 1491987.

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[29] S. H. Mahdavi and P. J. Bentley, Evolving noise tolerant antenna con-figurations, using shape memory alloys, presented at the 2nd Int. Conf.on Comp. Intel., Robotics and Auton. Syst. (CIRAS 2003), Dec. 2003.

[30] BMX Biometal Springs Datasheet. Toki, Japan [Online]. Available:http://www.toki.co.jp/BioMetal/

[31] J. Jayender, R. V. Patel, N. Nikumb, and M. Ostojic, Modeling andcontrol of shape memory alloy actuators, IEEE Trans. Control Syst.Tech., vol. 16, no. 2, Mar. 2008.

Shahrzad Jalali Mazlouman (M09) received theB.Sc. and M.Sc. degrees in electrical engineering(electronics) from Amirkabir University of Tech-nology (Tehran Polytechnic), Tehran, Iran, in 2001and 2003, respectively, and the Ph.D. degree inelectrical and computer engineering from Universityof British Columbia (UBC), Vancouver, BC, Canada,in 2008.

She has worked on several mixed-signal, RF,and antenna system designs. In 2007, she workedas a mixed-signal intern at PMC-Sierra, Burnaby,

BC, Canada. Since 2009, she has been a Postdoctoral Fellow at the School ofEngineering Science, Simon Fraser University (SFU), Burnaby, BC, Canada,where she is working on reconfigurable RF and antenna systems for wirelesscommunication devices, using smart material actuators.

Alireza (Nima) Mahanfar (S99M05) re-ceived the B.S. (honors) and M.S. degrees fromAmirkabir University of Technology (TehranPolytechnic), Tehran, Iran, in 1997 and 1999, respec-tively, and the Ph.D. degree from XLIM (formerlyIRCOM), Limoges, France, in 2005, all in electricalengineering.

From 2006 to 2007, he was with Simon Fraser Uni-versity, Burnaby, Canada, as a Research Associate.From 1998 to 2005, he was with a number of or-ganizations including Electromagnetics Lab (Tehran

Polytechnic), Tehran, and Wireless 2000, Sierra Wireless and Nokia MobilePhones, all in BC, Canada. Since December 2009, he has been with MobileDevice Strategy and Commercialization (MDSC) Division, Microsoft Corpora-tion, Redmond, WA, where he is involved in the research and development ofantennas for portable devices. His research interests are design of antennas andradio-frequency circuits.

Dr. Mahanfar is the recipient of an NSERC Postdoctoral Fellowship (2005),and URSI Young Scientist Award (2007).

Carlo Menon (M04) received the Laurea degree inmechanical engineering from the University of Padua,Italy, in 2001 and the Ph.D. degree in space sciencesand technologies from the Centre of Studies and Ac-tivities for SpaceG. Colombo, Italy, in 2005.

He was a Visiting Scholar at Carnegie Mellon Uni-versity, in 2004, and a Research Fellow at the Euro-pean Space Agency, The Netherlands, in 2005 and2006. Since 2007, he has been an Assistant Professorat Simon Fraser University (SFU), Burnaby, Canada,where he leads the MENRVA Research Group (http://

menrva.ensc.sfu.ca). He is an Associate Member to both the School of Biomed-ical Physiology and Kinesiology and the Institute of Micromachine and Micro-fabrication Research at SFU. His research team is focusing on mechatronics,smart materials and structures, robotics, and bioinspired systems with applica-tions especially in the biomedical and space sectors.

Dr. Menon is an AIAA, ASME, BIONIS, and IAF member. He received theInternational IAF Luigi G. Napolitano Award, Spain, in 2006, and the Interna-tional BIONIS Award on Biomimetics, U.K., in 2007. He is currently a Reviewerfor about 20 international journals and is on the editorial board of the Journalof Bionic Engineering.

Rodney G. Vaughan (F07) received the Bachelorand Masters degrees from the University of Canter-bury, New Zealand, in 1975 and 1976 respectively,and the Ph.D. degree from Aalborg University, Den-mark, in 1985, all in electrical engineering.

He worked with the New Zealand Post Office (nowTelecom NZ Ltd) and the NZ Department of Scien-tific and Industrial Research, and Industrial ResearchLimited (IRL). Here he undertook a wide variety ofpractical mechanical and electrical projects includingnetwork analysis and traffic forecasting, and devel-

oped microprocessor and DSP technology for equipment ranging from abattoirhardware to communications networks. He was an URSI Young Scientist in1982 for Fields and Waves, and in 1983 for Electromagnetic Theory. He devel-oped research programs and personnel working in communications technologyfor IRL, revolving around signal processing, multipath communications theory(electromagnetic, line and acoustic media), diversity design, signal theory, andDSP. Industrial projects included the design and development of specialist an-tennas for personal, cellular, and satellite communications, large-N MIMO com-munications systems design; and also capacity theory and spatial field theory.In 2003, he became Professor of Electrical Engineering and Sierra WirelessChair in Communications, at the School of Engineering Science, Simon FraserUniversity, Burnaby, BC, Canada. His current research for mobile communica-tions involves propagation theory, communications signal processing and theoryand design of antennas. Recent projects include compact mammalian bio-im-plantable antennas; multielement antenna design and evaluation; circularly po-larized antennas, multifaceted structures for large arrays; microelectronic an-tenna structures, MIMO capacity realization; and blind-, precoding- and inter-ference mitigation-techniques for OFDM.

Dr. Vaughan has guest-edited for several special issues including the IEEEANTENNAS AND PROPAGATION TRANSACTIONS Special Issue on Wireless Com-munications. He is a Fellow of the BC Advanced System Institute, an URSICorrespondent, and continues as the New Zealand URSI Commission B (Fieldsand Waves) representative.


Electrical Separation and Fundamental Resonance ofDifferentially-Driven Microstrip Antennas

Y. P. Zhang, Fellow, IEEE

AbstractThis paper studies the electrical separation and fun-damental resonance of differentially-driven microstrip antennaswith dual-probe feeds on both electrically thick substrate of highpermittivity and electrically thin substrate of low permittivity. Theelectrical separation is defined as the ratio of the distance ofthe dual-probe feeds to the free-space wavelength . It is foundthat the occurrence of resonance of the fundamental mode is re-lated with the electrical separation of the dual-probe feeds. Whenthe electrical separation is satisfied, the resonance oc-curs. Otherwise, the resonance does not occur. It is shown thatthe empirical factor is smaller for the electrically thicker sub-strate of higher permittivity than that for electrically thinner sub-strate of low permittivity and is smaller for the circular patch thanthat for the rectangular patch. To validate the relationship of theoccurrence of fundamental resonance with the electrical separa-tion, several differentially-driven microstrip antennas were fab-ricated on the electrically thin substrate of the low permittivityand measured. It is observed that the simulated and measured re-sults are in acceptable agreement for these differentially-driven mi-crostrip antennas. Thus, the electrical separation condition derivedin this paper should be very useful in guiding the design of differ-entially-driven microstrip antennas.

Index TermsInput impedance, microstrip antenna, resonance.

I. INTRODUCTION

M ICROSTRIP antennas have many unique and attractivepropertieslow in profile, light in weight, compactand conformable in structure, and easy to fabricate and to beintegrated with solid-state devices [1], [2]. Therefore, theyhave been widely used in radio systems for various appli-cations. Radio systems have been traditionally designed forsingle-ended signal operation, so have been microstrip an-tennas. Recently, radio systems have begun to be designed fordifferential signal operation [3]. This is because the differentialsignal operation is more suitable for high-level integration orsingle-chip solution of radio systems. Radio systems that adoptdifferential signal operation require differential antennas to getrid of bulky off-chip and lossy on-chip balun to improve thereceiver noise performance and transmitter power efficiency[4]. There have been a few papers about differential microstripantennas [5][10]. Of which [5][8] focus on integration with

Manuscript received January 29, 2010; revised August 13, 2010; acceptedNovember 23, 2010. Date of publication January 31, 2011; date of current ver-sion April 06, 2011.

The authors is with the Integrated Systems Research Lab, School of Elec-trical and Electronic Engineering, Nanyang Technological University, Singa-pore 639798, Singapore (e-mail: [email protected]).

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


solid-state circuits and only [9] extends the cavity model toanalyze differentially-driven microstrip antennas. The extendedcavity model provides physical insight into the differentialsignal operation of microstrip antennas but it fails to yieldaccurate prediction of the performance, especially when anelectrically thick substrate of high permittivity is used in at-tempting to achieve miniaturization and larger bandwidth. Forthese situations, a rigorous full-wave method has to be used[10]. In this paper we study differentially-driven microstripantennas using the HFSS simulator from Ansoft. The HFSSis a rigorous full-wave electromagnetic simulator based onthe finite element method. We analyze the relationship of theoccurrence of resonance of the fundamental mode with theelectrical separation of the differentially-driven microstripantennas in Section II. We describe the experiment and discussthe measured results to validate the analysis in Section III.Finally, we summarize the conclusions in Section IV.

II. ANALYSIS OF ELECTRICAL SEPARATION ANDFUNDAMENTAL RESONANCE

A microstrip antenna and a coordinate system are illustratedin Fig. 1(a). The microstrip patch located on the surface of agrounded dielectric substrate with thickness , dielectric rela-tive permittivity , and dielectric loss tangent is differentiallydriven at points and with dual-probe feeds. Inthis figure, denotes a shape for the microstrip patch andmeans its area. Typical rectangular and circular microstrip patchshapes as shown in Fig. 1(b) and (c) are considered in this paper.

The input impedance of the differentially-driven mi-crostrip antenna is given by [9]

(1)

where the parameters are defined at the driving pointsand and they can be easily calculated with the HFSSsimulator. If the differentially-driven microstrip antenna is in-deed symmetric, (1) simplifies to

(2)

which reveals that there is a cancellation mechanism, which mayimprove the impedance bandwidth. The value of is requiredin the design of matching network between the differentially-driven microstrip antenna and the differential active circuitry ina radio system. The calculated from is given by

(3)

0018-926X/$26.00 2011 IEEE

ZHANG: ELECTRICAL SEPARATION AND FUNDAMENTAL RESONANCE OF DIFFERENTIALLY-DRIVEN MICROSTRIP ANTENNAS 1079

Fig. 1. Differentially-driven microstrip antenna: (a) Arbitrary patch in three-dimensional view, (b) rectangular patch, and (c) circular patch.

where is 100 . When the imaginary part of the inputimpedance

(4)happens, the resonance occurs. The fundamental resonance is ofimportance because the microstrip antenna is usually designedto operate near the resonant frequency of the fundamental mode.It is found that the fundamental resonance is related with theelectrical separation of the dual-probe feeds. The electrical sep-aration is defined as the ratio of the distance between thedual-probe feeds to the free-space wavelength , which is sim-ilar to what we define the electrical thickness of a sub-strate. The substrate is electrically thick when andis electrically thin when . A microstrip antenna on

an electrically thick substrate of high permittivity has a smallerpatch size and a larger bandwidth; while a microstrip antenna onan electrically thin substrate of low permittivity achieves goodradiation efficiency and reasonable bandwidth. In the followingwe will analyze the relationship of the fundamental resonancewith the electrical separation of the dual-probe feeds of differen-tially-drive rectangular and circular microstrip antennas on bothelectrically thick substrate of high permittivity and electricallythin substrate of low permittivity, respectively.

A. Electrically Thick Substrate of High PermittivityConsider a square RT/duriod 6010 substrate of side length

(about one at 2.24 GHz), thickness, dielectric constant and dielectric loss

tangent . A rectangular microstrip patch that hasthe length in the Y direction 19 mm and the width in the X di-rection 30 mm is on the middle of the substrate. The diameterof the probes is 1.0 mm. Simulations show that the rectangularmicrostrip antenna driven at is matchedto a 50- single-ended signal source at 2.26 GHz. Measure-ments indicate that the rectangular microstrip antenna driven at

is matched to a 50- single-ended signalsource at 2.24 GHz [11], [12]. Hence, the simulator can sat-isfactorily predict the occurrence of resonance of the funda-mental mode of this rectangular microstrip antenna. We locatethe second driving point at the mirror point ofalong the line within the patch for the best differen-tial signal operation. It is found that the rectangular microstripantenna driven at and isalso matched to a 100- differential signal source at 2.26 GHz.

The simulated resonance of the fundamental mode ofthe differentially-driven rectangular microstrip antenna occursat 2.23 GHz. The electrical thickness is indicatingthat the differentially-driven rectangular microstrip antenna isindeed on an electrically thick substrate. Table I shows the sim-ulated input impedance as a function of electrical separation.Note that the resonance of the fundamental mode occursfor the electrical separation . The larger theelectrical separation, the lower the resonant frequency is and thehigher the resonant resistance is. For example, the resonant fre-quency is 2.22 GHz and the resonant resistance is 420 forthe electrical separation , while the resonant fre-quency decreases to 2.2 GHz and the resonant resistance in-creases to 935 for the electrical separation . Itis also seen that the resonance of the fundamental modedoes not occur for the electrical separation . Theinput resistance is quite small and the input impedance is in-ductive. For example, at 2.25 GHz for theelectrical separation .

Then consider a circular microstrip patch with the radius 9.92mm on the middle of the substrate that has the same electricalproperties as we used for the rectangular microstrip patch butslightly smaller side length 111 mm (about one at 2.71 GHz).The diameter of the probes is also 1.0 mm. It is found that thecircular microstrip antenna driven at ismatched to a 50- single-ended signal source. The simulatedresonance of the fundamental mode occurs at 2.58 GHz.


TABLE IRESONANCE AND ELECTRICAL SEPARATION OF THE DIFFERENTIALLY-DRIVEN

RECTANGULAR MICROSTRIP ANTENNA ON THE ELECTRICALLY THICKSUBSTRATE OF HIGH PERMITTIVITY

TABLE IIRESONANCE AND ELECTRICAL SEPARATION OF THE DIFFERENTIALLY-DRIVEN

CIRCULAR MICROSTRIP ANTENNA ON THE ELECTRICALLY THICKSUBSTRATE OF HIGH PERMITTIVITY

The measured resonance of the fundamental mode oc-curs at 2.71 GHz [11]. The simulator can predict the occur-rence of resonance of the fundamental mode of the circularmicrostrip antenna; however, the predicted resonant frequencyhas 4.8% error from the measured result. We locate the seconddriving point at the mirror point of along theline within the patch. It is found that the cir-cular microstrip antenna driven at and

is matched to a 100- differential signalsource.

The simulated resonance of the fundamental mode ofthe differentially-driven circular microstrip antenna occurs at2.575 GHz. The electrical thickness is indicatingthat the differentially-driven circular microstrip antenna is in-deed on an electrically thick substrate. Table II shows the simu-lated input impedance as a function of electrical separation.Note that the resonance of the fundamental mode occursfor the electrical separation . The larger theelectrical separation, the lower the resonant frequency is and thehigher the resonant resistance is. For example, the resonant fre-quency is 2.55 GHz and the resonant resistance is 545 forthe electrical separation , while the resonant fre-quency decrease to 2.49 GHz and the resonant resistance in-creases to 1200 for the electrical separation . Itis also seen that the resonance of the fundamental modedoes not occur for the electrical separation . Theinput resistance is small and the input impedance is inductive.For example, at 2.575 GHz for the electricalseparation .

TABLE IIIRESONANCE AND ELECTRICAL SEPARATION OF THE DIFFERENTIALLY-DRIVEN

RECTANGULAR MICROSTRIP ANTENNA ON THE ELECTRICALLYTHIN SUBSTRATE OF LOW PERMITTIVITY

B. Electrically Thin Substrate of Low PermittivityConsider a square RT/duriod 5880 substrate of side length

(about one at 3.8 GHz), thickness, dielectric constant and dielectric loss

tangent . A rectangular microstrip patch that hasthe length in the Y direction 25 mm and the width in the X di-rection 40 mm is on the middle of the substrate. The diameter ofthe probes is 1.0 mm. It is found that the rectangular microstripantenna driven at is matched to a 50-single-ended signal source. The simulated resonance of the fun-damental mode occurs at 3.83 GHz. The measured reso-nance of the fundamental mode occurs at 3.92 GHz [12].The simulator can acceptably predict the occurrence of reso-nance of the fundamental mode of the rectangular microstrip an-tenna. We locate the second driving point at the mirrorpoint of along the line within the patchfor the best differential signal operation. It is found that the rect-angular microstrip antenna driven at and

is matched to a 100- differential signalsource.

The simulated resonance of the fundamental modeof the differentially-driven rectangular microstrip antennastill occurs at 3.83 GHz, the same as that of the single-endedrectangular microstrip antenna. The electrical thickness is

indicating that the differentially-driven rect-angular microstrip antenna is indeed on an electrically thinsubstrate. Table III shows the simulated input impedanceas a function of electrical separation. Note that the resonanceof the fundamental mode occurs for the electrical sepa-ration . The larger the electrical separation,the lower the resonant frequency is and the higher the resonantresistance is. For example, the resonant frequency is 3.8 GHzand the resonant resistance is 280 for the electrical separation

, while the resonant frequency decreases to 3.78GHz and the resonant resistance increases to 488 for theelectrical separation . It is also seen that theresonance of the fundamental mode does not occur forthe electrical separation . The input resistanceis small and the input impedance is inductive. For example,

at 3.83 GHz for the electrical separation.

Then consider a square RT/duriod 5870 substrate of sidelength (about one at 3.8 GHz), thickness


TABLE IVRESONANCE AND ELECTRICAL SEPARATION OF THE DIFFERENTIALLY-DRIVEN

CIRCULAR MICROSTRIP ANTENNA ON THE ELECTRICALLYTHIN SUBSTRATE OF LOW PERMITTIVITY

, dielectric constant and dielectricloss tangent . A circular microstrip patch with theradius 14.85 mm is on the middle of the substrate. The diam-eter of the probes is also 1.0 mm. It is found that the circularmicrostrip antenna driven atis matched to a 50- single-ended signal source. The simulatedresonance of the fundamental mode occurs at 3.72 GHz.The measured resonance of the fundamental mode alsooccurs at 3.72 GHz [12]. Hence, the simulator can accuratelypredict the occurrence of resonance of the fundamental modeof the circular microstrip antenna. We locate the second drivingpoint at the mirror point of along the line

within the patch. It is found that the circularmicrostrip antenna driven at and

is matched to a 100- differentialsignal source.

The simulated resonance of the fundamental mode ofthe differentially-driven circular microstrip antenna still occursat 3.72 GHz, the same as that of the single-ended circular mi-crostrip antenna. The electrical thickness is indi-cating that the differentially-driven circular microstrip antennais indeed on an electrically thick substrate. Table IV shows thesimulated input impedance as a function of electrical separa-tion show that the resonance of the fundamental mode oc-curs for the electrical separation . The largerthe electrical separation, the lower the resonant frequency is andthe higher the resonant resistance is. For example, the resonantfrequency is 3.69 GHz and the resonant resistance is 550 forthe electrical separation , while the resonant fre-quency increases to 3.675 GHz and the resonant resistance de-creases to 800 for the electrical separation . Itis also seen that the resonance of the fundamental modedoes not occur for the electrical separation . Theinput resistance is quite small and the input impedance is induc-tive. For example, at 3.775 GHz for theelectrical separation .

C. On Electrical Separation and Fundamental ResonanceHaving observed the dependence of occurrence of resonance

of the fundamental mode on electrical separation of dual-probefeeds for differentially-driven microstrip antennas, we now ex-plain it as follows. For a dual-probe-feed microstrip antenna, itis known that the dual-probe feeds introduce not only the self

Fig. 2. Magnitude of electric field at 3.75 GHz on the patch of the circularmicrostrip antenna with dimensions given in this Section II-B.

and mutual inductances but also the capacitance between them.The mutual inductance and the capacitance depend on electrical(or physical) separation, the larger an electrical separation is,the smaller the mutual inductance and the capacitance are. Itis found that regardless of electrical separation, the dual-probefeeds contribute inductively rather than capacitively to the inputimpedance over the frequency range. This is because thecapacitance between the dual-probe feeds, although relativelylarger for a smaller electrical separation, is still too small; whilethe inductance of the dual-probe feeds, which is the sum of thepositive self and negative mutual inductances, is still quite largeeven for the smaller electrical separation. Hence, one can con-clude that it is not the inductance of the dual-probe feeds thatprevents the occurrence of resonance of the fundamental modefor the differentially-driven microstrip antenna when the elec-trical separation condition is satisfied. Rather, it is the funda-mental mode that cannot be well excited when the dual-probefeeds are brought physically closer to a certain extent or theelectrical separation condition is satisfied. Under such circum-stances, the dual-probe feeds are located in the weak field regionof the fundamental mode, thus making it impossible to stronglyexcite the fundamental mode but higher order modes. Since theresonant wavelength of higher order modes is shorter for thegiven microstrip patch dimension, the resistance generally de-creases with mode order, thus resulting in a smaller resistanceand inductive impedance [2].

Fig. 2 shows the magnitude of electric field on the patchof the circular microstrip antenna driven differentially with thedual-probe feeds and with a single-probe feed, respectively. Theweak field region for the single-probe feed, as predicted fromthe cavity model, is an approximately-elliptical zone near a di-ameter of the patch. The minor axis of a zone is always alongthe line drawn from the feed point to the patch center, whilethe major axis of the zone is, of course, along the patch di-ameter. The weak field region for the dual-probe feeds is alsoan approximately-elliptical zone but its position may not be al-ways near a diameter of the patch. It depends on the location


of the dual-probe feeds. For instance, the dual-probe feed lo-cation in Fig. 2(a) forces the zone in a vertical position; whilethe dual-probe feed location in Fig. 2(c) makes the zone in ahorizontal position. The zone is a consequence of the vectoraddition of the field components excited, respectively, by thedual-probe feeds. Hence, the zone may deviate from a diameterof the patch if the dual-probe feeds are located asymmetricallyto the diameter.

The distribution of the weak-field region of the fundamentalmode of the rectangular microstrip antenna driven differentiallywith the dual-probe feeds is more complicated than that drivenwith a single-probe feed. For the single-probe feed, the weak-field region of the excited fundamental mode is always in thevicinity of the patch middle line parallel to the X axis. This lineis defined here as the H line. While for the dual-probe feeds anddue to their differential nature, the weak-field region of the ex-cited fundamental mode may not be always in the vicinity of theH line. It is in the vicinity of the H line only if the dual-probefeeds are placed along the same line or respectively two dif-ferent lines parallel to the Y axis and symmetrically to the Hline as well. For such a case, the rectangular microstrip antennais an efficient differential radiator and the electrical separationis an important and useful design parameter. The differentialsignal from a practical circuit such as a power amplifier exhibitsthe amplitude difference and phase imbalance. If such an imper-fect differential signal is used to drive the rectangular microstripantenna, the dual-probe feeds should be placed along the sameline or respectively two different lines parallel to the Y axis andasymmetrically to the H line. If one feed is above and the otheris below the H line, the distribution of the weak-field regionof the excited fundamental mode will still be in between thedual-probe feeds but deviate from the vicinity of the H line, thefundamental mode still can be excited and the rectangular mi-crostrip antenna still radiate if the electrical separation conditionis still satisfied. However, the fundamental mode is not excitedas strong as the previous case and the rectangular microstrip an-tenna is not an efficient differential radiator any longer. If thedual-probe feeds are both either above or below the H line, thedistribution of the weak-field region of the fundamental modewill move as a function of time and not necessarily be in betweenthe dual-probe feeds. The fundamental mode cannot be well ex-cited and the microstrip patch antenna radiates quite poorly. Fur-thermore, for impedance matching the single-probe feed is oftenlocated at a point away from the patch middle line, which is per-pendicular to the X axis and is defined here as the V line. Thissuggests that the rectangular microstrip antenna be driven dif-ferentially with the dual-probe feeds away from the V line butsymmetrically to it. For this case, although the dual-probe feedsare located in the strong-field region of the fundamental mode,the fundamental mode cannot be excited but destroyed due to avertical weak-field region created by the differential dual-probefeeds. Since no fundamental mode is excited, neither does theresonance occur. The input resistance is near to zero and theinput impedance is inductive. The electrical separation becomesmeaningless.

The weak field region should be more appropriately termedas the non-resonant or inductive region. It is found that thenon-resonant region is smaller for the same microstrip antenna

Fig. 3. Slot effect on Magnitude of electric field at 3.75 GHz on the patches ofboth circular and rectangular microstrip antennas with dimensions given in thisSection II-B and the same color scale as in Fig. 2.

Fig. 4. Input impedance as a function of frequency with and without the slot:(a) circular and (b) rectangular microstrip antennas with dimensions given inthis Section II-B.

driven differentially with dual-probe feeds than that driven witha single-probe feed. This implies that the fundamental modecannot be well excited by the single-probe feed but still can bewell excited differentially by the dual-probe feeds with one lo-cated at the same place of the single-probe feed and the other atthe mirror image place if the electrical separation condition issatisfied.

Now that the electrical separation condition is related withthe weak field region, the perturbation of the weak field regionwill affect the degree of electrical separation and may causethe occurrence of resonance of the (quasi) fundamental modeeven if the electrical separation condition is not satisfied. Fig. 3


Fig. 5. Measured and calculated input impedance as a function of frequencyfor the rectangular differentially-driven microstrip antennas: (a) and (b) .

shows that the weak field regions on the patches of both cir-cular and rectangular microstrip antennas have been perturbedby the small rectangular slots [13]. Fig. 4 compares their inputimpedance as a function of frequency with and without theslots for fixed electrical separations. It is evident from these fig-ures that the slots do make the resonances of the (quasi) funda-mental modes occur, but at lower frequencies, as expected.

III. EXPERIMENTAL VALIDATION AND DISCUSSIONBoth rectangular and circular differentially-driven microstrip

antennas were constructed on the RT/duriod 5880 substratewith for experimental validation. To havea sufficient physical separation so as to make it possible tofeed the antennas with 3.5-mm SMA connectors, we designeddifferentially-driven microstrip antennas to operate at 2.4 GHz

. For rectangular microstrip antennas, patchesof and are on the middle ofthe substrates; while for circular microstrip antennas, patchesof are on the middle of the substrates. Thediameter of the feed probes is 1.0 mm. An Agilent networkanalyzer E5062A was used to measure their -parametersin an anechoic chamber. The measured -parameters can beconverted to the differential input impedance [9].

Fig. 5 shows the measured input impedance as a functionof frequency for the rectangular differentially-driven microstrip

Fig. 6. Measured and calculated input impedance as a function of frequencyfor the circular differentially-driven microstrip antennas: (a) and(b) .

antennas with electrical separations and 0.11, re-spectively. It is clear from the figure that the fundamental modedoes not resonate if the electrical separation condition is not sat-isfied but does resonate if the electrical separation condition issatisfied. Fig. 6 shows the measured input impedance as afunction of frequency for the circular differentially-driven mi-crostrip antennas with electrical separations and0.08, respectively. Again, when the electrical separation condi-tion is satisfied, the fundamental resonance occurs. Otherwise,it does not occur.

The simulated input impedance are also shown in Figs. 5and 6. There are small frequency (the resonant frequency or thefrequency at which the resistance reaches the peak) differencesless than 1% between the simulated and measured input im-pedances. They are mainly caused by the patch size tolerance[14]. One slightly reduces the circular patch diameter and in-creases the rectangular patch length, the frequency differencesdiminish. There are large magnitude differences between thesimulated and measured input impedances. The simulated mag-nitudes are generally smaller than the measured ones, whichcan be attributed to the enlarged electrical separation due towarpage. The different stresses between the metal ground planeand the dielectric substrate yield the noticeable warpage in thefabricated microstrip antenna. The warpage was not includedin simulations. However, the warpage effect was modeled by aslight increment in the electrical separation in our simulations.


As expected, the enlarged electrical separation makes the mag-nitude differences reduce significantly.

IV. CONCLUSION

The electrical separation, an important parameter in thedesign of differentially-driven microstrip antennas, has beendefined in this paper. It has been demonstrated that the occur-rence of the fundamental resonance of a differentially-drivenmicrostrip antenna is related with the electrical separation.When the electrical separation condition is satisfied, the res-onance occurs. Otherwise, the resonance does not occur. Theelectrical separation condition is an empirical factor . It hasbeen found for the first time that is smaller for electricallythicker substrate of higher permittivity than that for electricallythinner substrate of low permittivity and is smaller for circularpatch than that for rectangular patch. More importantly, ithas also been found that the electrical separation condition isrelated with the weak field region under the patch. A simpletechnique of cutting a slot in the patch to perturb the weakfield region so as to alter the degree of electrical separation hasbeen simulated. It has been shown that the slot in the patchcan cause the occurrence of the fundamental resonance evenif the electrical separation condition is not satisfied. The weakfield region is more appropriately termed as non-resonant orinductive region. It has been found that the non-resonant regionis smaller for the same microstrip antenna

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