IEEE Transactions on Antennas and Propagation [volume 58 number 9]

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Citation preview

SEPTEMBER 2010

VOLUME 58

NUMBER 9

IETPAK

(ISSN 0018-926X)

PAPERS

Antennas A Wideband Aperture-Coupled Microstrip Patch Antenna Employing Spaced Dielectric Cover for Enhanced Gain Performance ... ......... ........ ......... ......... ........ ......... ......... ........ ........ C. J. Meagher and S. K. Sharma Microstrip Patch Antennas With Enhanced Gain by Partial Substrate Removal . ......... . ....... S. B. Yeap and Z. N. Chen Broadband, Miniaturized Stacked-Patch Antennas for L-Band Operation Based on Magneto-Dielectric Substrates .... .. .. ........ ......... ......... ........ ......... ......... ........ .... F. Namin, T. G. Spence, D. H. Werner, and E. Semouchkina Wideband Phase-Reversal Antenna Using a Novel Bandwidth Enhancement Technique ........ ........ ......... ......... .. .. ........ ......... ......... ........ ......... ......... ........ ......... ......... ........ ......... ... N. Yang, C. Caloz, and K. Wu Design, Fabrication, and Measurement of a One-Dimensional Periodically Structured Surface Antenna .... .. H. R. Stuart Integrated Planar Monopole Antenna With Microstrip Resonators Having Band-Notched Characteristics ...... ......... .. .. ........ ......... ......... ........ ......... ......... ........ ....... D.-Z. Kim, W.-I. Son, W.-G. Lim, H.-L. Lee, and J.-W. Yu 3-D Radome-Enclosed Aperture Antenna Analyses and Far-Side Radiation .... ......... ......... ........ ......... ......... .. .. ........ ......... ......... ........ ......... ......... ........ ........ I. V. Sukharevsky, S. V. Vazhinsky, and I. O. Sukharevsky Platform Embedded Slot Antenna Backed by Shielded Parallel Plate Resonator ......... . ...... W. Hong and K. Sarabandi

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Arrays Low Probability of Intercept Antenna Array Beamforming ...... ......... ........ ......... ......... ........ .. D. E. Lawrence Analysis of a Wavelength-Scaled Array (WSA) Architecture .... ......... ........ ......... R. W. Kindt and M. N. Vouvakis Design of Broadband, Single Layer Dual-Band Large Reflectarray Using Multi Open Loop Elements . ......... ......... .. .. ........ ......... ......... ........ ......... ......... ........ ......... ... M. R. Chaharmir, J. Shaker, N. Gagnon, and D. Lee Near Field Focusing Using Phase Conjugating Impedance Loaded Wire Lens .. ......... ..... O. Malyuskin and V. Fusco

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Complex Media Electromagnetic Coupling Reduction in High-Profile Monopole Antennas Using Single-Negative Magnetic Metamaterials for MIMO Applications ......... ..... .... ........ M. M. Bait-Suwailam, M. S. Boybay, and O. M. Ramahi Diffraction by a Planar Metamaterial Junction With PEC Backing ....... ........ ......... .... G. Gennarelli and G. Riccio Sub-Wavelength Elliptical Patch Antenna Loaded With -Negative Metamaterials ..... ......... ... P. Y. Chen and A. Alù

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Electromagnetics Numerical Modeling for the Analysis of Plasmon Oscillations in Metallic Nanoparticles ....... ........ ......... ......... .. .. ........ ......... ......... ........ ......... ......... ........ ......... ......... ... G. Miano, G. Rubinacci, and A. Tamburrino

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(Contents Continued from Front Cover) Closed-Form Uniform Asymptotic Expansions of Green’s Functions in Layered Media ......... ........ ......... ......... .. .. ........ ......... ......... ........ ......... ......... ........ ......... ......... ........ .. R. R. Boix, A. L. Fructos, and F. Mesa

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Numerical High-Order Interface Treatment Techniques for Modeling Curved Dielectric Objects .. ......... ........ ......... ......... .. .. ........ ......... ......... ........ ......... ......... ........ ......... ......... .... J. Wang, W.-Y. Yin, P.-G. Liu, and Q.-H. Liu Analysis of Structures Containing Sharp Oblique Metal Edges in FDTD Using MAMPs .... C. J. Railton and D. L. Paul

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Propagation A Hybrid Model for Radio Wave Propagation Through Frequency Selective Structures (FSS) .. ........ ......... ......... .. .. ........ ......... ......... ........ ......... ......... ........ ......... ......... ........ ......... ....... M. Yang and A. K. Brown Broadband Antireflective Properties of Inverse Motheye Surfaces ....... ........ ......... ......... ........ ......... ......... .. .. ........ ......... ......... ........ ......... ......... .... M. S. Mirotznik, B. L. Good, P. Ransom, D. Wikner, and J. N. Mait Scattering A Novel Procedure for High Resolution Radar Signature Prediction of Near Field Targets ...... ........ M. Sui and X. Xu The First-Order High Frequency Radar Ocean Surface Cross Section for an Antenna on a Floating Platform .. ......... .. .. ........ ......... ......... ........ ......... ......... ........ ......... ......... ........ ......... J. Walsh, W. Huang, and E. Gill Fast Computation of Angular Responses of Large-Scale Three-Dimensional Electromagnetic Wave Scattering ........ .. .. ........ ......... ......... ........ ......... ......... ........ ......... ......... ....... Z. Peng, M. B. Stephanson, and J.-F. Lee Wireless A Novel Multilayer UWB Antenna on LTCC .... ........ ......... ......... ....... Y.-Q. Zhang, Y.-X. Guo, and M. S. Leong Self-Assembled Monopole Antennas With Arbitrary Shapes and Tilt Angles for System-on-Chip and System-in-Package Applications ... ......... ........ ......... ......... .... A. Mahanfar, S.-W. Lee, A. M. Parameswaran, and R. G. Vaughan A Wideband DVB Forked Shape Monopole Antenna With Coupling Effect for USB Dongle Application ...... ......... .. .. ........ ......... ......... ........ ......... ......... ........ ......... ......... ........ ......... ...... C.-H. Hsu and S.-J. Chung Planar UHF RFID Tag Antenna With Open Stub Feed for Metallic Objects .... ......... ......... ....... L. Mo and C. Qin

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COMMUNICATIONS

A Sparse Factorization for Fast Computation of Localizing Modes ...... ........ ......... ... Y. Xu, X. Xu, and R. J. Adams Active Integrated Wearable Textile Antenna With Optimized Noise Characteristics ..... ...... F. Declercq and H. Rogier A Printed, Broadband Luneburg Lens Antenna ... ........ ......... ......... ........ ......... ......... C. Pfeiffer and A. Grbic Reducing the Number of Amplitude Controls in Radar Phased Arrays .. ... M. D’Urso, M. G. Labate, and A. Buonanno Folded Reflectarrays With Shaped Beam Pattern for Foreign Object Debris Detection on Runways .... ......... ......... .. .. ........ ......... ......... ........ ......... ......... A. Zeitler, J. Lanteri, C. Pichot, C. Migliaccio, P. Feil, and W. Menzel Iterative Algorithm for Probe Calibration in Spherical Near-Field Antenna Measurement ....... ........ ......... ......... .. .. ........ ......... ......... ... D. Sánchez-Escuderos, M. Baquero-Escudero, J. I. Herranz-Herruzo, and F. Vico-Bondía A Modified Wheeler Cap Method for Efficiency Measurements of Probe-Fed Patch Antennas With Multiple Resonances ..... ......... ........ ......... ......... ........ ......... ......... ........ ......... ... C. Cho, I. Park, and H. Choo On the Accuracy of Three Different Six Stages SS-FDTD Methods for Modeling Narrow-Band Electromagnetic Applications ... ......... ........ ......... ......... ........ ......... ......... ........ ......... ......... ........ ..... O. Ramadan Error Analysis for Matrix Factorizations Using Non-Overlapped Localizing Basis Functions ... ........ ......... ......... .. .. ........ ......... ......... ........ ......... ......... ........ ......... ......... ........ ......... ... X. Xu, Y. Xu, and R. J. Adams Electromagnetic Scattering by Finite Periodic Arrays Using the Characteristic Basis Function and Adaptive Integral Methods ........ ......... ........ ......... ......... ........ ......... ......... ........ ......... .. L. Hu, L.-W. Li, and R. Mittra Applying the Optical Theorem in a Finite-Difference Time-Domain Simulation of Light Scattering ... ......... ......... .. .. ........ ......... ......... ........ ......... ......... ........ ......... ......... ...... C.-H. Tsai, S.-H. Chang, and S. H. Tseng Optimization of Reduced-Size Smooth-Walled Conical Horns Using BoR-FDTD and Genetic Algorithm ..... ......... .. .. ........ ......... ......... ........ ......... ......... ........ .. A. Rolland, M. Ettorre, M. Drissi, L. Le Coq, and R. Sauleau A Miniaturized Hilbert Inverted-F Antenna for Wireless Sensor Network Applications ......... ........ ......... ......... .. .. ........ ......... ......... ........ ......... ......... ........ ......... ......... ........ . J.-T. Huang, J.-H. Shiao, and J.-M. Wu

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Digital Object Identifier 10.1109/TAP.2010.2071010

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A Wideband Aperture-Coupled Microstrip Patch Antenna Employing Spaced Dielectric Cover for Enhanced Gain Performance Christopher J. Meagher, Member, IEEE, and Satish Kumar Sharma, Senior Member, IEEE

Abstract—A dielectric cover is used to enhance the gain of an aperture-coupled microstrip patch antenna. The cover is spaced off of the patch antenna by air and, as expected, is found to significantly increase antenna broadside directivity in some configurations. A parametric study on the effects of spacing height, cover size, and thickness of the cover are presented. This study uses a finite element method (FEM) based, commercial analysis tool to perform these parametric searches, and so accounts for finite size ground planes and dielectrics. The previous research work reported in literature considered infinite-area ground planes and dielectrics. The wide impedance matching bandwidth of the aperture-coupled microstrip patch also allows observation of the narrow-bandwidth effects of the added dielectric cover. Finally, a proposed design methodology is outlined, and a prototype of the antenna was fabricated and experimentally verified with a peak gain of 13.9 dBi. The measured results agree reasonably well with the simulated ones. Index Terms—Aperture antennas, dielectric radiation effects, electromagnetic reflection, microstrip antennas.

trading volume and potentially other antenna performance characteristics (i.e., impedance and gain bandwidths, beamwidths) for increased peak gain of a single radiating element. Doing so avoids the increased surface area, feed line loss, and mutual coupling between radiating elements in an array. For this paper, the starting antenna element is an aperture-coupled microstrip patch. While the seminal papers on enhanced gain through dielectric covers used Hertzian dipole elements [3], [4], a few subsequent studies focused on probe-fed microstrip patch antennas [6], [7]. We have extended the previous works in two major areas. First, since the aperture-coupled microstrip patch has much larger impedance bandwidth than previous printed antennas described in the literature (e.g., probe-fed patches), any impedance narrow-bandwidth effects may be better observed. Further, through the use of FEM analysis, our results focus on the effects of finite sizes of the ground plane and dielectric covers. II. ANTENNA GEOMETRY AND SIMULATION TOOLS

I. INTRODUCTION

A. Baseline (Uncovered) Antenna

G

AIN enhancement methods through the use of dielectric superstrates (covers) have been described in various manners for decades. Trentini [1] and, later Sasser [2], note that the multiple reflections off of a semi-transparent reflector can produce “images” of the original antenna that yield gain increases similar to that of arraying the antenna. Like the Fabry-Perot etalon or resonator used in optics, this configuration can increase gain for certain wavelengths (frequencies) at a particular angle. A thorough treatment of this configuration with dielectric/magnetic materials is provided in [3], where it is described as a “substrate-superstrate” effect. Further work described the gain enhancement through “leaky waves” [4], [5]. The goal of this and likely most of the previous studies is to provide an additional degree of freedom in antenna design: Manuscript received November 23, 2008; revised August 31, 2009; accepted March 19, 2010. Date of publication June 14, 2010; date of current version September 03, 2010. C. J. Meagher was with the Electrical and Computer Engineering Department, San Diego State University, San Diego, CA 92182 USA. He is now with the Tactical Edge Wireless Networking Branch, Space and Naval Warfare Systems Center Pacific (SSC PAC), San Diego, CA 92152 USA (e-mail: christopher. [email protected]). S. K. Sharma is with the Electrical and Computer Engineering Department, San Diego State University, San Diego, CA 92182 USA (e-mail: ssharma@mail. sdsu.edu). Digital Object Identifier 10.1109/TAP.2010.2052543

The baseline, uncovered antenna is a single aperture-coupled microstrip patch antenna on a finite ground plane and with finite substrate (lateral) sizes. Foam of thickness 0.724 cm was chosen as the patch substrate to maximize matching bandwidth [8], and, as per [9], the patch itself is attached to the bottom of a 0.0787 , ), mainly for ease cm FR-4 superstrate ( of fabrication. The antenna feed is realized on 0.159 cm FR-4. The target operating range of the antenna is around 5–6 GHz to support IEEE 802.11a communications. The cross section (side view) and metallic geometries of the antenna are shown in Fig. 1. The antenna is fed by a microstrip line, but a 50 grounded coplanar waveguide (CPW) section is employed to accept an edge-launch SMA connector, which will also be used when the antenna is fabricated. This allows for more accurate comparison between the simulated and measured results. Each of the coplanar ground pads are connected to the common ground plane through four vias. The CPW section then abruptly transitions to a 48.5 microstrip line. A 69 transmission line is then used as a quarterwave transformer to the 97 antenna feed line. The following dimensions are given both in centimeters and fractions of the reference wavelength, chosen . at the center of the band, 5.5 GHz As mentioned earlier, the antenna is modeled considering finite size structures. The - and -dimensions of the substrates to match with and ground plane are each 15.2 cm or

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MEAGHER AND SHARMA: A WIDEBAND APERTURE-COUPLED MICROSTRIP PATCH ANTENNA

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Fig. 2. Graphs showing the de-tuning effects of adding a dielectric cover with no spacing and small spacing height.

Fig. 1. Metallic geometries of the CPW-fed aperture-coupled microstrip patch antenna with finite sizes of the ground plane, substrate, and dielectric cover. Side view: The patch substrate and spacing to the dielectric cover are both in air. Exaggerated solid lines are used to show the location of the feed trace, ground plane with slot, and patch in the side view.

readily-attainable, copper clad boards. The ground plane rectangular aperture or coupling slot is 0.203 cm by 1.55 cm ( by ), and is tuned by a 0.239 cm open-circuited stub. The square microstrip patch is centered over the long. coupling aperture and each dimension is 1.52 cm bandThe FEM-calculated impedance matching width of this baseline, uncovered antenna is 28% (from 4.65 to 6.16 GHz). The electrically small stub, at under one-twelfth of a wavelength, and slightly longer slot compared with the patch were both found to increase the matching bandwidth of the antenna during a parametric study [10]. The combined use of a foam substrate and a higher dielectric constant superstrate (not the spaced cover) is also a likely contributor to the antenna’s wide matching bandwidth.

Fig. 3. Graphs showing impedance matching similarities between the uncovered antenna and ones with dielectric covers spaced 0:5 and 2 .





also studied, but the trends match closely with those presented in [6] and hence are not repeated here for the sake of brevity. III. EFFECTS OF VARYING SPACING HEIGHT

B. Simulation Tools Ansoft HFSS [11], a full wave FEM solver, was used for most of the simulations due to its ability to model finite dielectric structures and ground planes. Ansoft Designer [12], which employs a method of moments (MoM) solver for planar structures, was used only for initial pass simulations and to study the effects of infinitely large area spaced dielectric covers and ground planes. The simulated “Realized Gain” (absolute gain) values provided in this paper include mismatch loss effects so that they can be compared with the measured gain values. In Sections III–VIII, we present the effects of varying certain parameters of the dielectric cover on the antenna’s impedance matching and radiation characteristics. The spacing height, , cover size , and cover thickness, , are investigated. The effects of varying the cover material (i.e., dielectric constant) were

Spacing height of the dielectric cover off of the patch superstrate is an important parameter and therefore is investigated first. The dielectric material chosen for all of the height variation , tests was 0.254 cm thick Rogers TMM10 ( ), with the same lateral size as the ground plane (15.2 cm by 15.2 cm). Initial simulations were run for spacing heights of , 0.635 cm , 1.27 cm 0 (touching), 0.318 cm , 2.54 cm , 5.08 cm , and 10.16 cm . A. Impedance Matching Fig. 2 shows the magnitude of reflection coefficient versus frequency for the antenna with no cover, a touching cover, and a cover spaced . The match around 7 GHz is present in all simulated results throughout this paper and is

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TABLE I RADIATION CHARACTERISTICS WITH SPACING HEIGHT VARIATIONS



Fig. 4. Matching (VSWR 2) and half-power (3 dB) gain bandwidths versus spacing height for a 2.54 mm thick TMM10 dielectric cover.

most likely caused by the CPW feed. In the frequency range of interest, 5–6 GHz, the addition of a dielectric cover directly on top of the patch antenna detunes it, i.e., the matching bandwidth reduces from 27.8% to 10.2%. Also, as was found for the probe-fed patch [6], the resonances appear to drop in frequency for the covered cases, compared with the baseline antenna. However, the overall impedance matching is very good for spacings 2.54 cm and higher (apand above) and, in fact, is very similar to proximately that of the uncovered case (Fig. 3). Thus, at these taller heights, the spaced-off dielectric cover is far enough to be ignored for antenna matching purposes. The spacing height that leads to bandwidth is 5.08 cm the widest , yielding 27.6% bandwidth, which is very close to the 28.0% bandwidth of the antenna without the spaced-off cover. Fig. 4 is a shared graph showing both the matching and half-power (3 dB) gain bandwidths with respect to the spacing height. Note the general trend that the matching bandwidth and decreases for spacing heights up to and including spacing, the match at 5.1 increases beyond that. At which causes the apparent GHz is slightly above

Fig. 5. Broadside radiation efficiency at 5.5 GHz versus spacing height.

drop in matching bandwidth. Though the low sampling of spacing heights may cause the impedance matching graph to appear periodic, the effect is different from the periodic input impedance-versus-superstrate thickness described in [13], which investigates a finite-sized dielectric cover directly on top of a microstrip patch. In our case, there is an air gap between the patch and dielectric cover. At the limit of infinite spacing, the cover does not affect the input impedance of the antenna. B. Radiation Performance The promised increased gains are listed in Table I. This gain enhancement comes at the cost of a monotonically-decreasing gain bandwidth (Fig. 4) as expected from [3]. The radiation , for 5.5 GHz, is efficiency at the broadside angle plotted in Fig. 5. As with the impedance match, the radiation and recovers at efficiency drops dramatically around higher spacing. Although the efficiency does not increase beyond that of the uncovered antenna in this case, it is possible to use dielectric covers to improve antenna efficiency [14]. Since [3] provides us with design equations for the substrate-superstrate configuration, the predicted frequencies of

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maximum gain are listed in Table I for each spacing height. It is important to note that, in accordance with [3]–[7], the “substrate” thickness is equal to the distance between the ground plane of the patch and the dielectric cover/superstrate. Thus, our calculations include the spacing height, patch superstrate (FR-4) thickness, and patch substrate (air) thickness. The predicted frequency of maximum gain is consistently lower than that calculated in HFSS. This is due to the finite cover and ground plane size. Another observation regarding these sizes involves 3 dB beamwidths, which are also listed in Table I. The beamwidths generally decrease with increasing gain. The exception is the case, which has lower than expected gain for its small beamwidths due to high sidelobes and backlobe. The backlobe is only 4.07 dB below the mainlobe in this case, compared with and cases. In a similar 7.89 dB and 7.44 dB in the geometry, Nakano et al. [15] show that a further increase in spacing height (their top dielectric thickness) also leads to higher sidelobes and less gain. IV. EFFECTS OF VARYING COVER SIZE There may be applications which allow the cover size of the spaced dielectric cover to be varied, and so this parameter is studied next. For simplicity, we keep the square shape of the cover so the following variations list only one side length but represent changing the cover size in both dimensions. Three sets of finite spaced dielectric cover simulations were run: FR-4 at and total cover-to-ground plane distance and TMM10 at total distance, all at 5.5 GHz and with 0.254 cm dielectric thickness. Seven cover sizes were simulated for each set, the , 2.54 cm , lengths of each side being 1.52 cm , 5.08 cm , 7.62 cm , 10.2 3.81 cm , and 15. 2 cm . The sizes are given in free cm space wavelengths since the cover is above an air gap and so may be counted as a certain lateral size regardless of dielectric constant. This is not the case with cover thickness, which is a dimension that should account for dielectric constant since its effect is based on waves propagating through the material. A. Impedance Matching For the FR-4 sets, the matching remains essentially the same, between 27.3% and 28.5%. The matching bandwidths of the TMM10 sets are all very similar, within 2.3% around 28.0% fractional bandwidth, except for the side length case, whose the reflection coefficient peaks slightly above at 5.3 GHz. Considering the wide range of sizes tested, these results show that cover size is not a major design parameter affecting the impedance matching of the antenna. B. Radiation Performance Fig. 6 shows a plot of the maximum broadside gain and 3 dB gain bandwidth versus side length for the three simulation sets mentioned above. In all cases, the frequency of the maximum broadside gain remains essentially the same: 5.4–5.9 GHz for the FR-4 cases and 5.7–6.0 GHz for the TMM-10 cases. It is interesting to note that the gain bandwidth decreases monotonically with increasing cover size. The nature of this decrease is that the low frequency end of each gain profile remains nearly

Fig. 6. Maximum broadside gain values and 3 dB gain bandwidths for varying cover sizes, 0.254 cm thick, and with different cover materials and total distance: FR-4 spaced to 0:5 and  and TMM10 spaced to .

unaffected while high frequency gain drops with increasing cover size. More on this will be covered in Section IV-C. Additionally, the maximum gain appears to increase and peak side length, after which it decreases for all simat about ulation sets. Thus, in terms of maximizing gain performance (both magnitude and bandwidth), there appears to be an “optimum” size for the dielectric cover. Simulations with other spacing heights and with smaller ground plane sizes showed that the maximum gain was always achieved when using cover sizes slightly smaller than the total ground plane size. However, these results are not shown here for the sake of brevity. Radiation efficiency at broadside generally dropped with increasing cover size, and the drop was more pronounced for the spacing TMM10 set in comparison to the FR-4 and for compared with spacing. For the TMM10 set, the radiation efficiency at 5.5 GHz drops from 74% (1.52 cm cover) to 68% (15.2 cm cover) to 54% (infinite extent cover). C. Infinite Cover Size The limit of increasing the cover size is to have an infinite cover. This was simulated using Ansoft Designer, which models all dielectrics and ground planes as infinite in the plane. We re-simulated the spacing height variations from Section III (0.254 cm thick TMM10 cover dielectric) and found that the frequencies and values of maximum gain matched well for the uncovered case and for those at which the cover was spaced or higher. The infinite cover results for the touching and two smallest spacing height cases differed significantly in gain but were comparable in terms of matching when compared with the finite cover simulations. This is because surface waves are more prevalent for the lower spacing heights and their effects differ depending on whether the substrate in which they propagate is finite or infinite. Surface waves in the infinite dielectric cover act purely as a loss, whereas they can reflect/diffract on the boundaries of the finite cover and either cause more severe

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Fig. 7. Broadside, co-polarization realized gain versus frequency for (a) 0:23 , (b) 0:47 , (c) 0:93 , and (d) 1:9 spacing with finite 2:8 2:8 (no markers) and infinite cover sizes (triangle markers).

2

loss or yield some gain depending on the frequency and observation angle. The broadside gain values versus frequency for four spacing sides) and inheights are compared in Fig. 7 for finite- ( finite-sized covers. For the high spacing, high gain cases, the broadside gain drops faster at higher frequencies when using an infinite cover. In their modeling of infinitely large substrate-superstrate configurations, Jackson and Alexopoulos [3] attribute the more rapid decrease in gain at higher frequencies to frequency scanning. Thus, applications that allow for small dielectric covers can yield antennas with wider gain bandwidths than if they were implemented as part of the platform itself (acting as a large, approximately infinite dielectric cover). As seen in Section III, it is also important to note for design purposes that non-infinite covers tend to yield maximum gain at slightly higher frequencies than infinite covers. V. EFFECTS OF VARYING COVER THICKNESS The final parameter to check for a flat, spaced-off dielectric cover is cover thickness. For these tests, we chose to use FR-4 total cover-to-ground plane distance to see if its gain at performance could be improved by properly choosing a cover thickness. Previous analysis of infinite substrate/ground plane configurations [3] determined that maximum broadside gains . occur at cover thicknesses that are an odd multiple of

Fig. 8. (a) Matching and 3 dB gain bandwidths, (b) maximum broadside gain values and frequencies, and (c) broadside radiation efficiency at 5.5 GHz versus cover thickness for FR-4 covers at 0:5 total distance.

The following simulation set shows how finite sizes affect this thickness-based resonance and the effects on impedance to , matching. The cover thickness is varied from at 5.5 GHz, the intended resonant in increments of frequency. A. Impedance Matching A plot of the matching bandwidth and 3 dB gain bandwidth versus cover thickness is shown in Fig. 8(a). The matching bandwidth varies significantly with changing cover thickness, ranging from 14% to 30%. For the lower matching bandwidth

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cases, the reflection coefficient increases slightly near the center of the band (at 4.8–5.4 GHz of the 4.6–6.2 GHz range). This effectively halves the matching bandwidth. The variation from high to low matching bandwidth over changing cover thickness . occurs with a period of about B. Radiation Performance The half-power gain bandwidth in Fig. 8(a) is a nearly monotonically decreasing function, with the worst performance cover thickness. On the other hand, the periodicity at seen in the matching bandwidth is also present in the plots of Fig. 8(b) and (c): maximum, co-polarization realized gain at broadside; the frequency of this maximum gain; and broadside radiation efficiency at 5.5 GHz versus cover thickness. Unfortunately, large gain increases appear to come at the cost of reduced matching bandwidth. Furthermore, the frequency of maximum gain varies almost over the entire matching bandwidth, with the largest gain values lying near the intended center frequency of 5.5 GHz. and The maximum broadside gain values are found at cover thicknesses, slightly thicker than the and determined in [3]. The gain is larger for the thicker cover, indicating that the thickness of the cover creates an additional resonance in the broadside direction whose effect on gain is greater than the increase in dielectric loss. However, the downward trend of the radiation efficiency and nearly monotonic decrease in gain bandwidth warns against unnecessarily thick dielectric covers. VI. DESIGN METHODOLOGY A simple flow chart of the methodology for designing an aperture-coupled microstrip patch antenna with a spaced dielectric cover is shown in Fig. 9. As is typical in antenna design, the steps are closely coupled and present several design tradeoffs. Assuming that the goal of the design is to achieve maximum gain with certain restrictions on minimum matching and half-power gain bandwidths, we suggest the following steps: Step 1 Following established design guidelines [16]–[18], optimize the aperture-coupled patch antenna for the required matching bandwidth and allowable size and materials of your application. This bandwidth can be preserved by proper choice of cover dielectric and spacing in Steps 3 and 4. Step 2 Choose the cover size. This and the final steps depend on the application or platform on which the antenna will be used. If it is possible to choose the size of the spaced cover dielectric, it should be chosen in conjunction with Step 3 (spacing height) to optimize for both gain and gain bandwidth. A dielectric cover slightly smaller than the ground plane of the patch antenna will yield the highest gain. Step 3 Choose the spacing height between the antenna and the spaced dielectric cover such that the total distance between the antenna’s ground plane and the cover is a multiple of a half wavelength at a frequency in the desired bandwidth. For implementations that result in a very large cover size (e.g., using

Fig. 9. Flow chart showing the choices (boxed) and considerations (gray) for designing an aperture-coupled patch antenna with a spaced dielectric cover.

the wall or window of a platform as the cover), this frequency should be in the middle-to-upper end of the band to properly place the gain bandwidth, since the gain will fall off sharply at higher frequencies. For finite covers roughly the size of the antenna ground plane or smaller, the frequency should be at the lower end of the bandwidth since the increased gain will be sustained at higher frequencies. The design trade-off for this and the cover size is that increased gain usually comes at the expense of narrower gain bandwidth. Of course, an additional constraint throughout this step is the available volume for the antenna. Step 4 If it is possible to choose the cover material, experiment with ones that have moderately high dielectric constants. This will allow high gain to be achieved with a thin cover. The limit of this effect is that, as the material becomes more reflective due to the high dielectric constant (which yields the higher gain), it tends to have more of an effect on the antenna matching and thereby reduces absolute gain. The 3 dB gain bandwidth also drops sharply with increasing cover permittivity [6]. Step 5 Lastly, if the spaced cover thickness can be chosen, it should be roughly an odd multiple —slightly thicker for finite covers. A of , the lowest odd multiple, is thickness of recommended to maintain gain bandwidth and radiation efficiency. The design process above is focused on maximizing the matching bandwidth, broadside gain, and gain bandwidth. For some applications, such as using these antennas as elements in a steerable array, the beamwidth becomes an important

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constraint. As seen in Section III, beamwidth is inversely proportional to the gain produced by the broadside resonance. So, along with the gain bandwidth, beamwidth constraints limit the maximum gain achievable in the design process. Nevertheless, it may still be possible to design higher gain elements for ), thereby an array that steers over modest angles (e.g., reducing the required surface area of the array. Also, while this paper focuses on broadside gain improvement, it is possible to improve antenna gain at scanned angles, for various benefits [19]. Dielectric cover (superstrate) optimization for scanned beams is covered in the seminal works [3], [4]. VII. EXPERIMENTAL VERIFICATION The baseline aperture-coupled microstrip patch antenna was fabricated using pre-sensitized FR-4 boards and amateur developing and etching processes. Styrofoam sheets stacked to 0.749 cm were used for the patch substrate, and the patch superstrate was about 22.5% thicker (0.0965 cm versus 0.0787 cm). Thus, we can expect the resonances to be shifted lower in frequency. The dielectric cover was created from a 0.254 cm thick sheet of Rogers Corporation TMM10, with its copper cladding completely etched away. The cover was spaced off from the antenna with sheets of expanded polypropylene foam stacked to 2.67 and 5.33 cm —inexact due to the discrete cm thickness of the sheets. Both the dielectric cover and the antenna have -plane dimensions of 15.2 cm by 15.2 cm, as did the preceding simulations. Three sets of measurements were taken: first with the uncovered baseline antenna and then with the dielectric cover at and spacing heights. The reflection coefficient measurements were taken on an HP8051C network analyzer at SPAWAR Systems Center Pacific, and gain measurements were performed at San Diego State University’s newly installed anechoic chamber. reA graph comparing the measured versus simulated sults are shown in Fig. 10. Only the results for the uncovered antenna are shown, but each of the three measurements compares well with the simulated results. In all cases, the measured match is slightly worse for the lower frequencies up to around 5.2 GHz and at the center frequencies around 5.6 GHz. The mea-spaced, sured matching bandwidths for the uncovered, -spaced cases are 28.0%, 20.9%, and 18.5%, respecand tively. These results compare well with the simulated bandwidths of 27.4%, 23.0%, and 21.0%, respectively (updated for the changes in material thicknesses). Plots of the broadside, co-polarization gain versus frequency for the uncovered antenna are shown in Fig. 10 and for the two covered cases are shown in Fig. 11. The overall shape and frequencies of the measured gain for the uncovered antenna agree well with the simulations. The data was limited to 5.85 GHz by the measurement method. For the two cases with spaced dielectric covers, the gain values appear to be shifted to lower frequencies than expected (after accounting for the increased foam and FR-4 thicknesses). This shift in frequency might be explained by a higher dielectric constant of the patch superstrate, as this specification tends to vary widely for FR-4, or by bowing in the dielectric cover and foam layers. The latter might be due to tight

Fig. 10. Measured and simulated reflection coefficient (S ; dB) and broadside co-polarization absolute gain for the baseline, uncovered aperture-coupled microstrip patch antenna.

Fig. 11. Plots of measured and simulated broadside, co-polarization absolute gain values versus frequency for the covered antennas.

taping of the stacked layers to the antenna by their ends. An alternative is to use rigid dielectric spacers to hold the cover at the corners, as in [7], but that runs the risk of reflections off of the spacers. Fig. 12 shows the measured and simulated co- and cross-polarization radiation patterns for both the E- and H-planes at -spaced dielectric cover. The maximum 5.2 GHz for the measured gain is 13.9 dBi with a 3 dB gain bandwidth of 8.43% (Fig. 11). The simulated maximum gain was 12.5 dBi, also at 5.2 GHz, but with a wider gain bandwidth of 13.5%. The measured 3 dB - and -plane beamwidths of 23 and 22 are comparable to the simulated 25 and 24 . The cross-polarization levels . Thus, the for both the - and -planes are very low measured results agree reasonably well with the simulations. The slight difference in impedance and radiation performance

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avoid having to array microstrip patch elements by 2 2 or larger. In this case, the trade-off is between surface area/feed loss/artwork complexity and volume, as the new antenna configuration requires a large spacing height. For many applications, the dielectric cover can be realized as part of the antenna’s housing or platform. ACKNOWLEDGMENT The authors would like to thank Dr. R. Olsen of SPAWAR Systems Center Pacific for providing access to the lab’s Ansoft Designer and HFSS software, circuit board fabrication chemicals, and network analyzer. They would also like to thank J. Church and A. Singh for their help with anechoic chamber measurements at San Diego State University. REFERENCES

Fig. 12. (a) E - and (b) H -plane gain radiation patterns at 5.2 GHz, both measured and simulated, for the aperture-coupled microstrip patch antenna with a 0.254 cm TMM10 dielectric cover spaced 0:98 .

can be attributed to fabrication (e.g., bowing) and material inconsistencies. VIII. CONCLUSION Use of a dielectric cover, spaced some distance from an aperture-coupled microstrip patch antenna, can yield a high gain antenna with matching and half-power gain bandwidths large enough to be useful in high speed communications and many other applications. We presented the results of several parametric studies on the dimensions of this antenna configuration: spacing height, cover size, and cover thickness. The focus on how this configuration affects the aperture-coupled patch’s wide matching bandwidth and the effects of finite-sized dielectrics builds on the results of previous studies. A general design process was suggested, and the patch antenna was fabricated along with a 0.254 cm TMM10 -spaced, and cover for measurement. The uncovered, -spaced cases were measured, and their results agree well with the simulations. The maximum measured gain was 13.9 dBi, compared with 6.67 dBi for the uncovered antenna. Therefore, an obvious use of this configuration might be to

[1] G. V. Trentini, “Partially reflecting sheet arrays,” IRE Trans. Antennas Propag., vol. 4, no. 4, pp. 666–671, Oct. 1956. [2] B. Sasser, “A highly thinned array using the image element,” in Proc. Antennas Propag. Society Int. Symp., Jun. 1980, vol. 18, pp. 150–153. [3] D. Jackson and N. Alexopoulos, “Gain enhancement methods for printed circuit antennas,” IEEE Trans. Antennas Propag., vol. 33, pp. 976–987, Sep. 1985. [4] D. R. Jackson and A. A. Oliner, “A leaky-wave analysis of the highgain printed antenna configuration,” IEEE Trans. Antennas Propag., vol. 36, no. 7, pp. 905–910, Jul. 1988. [5] H. Ostner, J. Detlerfsen, and D. R. Jackson, “Radiation from one-dimensional dielectric leaky-wave antennas,” IEEE Trans. Antennas Propag., vol. 43, no. 4, pp. 331–339, Apr. 1995. [6] X.-H Shen, G. A. E. Vandenbosch, and A. Van de Capelle, “Study of gain enhancement method for microstrip antennas using moment method,” IEEE Trans. Antennas Propag., vol. 43, no. 3, pp. 227–231, Mar. 1995. [7] X.-H Shen, P. Delmotte, and G. A. E. Vandenbosch, “Effect of superstrate on radiated field of probe fed microstrip patch antenna,” Inst. Elect. Eng. Proc. Microw. Antennas Propag., vol. 148, no. 3, pp. 141–146, Jun. 2001. [8] D. M. Pozar, “Microstrip antennas,” Proc. IEEE, vol. 80, pp. 79–91, Jan. 1992. [9] J.-F Zurcher, “The SSFIP: A global concept for high-performance broadband planar antennas,” Electron. Lett., vol. 24, no. 23, pp. 1433–1435, Nov. 1988. [10] C. J. Meagher, “Additional design parameters and low-cost fabrication techniques for aperture-coupled microstrip patch antennas,” presented at the San Diego State University Student Research Symp., San Diego, CA, Feb. 29, 2008. [11] Ansoft HFSS [Online]. Available: http://www.ansoft.com/products/hf/ hfss/ [12] Designer [Online]. Available: http://www.ansoft.com/products/hf/ansoft_designer/ [13] H. Nakano, P. Huang, H. Mimaki, and J. Yamauchi, “Radiation characteristics of a patch antenna with a top dielectric layer,” in Proc. IEEE Antennas Propag. Society Int. Symp., Jul. 3–8, 2005, vol. 1A, pp. 267–270. [14] N. G. Alexopoulos and D. R. Jackson, “Fundamental superstrate effects on printed circuit antenna efficiency,” in Proc. MTT-S Int. Microwave Symposium Digest, May 1984, vol. 84, pp. 475–476. [15] H. Nakano, P. H. Huang, H. Mimaki, and J. Yamauchi, “A patch antenna with a top dielectric layer,” in Proc. IEEE Antennas Propag. Society Int. Symp., Jun. 20–25, 2004, vol. 4, pp. 4016–4019. [16] P. Sullivan and D. Schaubert, “Analysis of an aperture coupled microstrip antenna,” IEEE Trans. Antennas Propag., vol. 34, no. 8, pp. 977–984, Aug. 1986. [17] F. Croq and D. M. Pozar, “Millimeter-wave design of wide-band aperture-coupled stacked microstrip antennas,” IEEE Trans. Antennas Propag., vol. 39, pp. 1770–1776, Dec. 1991. [18] S. D. Targonski, R. B. Waterhouse, and D. M. Pozar, “Design of wide-band aperture-stacked patch microstrip antennas,” IEEE Trans. Antennas Propag., vol. 46, pp. 1245–1251, Sep. 1998. [19] Y. Kazama, A. Sugawara, T. Takano, and D. Radenamad, “Novel phased array antenna with elements of conical beam patterns,” in Proc. IEEE Antennas Propag. Society Int. Symp., Jul. 5–11, 2008, pp. 1–4.

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Christopher J. Meagher (M’08) was born in Los Alamitos, CA, in June 1983. He received dual B.Sci. degrees in electrical engineering and English from the California Institute of Technology, Pasadena, in 2005 and the M.Sci. degree in electrical engineering from San Diego State University, San Diego, CA, in 2009. Currently, he works at the Tactical Edge Wireless Networking Branch, Space and Naval Warfare Systems Center Pacific (SSC PAC), San Diego. To date, he has published several conference papers including those for the IEEE Antennas and Propagation Society International Symposium and MILCOM. His current antenna-related interests are on planar arrays and RF lenses implemented in printed circuit board. Other interests include mobile ad hoc networking with directional antennas and concentrated solar power.

Satish Kumar Sharma (M’00–SM’04) was born in Sultanpur (Uttar Pradesh), India, in April 1970. He received the B.Tech. degree from Kamla Nehru Institute of Technology, Sultanpur and the Ph.D. degree from the Institute of Technology, Banaras Hindu University, Varanasi, India, in 1991 and 1997, respectively, both in electronics engineering. From February 1992 to December 1993, he was a Lecturer and Project Officer at Kamla Nehru Institute of Technology and the Institute of Engineering & Rural Technology, Allahabad, respectively. From December 1993 to February 1999, he was a Research Scholar, and then Junior/Senior Research Fellow of the Council of Scientific and Industrial Research (CSIR) in Department of Electronics Engineering, Institute of Technology, Banaras Hindu University. From March 1999 to April 2001, he was a Postdoctoral Fellow in the Department of Electrical and Computer Engineering, University

of Manitoba, Manitoba, Canada. He was a Senior Antenna Engineer with InfoMagnetics Technologies Corporation in Winnipeg, Manitoba, Canada, from May 2001 to August 2006. Simultaneously, he was also a Research Associate at the University of Manitoba from June 2001 to August 2006. In August 2006, he joined San Diego State University (SDSU), San Diego as an Assistant Professor in the Department of Electrical and Computer Engineering. Here, he has developed an Antenna and Microwave Laboratory (AML), teaches courses in Applied Electromagnetics, and advises several graduate students. He is the author/coauthor of more than 80 research papers published in the refereed international journals and conferences. He is the coauthor of the chapter “Printed Antennas for Wireless Applications” in the book Microstrip and Printed Antennas: New Trends, Techniques and Applications (Wiley Inter-Science, UK). He also holds 1 U.S. and 1 Canadian patent. His main research interests are in microstrip antennas, ultrawide bandwidth antennas, reconfigurable antennas, feeds for reflector antennas, waveguide horns and polarizers, phased array antennas, wire antennas, and RF MEMS microwave passive components. Dr. Sharma received the National Science Foundation’s prestigious faculty early development (CAREER) award in 2009 and the Young Scientist Award of URSI Commission B, Field and Waves, during the URSI Triennial International Symposium on Electromagnetic Theory, Pisa, Italy, in 2004. He is a reviewer for the IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS, and IET Microwave and Antennas Propagation journals. He has served on the Technical Program Committee and Steering Committee of the IEEE Antennas and Propagation Society’s Symposia and Steering Committee of the IEEE Microwave Theory and Techniques Society’s International Microwave Symposium (IMS). He was Chair of the Student Paper Contest of the IEEE Antennas and Propagation Society Symposium 2008 held in San Diego and currently serves on the sub-committee of the Education Committee for the IEEE Antennas and Propagation Society for the organization of the Student Paper Contest during the IEEE Antennas and Propagation Society. He is a full member of the USNC/URSI, Commission B, fields and waves.

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Microstrip Patch Antennas With Enhanced Gain by Partial Substrate Removal Siew Bee Yeap, Member, IEEE, and Zhi Ning Chen, Fellow, IEEE

Abstract—A method to enhance gain of a microstrip patch antenna is investigated by partially removing the substrate surrounding the patch. The partial substrate removal reduces the losses due to surface waves and dielectric substrate. The effects of substrate removal in different configurations on the gain of the antenna are studied numerically and validated experimentally. Compared to a conventional patch antenna, the antennas with partial substrate removal can enhance gain, for example, up to 2.7 dB. Furthermore, it is observed that the enhancement of gain is more due to loss reduction of surface waves and dielectric substrate than increased patch size when the effective dielectric constant of substrate is lowered. Such a technique can be applied in designs operating at higher frequencies whereby surface wave and substrate losses are more significant though the 2.4-GHz design is exemplified here for ease of fabrication and measurement purposes. Index Terms—Microstrip antennas, surface waves.

I. INTRODUCTION

M

ICROSTRIP patch antennas is widely used due to being compact, conformal, and low cost. However, three types of losses i.e. conductor loss, dielectric loss and surface wave loss will lower gain of a patch antenna. The conductor loss and the dielectric loss depend on the quality of the materials being used such as copper or gold, and the substrate, respectively. The dielectric loss is dependent on the loss tangent of materials and substrate thickness while the surface wave loss depends on the permittivity of materials and the substrate thickness [1]. While better quality selection of conductor and substrate can reduce the conductor and dielectric losses therefore improving the gain of the antenna, the gain of the patch antenna can be further enhanced by suppressing surface waves. Jackson, et al. reported the designs that excite very little surface waves based on the principle that a ring of magnetic current in the substrate has a critical radius [2]. Another easy method is to replace the substrate of patch antennas with air of or with very low dielectric constant material, well known as suspended patch antennas [3]. The suspended patch requires an air gap and this is formed by a spacing material such as foam for fabrication purposes or the patch being supported by posts [4]. Both types can Manuscript received September 27, 2009; revised January 31, 2010; accepted March 19, 2010. Date of publication June 14, 2010; date of current version September 03, 2010. This work was supported by the Agency for Science, Technology and Research (A*STAR), Singapore through the Terahertz Science & Technology Inter-RI Program under Grant 082 141 0040. The authors are with Institute of Infocomm, Singapore 138632, Singapore (e-mail: [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TAP.2010.2052572

be fragile and not very durable at times making it unsuitable for mass production. Electromagnetic band gap structures are also used to improve antenna gain [5]–[7]. The periodic structures block the surface waves from propagating in a certain band gap. The alternative is to perforate the substrate i.e. drill holes in the substrate hence synthesizing a lower dielectric constant substrate [8], [9]. For ease of fabrication, the latter concept of synthesizing a lower dielectric constant by partially removing the substrate surrounding the patch is more practical. The method has also been applied by referring to it as trenches which are quite narrow but not studied with more detailed information [10]–[13]. In this paper, the effects of partial substrate removal on the performance of microstrip patch antenna are investigated to explore an effective yet simple way to enhance the gain of the antenna. The basic idea is to improve the gain of a microstrip patch antenna by suppressing surface waves and reducing dielectric loss through partial substrate removal surrounding the antenna. We refer to this method as open air cavity since the removed substrate can be a large portion. The designs with different substrate removals are studied numerically and verified experimentally. As an example, a microstrip patch antenna is designed to operate at 2.4 GHz to demonstrate the mechanism and effect of the method by studying the near-field distribution around the patch in Section II. Also in Section II, the gain of some open cavity designs are investigated. Then, the mutual coupling between two patch antennas lay opposite each other along the radiating edge direction is examined in Section III [14]. Section IV summarizes the findings with conclusions. II. MICROSTRIP PATCH WITH AND WITHOUT SUBSTRATE REMOVAL A. Aperture-Coupled Microstrip Patch Consider a conventional aperture-coupled microstrip patch antenna at 2.4 GHz on a dielectric substrate of Roger 6006 with and loss tangent of 0.0027. The geometry of the aperture-coupled microstrip patch is shown in Fig. 1(a). The patch and is positioned in the center of of square ground plane. The thicknesses of the a substrate are and . The thickness of is achieved by stacking multiple thin dielectric sheets of identical dielectric property. The width of the feeding strip . The coupled on the bottom of the substrate is slot positioned right underneath the center of the patch measures and . The strip stub has length of . Fig. 1(b) shows the simulated impedance bandwidth of 10% (2.33–2.57 GHz) for and gain against frequency.

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TABLE I DESIGN PARAMETERS OF THE APERTURE-COUPLED PATCH WITH/WITHOUT SUBSTRATE REMOVAL. UNITS ARE ALL IN mm EXCEPT V IN%

Fig. 3. Gain increment of Designs B-H compared to Design A at 2.4 GHz. Fig. 1. (a) Geometry, (b) simulated jS crostrip patch antenna.

j

and gain of an aperture-coupled mi-

Fig. 2. Aperture-coupled microstrip patch antenna with substrate removal.

Fig. 4. Aperture-coupled microstrip patch antennas with different substrate removal configurations.

B. Microstrip Patch Aperture-Fed With Open Air Cavity In this section, the substrate surrounding the patch is removed to synthesize a lower dielectric substrate with an open air cavity. All the cavities have the same depth . The cavity with a width is cut from the edge of the patch as shown in Fig. 2. The effect of increasing on the gain of the antenna is studied. The dimensions of the antenna are accordingly adjusted to maintain the resonance at 2.4 GHz when changes. Table I shows the design parameters, including the original patch without any cavity , that is Design A. Since the patch is not namely square, is not the same value in the radiating and non-radiating edge when all the substrate is removed. This is shown in Table I where has two values in the edges, respectively. The ratio of the substrate’s volume after partial removal over the total sub, in percentage is strate’s volume included as well. Fig. 3 shows the gain changes of the designs listed in Table I compared to the gain of Design A at 2.4 GHz. It is observed that

when , the gain increment of Designs A-D are only for Designs F and G. When 0.3 dB but 1.5 dB as all the side substrate is removed, namely Design H, the gain increases over 2 dB. The increase in gain is due to the increase in overall dimensions of the patch, the reduction of dielectric loss and suppression of surface waves. C. Comparison of Patch Antennas With Varying Open Air Cavity Configuration Besides varying the open air cavity size as mentioned above, the effects of removing substrate in different configurations on the antenna gain are numerically investigated and validated experimentally as shown in Fig. 4. For comparison purpose, Designs A and H were fabricated as Designs I and II, respectively. In Design III, the dielectric substrate was removed from its radiating edges whereas the dielectric substrate was removed from the non-radiating edges in Design IV. The dimensions of the

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Fig. 6. Normalized electric field distributions of Designs I–VI (in dB). Fig. 5. Simulated and measured jS j of aperture-coupled microstrip patch antennas with different substrate removal configurations.

patch antennas were changed accordingly to keep their resonance at around 2.4 GHz. To confirm that the improved gain is also from the reduction of surface waves and not only from the increase in patch size, Design V with the same patch size as Design II was designed by changing the dielectric constant of substrate to keep the antenna operating at 2.4 GHz. The achieved dielectric constant of can be considered as the effective permittivity for Design II. For fabrication purposes, Roger 4003 substrate with and the same loss tangent of 0.0027 was used to approximate . the substrate with the effective dielectric constant of Design VI has an embedded air cavity right beneath the patch. The cavity size is the same as the patch. All the cavities have the same depth, . for the Fig. 5 compares the simulated and measured designs, which agree quite well. The simulation was carried out using CST Microwave Studio. The slight discrepancy between the achieved resonances in simulation and measurement is mainly caused by fabrication tolerance and, especially, air gap between the thin dielectric sheets which were used to form the desired thick dielectric substrate. The bandwidth for Designs I–VI is as follow: 8.3% (Design I), 5% (Design II), 5.1% (Design III), 6% (Design IV), 11.2% (Design V) and 12% (Design VI). Due to higher surface wave loss, Design I and Design V have wider impedance bandwidths than Design II–IV. Design VI has the highest impedance bandwidth which shows that the cavity in Design VI improves the

impedance bandwidth the most. However, Design II–IV can achieve wider gain bandwidths than the conventional ones and better radiation performance as will be shown later on. Fig. 6 illustrates the electric field distributions along the plane of the patch, for all the designs respectively, which are normalized by the maximum electric filed amongst the designs. Design I is used as reference. Some important observations can be deduced from Fig. 6. First, compared with Design I, Designs II and III have much weaker radiation from the edges of the ground plane/substrate whereas Designs V and VI also illustrate strong radiation from their edges. Compared with Design I, Design V has weaker radiation from its substrate edges due to its lower dielectric constant. Such radiation is mainly caused by surface waves. It proves the fact that the dielectric causes the surface waves and the higher the dielectric constant, the stronger the surface waves. Secondly, Design IV has stronger radiation from the edges of dielectric slab which are positioned along the radiating edges of the patch, whereas Design III has much weaker radiation from the edges of the dielectric slab which is positioned along the non-radiation edges of the patch. It suggests that the majority of surface waves stems from the radiating edges of the patch. Table II compares the simulated and measured gain and halfpower beamwidths (HPBW) of Designs I–VI at their simulated and measured resonance frequency, respectively. The measured resonance frequency slightly shifts from the simulated due to fabrication tolerances as mentioned previously. From both simulated and measured gain against frequency, it is found that the achieved gain slightly changes around 2.4 GHz where the designs realized impedance matching. Designs II and III have the

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TABLE II APERTURE-COUPLED PATCH ANTENNAS WITH DIFFERENT SUBSTRATE REMOVAL CONFIGURATIONS

Fig. 7. (a) Measured gain of Design I–VI, (b) Gain increment of Designs II–VI at their respective resonance frequencies compared to Design I at 2.4 GHz.

narrowest HPBW due to less surface waves hence achieving the highest gain. Fig. 7(a) shows the measured gain for Design I–VI while Fig. 7(b) shows the gain increment of Designs II–VI with different substrate removal configurations at their respective resonance frequencies compared to Design I at 2.4 GHz. As mentioned earlier on, Design II–IV can achieve wider gain bandwidths than the conventional ones (gain above 4 dBi). The gain of 4 dBi is chosen as Design I has almost a flat gain response. Designs II–VI achieved higher gain at their respective resonance than Design I at 2.4 GHz. In particular, Design II realized the highest gain increment while Design III is not far off. By comparing Design II with partial substrate removal and Design V with the similar effective dielectric constant and loss tangent as Design II but without any substrate removal, the former is 2.7 dB higher gain than Design I whereas Design V has the 1.3 dB higher gain than Design I. Again, it suggests that the extra gain obtained is due to the reduction of surface waves and dielectric loss, not only from the increase in patch size. Gain of 6.7 dB for Design III and 5.2 dB for Design IV demonstrates that the surface wave loss caused from the radiating edges is much more than that from the non-radiating edges. Also, comparing 2.7 dB and 2.4 dB gain improvement for Design II and Design III suggests that the presence of substrate in the non-radiating edge is not as critical as the radiating edge for surface wave loss. Therefore, it will be reasonable to remove the dielectric substrate from the radiating edges instead of non-radiating edges if partial substrate removal is allowed in antenna fabrication. Finally, the gain enhancement for Design VI indicates that the introduction of the embedded cavity may reduce dielectric loss but not substantial surface wave loss compared to Designs II–IV.

It should be noted that the suspended design does not suffer any loss caused by surface waves and dielectric substrate. However, they have weakness in fabrication tolerance and installation robustness as well as ease of integration into other planar circuits, in particular at higher operating frequency, such as millimeter wave and sub-millimeter wave bands. Fig. 8 shows the measured radiation patterns for the designs at their respective resonant frequencies in the E- and H-planes. The measured results agree well with simulations as shown here. The cross-polarization levels are less than 20 dB for Designs II, III, and IV. Designs II and III have the narrowest beamwidths in both E- and H-planes as well as better front to back ratio. The reduced surface wave loss in Design II–IV does leads to improved quality factor. This in turn reduces the bandwidth as shown in Fig. 5. The design trade-offs would then be a compromise between bandwidth and the other antenna performance such as gain, beamwidth and front to back ratio for this type of design. III. MUTUAL COUPLING In this section, the inter-element mutual coupling between two adjacent patch antennas with/without substrate removal (Designs I and II as tabulated in Table II) along their E-planes is examined. The antennas are placed opposite to each other as shown in Fig. 9 at a distance of away from each other. The . separation is chosen at 0.1, 0.25, 0.5, 0.75, and Fig. 10 shows the isolation for a pair of Designs I and II for the varying at 2.4 GHz, respectively. Design II achieves better isoand a maximum for with lation for

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Fig. 9. Two aperture-coupled patch antennas placed opposite to each other with separation d.

Fig. 10. Comparison of isolation at 2.4 GHz for Designs I and II with varying separation d.

Fig. 11. Comparison of normalized electric field distributions at 2.4 GHz as d :  for (a) Design I—top view, (b) Design II—top view, (c) Design I—side view, and (d) Design II—side view.

= 05

Fig. 8. Measured radiation patterns of the patch antennas with different substrate removal configurations (Designs I–VI).

difference in isolation of 9.4 dB. The isolation then becomes almost similar for when the surface waves strength starts

to deteriorate. Another point to note is that Designs I and II as space have the same isolation when spacing is around waves dominate the mutual coupling. Fig. 11 compares the normalized electric field distributions of the scenarios with a pair of Designs I and Design II as . It is found that the substrate removal in Design II reduces the surface waves from the radiating edges of the excited patch (left-hand side) so that the coupled field at the radiating edges

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of the patch (right-hand side) is weakened. Therefore, the substrate removal greatly reduces the mutual coupling by 6.9 dB compared to Design I.

IV. CONCLUSIONS The effects of partial substrate removal on the gain of microstrip patch antennas have been investigated numerically and validated experimentally. It has been seen that by suppressing surface waves and reducing dielectric loss, the gain of the microstrip patch antenna, especially with high permittivity has been improved up to 2.4–2.7 dB when the substrate surrounding the radiating edges of the patch antenna have been fully or partially removed. Meanwhile, the E-plane mutual coupling between the two identical patch antennas at a distance of a half operating wavelength has been reduced by 6.9 dB. Therefore, the partial substrate removal is capable of improving gain and maintaining mechanical robustness of patch antennas.

REFERENCES [1] R. B. Waterhouse, Microstrip Patch Antennas—A Designer’s Guide. Boston, MA: Kluwer Academic Publishers, 2003, ch. 4. [2] D. R. Jackson, J. T. Williams, A. K. Bhattacharyya, R. L. Smith, S. J. Buchheit, and S. A. Long, “Microstrip patch designs that do not excite surface waves,” IEEE Trans. Antennas Propag., vol. 41, no. 8, pp. 1026–1037, Aug. 1993. [3] Z. N. Chen, “Broadband probe-fed plate antenna,” in Proc. 30th Eur. Microwave Conf., Oct. 2000, pp. 1–5. [4] H. S. Lee, J. G. Kim, S. Hong, and J. B. Yoon, “Micromachined CPW-fed suspended patch antenna for 77 GHz automotive radar applications,” in Proc. Eur. Microwave Conf., Oct. 2005, vol. 3, pp. 4–6. [5] R. Gonzalo, P. de Maagt, and M. Sorolla, “Enhanced patch-antenna performance by suppressing surface waves using photonic-bandgap substrates,” IEEE Trans. Microw. Theory Tech., vol. 47, no. 11, pp. 2131–2138, Nov. 1999. [6] H. Boutayeb and T. A. Denidni, “Gain enhancement of a microstrip patch antenna using a cylindrical electromagnetic crystal substrate,” IEEE Trans. Antennas Propag., vol. 55, no. 11, pp. 3140–3145, Nov. 2007. [7] N. Llombart, A. Neto, G. Gerini, and P. de Maagt, “Planar circularly symmetric EBG structures for reducing surface waves in printed antennas,” IEEE Trans. Antennas Propag., vol. 53, no. 10, pp. 3210–3218, Oct. 2005. [8] G. P. Gauthier, A. Courtay, and G. M. Rebeiz, “Microstrip antennas on synthesized low dielectric-constant substrates,” IEEE Trans. Antennas Propag., vol. 45, no. 8, pp. 1310–1314, Aug. 1997. [9] J. S. Colburn and Y. Rahmat-Samii, “Patch antennas on externally perforated high dielectric constant substrates,” IEEE Trans. Antennas Propag., vol. 47, no. 12, pp. 1785–1794, Dec. 1999. [10] R. A. R. Solis, A. Melina, and N. Lopez, “Microstrip patch encircled by a trench,” in Proc. IEEE Int. Symp. on Antennas Propag. Society, Jul. 2000, vol. 3, pp. 1620–1623. [11] Q. Chen, V. F. Fusco, M. Zheng, and P. S. Hall, “Micromachined silicon antennas,” in Proc. Int. Conf. on Microwave and Millimeter-Wave Tech., Aug. 1998, pp. 289–292. [12] Q. Chen, V. F. Fusco, M. Zhen, and P. S. Hall, “Trenched silicon microstrip antenna arrays with ground plane effects,” in Proc. 29th Eur. Microwave Conf., Oct. 1999, vol. 3, pp. 263–266.

[13] Q. Chen, V. F. Fusco, M. Zheng, and P. S. Hall, “Silicon active slot loop antenna with micromachined trenches,” in Proc. Inst. Elect. Eng. National Conf. on Antennas and Propagation, April 1999, no. 461, pp. 253–255. [14] J. G. Yook and L. P. B. Katehi, “Micromachined microstrip patch antenna with controlled mutual coupling and surface waves,” IEEE Trans. Antennas Propag., vol. 49, no. 9, pp. 1282–1289, Sept. 2001. Siew Bee Yeap (M’07) received the B.Sc. degree (with honors) from the University of Malaya, Kuala Lumpur, in 1996, the M.Sc. from the National University of Singapore, in 1998, and Ph.D. degree from Queen Mary, University of London, London, U.K., in 2003. From 2003 to 2004, she was a Postdoctoral Fellow at Queen Mary, University of London, where she was involved in multiple input and multiple output antenna design. She later joined Laird Technologies, from 2006 to 2007, as a staff antenna Design Engineer from which she holds a U.S. patent. In 2007, she joined the Institute of Infocomm Research, Singapore, as a Senior Research Fellow. Her current research interests include design, modeling and measurements of millimeter-wave and terahertz antennas. She has authored more than 10 international journals and conferences.

Zhi Ning Chen (F’07) received the B.Eng., M.Eng., Ph.D. and Do.E. degrees all in electrical engineering from Institute of Communications Engineering (ICE), China and University of Tsukuba, Japan, respectively. From 1988 to 1995, he worked at ICE as a Teaching Assistant, Lecturer and Associate Professor as well as at Southeast University, China, as a Postdoctoral Fellow and later Associate Professor. From 1995 to 1997, he was with City University of Hong Kong, China, as a Research Assistant and later a Research Fellow. In 1997, he was awarded a JSPS Fellowship to conduct his research at the University of Tsukuba, Japan. In 2001 and 2004, he visited the University of Tsukuba under a JSPS Fellowship Program (at senior level). In 2004, he worked at IBM T. J. Watson Research Center, New York, as an Academic Visitor. Since 1999, he has worked at the Institute for Infocomm Research (formerly known as Center for Wireless Communications and Institute for Communication Research) as a Member of Technical Staff (MTS), Principal MTS, Senior Scientist, and Lead Scientist. He was currently appointed Principal Scientist and Department Head for RF & Optical. Concurrently he was/is an Adjunct/Guest Professor at Southeast University, Nanjing University, Shanghai Jiao Tong University, Tongji University, Zhejiang University, National University of Singapore, and Nanyang Technological University. He has published and presented 275 papers in journals and at conferences as well as authored and/or edited the books Broadband Planar Antennas, UWB Wireless Communication, Antennas for Portable Devices, and Antennas for Base Station in Wireless Communications. He also contributed chapters to the books UWB Antennas and Propagation for Communications, Radar, and Imaging, and the Antenna Engineering Handbook. He is holding 25 granted and filed patents with 15 licensed deals with industry. His current research interests are in applied electromagnetics as well as antennas for microwave, mmW, submmW, and THz communication and imaging systems. Dr. Chen was nominated a Fellow of the IEEE for his “contribution to small and broadband antennas for wireless applications” and is also an IEEE AP-S Distinguished Lecturer. He has organized many international technical events as General Chair, Technical Program Committee Chair, and has been a key member of organizing committees. He is the founder of the International Workshop on Antenna Technology (iWAT). He is the recipient of the CST University Publication Award 2008, IEEE AP-S Honorable Mention Student Paper Contest 2008, IES Prestigious Engineering Achievement Award 2006, I2R Quarterly Best Paper Award 2004, and IEEE iWAT 2005 Best Poster Award.

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Broadband, Miniaturized Stacked-Patch Antennas for L-Band Operation Based on Magneto-Dielectric Substrates Farhad Namin, Student Member, IEEE, Thomas G. Spence, Douglas H. Werner, Fellow, IEEE, and Elena Semouchkina, Member, IEEE

Abstract—Design of stacked-patch antennas using magneto-dielectric substrates was investigated. In particular, special types of substrates with identical relative permittivity and permeability were considered. The optimal design parameters were determined using a genetic algorithm. It will be shown that by employing these matched magneto-dielectric substrates, a significant miniaturization of up to 60% can be achieved while providing a large operating bandwidth (20%). Several design examples were considered and their performance was evaluated using a full-wave analysis technique based on the method of moments. The tradeoff between antenna gain and degree of miniaturization for a fixed bandwidth was also investigated. A fabrication methodology for obtaining the required matched magneto-dielectric substrate materials is also proposed. Index Terms—Antenna miniaturization, genetic algorithms, magneto-dielectric material, stacked-patch antennas.

I. INTRODUCTION HE low profile and wide bandwidth of microstrip stacked-patch antennas makes them an attractive choice for many RF applications, especially in the UHF and L bands. There are several competing factors that impact the design of these antennas. For instance, miniaturization can be achieved through the use of substrates with a high permittivity. When using high permittivity substrates, the reduction in antenna size . However the size reduction is roughly proportional to tends to come at the expense of increased coupling between the patches and the ground plane, and consequently a reduced bandwidth. High permittivity dielectric materials can also be heavy (e.g., ceramics) and are therefore not suitable for many applications where light weight antenna structures are required. One proposed solution to these problems is the application of magneto-dielectric substrates.

T

Manuscript received October 10, 2009; revised February 24, 2010; accepted March 22, 2010. Date of publication June 14, 2010; date of current version September 03, 2010. F. Namin and D. H. Werner are with the Computational Electromagnetics and Antenna Research Lab (CEARL), Department of Electrical Engineering, The Pennsylvania State University (Penn State), University Park, PA 16802 USA (e-mail: [email protected]). T. Spence is with Northrop Grumman Electronic Systems, Baltimore, MD, MD 21240 USA. E. Semouchkina is with Michigan Technological University, Houghton, Michigan 49931-1295 USA. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TAP.2010.2052574

and ) In [1], a magneto-dielectric substrate ( was used in the design of a single-layer patch antenna. It was and provide a sigshown that even moderate values of nificant degree of miniaturization that typically comes about through the use of high permittivity substrates. Moreover, it was demonstrated theoretically that the bandwidth of the magneto-dielectric designs exceeds that of the dielectric-only ( and ) designs. The reduction in size that is obtained using magneto-dielectric substrates was shown to be roughly . In [2], Mosallaei and Sarbandi introproportional to duced an artificial anisotropic meta-substrate to maximize the bandwidth of a miniaturized patch antenna and validated its performance through numerical simulations. There are no natural materials having moderate and equal values of relative permittivity and permeability known to exist for application within the L-band. One possible solution to the fabrication of such substrates would be utilizing microwave composites of dielectric and magnetic materials as suggested in [3]. Another possible way to design magneto-dielectric substrates involves using periodic structures composed of dielectric and magnetic materials. To obtain the effective properties of these composite substrates, a quasi-static mixing model [4], [5] can be employed when the unit cell is much smaller than the wavelength in the medium. For the general case, a design methodology based on anisotropic effective medium theory was developed in [2]. A more recent approach utilizes ferromagnetic thin films based on metals such as Fe and Co. This technology has been used to design and fabricate bulk laminates exhibiting in the range 100 MHz–2 GHz [6]. In this paper, the use of magneto-dielectric layers will be extended to the application of stacked-patch antenna designs. In , which we call the particular we examine the case when matched magneto-dielectric condition. Consequently the characteristic impedance of the substrate will be identical to that of free space and it allows for better matching over the bandwidth of the antenna. Moreover, the magnetic property of the substrate provides an additional degree of miniaturization compared to non-magnetic (dielectric-only) substrate materials. It and will be shown that even with moderate values of it is possible to considerably reduce the size (length, width, and thickness) of these antennas while retaining their attractive wideband characteristics. We also explore the tradeoff between the size and gain of these antennas. Finally, a possible fabrication methodology for the magneto-dielectric substrate is proposed.

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II. MATERIALS There are no known natural materials having moderate (3–5) and equal values of relative permittivity and permeability within the L-band. The frequency range for magnetic materials is primarily limited by their ferromagnetic resonances. For most magnetic materials the relationship between the static and the ferromagnetic resonant frequency permeability is given by Snoek’s law [3] (1) where GHz/kOe. However for ferromagnetic films and hexagonal ferrites this law is replaced by Acher’s relation, which is given by [7], [8] (2) where is traditionally known as Acher’s constant which has units of GHz . Ferromagnetic films have much larger Achers constants (up to 4000 GHz ) due to higher saturation magnetization compared to 200 GHz for ferrites. However if the thickness is greater than 0.5 microns, the performance is deteriorated due to eddy currents. Therefore, films should be integrated with other materials into laminates to produce usable composites. The laminates can be made by sputtering ferromagnetic films onto thin polymer or silica layers followed by stacking the resulting elements together [6]. An estimate for the effective parameters of the resulting laminates is given in [9]. For either or we have (3) where for permittivity (layers perpendicular to the electric field) and for permeability (layers parallel to are the intervening the magnetic field). Moreover and denote the thicknesses of volume fractions. Letting the polymer and the ferromagnetic layers respectively, then the permittivity and the permeability can be expressed in the following form:

Fig. 1. Effective relative permittivity and permeability of laminate as a function of the thickness of the polymer layer from (6) and (7).

Fig. 2. Exploded and collapsed view of a stacked-patch antenna.

The resulting effective parameters of the laminate as a function of the polymer layer thickness are shown in Fig. 1. At a polymer layer thickness of roughly 38 m the resulting laminate will have identical relative permittivity and permeability . Moreover, different values of permittivity and permeability can also be achieved. However the parameters of the ferromagnetic film and the polymer layer need to be adjusted accordingly. Using this method, Osipov et al. [10] were able to fabricate and characterize laminates which had a relative permittivity and permeability of roughly 3 in the frequency range of 100 MHz–2 GHz without dispersion and with very small loss. III. DESIGN PROCESS

(4) (5) (6) (7) and correspond where the material parameters to the polymer and the ferromagnetic layer respectively. Also m. As an example consider as mentioned previously a polymer layer with and and a ferromagnetic and . The value of is fixed at film with to determine what 0.5 m and, from (6) and (7), we set value of will be required for the laminate to meet this matched condition.

The geometry of a stacked-patch antenna along with its design parameters is shown in Fig. 2. As mentioned in the introduction, this paper considers the design of stacked-patch antennas using magneto-dielectric substrates with identical (matched) permittivity and permeability. The design of a probe-fed stacked patch antenna involves the selection of several parameters. A total of nine parameters have been identified for each design including the dimensions of the lower and upper patches, the thickness and permittivity (permeability) of the lower and upper layer, and the probe feed location. While these parameters lend the antennas a degree of design flexibility, they also make for a more complicated design process than a standard single-layer patch antenna. The design procedure can be carried out manually based on a combination of physics-based reasoning and trial and error. However, due

NAMIN et al.: BROADBAND, MINIATURIZED STACKED-PATCH ANTENNAS FOR L-BAND OPERATION

TABLE I OPTIMAL DESIGN PARAMETERS FOR STACKED-PATCH ANTENNAS WITH COST FUNCTION F

to the large number of design parameters involved, the process can become cumbersome and very tedious. Thus the design approach used for this paper was carried out via a genetic algorithm (GA). The genetic algorithm is robust and lends itself very well to this multi-parameter multi-objective problem. A more detailed and complete description of genetic algorithms and their applications in solving electromagnetic optimization problems is given in [11], [12], and [13]. The GA that was utilized for this particular design was binary coded with each design parameter being quantized into 16 bits. Single point crossovers were used and tournament selection was employed for the mating process. The typical population size was 50. The maximum number of generations for the GA was set at 200. The mutation rate was fixed at 8% and a selection ratio of 0.5 was used. One of the key aspects of a GA is in the definition of its cost function. The cost function in our investigation incorporated three attributes of the antenna, namely VSWR over a prescribed bandwidth, broadside gain at a center frequency, and the overall thickness of the antenna. The center frequency was 1.2 GHz (L-band) and the targeted bandwidth was roughly 20% with a VSWR less than 2:1. Over this range (1.1 GHz–1.3 GHz) the VSWR was sampled at equally spaced frequency points. The particular implementation of the cost function that was utilized in this paper is given below (8) where denotes the VSWR of the antenna at the sampling frequency is the gain (in dBi) at the center is a targeted value of gain (in dBi) at the center frequency, is the thickness of the antenna. Also, frequency, and , and denote weighting factors for each of the three terms in the cost function. As it will be shown in some of the designs, tailoring the values of the targeted gain and the weighting on the thickness provides some insight into the tradeoffs between these characteristics. As mentioned previously, the permeability of each substrate layer is set equal to its permittivity. For our magneto-dielectric designs, we limited the range of relative permittivity between 1 and 5. The dynamic range for the upper and lower patch dimensions were initially set according to traditional guidelines for

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[14] where rectangular patch antennas denotes the wavelength in the magneto-dielectric substrate by and it is related to the free space wavelength . Additionally, the probe-feed was only permitted to be adjusted along the center-line of the lower patch. The analysis of the stacked-patch antenna was carried out through the application of full-wave method-of-moments (MoM) software (FEKO [15]). The numerical modeling assumes uniform substrates with effective permittivity and permeability, rather than laminates. This assumption greatly reduces the complexity of the problem. In our analysis, the antenna is modeled assuming that the substrate layers and the ground plane are infinite in extent. The MoM code calculates the reflection coefficient and the gain of the antenna. As mentioned earlier, a return-loss of dB is targeted to determine the bandwidth of the less than antenna. The GA algorithm was written in C++. During each generation, the MoM code is called from the GA to evaluate antenna performance for each member of the population. Once all members have been evaluated, the cost function associated with each member is calculated. The best performing member of each generation advances to the next generation without any mutation. Since the selection ratio for the GA is 0.5, half of the population with the highest cost functions are discarded and the other half advances to the next generation, where mating and mutation is applied to them to replenish the population. The GA will terminate under two conditions. First if it reaches the maximum number of prespecified generations (200), and second if the lowest cost function has reached a plateau and has not changed for 20 generations. In all of our examples, the GA converged prior to reaching the maximum number of generations allowed. Furthermore, each GA was run at least 3 times. IV. RESULTS In this section we will consider stacked-patch antenna designs that have been optimized based on several different variations of the cost function defined in (8). Both dielectric-only and magneto-dielectric loaded designs were considered in order to make direct comparisons. For all cases a total of 5 equally spaced frequency points where chosen in the required bandwidth (1.1 GHz–1.3 GHz). For the first design, the weighting terms in the cost function , and . This version of the cost were set to function is denoted by , which is used to determine what kind of miniaturization in terms of thickness can be obtained without taking the gain of the antenna into account. The material parameters were constrained to be within the range of 1–5 for both ) and the dielecthe magneto-dielectric (i.e., and ) designs. The optimal patric-only (i.e., rameters determined by the GA for the two types of designs are listed in Table I. It can be observed that through the use of magneto-dielectric substrates we were able to obtain a miniaturization factor of almost 2.4 in terms of the total thickness (roughly 60% reduction) compared to a conventional dielectric-only design. Plots of the return loss and the broadside gain of the two designs are shown in Figs. 3 and 4 respectively. As it can be seen from Fig. 4, while considerable miniaturization was achieved using magneto-dielectric substrates, the gain of the miniaturized antenna was much lower than its dielec-

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TABLE II OPTIMAL DESIGN PARAMETERS FOR MAGNETO-DIELECTRIC STACKED-PATCH ANTENNAS WITH COST FUNCTION F

Fig. 3. Reflection coefficient (dB) versus frequency of the magneto-dielectric and dielectric-only designs obtained by optimizing F . Fig. 5. Reflection coefficient (dB) versus frequency of the magneto-dielectric . The numbers designs obtained by optimizing F with increasing values of in the plot legend correspond to the total thickness of the design.

G

Fig. 4. Broadside gain (dBi) versus frequency of the magneto-dielectric and dielectric-only designs obtained by optimizing F .

tric-only counterpart. Using another variation of the cost function (8) it is possible to target bandwidth and thickness, as well as a certain desired value of broadside gain. In order to minimize the thickness of the antenna while (in dBi), a simultaneously maintaining a specified gain , and are second variation of (8) is considered in which all greater than zero. The exact values have been determined

through numerical experimentation. After considering several different combinations of the weighting parameters it was , and usually provided found that using the best results. For reference purposes this second version of the cost function (8) is denoted by . Here we were interested might in investigating how increasing the targeted value of affect the miniaturization of the magneto-dielectric loaded antenna design. Also for each antenna the miniaturization factor was defined as the ratio of the total thickness of the optimized dielectric-only antenna to that of the magneto-dielectric loaded antenna. It was of interest to see if a trend would emerge between the gain and the miniaturization factor. In this study, : 2 dBi, 3 dBi, 4 dBi, the following values were used for 5 dBi and 6 dBi. The optimal design parameters obtained for each of these five cases are listed in Table II. Table II also includes a miniaturization factor for each design, in terms of the total thickness of the design compared to the dielectric-only design obtained using . Plots of the return loss and the broadside gain for each of these designs are shown in Figs. 5 and 6, respectively, and labeled according to the

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which minimized the thickness of the antenna while simultaneously obtaining a certain broadside gain and a wide bandwidth. Two versions of the cost function were considered. The first version did not take the broadside gain into account. It was shown that if the broadside gain was not taken into account a roughly 60% reduction in thickness could be achieved using magneto-dielectric substrates compared to the dielectric-only antennas. The second version of the cost function targeted a specific broadside gain to determine what kind of size reduction would be possible in such a case. It was shown that significant miniaturization could be achieved while still obtaining moderate values of broadside gain. REFERENCES

Fig. 6. Broadside gain (dBi) versus frequency of the magneto-dielectric and . dielectric-only designs obtained by optimizing F with increasing values of The numbers in the plot legend correspond to the total thickness of the design.

G

Fig. 7. Miniaturization factor versus the broadside gain at the center frequency obtained for several designs.

total thickness of the antenna. The tradeoff between the broadside gain and the achieved miniaturization is better illustrated in Fig. 7 which plots the miniaturization factor against the gain (relative to an isotropic antenna) at the center frequency for each of the optimal designs included in Table II. As illustrated in this figure the data can be represented fairly accurately by a quadratic fitting model, which provides a useful design equation for trading off the amount of miniaturization with the gain of the antenna. V. CONCLUSION In this paper the design of wide-band stacked-patch antennas using matched magneto-dielectric substrates was considered. A fabrication methodology for such substrates was presented based on very thin ferromagnetic films on top of polymer layers. The design parameters for the antenna were obtained by applying a genetic algorithm to a multi-objective cost function

[1] R. C. Hansen and M. Burke, “Antennas with magneto-dielectrics,” Microwave Opt. Tech. Lett, vol. 26, no. 2, pp. 75–78, July 2000. [2] H. Mosallaei and K. Sarabandi, “Magneto-dielectrics in electromagnetics: concept and applications,” IEEE Trans. Antennas Propag., vol. 52, pp. 1558–1567, June 2004. [3] P. M. T. Ikonen, K. N. Rozanov, A. V. Osipov, P. Alitalo, and S. A. Tretyakov, “Magnetodielectric substrates in antenna miniaturization: potential and limitations,” IEEE Trans. Antennas Propag., vol. 54, no. 11, pp. 3391–3399, Nov. 2006. [4] S. Datta, C. T. Chan, K. M. Ho, and C. M. Soukoulis, “Effective dielectric constant of periodic composite structures,” Phys. Rev. B., vol. 48, no. 20, pp. 14936–14943, Nov. 1993. [5] T. Sondergaard, J. Broeng, A. Bjarklev, K. Dridi, and S. E. Barkou, “Suppression of spontaneous emission for a two-dimensional honeycomb photonic bandgap structure estimated using a new effective index model,” IEEE J. Quantum Electron., vol. 34, pp. 2308–2313, Dec. 1998. [6] K. N. Rozanov, I. T. Iakubov, A. N. Lagarkov, S. A. Maklakov, A. V. Osipov, D. A. Petrov, I. A. Ryzhikov, M. V. Sedova, and S. N. Starostenko, “Laminates of the ferromagnetic films for microwave applications,” in Proc. Symp. MSMW, Kharkov, Jun. 2007, pp. 168–173. [7] O. Acher and A. L. Adenot, “Bounds on the dynamic properties of magnetic materials,” Phys. Rev. B, vol. 62, no. 17, pp. 11324–11327, 2000. [8] A. L. Adenot, O. Acher, T. Taffary, and L. Longuet, “Sum rules on the dynamic permeabiltiy of hexagonal ferrites,” J. Appl. Phys., vol. 91, no. 10, pp. 7601–7603, 2002. [9] C. J. Dias and D. K. Das-gupta, “Inorganic ceramic/polymer ferroelectric composite electrets,” IEEE Trans. Dielectr. Electr. Insul., vol. 3, no. 5, pp. 706–734, Oct. 1996. [10] A. V. Osipov, I. T. Iakubov, A. N. Lagarkov, S. A. Maklakov, D. A. Petrov, K. N. Rozanov, and I. A. Ryzhikov, “Multi-layered fe films for microwave applications,” Piers Online, vol. 3, no. 8, pp. 1303–1306, 2007. [11] R. L. Haupt, “An introduction to genetic algorithms for electromagnetics,” IEEE Antennas Propag. Mag., vol. 37, pp. 7–15, Apr. 1995. [12] D. S. Weile and E. Michielssen, “Genetic algorithm optimization applied to electromagnetics: A review,” IEEE Trans. Antennas Propag., vol. 45, pp. 343–353, Mar. 1997. [13] R. L. Haupt and D. H. Werner, Genetic Algorithms in Electromagnetics. Hoboken, NJ: Wiley, 2007. [14] C. A. Balanis, Antenna Theory, Analysis, and Design. Hoboken, NJ: Wiley, 2005. [15] Feko User’s Manual [Online]. Available: http://www.emssusa.com FEKO. EM Software and Systems Frank (Farhad) Namin (S’09) was born in Denton, Texas, and grew up in Tehran, Iran. He received the B.S.E.E. and M.S.E.E. degrees in electrical engineering from the University of Texas at Dallas. He is currently working toward the Ph.D. degree at The Pennsylvania State University (Penn State), University Park. He has been a Research Assistant for the Computational Electromagnetics and Antenna Research Lab (CEARL), Department of Electrical Engineering, Penn State, since 2008. His research interests include

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ultra-wideband aperiodic antenna arrays, tiling theory, metamaterials, photonic crystals, dielectric filters, evolutionary algorithms, and wireless ad-hoc networks. Mr. Namin is the recipient of the Exploratory and Foundational Program Fellowship from the Applied Research Laboratory (ARL) at The Pennsylvania State University.

Thomas G. Spence received the B.S. degree in electrical engineering from the University of Rhode Island, in 2002, and the M.S. and Ph.D. degrees in electrical engineering from The Pennsylvania State University, University Park, in 2004 and 2008, respectively. From 2002 to 2008, he was a Research Assistant in the Computational Electromagnetics and Antennas Research Laboratory (CEARL), Department of Electrical Engineering, Penn State. He is currently with Northrop Grumman Electronic Systems, Baltimore, MD. He coauthored a chapter on Fractal Antennas in the fourth edition of the Antenna Engineering Handbook (New York: McGraw-Hill, 2007). His research interests include antenna theory and design, phased antenna arrays, computational electromagnetics, and optimization algorithms. Dr. Spence is a member of Tau Beta Pi and Eta Kappa Nu. He is the recipient of the 2007 Anthony J. Ferraro Outstanding Research Award for Ph.D. Research. His Ph.D. research was funded through the Exploratory and Foundational Program Fellowship from the Applied Research Laboratory (ARL), The Pennsylvania State University.

Douglas H. Werner (F’05) received the B.S., M.S., and Ph.D. degrees in electrical engineering and the M.A. degree in mathematics from The Pennsylvania State University (Penn State), University Park, in 1983, 1985, 1989, and 1986, respectively. He is a Professor in the Department of Electrical Engineering, Penn State, where he is the Director of the Computational Electromagnetics and Antennas Research Lab (CEARL) (http://labs.ee.psu.edu/labs/dwernergroup/) as well as a member of the Communications and Space Sciences Lab (CSSL). He is also a Senior Scientist in the Computational Electromagnetics Department, Applied Research Laboratory, and a faculty member of the Materials Research Institute (MRI), Penn State. He has published over 400 technical papers and proceedings articles and is the author of eight book chapters. He edited a book entitled Frontiers in Electromagnetics (Piscataway, NJ: IEEE Press, 2000). He has also contributed a chapter for the book Electromagnetic Optimization by Genetic Algorithms (New York: Wiley Interscience, 1999) as well as for the book Soft Computing in Communications (New York: Springer, 2004). He coauthored the book Genetic Algorithms in Electromagnetics (Hoboken, NJ: Wiley/IEEE, 2007). He has also contributed an invited chapter on Fractal Antennas for the popular Antenna Engineering

Handbook (New York: McGraw-Hill, 2007). His research interests include theoretical and computational electromagnetics with applications to antenna theory and design, phased arrays, microwave devices, wireless and personal communication systems, wearable and e-textile antennas, conformal antennas, frequency selective surfaces, electromagnetic wave interactions with complex media, metamaterials, electromagnetic bandgap materials, zero and negative index materials, fractal and knot electrodynamics, tiling theory, neural networks, genetic algorithms and particle swarm optimization. Dr. Werner is a Fellow of the IEEE, IET, and ACES, and a member of the American Geophysical Union (AGU), URSI Commissions B and G, the Applied Computational Electromagnetics Society (ACES), Eta Kappa Nu, Tau Beta Pi and Sigma Xi. He was presented with the 1993 Applied Computational Electromagnetics Society (ACES) Best Paper Award and was also the recipient of a 1993 International Union of Radio Science (URSI) Young Scientist Award. In 1994, he received the Pennsylvania State University Applied Research Laboratory Outstanding Publication Award. He was a coauthor of a paper published in the IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION which received the 2006 R. W. P. King Award. He has also received several Letters of Commendation from the Pennsylvania State University Department of Electrical Engineering for outstanding teaching and research. He is a former Associate Editor of RADIO SCIENCE, an Editor of the IEEE Antennas and Propagation Magazine. He was the recipient of a College of Engineering PSES Outstanding Research Award and Outstanding Teaching Award in March 2000 and March 2002, respectively. He was also presented with an IEEE Central Pennsylvania Section Millennium Medal. In March 2009, he received the PSES Premier Research Award.

Elena Semouchkina (M’04) received the M.S. degree in electrical engineering and the Ph.D. degree in physics and mathematics from Tomsk State University, Tomsk, Russia, in 1978 and 1986, respectively, and the Ph.D. degree in materials from The Pennsylvania State University, University Park, in 2001. She is currently an Associate Professor of electrical engineering at Michigan Technological University, Houghton, and an Adjunct Professor with Pennsylvania State University, University Park. From 1997 to 2009, she working at the Materials Research Institute, Pennsylvania State University, initially as a Graduate Research Assistant, then as a Postdoctoral Scholar, Research Associate, Senior Research Associate and Associate Professor. Prior to that, she was a Scientist with Russian academic centers, such as the Siberian Physics-Technical Institute, St. Petersburg State Technical University, and Ioffe Physics-Technical Institute, where she was involved with the investigation of metal-oxide-semiconductor devices and the development of infrared photodetectors. She has authored and coauthored over 70 publications in scientific journals. Her current research interests are focused on electromagnetic analysis of microwave materials, metamaterials and devices. Dr. Semouchkina was a recipient of the best Ph.D. thesis Award of the Materials Research Institute at The Pennsylvania State University in 2001 and the National Science Foundation 2004 Advance Fellows Award.

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Wideband Phase-Reversal Antenna Using a Novel Bandwidth Enhancement Technique Ning Yang, Member, IEEE, Christophe Caloz, Fellow, IEEE, and Ke Wu, Fellow, IEEE

Abstract—A novel bandwidth enhancement technique for phase-reversal Franklin-type antennas is proposed. Impedance bandwidth enhancement is achieved by combining several coupled modes of the antenna structure through periodic loading provided by radiating crossover dipoles. This technique is explained by the theory of periodically loaded transmission lines. Radiation pattern bandwidth enhancement is achieved by exciting the antenna in its center so as to suppress beam squinting by superposing the tilted beams of two resulting sub-arrays on either side of the feed. An offset parallel stripline (OPS) phase-reversal antenna using these bandwidth enhancement techniques is demonstrated theoretically and experimentally at 35 GHz. The antenna is printed on a thin substrate suspended over a micro-machined conductor-backed cavity for unidirectional radiation. The overall fractional bandwidth of the antenna is increased from 3% to over 11% compared to the conventional design and the antenna efficiency exceeds 80%. Index Terms—Coplanar stripline (CPS), Franklin-type antenna, offset parallel stripline (OPS), phase reversal.

I. INTRODUCTION

N the past few years, millimeter-wave circuits and systems have evolved into a promising technology for many wireless applications, such as automotive radars, remote sensing, and high-speed wireless local area networks (WLANs). The main requirements for antennas in such applications, besides lowprofile and low-cost, are wide frequency bandwidth (e.g., 10% for WLAN), high efficiency and low interconnect loss to allow low-cost integration with transceiver front-ends [1]. Achieving 10% or higher antenna bandwidth, while maintaining high antenna efficiency, represents a major challenge. Because of their convenient integration capability, the microstrip and slot arrays are most-widely used antennas. In these antennas, the simplest feeding system is the series feeding network, where transmission and leakage losses from the feeding lines are reduced compared to the case of the corporate feeding network, and in addition, the overall antenna uses a much smaller board area [2]. The bandwidth of a patch antenna or a slot antenna printed on substrate is typically limited to a few percents. Some techniques,

I

Manuscript received March 23, 2009; revised December 04, 2009; accepted March 18, 2010. Date of publication June 14, 2010; date of current version September 03, 2010. This work was supported in part by the National Science and Engineering Research Council (NSERC). The authors are with the Ecole Polytechnique de Montreal, Montreal, QC H3T 1J4, Canada (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TAP.2010.2052550

such as increasing the substrate’s height [3], using air as the substrate, adding multilayer parasitic patch elements [4], [5] and resorting to complex 3D feeding structures [6], can improve the bandwidth, but they create signal integrity problems and compromise the low profile benefit of the antenna. Furthermore, the connecting transmission lines of the series feeding network pose two major problems as frequency increases toward millimeter waves, namely, 1) due to their narrow strip width, they become highly lossy, 2) due to the fact that the patch-to-line width ratio decreases, the radiation efficiency is further decreased by the aperture blocking of the patches from the lines, which increases cross-polarization from parasitic radiation. The authors proposed in [7] a coplanar strip (CPS) phase-reversal antenna following the principle of the Franklin antenna [8], the Wheeler’s COCO (colinear coxial) antenna [9] and their various microstrip variations [10]–[12]. This antenna has the advantages of planarity, easy integration and smaller lateral footprint. Furthermore, the antenna exhibits the benefit of a balanced configuration, allowing the convenient integration with differential active circuits for low-cost transceiver front end. This antenna can be modeled as a high-order mode transmission line resonator terminated with shorted-end, and therefore exhibits a relatively narrow bandwidth. The measured impedance bandwidth reported in [7] is around 2–3%, which is comparable to the bandwidth of a series microstrip array. In this paper, we propose a novel technique to increase the bandwidth of this phase-reversal antenna. The key concept is to couple and combine several resonant modes, namely the modes , of the antenna to achieve a wider bandwidth. This is accomplished by crossover strips, the phase reversing and radiating elements of the array, which are arranged to couple to each other through parallel-plate coupling. Since coupling is periodically distributed along the transmission line antenna, a periodically loaded transmission line model is used to analyze the proposed antenna. The analysis demonstrates that the resonant frequency of the th mode is fixed, while the other resonant modes shift toward this frequency as coupling increases, as a result of compression in the dispersion curve. By adjusting the coupling parameters, impedance matching may be achieved over a very wide bandwidth. The proposed antenna is essentially a series-fed array. Series-fed array typically suffers from beam squinting as frequency varies, which is a serious drawback of such architectures. In this paper, by exciting the antenna in its center, broadband broadside radiation is achieved by superposing the tilted beams of two resulting sub-arrays on either side of the feed.

0018-926X/$26.00 © 2010 IEEE

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Fig. 2. (a) Two-ends shorted radiator with current and electric field distributions. (b) Structure of the proposed antenna array with its phase-reversing crossovers, and current and electric field distributions.

Fig. 1. Field patterns in the cross-section of (a) a coplanar stripline (CPS) structure, and (b) an offset parallel stripline (OPS).

II. PRINCIPLE OF THE PHASE-REVERSAL ANTENNA A. CPS and OPS Fig. 1(a) shows the cross-section of a CPS with its electric and magnetic fields distributions. A variation of the CPS is a offset parallel stripline (OPS), shown in Fig. 1(b). The common feature of the two structures is that both are balanced transmission lines [13], [14], capable of easily achieving high impedance, while the only difference is that CPS is perfectly coplanar while the OPS is not. Any antenna built in CPS can be transposed to OPS with very similar performance, and this also holds for the phase-reversal antenna, with some design and manufacturing advantages to be described later. B. Phase-Reversal Antenna The proposed phase-reversal antenna or antenna array of [7] is composed of a short-ended CPS transmission line resonator, , where is the number of half-wavewith a length length sections and is the physical length of these sections. It is well-known that an infinite number of resonant modes exist in such resonator, satisfying (1) where is the propagation constant or dispersion relation of the transmission line forming the resonator, and is the , corresponding to th resomodel index number. For from (1). This resonator is shown nance mode, we have in Fig. 2(a), along with its vector current and electric field distributions. The shorting ends have a nonzero length, which grows as the impedance of the transmission line increases (increasing gap ). In this case, maximal currents flow along the vertical shorted ends and therefore these ends operate as short dipole radiators. The structure is thus transformed into an antenna, which

will constitute an element of the overall phase-reversal array. To form a Franklin-type array, crossover strips are introduced along the resonator every length (or half-wavelength), as shown in Fig. 2(b). These crossovers act as phase-reversals and radiating elements at the same time, while the transmission line sections in between do not radiate. As displayed in Fig. 2(b), the currents flowing in the crossovers are all parallel, which can be modeled as arrayed infinitesimal dipole elements. The radiation resistance of each crossover dipole decides the illuminated power over the elements for array synthesis. The radiation resistance can be estimated from

(2) where is the length of the crossovers, is the free space wave. All the sections are excited with the same length and polarity, which produces radiation with transverse polarization. In Fig. 2(b), the antenna is fed from left end, which is very convenient for system integration. C. Crossover Phase-Reversals and Equivalent Circuit The crossovers can take various shapes. In [7], they are implemented under the form of printed via bridges, as shown in Fig. 3(a). In this paper, an offset parallel stripline (OPS) configuration, resulting in a simpler crossover structure, shown in Fig. 3(b), is preferred. The advantages of this modification is twofold: first, no vias are required, which represents an important benefit at millimeter-waves where parasitic effects play a serious role; secondly, it is easier to arrange the strips in two different layers to accurately control the coupling area and the orientation of the strips. This antenna in Fig. 2(b) is equivalent to an array of in-phase short dipoles. According to antenna array theory, the beam radiated by the overall structure is directed toward broadside and the polarization is in the transverse plane. In addition, the antenna is bidirectional. The equivalent circuit of the antenna, initially proposed in [7], is shown in Fig. 4(a). This circuit neglects the

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Fig. 3. Phase-reversals using crossovers with (a) a CPS via bridge [7] and (b) its variation with an OPS (this paper).

Fig. 4. Equivalent circuit for the phase-reversal antenna array of Fig. 2(b). (a) Initial model neglecting the couplings of the phase-reversal strips. (b) More accurate model considering the coupling of the phase-reversal strips, where the ideal 1:1 transformer, only responsible for the 180 phase reversal, may be suppressed.

couplings between the crossover strips. It models the phase reversals by ideal transformers and serial resistances, , the radiation resistances of the crossover dipoles. At the th mode res, onant frequency, where the electric length of each cell, . is , the input impedance is purely resistive, If the coupling of the crossover strips is significant, the equivalent circuit of Fig. 4(a) transforms into the circuit in Fig. 4(b), represents where the periodically loading shunt capacitance the coupling of the crossover strips, which can be estimated by quasi-static formula of parallel-plate capacitance or from a full-wave calibration technique.

III. MODE COUPLING AND COMBINING BANDWIDTH ENHANCEMENT TECHNIQUE From (1), the phase-reversal antenna resonates at a series of discrete frequencies distributed along the dispersion relation . Suppose the transmission line in Fig. 4(a) is a pure TEM line, the resonant frequencies , are then evenly distributed as shown in Fig. 5(a), satisfying the condition

(3)

Fig. 5. Dispersion curves and short-ended resonances of (a) an unloaded-TEM transmission line and (b) a periodically loaded transmission line computed by (4).

where is speed of light and is the effective dielectric constant of the transmission line. When the number of unit cells increases, with a fixed period , the th resonant frequency is unaffected, while the distance between all the resonant frequencies becomes smaller. This usually results in a series of independent matched frequencies with narrow bandwidth without any coupling because all the modes are orthogonal to one another. However, if the coupling capacitances of the crossover strips are included, as in Fig. 4(b), the equivalent circuit of the phasereversal antenna becomes a periodically loaded transmission line, terminated by a short, with the modified dispersion curves and resonances showed in Fig. 5(b). The computation of this graph will be explained below. The resonant modes are then able to couple to one another through these capacitances, as illustrated in Fig. 6. The coupling between resonators is the fundamental mechanism used in band-pass filters. Here, this mechanism is used to enhance the bandwidth of the phase-reversal antenna array. To determine the dispersion relation and resonances of the periodically loaded transmission line, we neglect the radiation resistances in a first step. They may be considered later, as they do not affect the resonant frequencies. The dispersion relation

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Fig. 6. Principle of the proposed bandwidth enhancement technique using mode coupling and combining.

of an infinite periodic transmission line loaded with shunt capacitance reads [15]

(4) is the characteristic impedance of the unloaded transwhere is the propagation constant of the unloaded mission line, is its phase velocity, is the period, is transmission line, is the propagation constant of the speed of light and the periodic line. The dispersion curve is shown in Fig. 5(b). As a consequence of the periodic loading, the dispersion curve has become nonlinear, and it exhibits a stop-band. As the capaciincreases, the slope of the curves becomes flatter tance and the stop-band, which divides the spectrum into two parts, increases. As in Fig. 4(b), the elements periodically line is then terminated by a short circuit. This yields a series of resonances correspond to . As shown in Fig. 5(b), these resonant frequencies are more and more conincreases, especially gregated as the coupling capacitance for the resonant frequencies close the stop-band. , by impleLet us now include the radiation resistances, menting the circuit of Fig. 4, for obtaining the input impedance of the antenna. Fig. 7(a) shows the input impedance and reflection coefficient, corresponding to the antenna model shown in Fig. 4(a), neglecting the coupling capacitances of the crossover . The resonant frequencies of each mode or the strips matched frequency bands are almost evenly distributed, each with a 10-dB fractional impedance bandwidth of less than 2%. Fig. 7(b)–(c) displays the input impedance and reflection coefficient for the antenna model of Fig. 4(b), where the couof the crossover strips are 0.03 pF and pling capacitances for 0.12 pF, respectively. The resonant frequencies , are congregated and shifted to lower frequencies. , does not change, The resonant frequency of th mode, , the resonant frequencies are shifted toward while for . Since these discrete resonant modes are electrically coupled to one another through the periodically distributed coupling capacitances, the antenna can be matched over a wider bandwidth, benefiting from these combined multi-mode resonances. Shown th modes are coupled and comin Fig. 7(b), the th and bined to form a wider bandwidth. By selecting pF. A wide bandwidth of 8% for 10 dB reflection is obtained. By value and with proper impedance matching, increasing the further increase in bandwidth is achieved, as shown in Fig. 7(c) pF which leads to a bandwidth of 12%. The for

Fig. 7. Input impedance and reflection coefficient of the phase-reversal antenna obtained with the equivalent circuit of Fig. 4(b): (a) without any coupling (C = 0), (b) with the coupling capacitance C = 0:03 pF, and (c) C = 0:12 pF, respectively.

impedance bandwidth could be further increased by further increasing since this would pack more resonant modes around the center frequency of operation. IV. DESIGN, PROTOTYPE, AND RESULTS To validate the proposed bandwidth enhancement technique and theory, a phase-reversal antenna is designed and fabricated

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Fig. 9. Antenna prototype. l = 2:7 mm, w = 1:2 mm.

Fig. 8. Structure of the designed phase-reversal antenna with crossover strips coupling for bandwidth enhancement. (a) Overall structure. (b) Zoom of part-1: crossover. (c) Zoom of part-2: =4 open-ended virtual short. (d) Zoom of part-3: parallel strip—microstrip transition, impedance matching section and T-junction excitation.

at 35 GHz. The layout of the antenna is shown in Fig. 8. The antenna is designed in parallel-strip technology [Figs. 1(b) and 3(b)] and the two parallel strips are printed on the opposite side of the substrate. As shown in Fig. 8(b), the crossovers are implemented with two perpendicular short parallel strips which fulfill the following three distinct functions: 1) phase reversal, by inverting the connections of the parallel strips; 2) radiation, under the form of two parallel small perpendicular dipoles; 3) parallel-plate coupling capacitance for bandwidth enhancement. As shown in Fig. 8(b), the coupling capacitance can be adjusted by varying the offset of the coupling strips, , and the width of . This does not change the radiation resistances the strips, , since it is mainly set by the length of the short dipoles. As open-ended parallel stripline is conshown in Fig. 8(c), a nected at the end to realize a virtual short, which is important for the resonance of the structure, rather than using direct via connections, to reduce cost and sensitivity to fabrication tolerance. The antenna is fed at the center by a parallel-stripline T-junction [Fig. 8(d)], which is then transformed to a microstrip line through an impedance matching transition. In a typical series-fed array, the input port is generally set at one end of the structure, and the main beam angle is then tilted as frequency changes. This is called beam squinting. The use of a center-feeding scheme, resulting in two back-to-back combined sub-arrays [Fig. 8(a)], mitigates this effect. Indeed, although each of the two sub-arrays squint away from broadside, in opposite direction, the superposition of these two beams

Fig. 10. (a) Return loss. (b) Simulated efficiency, measured gain and side-lobe level (SLL).

yields a maximum of radiated power at broadside, leading to a broadside antenna across a broad bandwidth. With the radiation resistances of the crossovers approximated by (2), the circuit model of Fig. 4(b) is combined with the T-junction to optimize the antenna performance in circuit level. Theoretically, the radiation resistances of the cross-over radiators are mainly decided by their length. Using this value for the circuit simulation gives an initial guess of the required equivalent capacitance value for a specified bandwidth. The formula for calculating parallel plate capacitance is then used to estimate the overlap area of the cross-over. And thereafter, full-wave simulation is applied to optimize the layout. To

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Fig. 11. Simulated and measured radiation patterns of the antenna array at frequency 34 GHz. (a) -plane ( ) E (Co-pol) and E (Cx-pol). (b) -plane ( ) E (Co-pol) and E (Cx-pol).

Fig. 12. Sensitivity (tolerance) analysis. (a) For a variation of of 2 2 (b) for a variation of the cross-over width of 0 15 mm 10%.

obtain 10% bandwidth, the coupling capacitance is chosen as pF. The prototype of the fabricated antenna array is shown in Fig. 9. The substrate used is Roger RO5880, with dielectric conand height of 10 mil. The antenna has an area stant of of 4.3 cm 0.3 cm and it is mounted on top of an alumina base with a micro-machined cavity at the center. The height of the cavity is almost a quarter of free space wavelength at the center frequency (2.3 mm @35 GHz), which reflects the lower space radiation of the antenna to the upper half space, and therefore forms a unidirectional radiation pattern. The gain of the antenna array is subsequently increased by 3 dB. The return loss of the antenna is measured with a network analyzer, and the results are plotted in Fig. 10(a) in comparison with full-wave simulation results obtained by IE3D and Ansoft HFSS. The measured impedance bandwidth is around 11%. The simulated radiation efficiency and measured gain versus frequency are shown in Fig. 10(b). The antenna efficiency is higher than 80% over the band extending from 32.6 to 37 GHz. The measured gain varies from 12 to 14.7 dBi across this bandwidth. The radiation patterns are computed by the HFSS and measured in the anechoic chamber. They are shown and compared in Fig. 11(a)–(b). Fig. 11(a) shows the co-polarization and crosspolarization radiation patterns in the -plane ( -plane) at the

frequency of 34 GHz, while Fig. 11(b) shows the co-polarization and cross-polarization in the -plane ( -plane). The measured gain is 14.4 at 34 GHz. The measured cross-polarization dB and dB at and plane respectively. At level is 34 GHz, the measured side-lobe level is around 20 dB, while as frequency increases, the side-lobe levels increases and reaches 13 dB at 35 GHz [Fig. 10(b)]. The pattern bandwidth (defined as the band over which the side-lobes level remains below 13 dB) is of around 4%. These performances represent a significant improvement over the single-ended phase-reversal array (impedance bandwidth of 3% [7]) and the traditional series-fed microstrip linear array (typically 2% of impedance bandwidth and 2.3% of pattern bandwidth [2], [16]). In general, the proposed antenna has a limited pattern bandwidth though the impedance bandwidth can be further . enhanced by further increasing the coupling capacitance And the pattern bandwidth is always narrower than impedance bandwidth. So, the practical bandwidth, which should include both the impedance and the pattern bandwidth, is limited by this fundamental problematic. Finally, a sensitivity analysis of some of the parameters, which may be practically critical in terms of tolerances, is performed using full-wave simulations. The most critical paand the width of rameters are the substrate permittivity

yz

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w

:

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: 6 10%;

YANG et al.: WIDEBAND PHASE-REVERSAL ANTENNA USING A NOVEL BANDWIDTH ENHANCEMENT TECHNIQUE

cross-over strips . When the dielectric constant varies in %, the center operation frequency the range of %, as shown in Fig. 12(a), while the varies within fractional frequency bandwidth is almost unchanged. When varies in the range of %, no significant change appears, as shown in Fig. 12(b).

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[14] J.-X. Chen and Q. Xue, “Novel 5:1 unequal Wilkinson power divider using offset double-sided parallel-strip lines,” IEEE Microw. Wireless Compon. Lett., vol. 17, pp. 175–177, Mar. 2007. [15] R. E. Collin, Foundations for Microwave Engineering, 2nd ed. New York: McGraw-Hill, 1992. [16] D. M. Pozar and D. H. Schaubert, “Comparison of three series fed microstrip array geometries,” in Proc. IEEE Antennas and Propag. Soc. Int. Symp. Dig., Ann Arbor, MI, Jun.–Jul. 28–2, 1993, vol. 2, pp. 728–731.

V. CONCLUSION A novel bandwidth enhancement technique has been proposed and demonstrated theoretically and experimentally for the phase-reversal Franklin-type antennas. By exploiting the mechanism of coupling and combining among the discrete resonant modes with properly designed phase-reversal crossovers, this antenna exhibits a dramatically enhanced bandwidth. The 10-dB bandwidth of the fabricated antenna is 11% and the efficiency is over 80% across this bandwidth. This antenna may be easily integrated on a package and meet the bandwidth requirement of most millimeter-wave applications, such as radars and wideband point-to-point wireless communications.

ACKNOWLEDGMENT The authors thank Rogers Cooperation for donating PCB samples and Zeland Cooperation for donating IE3D software licenses.

REFERENCES [1] T. Zwick, D. Liu, and B. P. Gaucher, “Broadband planar superstrate antenna for integrated millimeterwave transceivers,” IEEE Trans. Antennas Propag., vol. 54, no. 10, pp. 2790–2796, Oct. 2006. [2] D. Pozar and D. H. Schaubert, Microstrip Antennas: The Analysis and Design of Microstrip Antennas and Arrays. New York: Wiley, 1995. [3] E. Chang, S. A. Long, and W. F. Richards, “An experimental investigation of electrically thick rectangular microstrip antennas,” IEEE Trans. Antennas Propag., vol. AP-34, no. 6, pp. 767–772, Jun. 1986. [4] P. S. Hall, C. Wood, and C. Garrett, “Wide bandwidth microstrip antennas for circuit integration,” Electron. Lett., vol. 15, pp. 458–460, 1979. [5] R. Q. Lee, K. F. Lee, and J. Bobinchak, “Characteristics of a twolayer electromagnetically coupled rectangular patch antenna,” Electron. Lett., vol. 23, no. 20, pp. 1070–1072, Sept. 1987. [6] Y. Guo, C. L. Mak, K. M. Luk, and K. F. Lee, “Analysis and design of L-probe proximity fed patch antennas,” IEEE Trans. Antennas Propag., vol. 49, pp. 145–149, Feb. 2001. [7] N. Yang, C. Caloz, and K. Wu, “Fixed beam frequency-tunable phase-reversal coplanar stripline antenna array,” IEEE Trans. Antennas Propag., vol. 57, no. 3, pp. 671–681, Mar. 2009. [8] C. S. Franklin, “Improvements in Wireless Telegraph and Telephone Aerials,” U.K. Patent 24232-1924, 1924. [9] H. Wheeler, “A vertical antenna made of transposed sections of coaxial cable,” IRE Convention Record, vol. 4, no. 1, pp. 160–164, 1956. [10] K. Solbach, “Microstrip-Franklin antenna,” IEEE Trans. Antennas Propag., vol. AP-30, no. 4, pp. 773–775, Jul. 1982. [11] M. L. Brennan, “Antenna having double-sided printed circuit board with collinear, alternating and opposing radiating elements and microstrip transmission lines,” U.S. patent 5 963, 168, Oct. 5, 1999. [12] R. Bancroft and B. Bateman, “An omnidirectional planar microstrip antenna,” IEEE Trans. Antennas Propag., vol. 52, no. 11, pp. 3151–3153, Nov. 2004. [13] S. G. Kim and K. Chang, “Ultrawide-band transitions and new microwave components using double-sided parallel-strip lines,” IEEE Trans. Microw. Theory Tech., vol. 52, no. 9, pp. 2148–2152, Sep. 2004.

Ning Yang (M’03) received the B.S. degree in electric engineering from Southeast University (SEU), Nanjing, China, and the Ph.D. degree in microwave engineering under a joint program between SEU and the National University of Singapore (NUS) in 2004. He began his career as an Engineer with the Center for Wireless Communications (CWC) in November 2001 and later as an Associate Scientist with the Institute for Infocomm Research (I2R), Singapore, in 2003. From 2005 to 2006, he was with Motorola, Inc., as a Senior RF Engineer engaged in the research and development of emergent RF and antenna technologies for cutting-edge mobile devices. Since October 2006, he has been a Researcher with the École Polytechnique de Montréal, Montréal, QC, Canada. He has authored or coauthored over 60 peer-reviewed technical papers, holds one patent, and had one invention disclosure accepted at Motorola. As one of the key participants, he contributed to the development of V360, V361, V367, and ROKR E8 mobile phones at Motorola. His current research interests include differentially integrated microwave circuits and antennas/arrays, metamaterials, SIW devices, and integrated active RF subsystems. Dr. Yang was the recipient of the Young Scientist Award in the General Assembly of the International Union of Radio Science (URSI), in 2008 and the Best Dissertation Award of 2005 by the Ministry of Education, Jiangsu, China. He was a TPC member of EuCAP’2009 and has served as a reviewer for several transactions, journals, and letters.

Christophe Caloz (S’99–M’03–SM’06–F’10) received the Diplôme d’Ingénieur en Électricité and the Ph.D. degree from the École Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland, in 1995 and 2000, respectively. From 2001 to 2004, he was a Postdoctoral Research Engineer with the Microwave Electronics Laboratory, University of California, Los Angeles (UCLA). In June 2004, he joined the École Polytechnique de Montréal, Montréal, QC, Canada, where he is now a Full Professor, a member of the Poly-Grames Microwave Research Center and the holder of a Canada Research Chair (CRC). He has authored and coauthored over 360 technical conference, letter, and journal papers, three books and eight book chapters, and he holds several patents. He is a member of the Editorial Board of the International Journal of Numerical Modelling, the International Journal of RF and Microwave Computer-Aided Engineering, the International Journal of Antennas and Propagation, and Metamaterials of the Metamorphose Network of Excellence. His research interests include all fields of theoretical, computational and technological electromagnetics engineering, with strong emphasis on emergent and multidisciplinary topics. Dr. Caloz is a member of the IEEE Microwave Theory and Techniques Society (IEEE MTT-S) Technical Coordinating Committee (TCC) MTT-15 and MTT-25, a Speaker of the MTT-15 Speaker Bureau, and the Chair of the Commission D (Electronics and Photonics) of the Canadian Union de Radio Science Internationale (URSI). He was the recipient of the UCLA Chancellors Award for Postdoctoral Research in 2004 and the MTT-S Outstanding Young Engineer Award in 2007.

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Ke Wu (M’87–SM’92–F’01) is a Professor of electrical engineering and a Tier-I Canada Research Chair in RF and millimeterwave engineering with the École Polytechnique de Montréal, Montréal, QC, Canada. He holds the first Cheung Kong endowed chair professorship (visiting) at Southeast University, Nanjing, China, the first Sir Yue-Kong Pao chair professorship (visiting) at Ningbo University, and an honorary professorship with Nanjing University of Science and Technology and the City University of Hong Kong, China. He has been the Director of the Poly-Grames Research Center and the founding Director of the Center for Radiofrequency Electronics Research of Quebec (Regroupement stratégique of FRQNT). He has also held Guest and Visiting Professorships with many universities around the world. He has authored or coauthored over 710 refereed papers and a number of books/book chapters and patents. His current research interests involve substrate integrated circuits, antenna arrays, advanced computer-aided design and modeling techniques, and development of low-cost RF and millimeter-wave transceivers and sensors for wireless systems and biomedical applications. He is also interested in the modeling and design of microwave photonic circuits and systems.

Dr. Wu is a member of the Electromagnetic Academy, Sigma Xi, and URSI. He is a Fellow of the Canadian Academy of Engineering (CAE) and a Fellow of the Royal Society of Canada (The Canadian Academy of the Sciences and Humanities). He has held key positions in and has served on various panels and international committees including the Chair of technical program committees, international steering committees and international conferences/symposia. In particular, he will be the General Chair of the 2012 IEEE Microwave Theory and Techniques Society (IEEE MTT-S) International Microwave Symposium. He has served on the editorial/review boards of many technical journals, transactions, and letters as well as scientific encyclopaedias as well as serving as Editor or Guest Editor. He is currently the Chair of the joint IEEE chapters of MTTS/APS/LEOS in Montreal. He is an elected IEEE MTT-S Administrative Committee (AdCom) member for 2006–2012 and serves as Chair of the IEEE MTT-S Member and Geographic Activities (MGA) Committee. He is an IEEE MTT-S Distinguished Microwave Lecturer from January 2009 to December 2011. He was the recipient of many awards and prizes including the first IEEE MTT-S Outstanding Young Engineer Award, the 2004 Fessenden Medal of the IEEE Canada, and the 2009 Thomas W. Eadie Medal of the Royal Society of Canada.

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Design, Fabrication, and Measurement of a One-Dimensional Periodically Structured Surface Antenna Howard R. Stuart, Member, IEEE

Abstract—A radiating periodically structured surface resonator is studied from the point of view of minimizing the radiation -factor of the fundamental mode of the resonator. Structures with a one-dimensional array of gaps are considered, where the resonant mode is formed by the capacitance of the gaps resonating with the inductance of the conducting pathways. An eigenmode study of a range of designs of identical size demonstrates that increasing the number of gaps does not lower the . The results show that this family of resonators has a radiation that is typically 2 lower than a simple patch antenna occupying the same electrical volume. The improvement in is accompanied by a corresponding reduction in the directivity gain of the broadside radiation, confirming the inherent bandwidth/directivity trade-off in radiators of identical size and shape. A three-period resonator is made into an antenna by driving it from underneath the surface. The fabricated antenna has dimensions of 0 40 0 26 , a thickness of 34, and a measured 10 dB return loss bandwidth of 12.4%, 4 5 wider than a simple patch antenna of the same size. These antennas can replace patch antennas in applications demanding the widest possible impedance bandwidth from a thin antenna. Index Terms—Periodic structures,

-factor, resonant antennas.

results, in part, because the resonator has a fundamental radiation mode with a lower radiation -factor than the simple is accompatch of the same electrical volume. The lower panied by a lower broadside directivity gain, revealing the inherent bandwidth/directivity trade-off in structures of identical size and shape. This tradeoff may be acceptable for applications demanding the widest possible impedance bandwidth from a thin antenna, and desirable for applications requiring a wider beam width. We first present the results of a -factor study comparing the fundamental radiation modes of various resonator structures to those of identically-sized patch antennas. One example of the periodic surface resonator is then fabricated into an impedance-matched antenna. Separating the resonator design problem from the impedance matching problem enables a rapid comparison of a wide range of structures and provides additional physical insight into the mechanisms affecting performance. The impedance matching problem need only be solved on the optimized resonator structure. II. RESONATOR DESIGN AND

I. INTRODUCTION

I

T is well known that the bandwidth of a patch antenna decreases as the thickness of the patch is made smaller [1]. For many applications, it is desirable to have an antenna with the radiation characteristics of a patch (horizontally polarized broadside emission off an extended ground plane) with as low a profile as possible (minimal thickness). Whether or not the patch antenna represents a bandwidth-optimized solution to this problem is not clear. When exploring alternatives to the patch antenna, it is important to compare not only the performance of the full antenna designs, but also the physical properties of the resonant modes of the alternative structures directly with those of the patch. A direct comparison of the resonant modes enables the physical origin of any bandwidth improvements to be clearly revealed. In this paper, we study a periodically structured surface resonator that is used to provide a wider bandwidth alternative to a simple patch antenna with a thickness of less than 1/30 of a wavelength. The bandwidth improvement Manuscript received September 22, 2008; revised June 04, 2009; accepted March 18, 2010. Date of publication June 14, 2010; date of current version September 03, 2010. The author is with LGS, Bell Labs Innovations, Florham Park, NJ 07932 USA (e-mail: [email protected]). Digital Object Identifier 10.1109/TAP.2010.2052541

-FACTOR STUDY

The periodically structured resonator considered here is illustrated in Fig. 1. For all cases studied, the resonator has dimensions of 38 60 mm, with a height of 4 mm, and sits on a large ground plane. The top surface of this structure is covered with a conductor, and at the two edges of the 60 mm length the conductor is folded down and connected to ground. The top surface of the resonator has a periodic array of gaps, and Fig. 1(a)–(c) illustrate examples of one-, three-, and five-period resonators. The space inside the resonator can be air, or can be partially or completely filled with a dielectric material. We consider here the case of a thin dielectric layer suspended just underneath the top surface (in the experimental realization, this is the printed circuit board onto which the periodic pattern is printed), and the underlying space is air. For the case of a resonator with no gaps there is a cavity resonance at the frequency where the resonator is a half wavelength (2500 MHz). Adding a 0.64 mm substrate layer with a dielectric constant of 10.2 to the underside of the cavity surface lowers the cavity resonance to 2265 MHz (the radiation -factor of the mode at this frequency is 33.6). The electric field of the basic cavity mode is illustrated in Fig. 2(a). If we introduce a single gap of 8 mm width at the center of the top surface (creating a one-period resonator), we find two resonant modes in the new structure. The first mode, illustrated in Fig. 2(b), is a modified version of the cavity mode of Fig. 2(a); it has a slightly higher resonant frequency of 2313 MHz, and

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Fig. 1. (a) The one-period periodic surface resonator (the underlying ground plane is not shown). (b) The three-period resonator, with the dimensions indicated (the same dimensions are used in all of the resonators discussed here). (c) The five period resonator.

a radiation -factor of 30.7. The second mode of the one-period resonator is illustrated in Fig. 2(c). This mode is different in structure from the cavity mode, and shows notably improved coupling to radiation. The mode has a resonant frequency of 1865 MHz, and a much lower -factor of 16.0. It is characterized by a strong -directed field in the gap region, and inside the cavity the -directed component displays opposite polarities about the center. The magnitude of the electric field is plotted on a logarithmic scale in Fig. 3(a) to illustrate the modal field pattern in detail. One interesting aspect of the low- mode of Fig. 2(c) is that its resonant frequency can be varied over a wide range by simply varying the width of the gap at the center of the top surface. Reducing the gap size from 8 mm to 0.75 mm, for example, moves the resonant frequency from 1865 MHz to 1053 MHz, whereas the cavity mode corresponding to Fig. 2(b) remains close to 2265 MHz. This makes sense based upon the electric field profiles: the cavity mode has a very small field inside the gap, and is relatively insensitive to variations in gap size; its resonant frequency is determined by the half-wavelength cavity criterion. The low frequency mode, by contrast, is formed by the gap capacitance resonating with the inductance of the conducting pathway to ground; this resonance is moved to lower frequencies by increasing the gap capacitance (either by reducing the gap size, or by increasing the permittivity or

Fig. 2. The electric field for the resonant modes of several structures. (a) The cavity mode of the resonator with no surface gaps, which occurs at the frequency where the cavity length is =2. (b) The modified cavity mode of the one-period resonator, which is nearly identical to the mode in (a). This is not the mode that will be used for radiation. (c) The fundamental radiation mode of the oneperiod resonator, which appears at a lower frequency and has a lower Q than the modified cavity mode. The resonant frequency of this mode is formed by the gap capacitance resonating with the inductance of the conducting pathways to ground. (d) The fundamental radiation mode of the three-period resonator.

Fig. 3. The magnitude of the electric field for the fundamental radiation mode of the (a) one period, (b) three period, and (c) five period resonators. The field is plotted on a logarithmic scale with the lighter regions representing areas of higher magnitude.

thickness of the substrate layer underneath the gap). One consequence of moving the resonance to much lower frequencies is

STUART: DESIGN, FABRICATION, AND MEASUREMENT OF A 1-D PERIODICALLY STRUCTURED SURFACE ANTENNA

that its radiation -factor increases to . This is expected because the physical size of the resonator has not changed; its electrical size is therefore much smaller at the lower resonant frequency and the must be higher. Similar behavior is observed in the three-period and five-period resonators of Fig. 1(b) and (c). In a three-period resonator with identical overall dimensions (38 60 4 mm), using a gap size of 0.75 mm and a 0.64 mm substrate with permittivity 10.2 just underneath the top surface, the low- resonant mode is . Although the gap size found at 1970 MHz with a and substrate parameters are identical to the one-period case, the three-period resonator has three gap capacitances wired in series, resulting in 1/3 the overall capacitance, yielding a higher resonant frequency (the inductance is reduced slightly as well, due to the currents going to zero at three points along the surface rather than one). The electric field profile of this mode is shown in Fig. 2(d). The mode is characterized by strong in-phase and equal magnitude -directed electric fields in the three gap regions. The magnitude of the electric field is shown on a logarithmic scale in Fig. 3(b) to illustrate the detailed structure of the mode. In each region of the cavity underneath a gap, the mode shows a structure similar to that seen in the one-period resonator, with this pattern now repeated three times. Likewise, in the five-period resonator mode [see Fig. 3(c)] the pattern is repeated five times, with in-phase equal magnitude -directed electric fields in each of the five gaps. For the three-period resonator, there is also a modified cavity resonance similar in structure to the basic cavity mode of Fig. 2(a), but this mode appears at 2941 MHz (well above the half wavelength frequency . For the five-period resonator of 2500 MHz) and has a example illustrated in Fig. 3(d), the overall dimensions remain identical, the gap size is reduced to 0.5 mm and a 1.28 mm substrate with permittivity of 20 is used to increase the capacitance; . this results in a resonant mode at 1589 MHz with a The higher modified cavity mode for this example is found at 2580 MHz with . In order to assess the performance of these resonators as potential antenna elements, the -factor must be evaluated for a range of designs. A comparison of among different designs is complicated by the fact that the will naturally increase as the electrical size of the resonator is made smaller. In order to compare designs of different electrical size, we plot versus resonant frequency for a wide range of design variations all occupying the same physical volume. The resulting scatter plot produces a clear visualization of the relative behavior of different designs. (This technique was used previously in studies of multi-element spherical antennas [2]). For this study, the overall size was held constant (38 60 4 mm) and only the permittivity and thickness of the thin dielectric layer underneath the top surface, and the gap size, were varied. One-, two-, three-, and five-period designs were considered. For a three-period resonator, a 1.5 mm gap size, and a 0.64 mm dielectric layer of permittivity 10.2, the resonant frequency is 2360 MHz. Gradually reducing the gap to 0.5 mm lowers the resonance to 1828 MHz. Increasing the permittivity to 15 enables the same resonator to vary over a 1577–2287 MHz range for gap values between 0.5-1.5 mm; a permittivity of 17 and a gap size of 0.5 mm has a resonance at 1499 MHz. Similar variations are done

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Q

Fig. 4. The radiation -factor of the fundamental mode versus resonant frequency for a range of resonator designs of identical size and shape. The corresponding results for a simple patch occupying the same volume are shown for comparison (the dielectric constant of the substrate is varied to change the resonant frequency). The normalized length and height at various frequencies is included at the top of the plot. The solid lines are shown to illustrate trends.

for the other resonators, where the parameters were chosen to obtain a sampling of results covering a similar frequency range. (The one-period resonator, for example, required permittivities from 10.2 down to 1 and gap sizes from 2–11 mm to cover a similar range; the five-period resonator required larger permittivities and a 0.128 mm thick substrate to hit the low end of the target frequency range). The resonant frequency and of the fundamental mode of each resonator (i.e., the low frequency, low- mode) were computed using numerical eigenmode analysis. Fig. 4 plots the versus frequency for all of the simulation results. The versus frequency curve for the fundamental mode of a simple patch antenna of the identical size and shape is shown for comparison. The reference patch consists of a 38 60 mm rectangular conducting sheet sitting 4 mm over a ground plane (a 38 50 mm sheet was used for some cases to extend to higher frequencies). For the patch, the entire region directly under the patch is filled with dielectric, and the permittivity is varied in order to vary the resonant frequency. In all cases the resonators sit over an infinite ground plane and the conductors and dielectrics are assumed to be lossless The results in Fig. 4 yield several insights. The -factors for the periodic surface resonators all fall close to the same line. Increasing or decreasing the number of gaps does not significantly change the performance with one exception: the one-period resonator has a slightly lower than the multi-period structures. The of all of the periodic structures, however, is notably lower than the of the patch antenna. Over much of the plotted frequency range, there is roughly a 2 improvement in for the periodic surface resonator as compared to the patch. Some insight into this behavior is gained by comparing the radiation pattern of the periodic surface mode to that of the patch. Fig. 5(a) illustrates the far-field radiation in the - plane (plane

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Q

Fig. 6. The resonant frequency, -factor, and directivity for the two-period resonator when the position of the two gaps about the center is varied. The gap position represents the distance from each gap to the center of the surface. For this resonator, the gap size is 1 mm, and the substrate has a thickness of 0.64 mm and a permittivity of 3 (the substrate sits just under the top surface and the for these results was total thickness of the resonator is 4 mm). The ratio of shown in Fig. 5.

D=Q

Fig. 5. (a) The far-field radiation pattern of the fundamental modes of the periodic surface resonator (the solid line is the three period resonator at 1976 MHz, the dashed line is the one-period resonator at 2327 MHz) and the patch (60 mm length patch at 2148 MHz). These are simulated E-plane patterns on an infinite ground plane. (b) The ratio of directivity to for a subset of the results from Fig. 4 and for the two-period gap position variation results from Fig. 6.

Q

of polarization) for the one- and three-period structures and for the patch structure. Near 2 GHz, the directivity of the patch is 9.1 dBi, whereas the directivity of the fundamental mode of the three-period resonator is 5.4 dBi. The one-period resonator is similar to the three-period, though it radiates a slightly higher power level towards the horizon as compared to zenith (which as compared to the three-period explains its slightly lower structure). These results suggest an inherent tradeoff between directivity and -factor, and this is confirmed by plotting the ) for a subset of the simulation ratio of directivity to ( results, shown in Fig. 5(b). By this measure, the patch and the periodic surface resonators behave comparably (for the case of an infinite ground plane). The variation in directivity between the periodic resonator and the patch is easily understood by considering the periodic resonator structure as an array of radiating slots. For the fundamental mode of the periodic surface resonator, each slot radiates with equal magnitude and phase. To illustrate the effects of this, we consider the two-period resonator. In the structure considered in the eigenmode study in Fig. 4, the two gaps are located 15 mm to either side of the center, but the location of these two gaps can be varied. The effects of varying the gap position on the resonant frequency, , and directivity are shown in Fig. 6. As the gaps are moved towards the outer edges of the structure, the path difference between the fields radiating from the two slots towards the horizon approaches a half-wavelength, whereas the radiated fields are always in phase at zenith.

Fig. 7. (a) The three period antenna, and its normalized dimensions at the operating frequency. (b) Side view of the antenna structure. The antenna is constructed from two separate printed circuit boards, and is fed through the ground plane.

Therefore, the horizon radiation is subject to destructive interference and the directivity at zenith increases as the gaps are moved apart, and the likewise increases. In the limit where the gaps are a the outer edge of the structure, the two-period results surface resonator looks like a patch antenna. The for the various gap positions are also plotted in Fig. 5(b), and follow the same trend line as the other structures. III. ANTENNA DESIGN AND MEASUREMENTS In order to form an antenna from the resonator, a feed must be introduced. The feed structure is located underneath the periodic surface as illustrated in Fig. 7(a) (a three-period resonator is used to form the antenna). The antenna is fed through the underlying ground plane by a short pin that is connected to a 1.5 mm wide conducting strip running parallel to the ground plane. This strip is left open-circuited at the end point opposite

STUART: DESIGN, FABRICATION, AND MEASUREMENT OF A 1-D PERIODICALLY STRUCTURED SURFACE ANTENNA

Fig. 8. Measured return loss versus frequency for the three-period antenna and the patch antenna of identical size.

the feed. The feed current in the conducting strip electromagnetically couples to the resonant modes of the resonator (in a manner similar to that seen in an L-probe fed patch antenna [3]). The antenna is impedance matched to 50 ohms by choosing the appropriate length, position above the ground plane, and permittivity of the material under the strip. For the antenna presented here, a shunt capacitor at the feed point was also used to assist in the matching. We note that at the operating frequency of this . antenna, its thickness is The antenna is assembled from two separate printed circuit board (PCBs), with a side view of the structure shown in Fig. 7(b). The top conducting layer (with the three gaps) is fabricated on a 0.64 mm thick layer of RO3010 ) and the feed strip is fabricated on a ( ). The 1.524 mm thick layer of RO4003 ( top PCB sits on two metallic pieces located at each end of its length; these serve both to suspend the top PCB at a specified height (such that the top is 4 mm above the ground) and to provide a conductive connection between the ends of the top conductor and the ground plane. The electrical connection between the top layer and the supporting pieces is achieved using an array of vias along the edges of the PCB and a continuous narrow conductive layer along the bottom of the PCB at the ends. The top PCB is screwed down onto the supporting pieces at three points on each edge, insuring a good electrical connection. The feed PCB is attached directly to the ground plane and fed by a short pin through an SMA connector on the underside of the structure. The return loss versus frequency for the measured antenna is shown in Fig. 8. For this antenna, the gaps are 0.75 mm, the feed strip is 25.5 mm long (centered within the structure), and 1.7 pF of capacitance is shunted across the feed to ground. The antenna achieves a 10 dB return loss bandwidth of 12.4%. At the center of the band, the of the fundamental mode of this antenna is ; the presence of a higher order resonant expected to be over that mode broadens the impedance bandwidth by expected for a single resonance antenna with this [2]. The higher order mode results from the interaction of the feed line with the fundamental mode of the resonator, in a manner similar to that seen in a patch antenna fed with an L-shaped probe

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[3]. An L-probe is effective in broadening patch antenna band[3]. For the pewidth when the thickness of the patch is riodic surface antenna (PSA), the L-probe is effective at broad(this ening the bandwidth at a much smaller thickness of does not occur in L-probe fed patch antennas of this thickness). There are other higher-order resonant modes in the three-period resonator [including the modified cavity mode similar to that shown in Fig. 2(b)], but these occur at higher frequencies and do not contribute to the bandwidth broadening. We have also designed a one-period PSA of the same size and operating frequency, and observe a similar multi-resonant impedance (with a slightly wider bandwidth due to the lower -factor of the fundamental mode in the one-period resonator). The measured performance of a conventional patch antenna occupying the same volume is shown in Fig. 8 for comparison. The patch was fabricated using a 0.64 mm thick layer of RO3010 ) which is suspended by non-conducting ( posts such that the thickness of the patch is 4 mm, with most of that thickness being composed of air. It is fed with a pin through the underlying ground plane. The patch antenna exhibits single resonance behavior with a 10 dB return loss bandwidth of 2.4%. The 5.1 bandwidth improvement factor of the PSA is derived from a patch operating at the low edge of the PSA bandwidth. A patch operating at the center of the band would have a wider bandwidth; this comparison would yield an improvement factor . closer to The radiation patterns of the PSA and patch antenna are shown in Fig. 9. The measurements were performed with the antennas mounted on a two foot diameter circular ground plane. The most notable difference in the patterns is seen within the -plane, where the PSA has relatively strong radiation at the horizon, as expected from the simulated patterns of the fundamental resonant mode on an infinite ground plane, shown in Fig. 5 (where the power at the horizon in the -plane is within a few dB of the value at zenith). The strong power at the horizon is not due to surface waves (perfectly conducting surfaces are assumed in the simulations) but is simply a characteristic of the fundamental radiation mode, which resembles a horizontal magnetic dipole. In the measured structure, which has a finite ground, some of this energy diffracts off the edges of the ground plane, producing ripple in the far-field pattern at 2250 MHz, and yielding peak gain values at this frequency roughly equal ). The ripple effect is not to that of the patch antenna ( as pronounced at 2050 MHz, where a peak gain of is observed, closer to the value predicted by simulations on an infinite ground. The patch antenna has a much smaller radiation component along the horizon, and likewise does not exhibit the far-field ripple. IV. DISCUSSION The periodic surface structure studied here offers improved bandwidth compared with a patch antenna of the same size. This improvement results from two components: the lower of the PSA, and the multi-resonant impedance response. Though it is possible to improve the patch bandwidth by making it multi-resonant (using either a higher order tuning circuit or a more complex design), this would only make up for roughly half of the observed improvement. This is because the of the fundamental

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tennas, these surfaces can be viewed simply as radiating resonators, with a characteristic resonant frequency and -factor. Antennas using complex periodic structures as substrates are ullimitations versus electrical timately limited by the same size that we have observed in the PSA. For linearly polarized antennas, there is not a compelling reason to use two-dimensional periodicity; one-dimension suffices to generate the appropriate resonant mode. The results presented here suggest that complex designs do not yield improved bandwidth over simpler designs for miniaturization and height reduction. ACKNOWLEDGMENT The author thanks C. Tran of Bell Laboratories, Alcatel-Lucent, for fabrication of the antennas, and P. Canales and J. Hoppe, of the U.S. Army CERDEC, for assistance in performing the antenna measurements. REFERENCES

Fig. 9. Measured far-field radiation patterns for the three-period antenna (at two frequencies) and the patch (at 2030 MHz). The antennas were mounted on a 2 foot diameter circular ground plane.

mode of the patch is larger than that of the PSA. The reduction in comes at the expense of a reduction in the directivity of the antenna, a tradeoff likely to be acceptable for applications where an optimized impedance bandwidth from a low profile radiator is desired. The one-period PSA is similar to the “flush strip inductor” antenna described by Wheeler [4]. In Wheeler’s version, the top surface is flush with the surrounding ground plane and the depth of the resonator is sunk into a cavity below the surface. Wheeler briefly mentions the feed, which is described as “another (smaller) resonator located within the cavity,” and which yields a double resonant impedance response. (Another version of the one-period structure was recently studied by Erentok et al. [5], though in a different aspect ratio and electrical volume than considered here.) The primary advantage to the multi-period antenna over the one-period antenna is its improved broadside gain relative to the horizon gain [see Fig. 5(a)], and the ability to explicitly trade off directivity and bandwidth over a range of values in the two-period version. The resonant modes of the one-dimensional periodic surface resonators are similar to the resonant modes found in other types of more complex periodic structures that have been studied to improve the bandwidth performance of low-profile, broadside radiating antennas [6]–[10]. When used solely for the purpose of improving the bandwidth characteristics of thin resonant an-

[1] D. R. Jackson and N. G. Alexopolous, “Simple approximate formulas for input resistance, bandwidth, and efficiency of a resonant rectangular patch,” IEEE Trans. Antennas Propag., vol. 39, pp. 407–410, Mar. 1991. [2] H. R. Stuart, “Eigenmode analysis of small multielement spherical antennas,” IEEE Trans. Antennas Propag., vol. 56, pp. 2841–2851, Sep. 2008. [3] C. L. Mak, K. M. Luk, K. F. Lee, and Y. L. Chow, “Experimental study of a microstrip patch antenna with an L-shaped probe,” IEEE Trans. Antennas Propag., vol. 48, pp. 777–783, May 2000. [4] H. A. Wheeler, “Small antennas,” IEEE Trans. Antennas Propag., vol. AP-23, pp. 462–469, Jul. 1975. [5] A. Erentok and R. W. Ziolkowski, “Metamaterial-inspired efficient electrically small antennas,” IEEE Trans. Antennas Propag., vol. 56, pp. 691–707, Mar. 2008. [6] D. Sievenpiper, L. J. Zhang, R. F. J. Broas, and N. G. Alexopolous, “High-impedance electromagnetic surfaces with a forbidden frequency band,” IEEE Trans. Micro. Theory Tech., vol. 47, p. 2059, Nov. 1999. [7] F. Yang and Y. Rahmat-Samii, “Reflection phase characterizations of the EBG ground plane for low profile wire antenna applications,” IEEE Trans. Antennas Propag., vol. 51, pp. 2691–2703, Oct. 2003. [8] H. Mosallaei and K. Sarabandi, “Antenna miniaturization and bandwidth enhancement using a reactive impedance substrate,” IEEE Trans. Antennas Propag., vol. 52, pp. 2403–2414, Sep. 2004. [9] A. Erentok, P. L. Luljak, and R. W. Ziolkowski, “Characterization of a volumetric metamaterial realization of an artificial magnetic conductor for antenna applications,” IEEE Trans. Antennas Propag., vol. 53, pp. 160–172, Jan. 2005. [10] P. M. T. Ikonen, S. Maslovski, C. R. Simovski, and S. A. Tretyakov, “On artificial magnetodielectric loading for improving the impedance bandwidth properties of microstrip antennas,” IEEE Trans. Antennas Propag., vol. 54, pp. 1654–1662, Jun. 2006. Howard R. Stuart (M’98) received the S.B. and S.M. degrees in electrical engineering from the Massachusetts Institute of Technology, Cambridge, in 1988 and 1990, respectively, and the Ph.D. degree in optics from the University of Rochester, Rochester, NY, in 1998. From 1990 to 1993, he worked as a Research Scientist for the Polaroid Corporation in Cambridge, MA. In 1998, he joined Bell Laboratories, Lucent Technologies, as a Member of Technical Staff in the Advanced Photonics Research Department in Holmdel, NJ. Since 2003, he has worked in the Bell Labs Government Communications Laboratory, which became part of LGS Innovations in 2007. He has published papers on a variety of research topics, including small resonant antennas, metal nanoparticle enhanced photodetection, multimode fiber transmission, optical waveguide interactions and devices, optical MEMS, and optical performance monitoring. Dr. Stuart served as the Integrated Optics Topical Editor for the OSA journal Applied Optics from 2002–2008.

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Integrated Planar Monopole Antenna With Microstrip Resonators Having Band-Notched Characteristics Dong-Zo Kim, Wang-Ik Son, Won-Gyu Lim, Han-Lim Lee, and Jong-Won Yu, Member, IEEE

Abstract—Novel integrated planar monopole antennas with various microstrip resonators are presented. The proposed integrated antennas consist of wideband planar monopole antennas and electromagnetically coupled microstrip resonators producing band-notched characteristics. Various types of microstrip resonators such as open-circuited line resonator, short-circuited line resonator, closed-loop resonator and open-loop resonator are described. The proposed designs are suitable for wideband antennas with narrowband interferer rejection characteristic or multi-band antennas. Index Terms—Band-notched filter, integrated antenna, microstrip resonator, multi-band antenna, planar monopole antenna.

I. INTRODUCTION

band-notched characteristic while maintaining a wideband performance by etching particular features on radiating elements. In most communication systems, an antenna is followed by a filter or vice versa. In microwave band, distributed filters are normally used and implemented by transmission line resonators. However, the transmission line filters are not compact and thus their sizes become an issue for many applications. Since the transmission line filters are probably not the best choice when size matters, it is extremely desirable to integrate an antenna and a microstrip filter into a single module. In this paper, various antenna-filter structures which integrate wideband planar monopole antennas with microstrip resonators are developed. The parameters that affect the operation of the antenna-filter devices are analyzed both theoretically and experimentally.

T

HE increasing demand for communication systems has been emphasizing the design of low-cost and small-size RF/microwave transceivers. One of the design approaches is to integrate different components into a single element so that fewer components are used. Integrated or active-integrated antennas receive a great deal of attention because they can reduce size, weight and cost of many transmit and receive systems. Passive devices and active solid-state devices can be configured to provide several component functions at terminals of antenna. Active solid-state devices, for example, can be used to design active-integrated antenna oscillators, amplifiers and multipliers. Passive devices can be used to design filters/antennas [1], [2], bandpass frequency selective surfaces [3] and rectifying antenna [4]. With the advent of ultra wideband technology, wideband devices have received increased attention. However, wideband systems are faced with the overlapping frequency bands with narrowband wireless technologies. Thus, filtering out the overlapped bands to avoid the interference between wideband and narrowband devices has become necessary. In [5]–[8], it was shown that a planar monopole could achieve a narrow frequency

Manuscript received February 18, 2009; revised November 02, 2009; accepted November 08, 2009. Date of publication March 01, 2010; date of current version September 03, 2010. This work was supported by the IT R&D program of MKE/KEIT (2009-S-025-01, Development of Common Platform for 60 GHz CMOS Beam Forming Application). D.-Z. Kim, W.-I. Son, H.-L. Lee and J.-W. Yu are with the Department of Electrical and Computer Engineering, Korea Institute of Science and Technology (KAIST), Daejeon, Korea (e-mail: [email protected]; [email protected]; [email protected]; [email protected]). W.-G. Lim is with Korea Aerospace Research Institute, Daejeon, Korea (e-mail: [email protected]; [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TAP.2010.2044327

II. ANTENNA-FILTER DESIGN A. Microstrip Resonators A microstrip resonator is based on the structure having at least one oscillating electromagnetic field. Among many types of resonators, microstrip resonators for filter designs may generally be classified into distributed line or patch resonators. Some typical configurations of these resonators are illustrated in Fig. 1. The distributed line resonators shown in Fig. 1(a) and (b) can be named as quarter-wavelength resonators since they are long ( is the guided wavelength at the fundamental resonance frequency, ). They can also resonate at other frequencies, for . Another typical distributed line resonator is a half-wavelength resonator as shown in Fig. 1(c). in length at its fundamental resonance This resonator is for . frequency and can also resonate at This type of resonators can be configured into many different shapes such as an open-loop resonator when implementing filters. The ring resonator shown in Fig. 1(d) is another type of distributed line resonators for which is the median radius of the ring. The ring resonator resonates at its fundamental frequency, , when . Higher resonance frequencies also occur at for . Similarly, it is possible to implement this type of line resonators with different configurations such as square and meander loops. B. Planar Monopole Antenna Planar monopoles in various radiator shapes such as circular, rectangular, elliptical, pentagonal and hexagonal have been widely discussed and used [9]–[14]. These broadband monopoles are characterized by wide operating bandwidth, satisfactory radiation properties, simple structure and easy

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Fig. 1. Some typical microstrip resonators: (a)  =4 line resonator (shunt series resonance); (b)  =4 line resonator (shunt parallel resonance); (c)  =2 line resonator; (d) ring resonator.

Fig. 3. Conceptual equivalent lumped-element circuit model at the passband in (a), and at the bandstop in (b).

Fig. 2. Geometry of the planar monopole antennas with open/short-circuited microstrip resonators: (a), (c), (e), (g) for open-circuited and (b), (d), (f), (h), (i) for short circuited.

of fabrication. In this paper, a rectangular planar monopole with antenna is used. The rectangular patch of the microstrip feed line is implemented on Taconic’s RF35 and ). As shown substrate ( in Fig. 2, the length and width of the dielectric substrate are and , respectively. On the other side of the substrate, the conducting ground plane with a length of is implemented. denotes the distance between the feed point and the ground plane. C. Integrated Antenna With Microstrip Resonators Fig. 2 shows the geometry of the integrated antenna with microstrip resonators in various geometries: plain open-circuited half wavelength resonator (a), plain short-circuited quarter wavelength resonator (b), open-circuited -shaped resonator (c), short-circuited -shaped resonator (d), open-circuited L-shaped resonator (e), short-circuited L-shaped resonator (f), open-circuited -shaped resonator (g), short-circuited

-shaped resonator (h) and short-circuited -shaped resonator (i). The microstrip resonators are placed on the opposite side of the planar monopole antenna and coupled to a return signal on the ground (or imaging part) of the planar monopole antenna. In Fig. 2, is the distance (or coupling gap) between and denote the the resonator and the ground plane. length and width of the resonator, respectively. The conceptual equivalent lumped element circuit model for the integrated antenna with the electrically coupled resonator of Fig. 2(a) is shown in Fig. 3. The capacitively coupled open-circuited half wavelength resonator is modeled by a lumped capacitor in series with a transmission line inductor (open-circuited transmission line) which is less than a half wavelength long at is equal to , no current the resonance frequency. When flows to the antenna when current is induced in the resonator as shown in Fig. 3(b). Consequently, no radiation can be made by the antenna at this frequency (i.e., notch characteristic). The parameters of the integrated monopole antennas with microstrip resonators in Fig. 2 are summarized in Table I. As , are found to be shown in Table I, the parameters, G and the same for all resonators. Fig. 4 shows the variation of the antenna characteristic as G varies and the notch-level seems to . Since the surface current of the be ideal when resonator is coupled to the ground at resonance frequency, the coupling between the resonator and the ground decreases as G increases and, consequently, the notch-level is also decreased. is found to be identical for all resonators. Fig. 5 Similarly, and Fig. 6 show the measured for the rectangular planar monopole antennas integrated with open-circuited resonators and short-circuited resonators of Fig. 2, respectively. It is obless than 10 dB is served that the frequency band for

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TABLE I PARAMETER SUMMARY FOR MICROSTRIP RESONATORS (A) TO (O)

Fig. 5. Measured jS j for the integrated planar monopole antennas with the open-circuited resonators of Fig. 2(a), (c), (e) and (g).

Fig. 4. Variation of jS j for the integrated planar monopole antenna with the resonator (a) according to G.

from about 2.2 GHz to 5.9 GHz and a band-notched characteristic is created around 4.5 GHz. The fundamental resonance frecan be empirically quency of the open-circuited resonators approximated by (1) are the speed of light and the approximated where and effective dielectric constant, respectively. Also, the fundamental can be resonance frequency of short-circuited resonators empirically approximated by

Fig. 6. Measured jS j for the integrated planar monopole antennas with the short-circuited resonators of Fig. 2(b), (d), (f), (h) and (i).

of the integrated antennas with closed and open-loop microstrip ring resonators in different shapes: open-circuited closed-loop ring resonator (j), open-circuited open-loop rectangular ring resonators (k) and (l), open-circuited closed-loop rectangular ring resonator (m), short-circuited open-loop rectangular ring resonator (n) and short-circuited closed-loop rectangular ring resonator (o). A simple equation of the circular ring as in Fig. 7(j) is given by (3)

(2) According to (1) and (2), the resonance frequency shifts to lower increases. frequencies as

where , and are mean radius, mode number and resonance frequency of the circular ring resonator. Also, the closedor open-loop rectangular ring resonator of Fig. 7(k), (l) and (m) can be expressed as

D. Integrated Antenna With Ring Resonators The microstrip ring resonator has been actively used in filters, oscillators, mixers and antennas [15]–[17] because of its advantages in compact size, ease of fabrication, narrow passband bandwidth and low radiation loss. Fig. 7 shows the geometry

(4) where, is the resonance frequency of rectangular ring resonator. From (3) and (4), the resonance frequency shifts to lower

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Fig. 9. Rectangular planar monopole antenna with the resonator (p).

Fig. 7. Geometry of the integrated antennas with closed and open-loop microstrip ring resonators.

Fig. 10. Simulated and measured antenna with the resonator (p).

j

S

j

for the rectangular planar monopole

Fig. 8. Measured jS j for the rectangular planar monopole antenna with resonators (j), (k), (l), (m), (n) and (o).

frequencies as or increases. Also, parameters, and , in Fig. 7 affect the level of notch created at the resonance frequency. All the parameters in Fig. 7 are summarized in Table I for the rectangular planar monopole anand the measured tennas with circular ring resonators is shown in Fig. 8.

Fig. 11. Fabricated rectangular planar monopole antenna with resonators (a), (b), (g), (k) and (o) from Table I.

E. Integrated Antenna With Multiple Resonators Fig. 9 and Fig. 10 show the geometry and the measured/simulated for the rectangular planar monopole antenna with -shaped resonator (p) (a combination of filter (c) and (g) whose geometry is similar to a hairpin-type resonator [18]), -shaped resonator can create a respectively. It is noted that a triple-band antenna having a dual-band rejection characteristic. , it is observed that the -shaped From the measured microstrip resonator with , , makes one notch-band at 4.05 GHz and the other -shaped microstrip resonator with , , makes the second notch-band at 4.88 GHz.

III. MEASUREMENTS Fig. 11 illustrates the fabricated rectangular monopole antennas with the previously discussed resontors. Fig. 12 shows of the proposed antennas the measured transmission loss with resonators (a), (c) or (e). A sharp fall in the antenna gain at the notch frequency of 4.5 GHz is shown. At passband frequencies, the antenna gains with notch filters are similar to those without notch filters. The simulated radiation efficiencies for the antennas with resonators (a), (c) and (e), and for the antennas without the resonators are both about 93%. That is, there is no effect by resonators on the radiation efficiency. Fig. 13 shows

KIM et al.: INTEGRATED PLANAR MONOPOLE ANTENNA WITH MICROSTRIP RESONATORS

Fig. 12. Measured transmission loss (jS (c) and (e).

j)

between antennas with filters (a),

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Fig. 14. Measured and simulated radiation patterns for the antenna with a resonator (a): (a) x-z plane at 2.8 GHz, (b) y-z plane at 2.8 GHz, (c) x-z plane at 4.5 GHz (d) y-z plane at 4.5 GHz, (e) x-z plane at 5.2 GHz, (f) y-z plane at 5.2 GHz.

IV. CONCLUSION In this paper, integrated wideband planar monopole antennas with microstrip resonators have been proposed. Single band-notched and multi-band notched antennas have been implemented by integrating wideband planar monopole antennas with various types of microstrip resonators. The ability to integrate an antenna with a filter can significantly relax the requirements imposed upon complex wireless systems such as ultrawideband (UWB) and software-defined radio (SDR) systems. REFERENCES Fig. 13. Measured radiation patterns for the antenna without a resonator: (a) x-z plane at 2.8 GHz and 4.5 GHz, (b) y-z plane at 2.8 GHz and 4.5 GHz.

the radiation pattern of the antenna without a resonator at 2.8 GHz and 4.5 GHz. Here, 2.8 GHz and 4.5 GHz are selected since they are passband and stopband for the case that a notch filter is integrated. Finally, Fig. 14 shows the simulated and measured radiation patterns for the integrated antenna with resonator (a) at 2.8 GHz, 4.5 GHz and 5.2 GHz. As shown from Fig. 13 and Fig. 14, the radiation pattern in the passband has no changes.

[1] T. Le Nadan, J. P. Coupez, S. Toutain, and C. Person, “Integration of an antenna/filter device, using a multi-layer, multi-technology process,” in Proc. 28th Eur. Microw. Conf., Oct. 1998, pp. 672–677. [2] G. Goussetis and D. Budimir, “Antenna filter for modern wireless systems,” in Proc. 32nd Eur. Microw. Conf., Oct. 2002, pp. 1–3. [3] A. A. Tamijani, K. Sarabandi, and G. M. Rebeiz, “Antenna-filter-antenna arrays as a class of bandpass frequency-selective surfaces,” IEEE Trans. Microw. Theory Tech., vol. 52, no. 8, pp. 1781–1788, 2004. [4] C. H. K. Chin, Q. X. Xue, and C. H. Chan, “Design of a 5.8-GHz rectenna incorporating a new patch antenna,” IEEE Antennas Wireless Propag. Lett., vol. 4, pp. 175–178, 2005. [5] H. G. Schantz, G. Wolence, and E. M. Myszka, “Frequency notched UWB antennas,” in Proc IEEE Conf. on Ultra Wideband Systems and Technologies, Raston, VA, Nov. 2003, pp. 214–218.

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[6] S. W. Su, K. L. Wong, and C. L. Tang, “Band-notched ultra-wideband planar monopole antenna,” Microw. Opt. Technol Lett, vol. 44, pp. 217–219, 2005. [7] W. S. Lee, W. G. Lim, and J. W. Yu, “Multiple band-notched planar monopole antenna for multi-band wireless systems,” IEEE Microw. Wireless Compon. Lett., vol. 15, pp. 576–578, Sep. 2005. [8] W. S. Lee, D. Z. Kim, K. J. Kim, and J. W. Yu, “Wideband planar monopole antennas with dual band-notched characteristics,” IEEE Trans. Microw. Theory Tech., vol. 54, no. 6, pp. 2800–2806, 2006. [9] M. J. Ammann and Z. N. Chen, “Wideband monopole antenna for multiband wireless systems,” IEEE Antennas Propag. Mag., vol. 45, pp. 146–150, 2003. [10] N. P. Agrawall, G. Kumar, and K. P. Ray, “Wide-band planar monopole antennas,” IEEE Trans. Antennas Propag., vol. 46, pp. 294–295, 1998. [11] Z. N. Chen, M. Y. W. Chia, and M. J. Ammann, “Optimization and comparison of broadband monopoles,” IEE Proc. Microw. Antennas Propag., vol. 150, pp. 429–435, 2003. [12] G.-M. Yang, R. Jin, C. Vittoria, V. G. Harris, and N. X. Sun, “Small ultrawideband (UWB) bandpass filter with notched band,” IEEE Microw. Wireless Compon. Lett., vol. 18, no. 3, pp. 176–178, Mar. 2008. [13] M. Ojaroudi, C. Ghobadi, and J. Nourinia, “Small square monopole antenna with inverted T-shaped notch in the ground plane for UWB application,” IEEE Antennas Wireless Propag. Lett., vol. 8, pp. 728–731, 2009. [14] T.-N. Chang and M.-C. Wu, “Band-notched design for UWB antennas,” IEEE Antennas Wireless Propag. Lett., vol. 7, pp. 636–640, 2008. [15] K. Chang and L. H. Hsieh, Microw. Ring Circuits and Related Structures, 2nd ed. New York: Wiley, 2004. [16] J. Hong and M. J. Lancaster, Microstrip Filters for RF/Microw. Applications. New York: Wiley, 2001. [17] Y. Zhang, W. Hong, C. Yu, Z.-Q. Kuai, Y.-D. Don, and J.-Y. Zhou, “Planar ultrawideband antennas with multiple notched bands based on etched slots on the patch and/or split ring resonators on the feed line,” IEEE Antennas Propag. Mag., vol. 56, pp. 3063–3068, 2008. [18] J.-S. Hong and M. J. Lancaster, “Cross-coupled microstrip hairpin-resonator filters,” IEEE Trans. Microw. Theory Tech., vol. 46, no. 1, pp. 118–122, 1998.

Won-Gyu Lim received the B.S. degree in electrical engineering from Kyungpook National University, Daegu, South Korea, in 2002, and the M.S. and Ph.D. degrees and the postdoctoral in electrical engineering from KAIST, Daejeon, South Korea, in 2004, 2008 and 2009, respectively. He is currently with Korea Aerospace Research Institute, Daejeon, South Korea. His research interests are wireless transmitter/receiver front-end isolation, multilayer EMI/EMC analysis and small antenna.

Dong-Zo Kim received the B.S. and M.S. degrees in electrical engineering from Hanyang University, Seoul, South Korea, in 2004, and KAIST, Daejeon, South Korea, in 2006, respectively. He is currently working toward the Ph.D degree at KAIST. His research interests are direct conversion six-port transceiver, microwave/millimeter wave circuit (MMIC, Hybrid), wireless communication system and high directivity antenna.

Jong-Won Yu (M’98) received the B.S., M.S. and Ph.D. degrees in electrical engineering from KAIST, Daejeon, South Korea, in 1992, 1994 and 1998, respectively. From 1995 to 2000, he worked at Samsung Electronics. He also worked at Wide Tecom Head and Telson from 2000 to 2001 and from 2001 to 2004, respectively. In 2004, he joined KAIST as an Assistant Professor of electrical engineering and is currently an Associate Professor. His research interests emphasize microwave/millimeter wave circuit (MMIC, Hybrid), wireless communication system and RFID/USN.

Wang-Ik Son received the B.S. and M.S. degrees in electrical engineering from KAIST, Daejeon, South Korea, in 2006 and, 2008, respectively, where he is currently working toward the Ph.D. degree. His research interests are microwave/millimeter wave circuit (MMIC, Hybrid), wireless communication system and GPS antenna.

Han-Lim Lee received the BASc. degree in electronics engineering from Simon Fraser University, British Columbia, Canada, in 2008 and is working toward the M.S. degree at KAIST, Daejeon, South Korea. His research interests are microwave/millimeter wave circuit (MMIC, Hybrid), wireless communication system and RFID/USN.

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3-D Radome-Enclosed Aperture Antenna Analyses and Far-Side Radiation Ilya Vladimirovich Sukharevsky, Sergey V. Vazhinsky, and Ilya O. Sukharevsky, Student Member, IEEE

Abstract—Physical optics integral representations of the fields are given for the 3-D model of the aperture antenna with specified ampliphase excitation law enclosed in a radome. The problem is reduced to finding fields of a plane wave diffracted on the “symmetrized” radome. This model is used for calculations of radiation patterns and for analyses of far-field radiation. Peculiarities of the ray pattern and caustics are analyzed using geometrical optics (geometrical theory of diffraction) method. The contribution of the stationary phase points in the aperture to the far-side radiation has been investigated. Results of numerical calculations are presented. Index Terms—Aperture antenna, geometrical optics, geometrical theory of diffraction, physical optics, radomes, sidelobe supression.

I. INTRODUCTION

R

ADOMES are an inevitable component of antenna systems and radars, both airborne and ground-based. Reflections of an antenna field from the inner walls of the radome may cause significant pattern deformations and increase sidelobe levels. Although various integral equation techniques and FDTD methods [1]–[4] have been employed for radome simulation during the last decade, asymptotic approaches (see, for example, [5]–[10]) are still more suitable for 3-D modeling of electrically large radomes due to low computational costs. Aperture antennas in an inhomogeneous medium have been studied for various applications. In [11] the aperture antenna located below a linearly inhomogeneous semispace was studied in the context of hydroacoustic or troposphere wave propagation. The method proposed in [12] adopted a ray tracing technique to obtain a projected image of source distribution. Most of aperture antenna models (considered with respect to radomes, for example in [5]–[7]) can be interpreted as a flat aperture with a perfectly electrically conducting flange. However, this approximation provides valid results only for the main lobe and first sidelobes of directivity pattern. In contrast with this approach, another useful interpretation of aperture antenna as a hole in an ideally black screen was proposed in [13]. In this

Manuscript received February 15, 2009; revised March 10, 2010; accepted March 22, 2010. Date of publication June 14, 2010; date of current version September 03, 2010. I. V. Sukharevsky (retired) was with the Military Academy of Air Defence, Kharkov 61077, Ukraine (e-mail: [email protected]). S. E. Vazhinsky is with the National Academy of Defence of Ukraine, Kiev 03048, Ukraine (e-mail: [email protected]). I. O. Sukharevsky is with the Institute for Radiophysics and Electronics of National Academy of Sciences of Ukraine, Kharkov 61085, Ukraine (e-mail: [email protected]). Digital Object Identifier 10.1109/TAP.2010.2052548

case, the incident field is absorbed by flanges; hence, the reflection from “fictitious” flanges does not contribute to the far-side radiation of the antenna system. Here we employed a mathematically strict model of the radome-enclosed aperture antenna [14] based on the generalized principle of mirror images. It allows us to generalize the method of equivalent currents for aperture antenna calculations [13] in cases when the aperture antenna radiates to the semispace in the presence of arbitrary scatterers (dielectric, conducting or magnetic bodies). Simple, exact and approximate formulae have a clear physical interpretation and allow to calculate correctly directivity pattern in the whole semispace. The problem of antenna radiation is reduced to the diffraction of a plane wave on the “symmetrized” radome (the similar “symmetrized” model was used in [15] for simulating of a radome-enclosed dipole array backed by a ground plane in 2-D, and in [16] for representations of the fields of an aperture antenna enclosed in a spherical chiral radome). The electromagnetic wave incidence can be calculated with a conventional geometrical optics (GO) method or geometrical theory of diffraction (GTD) algorithm. The first GTD consideration of diffraction on the layer was made by J.B. Keller [17]. Keller supposed the layer to be homogeneous and equidistant and described the field via integral equations derived easily from Green’s formulae. Fixing (the wave number in a free space) and expanding all functions into series of (layer thickness), Keller obtained the first term of a diffracted field expansion and evaluated it with the stationary phase method for big . However, results obtained via this method are valid only when . The correct asymptotic consideration can be held only . The method with respect to a prior relations with respect to based on a combination of ray techniques and boundary-layer expansions allowed to solve this 3-D problem of diffraction on and [18], [19], and a thin layer in cases [20]. Heuristic assumption about the primary field representations in [18]–[20] was justified by the exact Green’s function asymptotics of a point source in the presence of a thin layer obtained in [21]. In [22] this method was applied for the purpose of acoustic diffraction. It should be noted, that the first term of the expansion of the diffracted plane wave coincides with GO solution on the flat layer, and the next terms of expansion give corrections on curvature, non-equidistance, etc. These GTD methods consider slightly curved layers. However, diffraction from a tightly curved tip can be taken into account, as shown in [23]. Here the wave passage through the radome layer is calculated with the same accuracy as in [5]. However, the caustic influence on the fields reflected from the radome is taken into account.

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Fig. 1. Problem geometry. Aperture antenna 6 enclosed in radome

G

.

Using the developed hybrid PO/GO (PO/GTD) algorithm we show that radar-induced distortions of the far-field pattern are mainly caused by the reflections from a small area of the radome wall associated with a stationary phase point in the aperture. This may open crucial opportunities to suppress far sidelobes (for example, by disconnecting corresponding elements of antenna array). Detection of stationary phase points can be also used for asymptotic approximation of the field by the method of stationary phase in 3-D, as it is done in [6] in 2-D case. Sections II is devoted to the integral representation of a field radiated by the discussed system. The ray pattern and caustics are analyzed by GO (GTD) techniques in Section III. The detection of the stationary phase points (SPPs) is analyzed in Section IV. The results of 3-D modeling of a circular aperture antenna enclosed with a parabolic radome in support of our concept about the significant SPP influence on the far-side radiation field are presented in Section V.

Fig. 2. “Symmetrized” radome.

, is the unit vector, normal to and directed where ; , is electromagnetic field induced by a point source to (electric dipole) in a space containing a closed dielectric shell, (Fig. 2). which is symmetrical with respect to plane From exact formulae (2) go to the approximation of physical optics. When edge effects in the aperture are small

Then, omitting indices A, B, we get

II. INTEGRAL REPRESENTATIONS OF THE FIELDS Introduce Cartesian coordinates . Let aperture is in the plane and radiates to the semi-space (Fig. 1). Radiated field , is induced by some sources in semi-space . Domain contains with permittivities , (generally, dielectric radome variable). Consider two assumptions about the physical properties of surface : A— is the ideally conducting surface ; B— is the ideally magnetic surface . Denote aperture in domain half sums

and for the fields induced by in problems A and B. Consider also their

(3) Right-hand integral (3) expresses field of the radiating aperture through the given distributions of , in the aperture, and the field, diffracted on the “symmetrized” radome. Equation (3) means that in the inhomogeneous medium the field, calculated by the method of equivalent currents, coincides (in PO approximation) with “averaged” field of Macdonald model. Thus, these formulae generalize results of [13] for the case of inhomogeneous medium. From (2) and (3), obtain formulae for complex directivity pat, where is a unit vector of an tern of radiating system observation point in far-zone

(1) “Averaged” field (1) can be interpreted as a field corresponded to Macdonald’s model [24] of ideally black surface . Using Lorentz lemma and generalized principle of mirror images [14], and any vector of receiving polarderive for any point ization

— Exact formulae

(4) (2)

— Approximate PO formula; , is aperture distribution of tangential field in Kirchhof’s approximation; , is a

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Fig. 4. Local coordinates.

The reflected field along the beam represent via the well-known expression [25]

Fig. 3. Ray pattern.

field of a plane wave propagating in the direction which passed through the radome

, (9) where is the Jacobian of transition from beam coordinates to Cartesian ones.

where , , are permittivities and a wavenumber in free space, respectively. , as a sum of the field reAssume flected from the inner wall S of the radome and the field passed through the radome directly to the aperture (Fig. 3). Multi-reflections provide scattered field corrections of a higher order, so can be neglected due to electrically large sizes of the radome.

A. The Development of

. Caustic Surfaces

Let S be a fairly smooth strictly concave surface. Assume that is a part of the surface S, where the normal unit forms an acute angle with the given unit vector (Fig. 3). ( ; ) be the main curvatures in point of Let , and , are the corresponding unit reflection vectors (Fig. 4). As we have described

III. PLANE WAVE PASSAGE THROUGH THE RADOME WALL For simplicity of presentation, let layer be equidistant. Take into consideration curvilinear coordinates counted along the lines of curvature in the point of reflection on the internal surface of the radome. Represent the incident wave, diffracted wave on the internal surface of the radome, and the reflected wave, respectively, as

(10) (11) on the surface , are angles bewith and vectors , respectively. tween vector The reflected beam can be given by equation

(5) (6) Taking into account (10) and (11), we derive (here

is the point of the reflection) (7)

In (7)

, where (8)

where is the normal unit vector; see Fig. 3. Phases of each of the fields (5)–(7) are equal to the same value in a point . Vectors , are GO vector amplitudes or the first terms ; , of asymptotic expansion [18] ( , where is the largest curvature of a radome surface and a wave-front).

where In particular 2D case (

. ;

) we have

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Thus, in formula (9)

, where From the balance

. it is easy to imply (14)

A discriminant of

can be presented either as (11a)

or

(11b) From (11b) follows that the roots of the considered polynomial are real:

With very broad assumptions about the surface , system of functions (14) is locally reversible in the neighborhood of each and inverse regular point , are differentiable in the correfunctions sponding point . derivatives. Go to the study of phase-function and In the vicinity of each regular point , so . Therefore, vector of a variable point on can be considered as a function and : , and the of curvilinear coordinates , are vectors tangential to . derivatives Taking into account that

but since (11a) shows that

Finally, we get

(15) Hence, in the discussed 3D case caustic surface is comprised of two connected components, described in the beam , . Asymptotic apcoordinates as proximation (9) is valid while moving along the reflected beam to the value (where is some fixed posfrom , beitive number), but loses its physical meaning nearby cause the one-to-one correspondence between the Cartesian and beam coordinates is not fulfilled. However [26], after passing the critical value the beam approximation is valid again, but in the modified form: after touching a beam caustic, wave phase . The similar phenomenon is occurring declines as a leap on in the transition through the critical value .

In consequence of (8) and the apparent equality , obtain

and since

,(

; 2), equality (15) becomes

Hence the following important sentence results. Theorem: If the system of equations

B. Stationary Phase Points of the Reflected Field be the equation of the inner surface S of Let the dielectric radome, either homogeneous or stratified. Suppose the incident wave field has a flat front with a phase and on (Fig. 3); so that in accordance to (7), the beam reflected from S in a point has the phase (12) For generality, assume the presence of currents performing electrical scanning in the direction . The corresponding math, in the ematical model is the additional term expression for the phase function. Instead of (12) we have (13)

(16) and , then has some solution the values , expressed through this solution via formulae (14), are the stationary coordinates of a phase function . Thus, the detection of SPP in the aperture and finding their coordinates reduce to the effective solving of system of (16). Turn now to this problem. Fix the unit vectors of radiation and scanning (17) where

;

;

.

SUKHAREVSKY et al.: 3-D RADOME-ENCLOSED APERTURE ANTENNA ANALYSES AND FAR-SIDE RADIATION

Using (8), (16), (17) and denoting system of (16) takes the form

;

, (18) (19)

where

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Substitution of expressions (23.1) and (23.2) in (24) provides ; . the following results: However, the second variant contradicts the problem geometry: reflected beam directed along is to be directed down to the antenna aperture. Thus, we have only one physically mean. ingful solution: IV. NUMERICAL RESULTS

It follows from (18), (19) that: (20)

( is the waveConsider circular aperture of radius length in the free space) with cosine-law amplitude distribution in (4)) placed symmetrically to the axis (represented by , of a parabolic radome, whose surface equation is

Denote the value of ratio (20) as (21) after substitution in (18) or (19), derive

where for

;

, and, finally, the equation

whence two solutions can be found

Substituting in formulae (21), we obtain the first solution of system of (18), (19) (22.1) Analogously, the second solution of (18), (19) can be obtained using (22.2) Therefore, (18), (19) has two solutions: (22.1) and (22.2). Physical meaning of this ambiguity is determined by conditions to obey the desired solution beside (18), (19). Demonstrate this fact for the case when azimuthal angles of vectors and co. As is easy to see incide: (23.1) (23.2) Look now at the expression for the component from (8), (17)

derived

(24)

Parameters of the radome are: , the depth of the , the dielectric permittivity , and the radome thickness is matched for the normal incidence. The unit polarization vector of currents in the aperture is . Using formula (4) we calculated radiation patterns in H-plane , ; Fig. 5) and compared ( them with the radiation patterns of the aperture enclosed in a . Scanning was semi-spherical radome, with radius . All radiation patterns carried by vector were normalized to the maximum of the radiation pattern without a radome. Note, that the radiation pattern of a circular aperture without electrical scanning [Fig. 5(a)] coincides with the corresponding pattern of [27], where it was computed by exponential approximation of Bessel function. A significant increasing of the sidelobe level in the far zone is observed in comparison with the radiation pattern of an aperture without radome in H-plane. Far sidelobes grow by 15–20 dB. This phenomenon is caused by reflections from the small area (less than 1% of surface of the radome inner wall), associated with a stationary phase points. For example, contribution of such without scanning is area to the total reflected field for equal to 85 per cents. The main lobe decreases by 0.6 dB. The radiation pattern for a semi-spherical radome is much more distorted compared to a parabolic radome for the case of a cosine-law distribution; however, this effect is less explicit for a constant amplitude and phase distribution [Fig. 5(b)]. With increasing of scanning angle, the pattern symmetry is breaking and far sidelobes are broaden and considerably distorted [Fig. 5(c)]. V. CONCLUSIONS The offered method allows to calculate the radiation field of an aperture antenna in the presence of arbitrary radome or (with some modifications) of any scatterers. It is equally applicable to study fields both in the near and far zones of a radome. For correct calculation of GO (GTD) passage of a wave through the radome, the caustic behavior is analyzed. The existence and coordinates of stationary phase points of can be recognized via the the reflected field in the aperture following developed algorithm.

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are quite small and do not overcome 2% of an aperture size. These results can be also used for field evaluation by the method of stationary phase. ACKNOWLEDGMENT The authors thank the anonymous reviewers, whose thorough consideration of the article helped to improve it significantly. I.O. Sukharevsky thanks his friend R. V. Berkeley Dennis for providing language help. REFERENCES

Fig. 5. Radiation patterns of the circular aperture antenna with the parabolic radome (black line), the semi-spherical radome (black dashed line), and without radome (gray line) in H-plane. (a) Without scanning for cosine amplitude distribution. (b) Scanning under an angle of 5 for cosine amplitude distribution. (c) Without scanning for constant distribution.

1) With given vectors of radiation and of scanning, solve the system of (18), (19) and choose the solutions lying in the domain . (points 2) Using formulae (19), determine the points of plane with coordinates corresponding to each found of (18), (19). solution 3) Among these points choose those that belong to the (i.e. the aperture of the considered antenna domain system) and thus obtain the desired set of stationary phase points of the field reflected from . A practical significance of these derivations is to build a grid of stationary phase points (SPP) whose local neighborhoods contribute significantly to the lateral radiation of the antenna system. In doing so may open opportunity of compensation of this contribution by technical devices. Neighborhoods of SPPs contribute significantly to the level of the reflected field (60–85% of the total value of reflections). Sizes of these areas

[1] C.-C. Lu, “A fast algorithm based on volume integral equation for analysis of arbitrarily shaped dielectric radomes,” IEEE Trans. Antennas Propag., vol. 51, pp. 606–-612, Mar. 2003. [2] V. B. Yurchenko, A. Altintas, and A. I. Nosich, “Numerical optimization of a cylindrical reflector-in-radome antenna system,” IEEE Trans. Antennas Propag., vol. 47, no. 4, pp. 668–673, Apr. 1999. [3] O. I. Sukharevsky, S. V. Kukobko, and A. Z. Sazonov, “Volume integral equation analysis of a two-dimensional radome with a sharp nose,” IEEE Trans. Antennas Propag., vol. 53, pp. 1500–1506, April 2005. [4] H. Jiang, H. Arai, and Y. Ebine, “FDTD analysis of input characteristic of monopole antenna covered with cylindrical radome,” in Proc. Antennas Propag. Symp., 2000, vol. 3, pp. 1480–1483. [5] G. Burks and E. R. Graf, “A high frequency analysis of radome-induced radar pointing error,” IEEE Trans. Antennas Propag., vol. 30, no. 9, pp. 947–955, Sep. 1982. [6] S. R. Rengarajan and E. S. Gillespie, “Asymptotic approximation in radome analyses,” IEEE Trans. Antennas Propag., vol. 36, no. 3, pp. 405–414, Mar. 1988. [7] R. Orta, R. Tascone, and R. Zich, “Performance degradation of dielectric radome covered antennas,” IEEE Trans. Antennas Propag., vol. 36, no. 12, pp. 1707–1713, Dec. 1988. [8] J. A. Shifflett, “CADDRAD: A physical optics radar/radome analysis code for arbitrary 3-D geometries,” IEEE Trans. Antennas Propag., vol. 39, no. 12, pp. 73–79, Dec. 1997. [9] A. Moneum, M. A. Z. Shen, J. L. Volakis, and O. Graham, “Hybrid PO-MOM analysis of large axi-symmetric radomes,” IEEE Trans. Antennas Propag., vol. 49, pp. 1657–1666, 2001. [10] O. I. Sukharevsky and V. A. Vasilets, “Scattering of reflector antenna with conic dielectric radome,” Progr. Electromagn. Res. B, vol. 4, pp. 159–169, 2008. [11] Y. I. Orlov and S. K. Tropkin, “Field of a planar aperture antenna in an inhomogeneous medium,” Radiophys. Quan. Electron., vol. 23, pp. 979–986, 1980. [12] H.-S. Lee and H. Park, “Prediction of radome bore-sight errors using a projected image of source distributions,” Progr. Electromagn. Res., vol. PIER 92, pp. 181–194, 2009. [13] Y. N. Feld, “Calculation of the fields of the aperture antennas,” (in Russian) Transl.: Radio Eng. Electron. Phys. Radiotekh. Electron., vol. 26, pp. 178–183, 1981. [14] I. V. Sukharevsky and O. I. Sukharevsky, “Calculation of a field induced by the radiating aperture in the presence of arbitrary system of scatterers,” (in Russian) Transl.:Soviet Journ. Commun. Technol. Electron. Radiotekh. Electron., vol. 1, pp. 8–13, 1986. [15] W.-J. Zhao, Y.-B. Gan, C.-F. Wang, and L.-W. Li, “Radiation pattern and input impedance of a radome-enclosed planar dipole array backed by a ground plane,” in Proc. Antennas Propag. Symp., Jul. 8, 2008, vol. 1A, pp. 350–353. [16] Li, M.-S. Leong, P.-S. Kooi, T.-S. Yeo, and Y.-L. Qin, “Radiation of an aperture antenna by a spherical-shell chiral radome and fed by a circular waveguide,” IEEE Trans. Antennas Propag., vol. 46, no. 5, pp. 664–671, May 1998. [17] J. B. Keller, “Reflection and transmission of electromagnetic waves by thin curved shells,” J. Appl. Phys., vol. 21, pp. 896–901, Sep. 1950. [18] I. V. Sukharevskii, “Passage of electromagnetic waves through a radiotransparent layer,” Radio Eng. Electron. Phys., vol. 12, pp. 191–197, Feb. 1967. [19] V. I. Zamiatin, “The diffraction of electromagnetic waves by radiotransparent layers of finite thickness,” Radio Eng. Electron. Phys., vol. 19, pp. 5–12, Nov. 1974. [20] E. N. Semeniaka, “Asymptotic solution of the problem of diffraction of electromagnetic waves from a slightly bent dielectric layer of much greater thickness than the wavelength,” Radio Eng. Electron. Phys., vol. 18, pp. 41–49, Jan. 1973.

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[21] S. I. Grinberg, E. N. Semenyaka, and I. V. Sukharevskii, “Short-wave asymptotic behaviour of Green’s function in the problem of diffraction at a plane layer,” USSR Comp. Math. Math. Phys., vol. 13, no. 3, pp. 170–186, 1973. [22] V. M. Babich, “Passage of a wave through a thin layer,” J. Math. Sci., vol. 55, no. 3, pp. 1656–1662, Jun. 1991. [23] J. A. Fozard, “Diffraction and scattering of high-frequency waves,” Ph.D. dissertation, Oxford, U.K., Sep. 2005. [24] H. M. Macdonald, Phil. Trans. Sec. A, vol. 12, no. 212, p. 337, 1912. [25] V. A. Fock, Electromagnetic Diffraction and Propagation Problems. New York: Pergamon, 1965. [26] V. M. Babich and V. S. Buldyrev, Asymptotic Methods in Short-Wave Diffraction Problems, ser. Springer Series on Wave Phenomena 4. Berlin: Springer, 1991. [27] E. J. Rothwell, “Exponential approximation of Bessel functions, with applications to electromagnetic scattering, radiation and diffraction,” IEEE Antennas Propag. Mag., vol. 51, no. 3, pp. 138–147, Jun. 2009. Ilya Vladimirovich Sukharevsky received the M.Sc. degree in mechanics and the Ph.D. degree in mathematical physics from Kharkov State University, Ukraine, and the D.Sc. degree in mathematical physics from the Military Academy of Air Defence, Kharkiv, in 1950, 1954, and 1967, respectively. He served in the Soviet Army during the Second World War. He was with Kharkov Polytechnical University from 1950 to 1958 and with Military Academy of Air Defence, Kharkiv, Ukraine, from 1959 to 1993. He was a Professor at Kharkiv Military University, Kharkiv, from 1993 to 2000. For 33 years from 1960 to 1993, he was the head of the Mathematics School of Military Academy of Air Defence. He held lectures on various mathematical courses (integral equations, mathematical statistics, computational mathematics, etc.) at the Mathematics and Mechanics Department of Kharkov State University and, for more than a decade, he was the head of the State Certification Commission. His early research interests (1953–1958) were mostly concentrated on the bounded problems and integral equation of the potential theory with applications to the hydrodynamics and elasticity theory. After 1958 he, in cooperation with Prof. A. Ya. Povzner, held a cycle of fundamental research of wave fronts and discontinuities of Green’s function on them in the case of the boundary value problem in a domain wholly illuminated by a source. This research became one of the first basic results in the microlocal analyses of partial differential

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equations, and have found wide use in acoustics and electrodynamics, in the problems of echolocation and radars. The vast number of his publications were dedicated to diffraction problems on radar-transparent stratified structures. The range of important asymptotic expansions with applications to antenna systems and radomes were obtained. The other direction of his scientific research was connected with operator, integral, in particular, equations. He was the author of papers dedicated to the stability of solutions of operator equations in Banach space, the stability of solutions of Fredholm equations under the discontinuous kernel variation, and the second kind integral equations of diffraction on open conducting surfaces. Prof. Sukharevsky was a member of the Methodological Commission of the Defense Ministry of the USSR and is a the permanent member of Presidium of Kharkov Mathematical Society since 1972. He was awarded the title of the Honoured Worker of Education of Ukraine in 1991.

Sergey E. Vazhinsky was born in 1961. He received the B.Sc. degree in electrical engineering from Kyiv Engineering Missile Academy, Ukraine, in 1985, and the M.Sc. and the Ph.D. degrees from the Military Academy of Air Defence and Kharkov Military University, in 1995 and 1997, respectively. He is now an Assistant Professor in the National University of Defence, Kiev, Ukraine. His current research interests include electronic systems and antennas.

Ilya O. Sukharevsky (S’08) was born in Kharkov, Ukraine, in 1984. He received the B.Sc. and the M.Sc. degrees in mathematical physics from Kharkov National University, Ukraine, in 2005 and 2006, respectively, where he is currently working toward the Ph.D. degree. He is now with the Institute for Radiophysics and Electronics of the National Academy of Sciences of Ukraine, Kharkov, Ukraine, as a Junior Scientist. His scientific interests are in the areas of antennas and computational electromagnetics.

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Platform Embedded Slot Antenna Backed by Shielded Parallel Plate Resonator Wonbin Hong, Member, IEEE, and Kamal Sarabandi, Fellow, IEEE

Abstract—A new cavity architecture for applications in design 15 of resonator-backed slot antennas with a height less than profile is presented. This architecture renders cavity heights as 130 and small lateral dimensions. Miniaturization low as of the supporting cavity resonator is achieved by meandering the passage from the bottom of the cavity resonator to the slot aperture. Unlike conventional cavity resonators, the proposed design operates in a TEM mode which allows for wider bandwidth operation and miniaturization of lateral dimensions. Ultrasonic consolidation technique is employed to fabricate the complicated cavity structure monolithically. Measurements verify the proposed antenna exhibits excellent gain and front-to-back ratio (FTBR). Wide-band mode of the antenna is achieved by using a carefully designed microstrip feed across the slot aperture which facilitates a fictitious short along the slot aperture. The antenna is then flush-mounted onto an arbitrarily built metallic platform and is shown to feature consistent impedance matching. The FTBR is found to improve when the antenna is embedded into the platform. The same antenna architecture is redesigned for VHF band operation using standard multi-layer PCB technology and consistent functionality is verified. Index Terms—Flush-mount antenna, parallel plate resonator, platform-embedded antenna, slot antenna.

I. INTRODUCTION NTENNAS are one of the most visual component in a wireless communication system. Historically, radiation performance of an antenna has been considered one of the highest priorities in determining antenna type and placement on a wireless communication system platform. At low RF frequencies such as HF-UHF bands, the size of antennas is relatively large. This has motivated significant research on antenna miniaturization. The literature concerning antenna miniaturization can be categorized into the following two, different general approaches: 1) techniques based on antenna topology [1]–[5] and 2) methods based on use of materials [6]–[10]. In this paper the focus is on miniaturizing the effect of the platform on antenna performance and reducing antenna effect on the platform

A

Manuscript received April 19, 2009; revised February 10, 2010; accepted February 19, 2010. Date of publication June 14, 2010; date of current version September 03, 2010. W. Hong was with the Radiation Laboratory, Department of Electrical Engineering and Computer Science, The University of Michigan, Ann Arbor, MI 48109-2122 USA. He is now with Samsung Electronics, Suwon 443-742, South Korea (e-mail: [email protected]). K. Sarabandi is with the Radiation Laboratory, Department of Electrical Engineering and Computer Science, The University of Michigan, Ann Arbor, MI 48109-2122 USA. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TAP.2010.2052551

aesthetic or other physical characteristics, such as aerodynamic drag. Significant interactions exist between the antenna and the platform where the antenna is placed. Such interactions can result in significant pattern, impedance matching, and gain degradation of the antenna once the antenna is integrated with the rest of the wireless communication system including the platform. Various studies have been done to characterize the effect of the platform for a variety of scenarios [11]–[13]. Practical problems are encountered when antennas are integrated with circuit boards [14]–[16]. These studies collectively indicate strong likelihood of radiation performance differences between an antenna in an open-space environment and the antenna integrated with the rest of the wireless communication system across a broad spectrum of scenarios. In addition to radiation performance of the antenna, the overall mechanical complexity, ergonomics, aerodynamic drag, etc., are considered during the antenna design process. For instance in aviation applications, low frequency SAR antennas are typically mounted onto the fuselage or the aircraft wings. At present it is very difficult to attain vertical polarization without significantly protruding the fuselage which adversely affects aerodynamic drag of the entire aircraft. Therefore system level approach in antenna design is becoming increasingly demanding as wireless communication systems become more diverse, versatile, and integrated. System level approach in antenna design can often require significant processing power beyond the capacity of commercial EM solvers. This problem is exacerbated for scenarios where the wireless communication platform is electrically large. Slot antennas are highly useful for platform-level integration scenarios due to its low profile. Slot antennas with high level of isolation do not require extensive system level design and the associated computational costs are favorable. Designing a shield (cavity) with dimensions comparable to wavelength to suppress backward radiation of a slot antenna is a common solution [17]. While this yields high isolation level, the design is intrusive because of it’s extensive height of the antenna platform. Height reduction of the cavity is achieved by operating a cavity-backed slot antenna above its second resonance in [18]. In [19], it is demonstrated that the profile of a conventional cavity can be further reduced through modification of the cavity topology. In [20], the dimension of the cavity-backed slot antenna is miniaturized by replacing the metal ground plane around the slot aperture with specially designed metallic patterns. This paper presents an antenna that features a low-profile dimension suitable for platform-embedded scenarios. The antenna consists of a slot aperture backed by a shielded parallel plate resonator. Integrated with the slot aperture, the proposed antenna functions similar to a conventional cavity-backed slot antenna while having small lateral dimensions as well as ver-

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tical height less than . To fabricate the structure of the shielded parallel plate resonator without material support, the structure is designed and fabricated using Ultrasonic consolidation technology. The details of the proposed antenna is presented in Section II. The measured antenna features high levels of gain, low levels of cross polarizations, and FTBR. The bandwidth of the antenna is enhanced by creation of an additional fictitious resonance close to the principle resonance and exhibits a wide-band mode. An arbitrary metallic platform is built and the shielded parallel plate resonator-backed slot antenna is flush-mounted on the platform and the isolation levels are evaluated in Section III. The proposed antenna is also redesigned and demonstrated for VHF applications using low-cost standard printed circuit board (PCB) technology. II. THE SHIELDED PARALLEL PLATE RESONATOR-BACKED SLOT ANTENNA For majority of application scenarios, the difficulties of implementing a slot antenna on a platform represent two challenges. Firstly, slot antennas at resonance will direct half of the radiated power in the undesired direction into the platform. Secondly, the backward radiation significantly increases the sensitivity of slot antenna to its environment. The input impedance, radiation pattern and gain of the slot antenna tends to significantly alter as a function of the platform. As a result, conventional slot antennas are generally designed to function in conjunction with a predefined platform. To mitigate these difresonant slot antennas are usually ficulties, unidirectional designed over a cavity resonator operating at a proper mode coherent with the field distribution over the slot. Consider a conventional cavity resonator-backed slot antenna as shown in for the cavity resonator diFig. 1. If we assume mension in Fig. 1, the propagating conditions within the cavity resonator can be expressed as (1) where (2) If we assume the cavity resonator-backed slot antenna operates in the lowest-order (dominant) mode then, , , . Classical studies by Cockrell [21] and Long [22] have shown theoretically and experimentally that the suscepslot antenna becomes tance of the cavity resonator backedwhere is the guided wavenegligible when becomes length. This can be explained by modeling the cavity resonator as a short-circuited transmission line of electrical length in parallel with the open slot antenna. However as previously shown, this can only be achieved for specific cavity resonator modes. As a result, conventional cavity resonator backed-slot antennas feature narrow antenna bandwidth. In addition, the height of the cavity resonator may be considered physically large especially at low frequencies when placed on a plattrench may also be difficult in many form. Excavation of a

Fig. 1. Topology of the cavity resonator-backed slot antenna. (a) 3-D view. (b) Topology in the y-z plane.

situations. The physical height of the cavity resonator can be further reduced using magneto-dielectric loading, but this leads to additional material loss and degradation of antenna gain. A. Design of the Shielded Parallel Plate Resonator We are looking for an alternative topology for a cavity resonator backed-slot antenna having small lateral dimensions and low vertical profile. For conventional cavity resonator-backed of the cavity resslot antennas shown in Fig. 1, the height onator is equal to the distance from the slot aperture to the cavity resonator ground. These two parameters can be differentiated as shown in Fig. 2(a), (b) by devising a cavity resonator consisting of metallic parallel plates with fixed spacing within the structure. By enclosing the parallel plate resonator in the z-x plane, the shielded parallel plate resonator operates in the TEM mode. Hence, proper operation is achieved by adjusting the distance from the slot aperture to the resonator to be where is free space wavelength. As ground of the cavity resonator is significantly a result, the height reduced through folding the parallel resonator multiple times. In addition, performance is independent of the longitudinal dimension since cutoff frequency is nonexistent for the shielded parallel plate resonator. The top ground plane supports electric currents moving perpendicular to the slot which are responsible for far-field radiation. The size of the slot ground plane and its symmetry around the slot determines the bandwidth and radiation efficiency [23]. The bandwidth is also determined by the volume occupied by the back resonator. To fully utilize the overall surface and increase the volume of the shielded parallel plate resonator without increasing the height profile, dual resonator architecture with a metallic center pillar that separates the resonators is conceived as shown in Fig. 2(c). The parallel plates combined with the center pillar forms two sub-resonators that are identical in dimension and each behave as a resonator. The dimensions and are further optimized by considering the effect of the spacing using Ansoft HFSS. The optimized shielded parallel plate resonator is presented in Fig. 3. The shielded parallel plate resonator is fabricated by

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TABLE I DESIGN PARAMETERS OF THE OPTIMIZED SHIELDED PARALLEL PLATE RESONATOR-BACKED SLOT ANTENNA (mm)

TABLE II SIMULATED GAIN AS A FUNCTION OF

Fig. 2. The rudimentary concept of the slot antenna backed by shielded parallel plate resonator. (a) 3-D view. (b) Topology in the y-z plane.

W

AND

g

the TEM waves travel from the slot aperture to the resonator . The length of the parallel plate is swept from ground 1.75 mm to 4.75 mm with an increment of 1.0 mm. Simulation increases over the sweep range, the resresults indicate as onance of the antenna decreases by approximately 20%. Hence increases, the TEM waves are forced to travel a longer as distance to the resonator ground. In contrast, the variation of from 0.3 mm to 1.2 mm spacing between the parallel plates with 0.3 mm increment has limited influence on the resonance of the antenna. However, as summarized in Table II, the simulated gain is proportional to . Therefore for a fixed shielded , the gain and resonance of the parallel plate resonator height proposed antenna can be optimized through modification of the and . aforementioned parameters B. Design of a Wideband Slot Aperture on the Shielded Parallel Plate Resonator

Fig. 3. The optimized shielded parallel plate resonator-backed slot antenna. (a) 3-D view. (b) Side view (y-z plane). (c) Top view (x-y plane).

Solidica of Ann Arbor, MI employing ultrasonic consolidation technique. The technique involves merging layers of metal from conventional aluminium foil sheets using an ultrasound welding method [24]. The process produces metallurgical bonds and is capable of fabricating complex 3-D metallic topologies monolithically. The height of the completed shielded parallel plate , and less than in width. The resonator ( ) is less than complete geometrical dimensions and physical parameters are listed in Table I. It is important to consider the effects of the length of the parand spacing between the parallel plates on allel plate the functionality of the proposed antenna. The length of the paris a key parameter in determining the distance allel plate

The slot aperture is designed and fabricated on the top surface of the shielded parallel plate resonator. An off-centered 50 microstrip feed connected to a open-circuited 110 microstrip is designed to excite the slot aperture. It has been reported in [25] that the bandwidth of a slot antenna in open-space can be enhanced to feature wide-band or dual-band behavior with consistent radiation behavior. Similarly, the microstrip feed can be adjusted so the shielded parallel plate resonator-backed slot antenna features a second fictitious resonant frequency slightly and shown above the first resonant frequency. Values for in Fig. 3 are chosen to merge the two resonances to achieve a wide-band mode. The simulated input reflection coefficients of is presented in Fig. 4. the antenna as a function of parameter and are 33 mm and 12.5 mm reThe optimized values of spectively. The microstrip feed is fabricated on a 0.8 mm thick RO4003 from Rogers Corp. substrate with dielectric constant of , and loss tangent of . The substrate is then placed on the shielded parallel plate resonator such that the slot aperture is sandwiched between the bottom of the proposed

HONG AND SARABANDI: PLATFORM EMBEDDED SLOT ANTENNA BACKED BY SHIELDED PARALLEL PLATE RESONATOR

Fig. 4. Simulated input reflection coefficients of the shielded parallel plate res: . onator-backed slot antenna as a function of L with L

= 12 5 mm

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Fig. 5. The measured and simulated input reflection coefficients of the shielded parallel plate resonator-backed slot antenna.

resonator and the microstrip feed susbtrate. The slot aperture excited by the microstrip feed is presented in Fig. 3(c). C. Measurements and Discussion An SMA connector is connected to the microstrip feed of the shielded parallel plate resonator-backed slot antenna. The measured input reflection coefficient is measured using a calibrated HP8729D vector network analyzer and the measured and simulated results are presented in Fig. 5. The difference in the overall shape of the input reflection coefficient curve can be mostly attributed to deviations caused during the fabrication process, the effect of the SMA connector, and material tolerance levels. Nonetheless simulated and measured results both display more than 14% 2:1 VSWR indicating that the measured result is a product of the merge of the two resonances that can be clearly observed in the simulated result. The far field co-polarized and cross-polarized radiation patterns of the antenna are measured in the E- and H-planes inside the anechoic chamber of the University of Michigan and the results are presented in Fig. 6. It is observed that the shielded parallel plate resonator-backed slot antenna has low levels of cross polarizations and features more than 7.0 dB front-to-back ratio (FTBR). The discrepancy between the measured and simulated cross-polarized radiation patterns is mainly attributed to the effect of the antenna feeding network used during the measurement. The gain of the antenna is measured in the anechoic chamber using a standard double-ridged horn antenna as a reference and the results are presented in Table III. The measurement indicates the proposed geometry of the shielded parallel plate resonator behaves similarly as an effective cavity resonator while featuring very low profile. As discussed earlier, since the shielded parallel plate resonator operates in the TEM mode, the longitudinal length of the structure can be further reduced without altering the functionality. Studies in [1] and [2] have devised methods of miniaturizing the longitudinal length of a slot antenna while preserving the radiation patterns. A similar miniaturized slot antenna topology is adapted and backed by a Shield parallel plate resonator with half of the original longitudinal length . The rest of the design parameters for the structure are unmodified. The miniaturized slot antenna backed by shielded

Fig. 6. Measured and simulated radiation patterns of the shielded parallel plate resonator-backed slot antenna studied in Section II. E-Plane (Left). H-Plane (Right).

TABLE III MEASURED GAIN AND FTBR OF THE SHIELDED PARALLEL PLATE RESONATOR-BACKED SLOT ANTENNA STUDIED IN SECTION II

parallel plate resonator is designed and the radiation patterns are simulated as shown in Fig. 7. The simulated patterns remain similar to that before miniaturization. The simulated bandwidth is found to decrease, which is in accordance with previous studies [1], [2]. III. APPLICATIONS OF THE SHIELDED PARALLEL PLATE RESONATOR-BACKED SLOT ANTENNA A. Demonstration of the Proposed Antenna Functioning as a Platform-Embedded Antenna The validity of the shielded parallel plate resonator-backed slot antenna was confirmed in the previous section. Now we return to the original objective of successfully mounting the proposed antenna on a platform. First, a metallic platform of arbitrary dimensions is built. A trench with identical volume as that of the shielded parallel plate resonator-backed slot antenna

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Fig. 7. Miniaturized slot antenna backed by shielded parallel plate resonator. (a) 3-D view. (b) Simulated radiation pattern (H-Plane). Fig. 8. The topology of the shielded parallel plate resonator-backed slot antenna with modified microstrip feed network discussed in Section III. (a) Side view. (b) Top view (Metallic platform omitted).

is then created on the top surface of the metallic platform. A small hole is drilled through the metallic platform for the placement of the semi-rigid feeding cable for the antenna structure. The antenna topology remains unmodified. The feeding network is redesigned using identical RO4003 substrate discussed of the microstrip feed substrate in Section II. The width is increased to accommodate for the semi-rigid coaxial cable which replaces the SMA connector. The modified feeding netand are slightly work is shown in Fig. 8. Parameters adjusted to achieve wide-band mode and the optimized values are 32.1 mm and 12.4 mm respectively. The input reflection coefficient, radiation patterns in the E- and H-planes, and the gain are measured for the modified shielded parallel plate resonator-backed slot antenna in open-space. The measurement process is repeated when the modified antenna is completely embedded into the metallic platform in a flush-mount fashion. The shielded parallel plate resonator-backed slot antenna is first flush-mounted into the trench of the metallic platform. Afterwards, the modified feed network substrate is placed above the slot aperture and secured. A small through hole is drilled at the edge of the microstrip feed substrate to ensure connection to the center conductor of the semi-rigid coaxial cable. Lastly, the semi-rigid coaxial cable is inserted through the small hole in the metallic platform from the bottom and the tip of the center conductor is soldered to the microstrip feed. The measured input reflection coefficients of the proposed antenna in open-space case and platform-embedded case are presented in Fig. 9(a). The measurement indicates that the resonant frequency and polarization of the antenna when embedded in the metallic platform are preserved. This confirms the proposed antenna features low levels of sensitivity to its platform while requiring minimum surface intrusion. When embedded, the modified shielded parallel plate resonator-backed slot antenna is observed to have more than 10% 2:1 VSWR bandwidth. The difference in the magnitude of the input impedance matching can be mostly attributed to the deviations during the assembly process as the microstrip feed substrate and the semi-rigid coaxial cable must be separated from the antenna to be embedded in the metallic platform and then reinstalled afterwards. The measured E- and H-Plane far-field radiation patterns (normalized) for both cases are presented in Fig. 9(b). As expected, it is observed that the metallic platform has significant effect on both planes of the far-field

patterns. The metallic platform behaves as an electrically large ground plane that further suppresses the backward radiation of the shielded parallel plate resonator-backed slot antenna. This is supported by the increase in directivity from 5.3 dBi to 6.4 dBi when the antenna is embedded in the platform compared to antenna in open-space. The FTBR is measured to be 8.2 dB in open-space. Measurements indicate the FTBR is enhanced to 22 dB for the embedded case. The cross polarizations are also affected by the presence of the metallic platform, resulting in a slight increase in the direction of boresight. The measured gain and FTBR for both cases are summarized in Table IV. B. Designing the Shielded Parallel Plate Resonator-Backed Slot Antenna Using Printed Circuit Board (PCB) Technology The physical dimension of a conventional cavity resonator becomes increasingly problematic as the frequency of operation decreases. The ultrasonic consolidation process employed in the previous section to fabricate the shielded parallel plate resonator-backed slot antenna proves to be precise and reliable. However the current fabrication time and cost necessitate to further examine whether the FWRA can be designed using conventional multi-layer Printed circuit board (PCB) technology. The proposed antenna is scaled to operate in the VHF band using the original topology. The parallel plates are printed on 1.6 , mm thick FR4 substrates with dielectric constant of . The center pillar and the and loss tangent of side walls are constructed using Plated Vias with outer radius of 2.5 mm. To avoid the usage of blind vias, the shielded parallel plate resonator is constructed by first fabricating two separate blocks, one representing the upper portion of the resonator, and the other representing the lower portion of the resonator that contains the center pillars. The fabrication process of the shielded parallel plate resonator using PCB technology is visualized in Fig. 10. Photograph of the fabricated shielded parallel plate resonator-backed slot antenna using PCB technology is presented in Fig. 11. The microstrip feed network is redesigned in a similar way as discussed in Section III using a 0.5 mm thick RO4003 from Rogers Corp. substrate with dielectric con, and loss tangent of . Constant of sidering the physical dimensions of a 50 microstrip feed at

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TABLE IV MEASURED GAIN AND FTBR OF THE SHIELDED PARALLEL PLATE RESONATOR-BACKED SLOT ANTENNA IN THE PRESENCE OF A METALLIC PLATFORM

Fig. 10. Side view of the shielded parallel plate resonator-backed slot antenna using PCB technology.

Fig. 9. (a) The measured input reflection coefficients of the shielded parallel plate resonator-backed slot antenna in the presence of the metallic platform. (b) Measured radiation patterns of the shielded parallel plate resonator-backed slot antenna in the presence of the metallic platform. E-Plane (Left). H-Plane (Right).

VHF band, the slot aperture is matched to the 110 portion of (length) the microstrip feed. The corresponding values for (position) defined in Section II for the microstrip feed and are 102 mm and 52 mm respectively. The antenna is completed by stacking the microstrip feed substrate on the resonator. The completed dimension of the antenna using PCB technology is . This corresponds to a cavity height of . The measured and simulated input reflection coefficients can be observed in Fig. 12. The measurement confirms the mechanism and functionality of the proposed antenna remain consistent after adapting a PCB technology approach. The operating frequency range of the redesigned shielded parallel plate resonator-backed slot antenna is below the operating range of the anechoic chamber and therefore the measured patterns are omitted. Nevertheless, the simulated far-field radiation patterns remain consistent with those previously presented in this paper. The simulated gain and directivity of the fabricated shielded parallel plate resonator-backed slot antenna using PCB technology is computed to be 6.2 dBi and 4.7 dBi respectively. The relatively low radiation efficiency is predominantly due to thermal (ohmic) loss at the surface of the PCB and high level of stored energy due to extremely small gaps between the parallel plates as discussed in Section II. It should be noted that design and fabrication of the proposed antenna in conjunction with PCB technology is most feasible for low-cost application scenarios where radiation efficiency requirements are relatively lax.

Fig. 11. The fabricated shielded parallel plate resonator-backed slot antenna using PCB technology.

Fig. 12. The measured and simulated input reflection coefficients of the shielded parallel plate resonator-backed slot antenna using PCB technology.

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IV. CONCLUSIONS A new class of low-profile resonator-backed slot antenna is presented and discussed. The proposed antenna is derived from a conventional cavity resonator-backed slot antenna. However, the proposed cavity resonator operates in the TEM mode. The proposed cavity resonator is modified to feature excellent gain and FTBR whilst having the height reduced to value as low as . The antenna bandwidth is further enhanced by the additional creation of a fictitious resonance that is merged with the principle resonance of the antenna. The electrically small dimensions of the antenna is advantageous for scenarios where the antenna must be integrated with the rest of the wireless communication platform with minimum intrusion. The shielded parallel plate resonator-backed slot antenna is fully embedded into an arbitrary metallic platform. Measurements show consistency in input impedance matching of the proposed antenna for platform-embedded scenario indicating high levels of isolation. Significant increase in FTBR is observed. The antenna is redesigned for VHF applications and fabricated using conventional printed circuited board (PCB) technology. Measurements support the possibility of using the shielded parallel plate resonator-backed slot antenna using PCB technology for relatively low-cost application scenarios. REFERENCES [1] R. Azadegan and K. Sarabandi, “A novel approach for miniaturization of slot antennas,” IEEE Trans. Antennas Propag., vol. 51, no. 3, pp. 421–429, Mar. 2003. [2] N. Behdad and K. Sarabandi, “Bandwidth enhancement and further size reduction of a class of miniaturized slot antennas,” IEEE Trans. Antennas Propag., vol. 52, no. 8, pp. 1928–1935, Aug. 2004. [3] C. Puente-Baliarda, J. Romeu, and A. Cardama, “The Koch monopole: A small fractal antenna,” IEEE Trans. Antennas Propag., vol. 48, no. 11, pp. 1773–1781, Nov. 2000. [4] J. Zhu, A. Hoorfar, and N. Engehta, “Bandwidth, cross-polarization, and feed-pont characteristics of matched Hilbert antennas,” IEEE Antennas and Wireless Propagation Letters, vol. 2, pp. 2–5, 2003. [5] J. McVay and A. Hoorfar, “Miniaturization of top-loaded monopole antennas using Peano-curves,” in IEEE Radio and Wireless Symp., Jan. 2007, pp. 253–256. [6] A. Buerkle, K. Sarabandi, and H. Mosallaei, “Compact slot and dielectric resonator antenna with dual-resonance, broadband characteristics,” IEEE Trans. Antennas Propag., vol. 53, no. 3, pp. 1020–1027, Mar. 2005. [7] H. Mosallaei and K. Sarabandi, “Antenna miniaturization and bandwidth enhancement using a reactive impedance substrate,” IEEE Trans. Antennas Propag., vol. 52, no. 9, pp. 2403–2414, Sep. 2004. [8] K. Buell, H. Mosallaei, and K. Sarabadi, “A substrate for small patch antennas providing tunable miniaturization factors,” IEEE Trans. Antennas Propag., vol. 54, no. 1, pp. 135–146, 2006. [9] Y. Hwang, Y. Zhang, G. Zheng, and T. Lo, “Planar inverted F antenna loaded with high permittivity material,” Electron. Lett., vol. 31, no. 20, pp. 1710–1712, Sep. 1995. [10] J. Colburn and Y. Rahmat-Sami, “Patch antennas on externally perforated high dielectric constant substrates,” IEEE Trans. Antennas Propag., vol. 47, no. 12, pp. 1785–1794, Dec. 1999. [11] D. Horn, “Selection of vehicular antenna configuration and location through use of radiation pattern,” in Proc. 24th IEEE Vehicular Technology Conf., Dec. 1973, vol. 24, pp. 45–51. [12] Z. Novacek, “Radiation of a whip antenna on the car body,” in Proc. 17th Int. Conf. Radioelektronika, Apr. 24–25, 2007, pp. 1–4. [13] S. R. Best, “On the use of scale brass models in HF shipboard communication antenna design,” IEEE Antennas Propag. Mag., vol. 44, no. 2, pp. 12–23, Apr. 2002. [14] B. Collins, “Embedding antennas in user equipments,” in Proc. IEEE Wireless Communications and Networking Con., March 11–15, 2007, pp. 2334–2337.

[15] S. Ponnapalli, “Design and packaging of antennas for wireless systems,” in Proc. Electrical Performance of Electronic Packaging, Oct. 2–4, 1995, pp. 157–159. [16] B. Collins, “Improving the RF performance of clamshell handsets,” in Proc. IEEE Int. Workshop on Antenna Technology Small Antennas and Novel Metamaterials, Mar. 6–8, 2006, pp. 265–268. [17] , J. D. Kraus, Ed., Antennas. New York: McGraw-Hill, 1988. [18] A. Vallecchi and G. Gentili, “Investigation of microstrip-fed slot antennas backed by shallow cavities,” in Proc. IEEE Antennas Propag. Society Int. Symp., Jul. 3–8, 2005, vol. 3B, pp. 373–376. [19] C. X. Lindberg, “A shallow-cavity UHF crossed-slot antenna,” IEEE Trans. Antennas Propag., vol. 17, no. 5, pp. 558–563, Sep. 1969. [20] W. Hong, N. Behdad, and K. Sarabandi, “Size reduction of cavitybacked slot antennas,” IEEE Trans. Antennas Propag., vol. 54, no. 5, pp. 1461–1466, May 2006. [21] C. Cockrell, “The input admittance of the rectangular cavity-backed slot antenna,” IEEE Trans. Antennas Propag., vol. 24, no. 3, pp. 288–294, May 1976. [22] S. Long, “A mathematical model for the impedance of the cavity-backed slot antenna,” IEEE Trans. Antennas Propag., vol. 25, no. 6, pp. 829–833, Nov. 1977. [23] R. Azadegan and K. Sarabandi, “A compact planar folded-dipole antenna for wireless applications,” in Proc. IEEE Antennas Propag. Society Int. Symp., Jun. 2003, pp. 439–442. [24] Solidica [Online]. Available: http://www.solidica.com [25] N. Behdad and K. Sarabandi, “A wide-band slot antenna design employing a fictitious short circuit concept,” IEEE Trans. Antennas Propag., vol. 52, no. 1, pp. 475–482, Jan. 2005. Wonbin Hong (S’05–M’08) received the B.S. degree in electrical engineering from Purdue University, West Lafayette, IN, in 2004, and the M.S. degree and Ph.D. in electrical engineering from the University of Michigan, Ann Arbor, in 2005 and 2009, respectively. He is currently a Senior Engineer at Samsung Electronics, South Korea. His current research involves the development and characterization of microwave and millimeter-wave front-end circuits and miniaturized antennas.

Kamal Sarabandi (S’87–M’90–SM’92–F’00) received the B.S. degree in electrical engineering from Sharif University of Technology, Iran, in 1980, the M.S. degree in electrical engineering in 1986, and both the M.S. degree in mathematics and the Ph.D. degree in electrical engineering in 1989 from The University of Michigan, Ann Arbor. He is the Rufus S. Teesdale professor of Engineering and Director of the Radiation Laboratory in the Department of Electrical Engineering and Computer Science, University of Michigan. His research areas of interest include microwave and millimeter-wave radar remote sensing, metamaterials, electromagnetic wave propagation, and antenna miniaturization. He has 25 years of experience with wave propagation in random media, communication channel modeling, microwave sensors, and radar systems and is leading a large research group including two research scientists, and 14 Ph.D. students. He has graduated 34 Ph.D. and supervised numerous postdoctoral students. He has served as the Principal Investigator on many projects sponsored by NASA, JPL, ARO, ONR, ARL, NSF, DARPA and a larger number of industries. Currently he is leading the Center for Microelectronics and Sensors funded by the Army Research Laboratory under the Micro-Autonomous Systems and Technology (MAST) Collaborative Technology Alliance (CTA) program. He has published many book chapters and more than 180 papers in refereed journals on miniaturized and on-chip antennas, metamaterials, electromagnetic scattering, wireless channel modeling, random media modeling, microwave measurement techniques, radar calibration, inverse scattering problems, and microwave sensors. He has also had more than 420 papers and invited presentations in many national and international conferences and symposia on similar subjects. Dr. Sarabandi is a member of NASA Advisory Council appointed by the NASA Administrator and is a member of Commissions F and D of URSI. He was the recipient of the Henry Russel Award from the Regent of The University of Michigan. In 1999 he received a GAAC Distinguished Lecturer Award

HONG AND SARABANDI: PLATFORM EMBEDDED SLOT ANTENNA BACKED BY SHIELDED PARALLEL PLATE RESONATOR

from the German Federal Ministry for Education, Science, and Technology and was also a recipient of the 1996 EECS Department Teaching Excellence Award and a 2004 College of Engineering Research Excellence Award. In 2005 he received the IEEE GRSS Distinguished Achievement Award and the University of Michigan Faculty Recognition Award. He also received the best paper Award at the 2006 Army Science Conference. In 2008 he was awarded a Humboldt Research Award from The Alexander von Humboldt Foundation of Germany and received the best paper award at the IEEE Geoscience and Remote Sensing Symposium. He was also awarded the 2010 Distinguished Faculty Achievement Award from the University of Michigan. . He is serving as a vice president of

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the IEEE Geoscience and Remote Sensing Society (GRSS) and is a member of the IEEE Technical Activities Board Awards Committee. He is serving on the Editorial Board of The IEEE Proceedings, and served as Associate Editor of the IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION and the IEEE SENSORS JOURNAL. In the past several years, joint papers presented by his students at a number of international symposia (IEEE APS’95,’97,’00,’01,’03,’05,’06,’07; IEEE IGARSS’99,’02,’07; IEEE IMS’01, USNC URSI’04,’05,’06,’10, AMTA ’06, URSI GA 2008) have received best paper awards.

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Low Probability of Intercept Antenna Array Beamforming Daniel E. Lawrence, Member, IEEE

Abstract—A novel transmit array beamforming approach is introduced that offers low probability of intercept (LPI) for surveillance radar systems employing phased array antennas. Radar systems are often highly visible to intercept receivers due to the inherent two-way versus one-way propagation loss. In this paper, the traditional high-gain antenna beam scanned across a search region is replaced with a series of low-gain, spoiled beams. Keeping the transmit antenna gain low reduces the radar visibility, but the radar’s antenna performance remains unchanged as the original high-gain beam can be formed by processing the set of spoiled beams. Large transient power density radiated in a traditional scan is replaced with low power density persistently radiated at the target throughout the scan time. The detection performance of the radar is not affected since the total energy on the target is the same. Derivation of the complex weights to synthesize the high-gain patterns from the low-gain basis patterns is presented for both one-way and two-way beam patterns. Index Terms—Antenna arrays, beamforming, low-probability of intercept, radar.

I. INTRODUCTION

O

N the modern battlefield, active surveillance radars are highly vulnerable to detection and exploitation by opposing forces. The ongoing battle between radar systems and the electronic devices used to exploit, degrade, or prevent radar operation has been termed electronic warfare (EW) and is divided into two broad categories: 1) Electronic support measures (ESM) and 2) electronic counter-measures (ECM). The distinction between the two is simply that ESM is typically used to search, identify, record, and analyze radiated radar signals for potential exploitation during military operations, while ECM involves the active approaches taken to degrade radar’s effectiveness [1], [2]. An ESM device could be realized as a basic radar warning receiver (RWR), but ESM is often cast in terms of the broader category of electronic intelligence (ELINT) encompassing both tactical and strategic information gathering [3], [4]. In this paper, the term ESM is used to denote any EW device used to intercept the radar transmission and potentially enable harmful ECM techniques. In light of the significant threat presented by ESM receivers, there has been a growing trend towards the development of Manuscript received October 06, 2009; revised February 12, 2010; accepted March 20, 2010. Date of publication June 14, 2010; date of current version September 03, 2010. The author is with the Phase IV Systems Operation of Technology Service Corporation, Huntsville, AL 35802 USA (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TAP.2010.2052573

low probability of intercept (LPI) radar systems. The underlying weakness of any monostatic radar system, whose theoretical performance is dictated by the radar range equation, is ) versus one-way ( ) propagathe classic two-way ( tion loss experienced by the radar and intercept receiver, respectively. The ESM receiver always has the upper hand when it comes to received power, and in most cases will be able to intercept the radar transmission well beyond the radar’s detection range. To overcome the inherent disadvantage of the radar, a number of techniques have been developed to reduce the radar visibility and enhance LPI performance. Many of these techniques are well documented in the open literature [5]–[15]. In general, the capacity to reduce radar visibility relies on three key areas: 1) spreading the energy in time with high duty cycle waveforms; 2) spreading the energy in frequency with wide bandwidth waveforms; and 3) spreading the energy in space through broad transmitter antenna beams. Often combinations of these techniques are used together to improve performance. Perhaps the most common LPI technique employs the use of high duty cycle, wideband waveforms. Phase modulated CW, FMCW, frequency hopping, and random waveforms have all been reported in terms of their LPI qualities [16]–[23]. There is an upper limit, however, on the bandwidth extent that is feasible to spread the transmitted waveform. If the bandwidth of the radar waveform is increased such that individual scatterers on the target are resolved in range, then the detection performance of the radar becomes compromised offsetting the benefits of LPI [24]. In conjunction with waveform design, transmit antenna modifications can also improve LPI performance. A novel switched antenna approach, called antenna hopping, has been proposed [25]. Fielded radar systems often use irregular scan patterns to reduce susceptibility to receivers that use scan rate information for detection. Additionally, suppressing antenna sidelobe levels reduces the probability of being detected in a sidelobe region. Even with suppressed sidelobes, however, a high gain scanning main beam is still likely to be detected. Thus, it is desirable to keep the transmit gain low to reduce the peak power available to an ESM receiver. To accomplish this, a corresponding increase in integration time is needed to compensate for the lost gain. In [26] a technique is introduced that applies a broad beam transmit antenna to reduce the peak radiated power and is referred to as the omnidirectional LPI (OLPI) radar. Specifically, an omnidirectional transmit antenna is used in conjunction with multiple, narrow beam receive antenna channels to cover the desired surveillance field of view. To make up for the lost transmit gain, the integration time is increased to be the same as what the scan time would have been for a traditionally scanned, high-gain transmit antenna

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Fig. 2. N-element linear phased array antenna. setting for the nth element.

Fig. 1. Reduction of ESM receiver intercept area when the peak radar transmit antenna gain is reduced by 10 dB.

beam [27]–[29]. The main drawback of this approach is the need for simultaneous receive beams which, for large arrays, significantly increases hardware complexity. In this paper, a beam-spoiling technique is introduced to provide good LPI performance that can be implemented with only a single receive antenna channel without sacrificing antenna gain. Rather than scanning a high-gain transmit beam, a series of low-gain spoiled beams covering the desired surveillance region are formed sequentially. The sequence of low-gain beams comprise a set of basis patterns that can then be weighted and coherently combined to form an ensemble of high-gain beams scanned across the prescribed field of view. In this way, the peak power radiated in any direction is significantly reduced while maintaining the same antenna performance as a traditional surveillance radar with scanned high-gain antenna. In essence, low power persistently radiated over the surveillance area has replaced the transient high power sweep. To the author’s knowledge, the LPI beamformer technique presented here is novel and offers the potential to significantly reduce the visibility of modern surveillance radar systems. It should be noted that a radar system enhanced by the LPI technique described here still might not be able to detect a target before being detected itself. Rather, the term LPI is used to denote that the intercept range of an ESM receiver has been greatly reduced or, equivalently, that the probability of intercept has been reduced at a particular standoff range. The potential impact of an LPI beamformer is illustrated in Fig. 1. It is shown that a reduction of 10 dB in the radar’s transmit antenna gain brings in the maximum intercept range of the ESM receiver by a factor , equating to a factor of 10 reduction in the intercept of area. Using the methodology presented in this paper, however, the radar detection range remains unchanged while limiting the intercept area of the ESM receiver. In what follows, a novel technique for spoiling the radar antenna pattern through judicious choice of phase shifter settings is described with the goal of enhancing LPI performance. The principle is initially applied in Section II to a one-way pattern in order to derive the fundamental beam spreading and recombination equations. It is demonstrated that complex weights can be applied to the set of spread patterns to synthesize any of



denotes the phase shifter

the desired high-gain, scanned patterns. Many radar applications use the same antenna for transmit and receive and, thus, the equations are extended in Section III for the two-way antenna pattern. Finally, an implementation discussion is provided in Section IV followed by a summary of the work in Section V. II. ONE-WAY PATTERN SYNTHESIS In this section, the high-gain pattern synthesis approach is presented for a set of low-gain transmit beams. When the pattern is only affected on transmit, it is referred to as a one-way synthesis. An example application of the one-way synthesis would be a spoiled-beam transmit array combined with multiple simultaneous receive beams. Consider the linear antenna array shown in Fig. 2. For a linear array of elements with uniform excitation, the far-field radiation pattern is expressed (1) where is the free-space propagation constant, is the array element spacing, and is the spatial angle measured from the array broadside. It is convenient for the following development to make a substitution for the relative phase between elements (2) The fundamental array pattern is now written (3) The pattern in (3) is characterized by a dominant mainlobe with high gain directed broadside to the array. The high-gain pattern can be scanned by applying a linear phase progression across the array. The set of scanned patterns, with the fundamental phase is written scan

.. . (4)

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.. . (6)

Fig. 3. Fundamental basis pattern and broadside high-gain pattern comparison for a 32 element linear phased array.

For LPI applications, it is desirable to form high-gain patterns by a linear combination of low-gain basis patterns. A fundamental basis pattern can be formed by applying a select phase shift to each array element. The set of phase shift values is chosen to create a low gain, “spoiled” beam pattern. The fundamental basis pattern is written

Since the basis patterns are steered versions of the fundamental, they all exhibit low gain and broad beamwidth. The ultimate goal of this development is to write the set of high-gain, scanned patterns as a linear combination of the low-gain basis patterns, . Suppose the original broadside pattern in (3) can be basis patterns where the th written as a summation of all basis pattern is weighted by the complex coefficient

(7) Furthermore, suppose the remaining scanned high-gain patterns can also be formed by linear combinations of the basis patterns with the appropriate complex coefficients,

(5) An example low-gain basis pattern for a 32 element array is shown in Fig. 3. This pattern is formed by computer optimization of a quadratic phase shift variation across the elements where the goal is to minimize the gain. Details of the phase shifter settings used for this paper are provided in the Appendix. Other techniques to form broad beam patterns are given in [30]–[33]. The peak gain is only 1.7 dB compared to 15 dB for the fundamental high-gain pattern. Additional patterns are formed by applying a linear phase progression to the fundamental basis pattern. The phase progression is in for the 2nd pattern and increments of for the 1st pattern, steered versions of the fundamental so on. This results in pattern. There are other possibilities for choosing the remaining basis patterns, but steered versions of the fundamental ensure linear independence. The set of basis patterns derived from the fundamental are expressed

.. . (8) By expanding the high-gain pattern and basis patterns in (7) and equating equal powers of , a matrix equation can be set up for the coefficients

.. .

.. .

(9)

where the matrix is defined in (10), shown at the bottom of matrix equations the page. Using (8), the remaining set of can be written for the complex coefficients to form each of the scanned beams remaining

.. .

..

.

.. .

(10)

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.. .

.. .

.. .

.. .

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.. .

(11)

.. .

.. .

The equation set (9) and (11) can be combined into a single matrix equation to solve for all coefficients simultaneously

.. .

..

Fig. 4. Illustration of scanned high-gain patterns (solid line) formed by linear combinations of 32 low-gain basis patterns (dashed lines) for a 32 element linear array.

.. .

.

(13)

.. .

..

.

If we let be expressed

.. .

, it is straightforward to show that (13) can

(12) Using the coefficients calculated in (12) in the synthesis (7) and (8) allows high-gain patterns to be formed by linear combinations of the basis patterns. It should be noted that once the set of basis patterns have been formed, all steered high-gain patterns can be synthesized at once. Fig. 4 demonstrates the high, gain patterns of a 32 element array steered to 0 deg, . The patterns are formed by linear combination of and the 32 basis patterns. Again, any of the 32 high-gain patterns can be formed once the basis patterns are available.

(14) where for (15) for Scanned versions of the squared high-gain pattern, having a fun, can be written damental phase scan

III. TWO-WAY PATTERN SYNTHESIS When the same antenna array is used for both transmit and receive, the one-way pattern formation is not sufficient since the target return is scaled by the square of the pattern. The synthesis of the two-way pattern is slightly more complex and is achieved by a linear combination of two-way basis patterns. In order to , represent the two-way pattern as a summation of powers of the squared version of the broadside high-gain pattern of (3) is written

.. .

(16)

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Note that there are scanned patterns corresponding to the terms in the squared pattern expansion. Fig. 5 number of shows several scanned high-gain patterns for a 32 element linear array. The fundamental two-way pattern can be synthesized by a weighted summation of two-way basis patterns

(17) Similarly, scanned versions of the high-gain pattern can also be synthesized

Fig. 5. Selected scanned two-way, high-gain patterns for a 32 element linear : . The entire constellation of array. The fundamental scan angle is  63 scanned patterns would fill the entire angular region from deg to .

= 3 6 deg

+90 deg

.. .

+90 deg

(18) Since the squared basis patterns are used to form the squared high-gain pattern, it is necessary to represent the squared basis terms. The squared fundamental patterns in a summation of basis pattern can be written

(19) By letting , (19) can be rewritten as a summation of weighted powers of

Fig. 6. Fundamental two-way basis pattern and broadside high-gain pattern comparison for a 32 element linear phased array.

mind that for LPI performance assessment we should only consider the transmit pattern which remains a one-way pattern. Similarly, the remaining squared basis patterns can be written

(20) where

for (21)

.. .

for The fundamental two-way basis pattern together with the broadside high-gain pattern are shown in Fig. 6 for a 32 element array. Although the two-way basis patterns are shown here, keep in

(22)

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where is defined in (21). Substituting (14), (20), and (22) into the pattern synthesis equation of (17) and equating equal results in equations for the complex basis powers of coefficients,

(23) In matrix form, the set of equations in (23) can be written

(24)

.. .

.. .

is defined to be

where the matrix

.. .

..

.. .

.

(25) Solving for the coefficients to form the remaining set of scanned patterns in (18) is accomplished through a combined matrix equation which allows simultaneous solution for the pattern weights, see (26) at the bottom of the page. Using the weights calculated in (26) and the synthesis equations of (17) and (18), any of the high-gain patterns can be synthesized by linear combinations of the basis patterns. Fig. 7 demonstrates the high-gain patterns of a 32 element array steered to 0 deg, , and where the patterns are formed by linear combination of the 63 basis patterns. IV. IMPLEMENTATION Some discussion is in order on the practical implementation of the LPI beamforming approach described in this paper. The theoretical antenna performance that can be achieved after generating the set of high-gain beams from the low-gain basis patterns is the same as an un-spoiled, high-gain beam scanned over the same coverage area. Transient peak power is traded for sustained low power on the target over the search region, resulting in equivalent total energy on the target. Since the phase relation-

.. .

..

.

.. .

Fig. 7. Illustration of scanned two-way, high-gain patterns (solid line) formed by linear combinations of 32 low-gain basis patterns (dashed lines) for a 32 element linear array.

ship between basis patterns is important, the target must remain coherent over the scan time of the radar. For long scan times, this may require motion compensation for the target dynamics. The coherency requirement is the same as that required by traditional Doppler processing over the same scan time interval. Also, if the radar system is limited by receiver thermal noise, rather than ground clutter for example, the two-way beam pattern formulation may not have sufficient integration time to overcome the two-way gain loss. The pattern performance remains the same, but the resulting signal-to-noise will be lower than if a one-way pattern formulation combined with a multi-channel receiver having high gain were used on receive. In order to fully utilize the LPI beamforming approach in a particular radar system, the beam switching methodology must first be integrated with the radar waveform. A vast number of waveforms exist for many different radar performance objectives, and it is beyond the scope of this paper to address them all. Instead, an implementation using a standard pulsed waveform is suggested. Specifically, consider a waveform consisting

.. .

..

.

.. .

(26)

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Fig. 8. Illustration of processing architecture to implement beamforming approach. Complex weights are applied to the matched filter output before summing across multiple PRIs.

of spoiled, low-gain basis patterns. The obvious advantage of the technique presented here is the significant reduction in ESM intercept range that accompanies the reduction in peak transmit gain. Although peak gain is reduced, the target detection performance of the LPI beamforming approach can be made identical to that of a traditional high-gain beam since the total energy on the target is the same. The advantages of using LPI beamforming come at the cost of increased memory and processing requirements as well as restrictions on the target dynamics since the target must remain coherent over the entire scan time. Overall, the technique offers a promising tool that can possibly be combined with other LPI waveform techniques to reduce radar susceptibility and visibility in the ongoing LPI battle. APPENDIX

Fig. 9. Phase taper for the fundamental low-gain basis pattern. Note that the phase shift values are in radians and have not been wrapped.

of consecutive pulses separated by the pulse repetition interval (PRI). A notional block diagram of a digital processing architecture for this waveform is shown in Fig. 8. Here each pulse is transmitted and received using phase-shifter settings for a particular low-gain basis pattern: beam #1 for pulse #1, beam #2 for pulse #2, and so on. Each pulse is processed through a matched filter and then fills a corner-turn memory where the rows represent different range samples and the columns of the corner-turn are used to store sequential PRI data. The complex weights calculated in (12) or (26) are applied across PRI samples and summed. For a particular set of weights, the weighted summation forms the equivalent range return of a single high-gain separate returns beam. Note that once the data is collected, can be formed simultaneously by applying weights from each column of (12) or (26). There is no extra scan time required separate when compared to the traditional method of using high-gain beams that scan across the same region. Other LPI beamforming implementations are possible and could potentially be integrated with waveforms also designed for LPI performance. This represents a promising area of future work. V. CONCLUSION In this paper, a novel transmit beamforming approach is presented that provides an LPI alternative to a traditional scanned high-gain antenna beam. Both one-way and two-way high-gain patterns can be synthesized by weighted combination

A low-gain basis pattern can be implemented by selecting phase shifter values that provide a broad, spoiled beam. A uniform or linear phase variation across the array results in a highgain beam steered in angle proportional to the slope of the phase variation. Alternatively, by introducing a quadratic phase variation, the beam becomes de-focused and the gain of the array is reduced. In this paper, the phase shifter values are selected by randomly choosing a quadratic phase slope across the array. Then, using the randomly selected quadratic phase as a starting value, a multi-dimensional gradient search routine is used to minimize the gain of the array. Minimizing the gain ensures that a broad beam is achieved. The specific phase shifter settings used for the fundamental basis pattern described in this paper are given by

These phase values are in radians. The values through are the same as above but in reverse order. This gives a symmetric array excitation. A plot of the phase shifter values is shown in Fig. 9 illustrating the quadratic nature of the phase. Another viable option is to randomly select the array phase shifter settings and then minimize the gain using a multi-dimensional gradient search. REFERENCES [1] D. C. Schleher, Introduction to Electronic Warfare. Boston, MA: Artech House, 1986. [2] M. Skolnik, Radar Handbook, 2nd ed. New York: McGraw-Hill, 1990. [3] J. Tsui, Microwave Receivers With Electronic Warfare Applications. New York: Wiley, 1986. [4] R. G. Wiley, Electronic Intelligence: The Interception of Radar Signals. Norwood, MA: Artech House, 1985. [5] A. G. Stove, A. L. Hume, and C. J. Baker, “Low probability of intercept radar strategies,” IEEE Proceedings-Radar Sonar and Navigation, vol. 151, no. 5, pp. 249–260, Oct. 2004. [6] G. Schrick and R. Wiley, “Interception of LPI radar signals,” in Proc. IEEE Int. Radar Conf., 1990, pp. 108–111. [7] G. T. Oreilly, T. C. Pierce, and R. R. McElroy, “Track-while-scan quiet radar,” in Proc. 15th Annu. Electronics and Aerospace Systems Conf., Washington, DC, Sep. 20–22, 1982, pp. 369–374.

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[8] A. G. Stove, “Radar and ESM: The current state of the LPI battle,” presented at the 1st EMRS DTC Technical Conf., Edinburgh, 2004. [9] K. L. Fuller, “To see and not be seen,” Proc. Inst. Elect. Eng. Radar and Signal Processing, F, vol. 137, pp. 1–10, Feb. 1990. [10] P. E. Pace, Detecting and Classifying Low Probability of Intercept Radar. Norwood, MA: Artech House, 2004. [11] D. C. Schleher, “LPI radar: Fact or fiction,” IEEE Aerosp. Electron. Syst. Mag., vol. 21, pp. 3–6, May 2006. [12] E. J. Carlson, “Low probability of intercept (LPI) techniques and implementations for radar systems,” in Proc. IEEE National Radar Conf., Apr. 1988, pp. 56–60. [13] A. Denk, “Detection and jamming low probability of intercept (LPI) radars,” Ph.D. dissertation, Naval Postgraduate School, Monterrey, CA, 2006. [14] G. Lui, H. Gu, W. Su, and H. Sun, “The analysis and design of modern low probability of intercept radar,” in Proc. CIE Int. Conf. on Radar, Oct. 2001, pp. 120–124. [15] P. Wu, “On sensitivity analysis of low probability of intercept (LPI) capability,” in Proc. IEEE Military Communications Conf., Oct. 2005, vol. 5, pp. 2889–2895. [16] K. E. Olsen, T. Johnsen, S. Johnsrud, R. Gundersen, H. Bjordal, I. Tansem, and P. Sornes, “Results from an experimental continuous wave low probability of intercept bistatic radar – The first steps toward multistatic radar,” in Proc. Int. Radar Conf., 2003, pp. 288–292. [17] N. Levanon and B. Getz, “Comparison between linear FM and phasecoded CW radars,” Proc. Inst. Elect. Eng.– Radar, Sonar, Navigation, vol. 141, no. 4, pp. 230–240, Aug. 1994. [18] A. G. Stove, “Linear FMCW radar techniques,” Proc. Inst. Elect. Eng. F, vol. 139, no. 5, pp. 343–350, Oct. 1992. [19] B. E. Anderson, M. Persson, and K. Boman, “FMCW and super resolution techniques applied to an LPI short range air search radar,” in Proc. Radar 97, Oct. 1997, pp. 406–410. [20] F. Gross and K. Chen, “Comparison of detectability of traditional pulsed and spread spectrum radar waveforms in classic passive receivers,” IEEE Trans. Aerosp. Elect. Sys., vol. 41, no. 2, pp. 746–751, Apr. 2005. [21] J. Vankka, “Digital frequency synthesizer/modulator for continuousphase modulation with slow frequency hopping,” IEEE Trans. Veh. Technol., vol. 46, no. 4, pp. 933–940, Nov. 1997. [22] M. Burgos-Garcia and J. Sanmartin-Jara, “A LPI tracking radar system based on frequency hopping,” in Proc. Int. Radar Symp., Munich, Germany, Sep. 1998, pp. 151–159. [23] G. Liu, H. Gu, W. Su, H. Sun, and J. Zhang, “Random signal radar – A winner in both the military and civilian operating environments,” IEEE Trans. Aerosp. Elect. Systems., vol. 39, no. 2, pp. 489–498, Apr. 2003.

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[24] Y. Shirman, S. Leshchenko, and V. M. Orlenko, “Advantages and problems of wideband radar,” in Proc. Int. Radar Conf., 2003, pp. 15–21. [25] E. J. Baghdady, “Directional signal modulation by means of switched spaced antennas,” IEEE Trans. Commun., vol. 38, no. 4, pp. 399–403, Apr. 1990. [26] W. D. Wirth, “Omni-directional low probability of intercept radar,” in Proc. Int. Conf. on Radar, Paris, 1989, pp. 25–30. [27] W. D. Wirth, “Long term coherent integration for a floodlight radar,” in Proc. IEEE Int. Radar Conf., May 1995, pp. 698–703. [28] W. D. Wirth, Radar Techniques Using Array Antennas. London, U.K.: IET, 2001. [29] G. Binias, “Target track extraction procedure for OLPI antenna data on the basis of Hough transforms,” IEE Proc. Radar Sonar Navig., vol. 149, pp. 29–32, Feb. 2002. [30] G. Brown, C. Kerce, and M. Mitchell, “Extreme beam broadening using phase only pattern synthesis,” in IEEE Sensor Array and Multichannel Sig. Processing Workshop Proc., 2006, pp. 36–39. [31] R. Kinsey, “Phased array beam spoiling technique,” in IEEE Antennas Propag. Society AP-S Int. Symp., 1997, vol. 2, pp. 698–701. [32] E. Bayliss, “Phase synthesis technique with application to array beam broadening,” in IEEE Antennas Propag. Digest, 1966, pp. 427–432. [33] S. Srinivasa and S. Jafar, “The optimality of transmit beamforming: A unified view,” IEEE Trans. Inf. Theory, vol. 53, no. 4, pp. 1558–1564, Apr. 2007.

Daniel E. Lawrence (S’98–M’02) received the B.E.E. and M.S. degrees in electrical engineering from Auburn University, Auburn, AL, in 1996 and 1998, respectively, and the Ph.D. degree in electrical engineering from the University of Michigan, Ann Arbor, in 2002. In 2002, he joined the Phase IV Systems Operation of Technology Service Corporation, Huntsville, AL and serves as a Subject Matter Expert in the area of radar and communication systems for a wide range of defense programs. He also serves as a part-time instructor with the Department of Electrical Engineering, University of Alabama in Huntsville, teaching both undergraduate and graduate courses in radar, antennas, and signal processing. His current research interests include low-probability of intercept radar techniques, high fidelity interferometric antenna design, electromagnetic scattering, and forward error correction techniques for robust missile communication links.

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Analysis of a Wavelength-Scaled Array (WSA) Architecture Rick W. Kindt, Member, IEEE, and Marinos N. Vouvakis, Member, IEEE

Abstract—Wavelength-scaled array architectures use scaled elements to achieve ultrawideband performance with significantly fewer overall radiators than traditional ultrawideband arrays based on a single element type. Compared to a conventional ultrawideband array with 8:1 bandwidth, a wavelength-scaled array that uses elements of three different sizes creates an aperture with fewer than 16% of the original element count, i.e., 6.4-times fewer elements, and by extension a comparable reduction in electronics required to feed the array. In this paper, a study of an asymmetric wavelength-scaled array architecture is presented for finite arrays of offset-centered dual-polarized flared-notch radiators. The unique element transitions within the finite array structure are modeled via a non-matching grid Domain Decomposition-Finite Element Method that allows for rigorous impedance and radiation pattern prediction of full-sized wavelength-scaled arrays. This design study shows that the wavelength-scaled array has comparable performance to traditional ultrawideband arrays in terms of VSWR, radiation patterns, array mismatch efficiency, and cross-polarization levels. Index Terms—Antenna arrays, domain decomposition, phased arrays, ultrawideband arrays, wavelength-scaled arrays.

I. INTRODUCTION

M

ULTI-FUNCTIONAL antenna arrays promise a larger number of applications with better performance at lower overall cost, weight, and installation space. A central component in these systems is the ultrawideband (UWB) phased antenna array. Traditional UWB arrays are very costly to build due to the high element density required for scanning across a wide range of frequencies. In order to make multi-functional apertures a viable option, there is significant interest in finding ways to reduce the cost of UWB array designs. UWB arrays are commonly based on flared-notch (Vivaldi) elements [1]–[4]. The flared-notch is popular because it is relatively easy to manufacture and provides wide bandwidth. Flared-notch arrays have been proposed for a wide range of systems and applications including communications, RADAR, electronic warfare, imaging, radio-astronomy, and multi-functional apertures [5]–[9]. In recent years, UWB array research has focused on developing large low-cost arrays Manuscript received August 26, 2009; revised February 17, 2010; accepted February 24, 2010. Date of publication June 14, 2010; date of current version September 03, 2010. This work was sponsored by the U.S. Office of Naval Research in 2007. R. W. Kindt is with the U. S. Naval Research Laboratory, Washington, DC 20375 USA (e-mail: [email protected]). M. N. Vouvakis is with the Center for Advanced Sensor and Communication Antennas, University of Massachusetts Amherst, MA 01003 USA (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TAP.2010.2052566

[10]. Significant effort has been directed towards lower cost elements, manufacturing technologies, and assembling techniques [11]–[15]. In part, UWB research has been directed towards lower-profile designs with better cross-polarization performance than flared-notches [16], [17]. This paper focuses on a design approach that cuts cost by reducing the overall element count in the UWB array. In previous work, the US Naval Research Laboratory (NRL) proposed a UWB array concept featuring a core of traditional wideband flared-notch elements surrounded by concentric rings of increasingly-larger elements that achieved relatively-constant electrical aperture size by selectively exciting portions of the array at different frequencies [18]. The initial concept was not practical for implementation due to the high number of different-size radiators and mutual coupling/structural integrity issues associated with element misalignment. In 2006, NRL initiated a follow-up study on a symmetric wavelength-scaled array (WSA) architecture comprised of different-sized single-polarized flared-notch radiators that lined up every-other row for electrical continuity between element regions [19]. Like thinned narrowband and sparse fractal arrays, WSA architectures lead to lower element counts [20], [21]. However, fractal arrays typically use identical elements in a fractal arrangement that is self-similar, whereas in the WSA, the elements are not identical, they are not scaled in a self-similar fashion, and the lattice does not follow a fractal arrangement. Further, fractal arrays typically include randomized effects or tapers designed to alleviate undesirable grading lobes, whereas in the WSA, the partial illumination strategy precludes the onset of grading lobes altogether. The preliminary study [19] of small infinite-by-finite array sections with scaling and scanning in the E-plane only was instructive, but left many questions about WSA design and operation unanswered. This current work summarizes a detailed study of a new asymmetric WSA architecture for full-sized finite arrays of dual-polarized radiators with vertical and horizontal wavelength-scaling. The WSA is designed to operate coherently in three overlapping frequency bands to create an 8:1 bandwidth array. Elements of three different sizes fill the aperture with 16% of the original element count—i.e., 6.4-times fewer elements than a traditional periodic array of equivalent aperture size—with a comparable reduction in electronics required to feed the array. This study examines important aspects of the array operation, including edge and corner truncation effects for scanning in the E-, H-, and D-planes. It is shown that VSWR and radiation characteristics of the WSA compare favorably with their traditional UWB counterparts, demonstrating symmetric patterns and sidelobe structures, excellent array mismatch efficiency and comparable cross-polarization levels.

0018-926X/$26.00 © 2010 IEEE

KINDT AND VOUVAKIS: ANALYSIS OF A WSA ARCHITECTURE

This new array architecture poses a unique set of challenges in both analysis and design. The interfaces between dissimilar WSA sub-arrays give rise to discontinuity effects not present in traditional arrays. Moreover, the co-existence of different periodicities and partial aperture illumination requires careful design to avoid onset of grating lobes or scan blindness [22]. Due to the non-periodic nature of the array architecture, the infinite Floquet cell approximation [23], [24] cannot be used for analysis. Rather, a rigorous full-wave analysis of the entire finite array must be performed. There are many full-wave numerical methods tailored to the analysis of finite array structures, some noteworthy examples given here [25]–[29]. For the analysis done in this paper, NRL developed a non-conforming Domain Decomposition-Finite Element Method (DD-FEM) based on a combination of techniques proposed in [30] and [25]. This fast and rigorous full-wave analysis of the WSA structure exploits array repetitions, storing in memory only unique geometry features. The method allows non-matching grids between element domains, meaning each element type can be meshed independently, greatly simplifying the synthesis/analysis of the WSA. The remainder of this paper is organized as follows. Section II-A presents an overview of the proposed asymmetric/ non-concentric offset-centered dual-polarized flared-notch WSA architecture and details element counts compared with alternative architectures. Section II-B introduces the design of the WSA and the UWB elements. In Section III, performance of the WSA architecture is evaluated in terms of VSWR, array mismatch efficiency, radiation patterns and cross-polarization levels for broadside and scanning in the E-, H- and D-planes. Sections IV and V conclude the paper with a brief discussion about options and advantages associated with WSA architectures, addressing future directions for this research.

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2

Fig. 1. UWB Option 1—single 32 32 array of 8:1 bandwidth, 1024 elements/ polarization, 6–48 GHz operation, 12-degree beam at 12 GHz.

2

Fig. 2. Option 2—three separate 8 8 arrays (192 elements/polarization total); (a) 3 mm elements, 12-degree beam at 48 GHz, (b) 6 mm elements, 12-degree beam at 24 GHz, (c) 12 mm elements, 12-degree beam at 12 GHz.

II. THEORY A. Overview of the WSA Architecture For illustrative purposes, this section begins by presenting a traditional UWB phased array with a 12-degree beamwidth requirement and coverage from 6–48 GHz (8:1 bandwidth). For operation at the high end of the frequency band (48 GHz), the array element must be roughly 3 mm in width for typical halflattice spacing requirements. For a 12-degree wavelength is rebeamwidth at this frequency, an aperture of roughly quired, or equivalently, an 8 8 array of 3 mm elements. Two octaves lower in frequency (12 GHz), an aperture of roughly is again required for a 12-degree beamwidth. Using 3 mm-wide elements, this equates to a 32 32 array with a total of 1,024 elements in each polarization. This summarizes the traditional UWB array, illustrated in Fig. 1 as Option 1. Alternatively, a relatively-constant 12-degree beamwidth can be achieved across the same frequency range using three 8 arrays of increasing size. Option 2—illustrated in 8 8 array of 3-mm wide elements Fig. 2—consists of an 8 8 array of 6-mm (12-degree beamwidth at 48 GHz), an 8 wide elements (12-degree beamwidth at 24 GHz), and an 8 8 array of 12-mm wide elements (12-degree beamwidth at 12

Fig. 3. Option 3—equivalent WSA architecture (160 elements/polarization, full 6–48 GHz operation), 6.4 times fewer elements than Option 1, 12-degree beam at 12 GHz, 24 GHz, and 48 GHz.

GHz). Option 2 has 192 elements in each polarization—more than 5 times fewer overall elements than Option 1. However, this option consists of three separate apertures operating independently over distinct bands (not a single multi-functional aperture), and because it requires additional installation space, may not be suitable for space-restricted applications. Option 3, depicted in Fig. 3, is the WSA architecture explored in this work. The WSA architecture achieves a more cost-effective solution than Option 1, assuming there are more elements

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TABLE I DIMENSIONS OF THE THREE UWB ELEMENTS OF THE WSA (IN MILIMETERS)

than necessary to satisfy the 12-degree beamwidth requirement at the high end of the frequency spectrum. Essentially, the three apertures of Option 2 have been integrated into a single aperture with even fewer overall elements—only 160 elements in each polarization. Option 3 has 20% fewer elements than Option 2 and 85% (6.4-times) fewer elements than Option 1. Elements of three different sizes (in this case—3 mm, 6 mm, 12 mm) function together coherently to create a continuous aperture with 8:1 bandwidth. It is important to understand that the apertures do not function independently. Rather, from 6–12 GHz, all the elements of the array are active, creating a single, coherently-radiating square aperture. From 12–24 GHz, only the 6 mm and 3 mm elements are active. From 24–48 GHz, only the 3 mm elements are active. Effectively, these three frequency bands have apertures of the same electrical size. The design and operation of this asymmetric/non-concentric array is considered below. B. WSA Design Details and Considerations In order for this architecture to work, several constraints need to be met. An element that can achieve 8:1 bandwidth is required—in this example the 3-mm wide element, operating from 6–48 GHz. The remaining 6 mm and 12 mm elements must be able to achieve 4:1 bandwidth and 2:1 bandwidth, respectively, overlapping the same low-end frequencies of the 3 mm element. The WSA architecture is based on UWB elements and cannot be pieced together with narrowband elements. To achieve uniform radiation patterns, the element excitations must be scaled based on their cell size to create uniform power density across the aperture. Further, mutual coupling is an important consideration. The configuration considered here follows a 2-to-1 scaling profile in which every-other row/column lines up exactly at the interface between element regions for proper coupling. Element reduction estimates are independent of array size, beamwidth and bandwidth, but assume three levels of element scaling, following a 2-to-1 scaling profile at each level. Using four levels of 2-to-1 element scaling would lead to greater savings in the number of elements, but requires a 16:1 bandwidth element. Other scaling options have been considered, such as a 3-to-1 scaling with every third row of elements aligned. Scaling can be chosen to meet aperture/bandwidth requirements, and may also depend on the type of array element and lattice arrangement. In this paper, the elements are scaled such that they are the same length and share a common ground plane, resulting in the low end frequency limit being similar for all elements. Alternatively, the elements could be scaled such that the larger

(outer) elements extend to a lower frequency for partial bandwidth overlap, increasing the overall design bandwidth. In this WSA implementation, the high-frequency elements are located in the lower right corner of the array (see Fig. 3), rather than symmetrically in the center. This asymmetric/nonconcentric design choice is made for two primary reasons. First, the elements are constructed in pairs, and placing the smaller elements in the center region does not allow for proper element pairing, leading to geometric interference. From Fig. 2 it can be seen how (if connected) smaller elements on the left would interfere with the radiating regions of the larger elements to the right. Secondly, compared to a concentric design, this layout has fewer transition regions, thereby reducing performance degradation due to mismatch at the element interfaces. Though asymmetric, it will be shown that this design has symmetric radiation patterns and cross-polarization levels comparable with conventional UWB designs. The WSA is built from three dual-polarized solid-metal flared-notch elements with dimensions given in Table I. The dual-polarized elements are constructed in horizontal/vertical pairs, and are backed by a common ground plane. All three elements are 17.8 mm long in the broadside radiation direction with 15.4 mm tapers, such that they provide roughly the same radiation path length. To facilitate proper geometric integration, the elements share common (0.76-mm diameter) post. This design choice allows the thickness of the individual element types to be manipulated for adjusting the impedance match. Additionally, the slot-line cavity dimensions and slot tapers have been adjusted for matching. Since the WSA architecture is being evaluated at the aperture level only, it is sufficient for the analysis to feed the elements with 50-Ohm lumped-element ports at the base of the slot-line cavity. Fig. 4 shows VSWR performance for each of the elements, computed using an NRL in-house Floquet cell analysis code. Though not shown here, these results have been validated against commercial software (Ansoft HFSS). The 3-mm wide flared-notch UWB element operates from roughly 6–48 GHz, while the 6-mm wide and 12-mm wide elements operate from 6–24 GHz, and 6–12 GHz respectively. The plots show broadside performance for each of the elements, plus scan performance at 45-degrees in three scan planes—E-plane (horizontal), D-plane (45-degree), and H-plane (vertical). While the 3 mm element has 8:1 bandwidth, the design process of scaling the element to 6 mm and 12 mm results in bandwidths of 4:1 and 2:1 respectively. The elements have the same low-end frequency limit, but the larger lattice spacing of the 6 mm and

KINDT AND VOUVAKIS: ANALYSIS OF A WSA ARCHITECTURE

Fig. 4. Simulated VSWR performance of the three elements (infinite cell), broadside, E-plane scan, D-plane scan, H-plane scan (to 45 degrees).

12 mm elements creates impedance anomalies and grating lobes that restrict high-end bandwidth. In the past, scan and impedance anomalies have been identified and studied in arrays of flared-notches [22], [32]. For the dual-polarized arrays studied here, intersecting horizontal and vertical elements create square waveguides that are terminated by the metal back of the array. At certain frequencies above cutoff, the fields excited in these structures become destructively out of phase with the radiating fields of the elements, causing scan anomalies. Though these anomalies typically occur above the upper operational frequency of the elements, in the WSA they are cause for concern. The impedance anomalies of the wider elements [see VSWR spikes in Fig. 4(b) and (c)] occur within the frequency range of the 3 mm element, and must be verified not to adversely affect the WSA operation. At broadside, all elements operate with VSWR below 2 within their specified frequency range, down to approximately 6 GHz. It is clear that scanning in the H-plane causes the worst degradation in VSWR. However, Fig. 4 shows that for most of the operational frequency range, scanning can be achieved out to 45 degrees with VSWR mostly below 3, with some loss of bandwidth at the low and high end. In the following sections the performance of the integrated WSA will be compared to these ideal performance metrics. III. RESULTS A. VSWR Performance The WSA analyzed here follows the layout of Fig. 3. It is constructed from a 32 32 core of 3 mm elements, three 16 16 cores of 6 mm elements, and three 16 16 cores of 12 mm elements. This array size is a good compromise that allows proper evaluation of the WSA nuances, without the data overload of larger array configurations or the dominance of truncation effects of smaller configurations. For the numerical analysis, the array is truncated in artificial absorber as a simple treatment to

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Fig. 5. VSWR sweep versus frequency for broadside operation of the WSA. The solid line corresponds to the infinite result from Fig. 4 and the dots represent individual element data. The average (dashed line) and standard deviation (dotted line) are also provided for statistical analysis.

improve matching at the array edge and allow behavior in the element transition regions to stand out more. First, the VSWR performance of the array at broadside (horizontal-polarization) radiation is evaluated. Fig. 5 shows the sweep of VSWR versus frequency. In the plots, the solid curve is the VSWR for the infinite cell (Fig. 4). This line is printed over a set of dots representing the VSWR measured at each horizontal element of the array across the frequency band. For statistical analysis, the dashed line gives the average VSWR across the aperture, while the standard deviation is plotted as a dotted line. These results show that the elements in the WSA are closely related to the ideal element, with very confined deviation (plus and minus) from the norm, slightly more variation at the low end. On average, the VSWR swings nearly equally higher and lower than the infinite case. Though not included here for brevity, results in traditional finite-sized UWB arrays (as in Fig. 1) show the same VSWR behavior. Fig. 5 shows that VSWR remains mostly below 2 at broadside, with some cresting above 2 at 13 GHz for the 3 mm and 6 mm elements. All element types have lost some low-end bandwidth, but the deviation is well below 0.5 across the band. It is important to point out that there is no evidence of the out-of-band impedance anomalies of the 6 mm elements affecting the operation of the 3 mm elements (Fig. 4(b), near 33 GHz), or the anomalies of the 12 mm element (Fig. 4(c), near 17 GHz) affecting the 6 mm elements. While the long channels between rows of elements in [19] made the WSA prone to impedance anomalies, the dual-polarized array lattice appears less affected. While the curves of Fig. 5 give a good sense of the array performance as a whole across the frequency band, from the data spectrum it is not possible to glean the spatial effects of the wavelength-scaling on the VSWR. Plots of the VSWR distribution for the WSA at 8 GHz and 12 GHz are given in Fig. 6. Each colored tile in the plot represents the active VSWR of the element at that spatial location. In finite arrays of flared-notches,

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Fig. 6. Spatial VSWR distribution on WSA at key frequencies for broadside radiation, horizontal polarization; each tile represents VSWR on horizontal element at that location (VSWR key beside plot).

outer edge truncation causes a ripple in the VSWR across the aperture that varies with frequency, array size, and truncation condition (cavity enclosure, open air, parasitic elements, material treatment, etc.), and differs for E-plane and H-plane truncation. While VSWR at the outer edge is typically worse than at the array center, the peaks and valleys of the ripple periodically result in VSWR at the array edges that could be lower than at the array center. A similar ripple effect occurs from the discontinuity between element regions of the WSA, as seen in Fig. 6. Within the WSA, every other row/column of smaller elements at an interface is discontinuous. For example, in Fig. 3, starting with rows of 6 mm elements and tracing left to where they meet the 12 mm elements, the rows either continue electrically into the 12 mm elements or come to an abrupt stop, similar to the outer edge of an array. Conversely, tracing rows of larger elements in the opposite direction to where they meet the smaller elements, every row continues electrically. Consequently, the smaller of the two elements at a given interface sees the greatest perturbation in VSWR, with the effect in the larger elements less severe. At vertical column (E-plane) interfaces, the VSWR in smaller elements often spikes higher than the VSWR at the array center, whereas at horizontal row (H-plane) interfaces, the VSWR in smaller elements tends to drop lower. At E-plane interfaces the smaller of the two elements tends to have relatively higher VSWR, whereas for H-plane interfaces, the smaller of the two elements tends to have relatively lower VSWR. In cases where the VSWR is lower for elements right at the interface, it is usually the case that the ripple creates a VSWR maximum some number of elements away. This phenomenon appears to be a consequence of the unique WSA geometry, and though these observations apply in this case, it may not be true for all architectures. Next, the scanning VSWR performance of the WSA is examined. From the results in Fig. 4, it is clear that the elements have the worst VSWR for scanning in the H-plane, better performance in the E-plane, and the D-plane scan performance falls in the middle of these two cases. Though the D-plane scan data were collected and analyzed, for brevity they are not presented. Because of the geometrical asymmetry introduced by the wavelength-scaling and the layout of the element pairs, there is the potential for asymmetric scan performance to consider. Therefore, plots of both the positive 45-degree scan results and the negative 45-degree scan are given.

Fig. 7. VSWR sweep versus frequency for 45-degree E-plane scan; individual dots represent spread of finite array data.

Fig. 8. Spatial VSWR distribution for 45-degree E-plane scans at 10 GHz; each tile represents VSWR on horizontal element at that location (VSWR key beside plot).

The case of E-plane scanning is considered in Fig. 7, where the VSWR versus frequency is plotted at a 45-degree scan. The response from the WSA array follows the same general trend as the ideal infinite element, with the VSWR swinging above and below the ideal case. There are two main items to point out here. First, under scan, the VSWR remains largely below 3 across the frequency band. Secondly, there appears to be groups of elements that stray from the rest, most notable at certain frequencies. For example, at 10 GHz, for each element type there is a group of elements with VSWR that is somewhat worse than the rest, most clearly visible in the group of 6 mm elements scanned to positive 45 degrees. From Fig. 8 it is clear that, for this scan direction, these elements are typically the ones along the left edge of the cores, where the smaller elements transition into regions of larger elements. Though clearly worse than central regions of the array, the VSWR at the interfaces remains within reasonable levels. Fig. 9 shows the VSWR for a 45-degree H-plane scan versus frequency. As before, the VSWR of the WSA largely follows the curves of the ideal infinite cell, with VSWR levels clearly higher for H-plane scanning. For the 3 mm elements, the VSWR is as high as 4 at some frequencies, with deviation roughly twice that

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Fig. 9. VSWR sweep versus frequency for 45-degree E-plane scan; individual dots represent spread of finite array data.

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Fig. 11. Array mismatch efficiency (versus frequency) of the WSA and two other array configurations for: (a) broadside scan, (b) E-plane scan to 45 degrees, (c) H-plane scan to 45 degrees.

B. Array Mismatch Efficiency

Fig. 10. Spatial VSWR distributions for 45-degree H-plane scans at 8 GHz; each tile represents VSWR on horizontal element at that location (VSWR key beside plot).

of the E-plane scan. For the 6 mm and 12 mm elements, while the majority of the elements follow the ideal curves on average, certain groups of elements have markedly worse behavior than the rest. To isolate these anomalies, Fig. 10 shows the VSWR distribution for the array scanned to 45-degrees in the H-plane at 8 GHz. For the H-plane scans, most of the array has similar VSWR behavior as the infinite array case, but effects at the transition regions are more pronounced. Fig. 10 shows that when the VSWR in elements is worse than average on one side of the element transition region, this is balanced out by the VSWR in elements on the other side of the interface being better. It is important to point out that while the peak/deviation in VSWR (dotted line) for H-plane scanning tends to be higher at the low frequencies, on average (dashed line), the elements perform better than the ideal case (solid line). This becomes important for the efficiency numbers considered in the next section. As a note, the difference in VSWR distribution for positive and negative scans can be partially attributed to the asymmetric arrangement of the elements pairs.

While the previous section examined phenomena in the WSA at the element level, it is also important at the system level to look at array mismatch efficiency—a statistical measure of the average mismatch seen at the antenna ports. Array mismatch ef, where is ficiency is computed as the active reflection coefficient at array port of an -element array. This gives a single-valued figure-of-merit to gauge how well an array performs, on average, compared to the ideal (infinite) case. Fig. 11 compares the efficiency of the WSA array to an equivalent size (finite) UWB array of 3 mm elements, and also the 3 mm element infinite (ideal) case. For broadside scan, Fig. 11(a) shows that the 3 mm finite array performs very close to ideal across the frequency band, and that the WSA—though it shows a slightly different efficiency versus frequency—is always within a few percent of ideal. The E-plane scan results of Fig. 11(b) indicate that WSA efficiency is as much as 4% worse than the 3 mm UWB at some frequencies, but also better at others. In the H-plane [Fig. 11(c)], though the overall numbers are lower, both the finite 3 mm UWB array and the WSA show better efficiency at low frequencies—on average—than the infinite cell. Fig. 11(c) shows that the WSA will function at better than 85% average efficiency for almost the entire 6–48 GHz at 45-degree H-plane scans. Because the D-plane efficiency falls somewhere between the E-plane and H-plane results, for brevity it is not included here. It should be pointed out that the jumps in efficiency for the WSA at 12 GHz and 24 GHz are a consequence of 12 mm elements turning off above 12 GHz and 6 mm elements turning off above 24 GHz. C. Radiation Characteristics of the WSA This section begins with broadside far-field radiation patterns (E-plane cut) at 12 GHz for the WSA compared to like-sized arrays of 3 mm, 6 mm, and 12 mm elements, as shown in Fig. 12.

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Fig. 12. Far-field radiation patterns (E-plane cut) at 12 GHz; comparisons for the WSA and equivalent-sized arrays of single elements.

Fig. 13. Comparison of the WSA far-field radiation patterns at 12 GHz, 24 GHz, and 48 GHz to demonstrate relatively-constant beamwidth versus frequency.

All patterns have nearly identical beamwidth and sidelobe structure, and similar cross-polarization levels. The upper left of the figure includes a zoomed-in view of the main lobe and first sidelobes, revealing a slight shift in the beam and imbalance in the sidelobe levels for the WSA. However, the difference is very minor, and though not attempted here, is easily corrected using amplitude/phase weighting. The WSA is intended to function with relatively constant beamwidth. Fig. 13 shows the beam structure of the WSA at three key frequencies across the 6–48 GHz range. At 12 GHz all the elements are active. At 24 GHz the 12 mm elements are not active, and at 48 GHz only the 3 mm elements are active. Fig. 13 shows that the beamwidth at these key frequencies is the same, and the lobe characteristics are quite similar as well. Further from the main beam, the lobe structure shows some differences in radiation level, but for the most part, the patterns are remarkably similar. At 48 GHz the first sidelobes are symmetric at 13.35 dB down. At 24 GHz, the right sidelobe is approximately 0.7 dB higher than the left, and at 12 GHz the right sidelobe is about 1.2 dB higher than the left. The cross-polarization levels, typical for the underlying element types, are considered in the next section. Fig. 14 shows the corresponding results for scans to 45 degrees in the E-plane. Again, the results are very reasonable, showing that symmetric beam structure can be achieved while scanning. Though not included here, other frequencies/scan angles also indicate very similar results. In summary, it is important to note that the asymmetric WSA design does not appear to have a negative effect on the beam structure, though some minor compensation for element differences may be required. D. Cross-Polarization (XPOL) Performance This section presents the XPOL data for the WSA. For this paper, XPOL is defined as the vertically-polarized field levels

Fig. 14. Far-field radiation patterns of the WSA at a 45-degree scan in the E-plane. Patterns show very similar beam structure even at high scan angles.

measured at a given scan angle relative to the horizontally-polarized field levels for an array of horizontally-polarized array elements. For brevity, only results for the two principle planes plus the D-plane are included, though data was collected for scanning in 15-degree increments from zero to 90 degrees. First, Table II shows the XPOL levels at three frequencies (12 GHz, 24 GHz, and 48 GHz) for a finite-sized UWB array (non-WSA) of 3 mm elements. The 3 mm element has very good polarization purity in the E- and H-planes—better than 39 dB for all scan angles and frequencies. However, in the D-plane, the XPOL degrades at high scan for higher frequencies. Scans to 45-degrees at 12 GHz, 24 GHz, and 48 GHz show XPOL levels of 11 dB, 4.5 dB, and 3 dB respectively. This table is included to show that poor XPOL at higher frequencies is a consequence of element properties and not attributable to WSA architecture. Table III gives the XPOL numbers for the WSA. At 48 GHz (where only 3 mm elements are active), the numbers are similar to Table II, including poor XPOL in the D-plane. However, at 12 GHz/24 GHz, the XPOL numbers for the WSA are slightly better, because the wider 6 mm/12 mm elements in the WSA have better XPOL, bringing down the total numbers. As pointed out earlier in this paper (and in several of the references), elements with a smaller height-to-width ratio tend to have better XPOL numbers. To highlight the dependence of XPOL on the element width, Table IV shows the XPOL numbers for arrays of 3 mm, 6 mm, and 12 mm elements at 12 GHz. Polarization purity in the E-/Hplanes is similar for all element types, but it is clear that the 6 mm/12 mm elements have better XPOL levels in the D-plane. At a 45-degree scan, the 12 mm elements have around 4 dB better XPOL. To summarize, this section shows that the WSA has slightly better XPOL characteristics than an equivalent traditional finite-sized UWB array (of 3 mm elements). However, because elongated UWB elements in general have poor XPOL for scans in the D-plane (for example, as pointed out in [11], [16]), future WSA work will likely involve lower-profile element designs that are known to have better XPOL numbers. IV. DISCUSSION The WSA architecture achieves a 6.4 times reduction in element count. However, combining active and passive electronics behind the elements could lead to additional savings. For example, at the lower frequencies, the 3 mm-element core of the WSA is oversampled. For receive applications from 6–12 GHz it is only necessary to collect signals from every fourth row, or equivalently, a single element in every 4 4 sub-array

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TABLE II CROSS-POLARIZATION LEVELS (IN dB) FOR A 32

2 32 ARRAY OF 3 mm ELEMENTS

TABLE III CROSS-POLARIZATION LEVELS (IN dB) FOR THE WSA

TABLE IV CROSS-POLARIZATION LEVELS (IN dB) AT 12 GHz FOR 32 32 ARRAYS OF 6 mm AND 12 mm ELEMENTS

2

of elements to meet sampling requirements (at the expense of some gain). Similarly, sampling requirements can be satisfied by collecting signals from every-other row of 6 mm elements, or equivalently, one element in every 2 2 sub-array. However, for transmit applications this reduced sampling will not work. The passive elements in the radiating environment of the active elements re-radiate energy out of phase with the original signal, causing significant performance degradation. Alternatively, at the lower frequencies it is also possible to passively combine the 4 4 sub-arrays of 3 mm elements and 2 2 sub-arrays of 6 mm elements into a single port. Though it could lead to worse noise figure, this option also works for transmit applications and could reduce the amount of electronics significantly. V. CONCLUSION This paper presents and demonstrates the viability of a new array architecture that significantly lowers implementation

costs of UWB arrays by lowering overall element count, thus making a significant step towards realizing low-cost multi-functional apertures. The purpose of this paper was to examine the performance of a finite asymmetric/non-concentric WSA design for offset-centered dual-polarized radiators. The conclusions reached from this study indicate that the examined WSA architecture is competitive with traditional UWB arrays, at the cost of some minor performance degradation, but with significantly reduced element counts. In the next phase of this research, a prototype array based on flared-notch radiators will be designed and built. Based on past experience working with flared-notch radiators and given the results of these studies, it is believed that a WSA consisting of scaled notch elements has a good chance of performing as indicated in these studies. However, the poor cross-polarization levels of these flared notches in D-plane scans suggests that ultimately, a lower-profile element with better cross-polarization performance may

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be needed. Currently, alternatives to the flared-notch element with better polarization purity and less sensitivity to electrical discontinuity between disjoint regions are being pursued [11]. REFERENCES [1] P. J. Gibson, “The vivaldi aerial,” in Proc. 9th Eur. Microwave Conf., 1979, pp. 101–105. [2] L. Lewis, J. Pozgay, and A. Hessel, “Design and analysis of broadband notch antennas and arrays,” in Proc. IEEE Antennas Propagation Symp., 1976, vol. 14, pp. 44–47. [3] D. H. Schaubert, S. Kasturi, A. O. Boryssenko, and W. M. Elsallal, “Vivaldi antenna arrays for wide bandwidth and electronic scanning,” in Proc. 2nd Eur. Conf. on Antennas and Propagation, EuCAP, 2007, pp. 1–6. [4] M. Kragalott, W. R. Pickles, and M. S. Kluskens, “Design of a 5:1 bandwidth stripline notch array from FDTD analysis,” IEEE Trans. Antennas Propag., vol. 48, no. 11, pp. 1733–1741, Nov. 2000. [5] S. Balling, M. Hein, M. Hennhofer, G. Sommerkorn, R. Stephan, and R. Thoma, “Broadband dual polarized antenna arrays for mobile communication applications,” in Proc. 33rd Eur. Microwave Conf., Oct. 7–9, 2003, vol. 3, pp. 927–930. [6] K. Trott, B. Cummings, R. Cavener, M. Deluca, J. Biondi, and T. Sikina, “Wideband phased array radiator,” in Proc. IEEE Int. Symp. on Phased Array Systems and Technology, 2003, pp. 383–386. [7] Y. Yang, C. Zhang, and A. E. Fathy, “Development and implementation of ultra-wideband see-through-wall imaging system based on sampling oscilloscope,” IEEE Antennas Wireless Propag. Lett., vol. 7, pp. 465–468, 2008. [8] D. H. Schaubert, A. O. Boryssenko, A. van Ardenne, J. G. Bij de Vaate, and C. Craeye, “The square kilometer array (SKA) antenna,” in Proc. IEEE Int. Symp. on Phased Array Systems and Technology, Oct. 14–17, 2003, pp. 351–358. [9] C. Hemmi, R. T. Dover, F. German, and A. Vespa, “Multifunction wide-band array design,” IEEE Trans. Antennas Propag., vol. 47, no. 3, pp. 425–431, Mar. 1999. [10] R. Maaskant, M. Popova, and R. van den Brink, “Towards the design of a low-cost wideband demonstrator tile for the SKA,” in Proc. 1st Eur. Conf. on Antennas and Propagation, EuCAP, Nov. 6–10, 2006, pp. 1–4. [11] M. W. Elsallal and D. H. Schaubert, “Reduced-height array of BAVA with greater than octave bandwidth,” in Proc. Antenna Applications Symp., Sep. 21–23, 2005, pp. 226–242. [12] W. Croswell, T. Durham, M. Jones, D. H. Schaubert, P. Frederich, and J. G. Maloney, “Wideband array,” in Modern Antenna Handbook, C.A. Balanis, Ed. : Wiley, 2008. [13] H. Holter, “Dual-polarized broadband array antenna with BOR-elements, mechanical design and measurements,” IEEE Trans. Antennas Propag., vol. 55, no. 2, pp. 305–312, Feb. 2007. [14] S. Nikolaou, G. E. Ponchak, J. Papapolymerou, and M. M. Tentzeris, “Conformal double exponentially tapered slot antenna (DETSA) on LCP for UWB applications,” IEEE Trans. Antennas Propag., vol. 54, no. 6, pp. 1663–1669, Jun. 2006. [15] M. Jones and J. Rawnick, “A new approach to broadband array design using tightly coupled elements,” in Proc. IEEE Military Communications Conf., Oct. 29–31, 2007, pp. 1–7. [16] J. J. Lee, S. Livingston, and R. Koenig, “A low-profile wideband (5:1) dual-pol array,” IEEE Antennas Wireless Propag. Lett., vol. 2, no. 1, pp. 46–49, 2003. [17] A. Neto, D. Cavallo, G. Gerini, and G. Toso, “Scanning performances of wideband connected arrays in the presence of a backing reflector,” IEEE Trans. Antennas Propag., vol. 57, no. 10, pp. 3092–3102, Oct. 2009. [18] B. Cantrell, J. Rao, G. Tavik, M. Dorsey, and V. Krichevsky, “Wideband array antenna concept,” IEEE Aerosp. Electron. Syst. Mag., vol. 21, no. 1, pp. 9–12, 2006. [19] R. Kindt, M. Kragalott, M. Parent, and G. Tavik, “Preliminary investigations of a low-cost ultra-wideband array concept,” IEEE Trans. Antennas Propag., vol. 57, no. 12, pp. 3791–3799, Dec. 2009. [20] R. Mailloux, Phased Array Antenna Handbook, 2nd ed. Boston, MA: Artech House, 2005. [21] J. B. Bregman, G. H. Tan, W. Cazemier, and C. Craeye, “A wideband sparse fractal array antenna for low frequency radio astronomy,” in Proc. IEEE Antennas Propagation Symp., 2000, vol. 1, pp. 166–169.

[22] G. J. Wunsch and D. H. Schaubert, “Full and partial crosswalls between unit cells of endfire slotline arrays,” IEEE Trans. Antennas Propag., vol. 48, no. 6, pp. 981–986, Jun. 2000. [23] T. F. Eibert, J. L. Volakis, D. Wilton, and D. Jackson, “Hybrid FE/BI modeling of 3D doubly periodic structures using triangular prismatic elements and a MFIE accelerated by the Ewald transformation,” IEEE Trans. Antennas Propag., vol. 47, no. 5, pp. 843–850, May 1999. [24] E. W. Lucas and T. P. Fontana, “A 3-D hybrid finite element/boundary element method for the unified radiation and scattering analysis of general infinite periodic arrays,” IEEE Trans. Antennas Propag., vol. 43, no. 2, pp. 145–153, Feb. 1995. [25] S. C. Lee, M. Vouvakis, and J.-F. Lee, “A non-overlapping domain decomposition method with non-matching grids for modeling large finite antenna arrays,” J. Computat. Phys., vol. 203, no. 1, pp. 1–21, Feb. 2005. [26] R. W. Kindt and J. L. Volakis, “Array decomposition-fast multipole method for finite array analysis,” Radio Scie., vol. 39, no. 2, Apr. 16, 2004. [27] R. Maaskant, R. Mittra, and A. Tijhuis, “Fast analysis of large antenna arrays using the characteristic basis function method and the adaptive cross approximation algorithm,” IEEE Trans. Antennas Propag., vol. 56, no. 11, pp. 3440–3451, Nov. 2008. [28] P. Pirinoli, L. Matekovits, F. Vipiana, G. Vecchi, and M. Orefice, “Multi-grid SFX-MR approach for the analysis of large arrays,” in Proc. 18th Int. Conf. on Applied Electromagnetics and Communications (ICECom), Oct. 12–14, 2005, pp. 1–4. [29] D. J. Bekers, S. J. L. van Eijndhoven, A. A. F. van de Ven, P.-P. Borsboom, and A. G. Tijhuis, “Eigencurrent analysis of resonant behavior in finite antenna arrays,” IEEE Trans. Microw. Theory Tech., vol. 54, no. 6, pp. 2821–2829, Jun. 2006. [30] R. W. Kindt, “Rigorous Analysis of Composite Finite Array Structures,” Ph.D. Dissertation, EECS Dept., Univ. Michigan, Ann Arbor, 2004. [31] S. Kasturi and D. H. Schaubert, “Effect of dielectric permittivity on infinite arrays of single-polarized Vivaldi antennas,” IEEE Trans. Antennas Propag., vol. 54, no. 2, pp. 351–358, Feb. 2006. [32] D. H. Schaubert, “A gap-induced element resonance in single-polarized arrays of notch antennas,” in Proc. IEEE Antennas Propagation Symp., Jun. 20–24, 1994, vol. 2, pp. 1264–1267. Rick W. Kindt received the B.S.E. degree in electrical engineering and the M.S.E. and Ph.D. degrees from The University of Michigan, Ann Arbor, in 1998, 2000, and 2004, respectively. He worked briefly as an Antenna Systems Engineer on airborne radar projects for Raytheon Systems Company, El Segundo, CA, before returning to the University of Michigan to complete his studies. As a graduate student, his research focused on hybrid finite element-boundary integral methods, with emphasis on domain decomposition techniques and fast methods for array-type problems. He worked as a Postdoctoral Researcher at The Ohio State University (2004–2005) where he did research on antenna design and hybrid numerical methods for array/platform analysis. Since 2005, he has been with the Electromagnetics Section, Radar Division, Naval Research Laboratory, Washington, DC. His current research interests include ultrawideband antenna array design as well as generalized computational methods for electromagnetic analysis with emphasis on domain decomposition techniques for very large structures.

Marinos N. Vouvakis (M’05) received the Diploma degree in electrical engineering from Democritus University of Thrace, Xanthi, Greece, in 1999, the M.S. degree electrical and computer engineering from Arizona State University, Tempe, in 2002, and the Ph.D. degree electrical and computer engineering from The Ohio State University, Columbus, in 2005. Since 2005, he has been an Assistant Professor with the Center for Advanced Sensor and Communication Antennas (CASCA), Electrical and Computer Engineering Department, University of Massachusetts Amherst. His research is primarily in the broader area of computational electromagnetics with emphasis on fast finite element method solvers such as domain decomposition, reduced modeling and multigrid, as well as fast integral equations and hybrid methods. Besides computational electromagnetics, his research focuses on the design of ultrawideband phased arrays.

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Design of Broadband, Single Layer Dual-Band Large Reflectarray Using Multi Open Loop Elements Mohammad Reza Chaharmir, Jafar Shaker, Nicolas Gagnon, and David Lee

Abstract—A novel method is introduced to design a single layer, dual-band large printed reflectarray with open loop elements of variable size for both bands. The reflectarray is designed for two frequency bands: 11.4–12.8 GHz for receive and 13.7–14.5 GHz for transmit. Different classes of open cross loop elements were used in the design of the receive band elements. Noting the larger relative bandwidth at the lower band as compared to the upper band, the dimensions of these cross loops are adjusted, using an optimization technique to achieve required phase distribution at the center frequency and minimize frequency dispersion at extreme frequencies of the lower band. Double square open loop elements with variable loop length were used for the transmit band elements. The reflectarray consists of 3 3 panels of 40 cm 40 cm, that are arranged side by side to construct the large 120 cm 120 cm reflectarray. The flat configuration and modular nature of this reflectarray gives it an advantage from the installation point of view as compared to conventional dish antennas. Index Terms—Cross loops, optimization, reflectarray, wideband.

I. INTRODUCTION ICROSTRIP reflectarray technology is rapidly becoming an attractive alternative to the more traditional parabolic reflector and phased array antennas due to its various advantages such as low profile, significant simplification of feed systems in the case of multi-polarization/multi-band antenna systems and low loss as discussed in [1], [2]. A printed reflectarray is a flat reflector composed of a planar array of microstrip cell elements on a grounded substrate. The cell elements are tuned to collimate or shape the radiated beam when illuminated by a feed horn as primary source. The most severe drawback of reflectarrays is their narrow-band performance and an intense effort has been made in recent years to overcome this shortcoming. The bandwidth performance of a microstrip reflectarray is limited primarily by two factors. The first is the inherent narrow bandwidth behaviour of microstrip elements themselves. The second is the differential spatial phase delay resulting from different path lengths for the rays emanating from the feed to each reflectarray element and is the most restrictive in the case of large-sized reflectarrays [3]. Several methods such as stacked patches of variable length [4], multi-resonant dipoles [5], artificial impedance surfaces [6]

M

Manuscript received September 02, 2009; revised January 28, 2010; accepted January 31, 2010. Date of publication June 14, 2010; date of current version September 03, 2010. The work was supported in part by C-Com Satellite Systems, located in Ottawa, Canada. The authors are with the Communications Research Centre Canada, Ottawa, Ontario K2H 8S2 (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TAP.2010.2052568

and multi loop reflectarrays [7]–[9] were introduced to address the first factor. A method was introduced in [10] to overcome the bandwidth limitation of large reflectarrays by using an optimization routine to adjust all the dimensions of a three-layer printed reflectarray to compensate for the frequency dispersion, but using a multilayer configuration leads to other shortcomings such as additional fabrication complexity, increased weight, and higher loss. The goal of this paper is to design a large 120 cm offset-fed reflectarray at Ku-band as a ground terminal for Direct Broadcast Satellite (DBS) applications. The conventional reflectors were satisfactorily used to fulfil all the electrical requirements for this particular application. However application of such reflectors in a portable scenario is a complicated task due to mechanical considerations. The reflectarray technology has been utilized in this design since it has a low profile as compared to a conventional reflector and is more amenable to portable terminal application by assembling multiple panels to construct the reflectarray. The antenna is designed at Ku-band with two frequency bands of 11.4–12.8 GHz for the receive band and 13.7–14.5 GHz for the transmit band. Because of the larger bandwidth requirement in the receive band, an optimization technique was introduced to minimize the frequency dispersion for this band [11], [12]. The design was etched onto 9 small substrate panels of 40 cm 40 cm each, which were finally assembled to realize the larger 120 cm 120 cm reflectarray, which is superior to its conventional reflector counterpart from portability point of view. It has to be noted that the optimization technique, presented in this paper is different from the one introduced in [10] in the type of objective function that is used and constraints that were implemented in the optimization process in order to control frequency dispersion. Different classes of multi-cross loop elements were utilized in this optimization. The selection criteria for the elements are the minimization of the phase error (difference of desired and realized phase) at the center and two extreme frequencies [12]. Several techniques have been introduced for designing multi-band reflectarrays [13], [14]. This paper presents application of open orthogonal loop elements interlaced on top of a single-layer, grounded substrate in the design of a dual-band reflectarray. II. OPTIMIZATION PROCESS The differential spatial phase delay is the main reason of bandwidth limitation of large reflectarrays [15]. Variation of the separation between the phase center of feed and each reflectarray element produces a different phase delay at each location, which is compensated with the reflected phase generated by reflectarray elements. This phase delay can be in a range of several

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Fig. 1. Schematic 1-D view of an offset-fed reflectarray.

multiples of 360 for a large reflectarray. The conventional technique of reflectarray design calls for adjustment of the elements to compensate the phase delay at the center frequency without , which taking into account the dispersion phase value is the variation of the phase as the frequency is swept across the band. Noting the appreciable amount of frequency dispersion for a large reflectarray, and very limited capability of the element to compensate for the dispersion, the antenna bandwidth suffers significantly. An optimization technique, introduced by the authors of this paper [16] was utilized here to address this problem. For an offset-fed reflectarray that is shown in Fig. 1 (for simplification only 1-D problem was addressed here), the phase value that is to be imparted by the elements of the reflectarray in order to transform the spherical phase front of the feed to plane wave at , can be calculated from the following equation: (1) where is x-coordinate of nth reflectarray element with respect to geometrical center of reflectarray, is the angle of is distance from the feed to the main beam from z-axis, element with minimum desired phase at the center frequency and and represent the operating frequency, and the speed of light, respectively. This phase can be normalized to the min) (global minimum of the required phase imum phase, shift throughout the reflectarray), for each frequency to impose 0 global minimum phase shift for the phase templates at all optimized frequencies. An arbitrary phase can be also added as shown in (2) to satisfy the dispersion frequency constraint as described as follows:

(2) is selected in a way to meet constraint for all the reflectarray elements (physical restriction). The maxis adjusted to get zero frequency dispersion for imum the elements at the reflectarray edge element while maintaining negative frequency dispersion for the rest of elements. This guarantees negative (or zero) frequency dispersion for all the reflectarray elements. Therefore, it is physically feasible to

Fig. 2. The desired on-axis phase of 120 cm square center-fed reflectarray with F=D = 1 for three different frequencies when 1' =1f is calculated according to the (3).

realize the required phase by appropriate choice of reflectarray elements. Negative frequency dispersion condition as discussed above is a universal condition that is to be met regardless of the type of element that is used. For a simple case of a broadside, , the can be calcucenter-fed reflectarray lated according to the following: (3) is distance from the feed to the edge of reflectarray where and F is reflectarray focal length. This equation was calculated for the element at the edge by assuming and in (2). Figs. 2 and 3 show the required phase on a row/column passing through the center of a center-fed reflectarray for the center frequency and extreme frequencies of 12, 11, and 12.8 GHz. These phases were calculated for two different values. The desired phase in Fig. 2 is calculated for the elements at based on (3) to get is not assigned the edge of reflectarray. In Fig. 3 correctly and it is slightly smaller than the one calculated in for some elements Fig. 2, therefore the at the edge, which cannot be compensated by any choice of reflectarray cell element. The phase of center element at center but it can be selected frequency (12 GHz) was set to in a manner to obtain a better convergence and less error as a result of frequency dispersion. An offset-fed reflectarray, shown in Fig. 4, was selected to verify the optimization routine. Different classes of double-cross loop elements [9] with variable loop length were used for designing the reflectarray (see Fig. 4). These different loop elements were defined by changing the , loops separation and cross width (e.g., line width Table I). All the simulations to generate phase-length curves in this paper were done in EMPIRE XCcel [17] using a waveguide simulator to emulate the periodic boundary condition for normal plane wave excitation. Since the loop elements are less sensitive to the angle of incidence [18] we did not take into account

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Fig. 5. Phase of the reflected wave versus loop length L for plane wave excitation with different incident angle d = d = 0:5 mm; g = 0:6 mm; w = 4 mm.

TABLE I PARAMETERS OF THE CELL ELEMENT FOR DIFFERENT CONFIGURATIONS Fig. 3. The desired on-axis phase of 120 cm square center-fed reflectarray with F=D = 1 for three different frequencies when 1' =1f is smaller than the one calculated in (3).

Fig. 4. A schematic view of the reflectarray and the cell element.

the effect of incident angle in designing of the reflectarray for both bands. Fig. 5 shows the phase of reflected wave versus loop length of a double cross loop element for different angles of incidence. This structure was simulated in HFSS [19] with periodic boundary condition. As shown in Fig. 5, there is a small variation as the incident angle changes. Similar cell size, substrate thickness and permittivity were used for all classes of cell elements, which are listed as follows: mm, mm. Cell element size The goal is to design a reflectarray at 12 GHz. First, the is deterdesired phase of the reflection coefficient , lower mined at three different frequencies of central and upper , frequencies in order to achieve a collimated is beam at the desired direction. The desired phase, calculated based on the antenna geometry and desired radiation

pattern. As was mentioned before, the , which for the offset case is the desired phase of the reference element (the element with minimum desired phase at the central frequency) could theoretically be chosen arbitrarily. To realize the desired phase at the center and edge frequencies, a search is conducted among cross loop elements with different geometrical parame, and ) in order to find an element that gives the ters ( best match for the desired phase shifts at given frequencies. In order to minimize the effect of frequency dispersion on radiating characteristics of the reflectarray, the candidate cell elements that produced the best achievable phase shifts, at center frequency ( GHz) and extreme frequencies of GHz and GHz are selected by minimizing which was first inthe following objective function troduced in [16]:

(4) refer to a particular location on the reflectarray where and reprelattice and sent desired and achievable phase delays at given frequencies and represent lower, center and upper frequencies, re( spectively). To select the appropriate cell element for a particon the reflectarray lattice, the above objecular location tive function is calculated for all members of the search space which is composed of classes of cross rings as described above. The particular ring element that minimizes the above objective

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Fig. 6. A view of the receive and transmit reflectarray elements.

function is selected as the optimum choice. This method was repeated for all the elements to get minimum frequency dispersion for all the reflectarray elements. In other words, from among all the members of the search space that provide a given phase at the center frequency, the one that minimizes the objective function is chosen as the optimum element.

Fig. 7. Phase versus loop length of double square open loop element.

III. RESULTS The goal is to design a 120 cm 120 cm dual-band offset-fed reflectarray. The polarization states are linear and orthogonal to each other. Noting the wider bandwidth requirement for the receive band, the optimization is only applied to this band. For the transmit band elements, double square loop elements [20] were used and conventional design rules for a reflectarray applied to adjust the dimensions of the cell elements. Double-cross open loop and double square open loop elements were used for the receive (Rx) and transmit (Tx) bands, respectively. The gaps in the receive and transmit elements are placed so as to ensure the orthogonality of the polarization states of the two bands with respect to each other (c.f., Fig. 6). The reflectarray was offset-fed consists of 9 small substrate panels of 40 cm 40 cm with a feed location of cm, cm and mm. The feed location was adjusted to achieve 10 dB tapering on the edges of the reflectarray. The elements were etched on a single layer substrate with perand thickness of mm. The mittivity of . reflectarray was designed to collimate the beam at IV. TRANSMIT BAND As mentioned earlier the optimization method was not applied to the transmit elements. Double open square loop elements were used for this band. To improve the bandwidth, the loop width of the cell element and also the gap between the loops were adjusted to maximize the linear range of the phase versus loop length curve [20]. A single Tx-band of the same specifications as given above (size, feed location, substrate permittivity, and thickness) was designed and fabricated to investigate the performance in the absence of lower band elements. Fig. 7 shows the phase of reflected wave versus loop length for different line widths ( and ) and loop separation . It can be observed that the slope of phase versus length curve becomes smoother as the line width were increased. ( and ) and gap between the loops

Fig. 8. A view of the single-band, 1.2 m reflectarray.

Based on the result shown in Fig. 7, optimal parameters of the open square loops that were used as the Tx-band cell element mm, mm, of the reflectarray were: mm. As noted in the introduction, a 120 cm 120 cm reflectarray was fabricated using a 3 3 assembly of 40 cm 40 cm panels as shown in Fig. 8. Radiation patterns of the reflectarray were measured in a compact range setup for three frequencies of 13.7, 14, and 14.5 GHz and the result is shown in Fig. 9. The measured data demonstrates that the reflectarray 1-dB gain bandwidth of the antennas meets requirements of the Tx-band. However, it should be noted that this result was obtained in the absence of Rx-band elements and the addition of these elements might deteriorate the Tx-band performance. The procedure of the reflectarray design in the Rx-band will be presented in the next subsection. The Tx-band design was then superimposed on the optimized Rx-band design to realize the dual-band reflectarray. The radiation patterns of the dualband reflectarray were measured and the results are shown in Fig. 10 for the upper band. Comparing the results with radiation pattern of the single Tx-band reflectarray of Fig. 9, it can be seen that the presence of the lower-band elements has only

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Fig. 9. Radiation pattern of the single band, 1.2 m reflectarray. Fig. 11. Phase of the reflected wave versus length for different loop configurad g . tions. d

=

=

The structure was simulated using different cross loop configurations. Fig. 12 shows the calculated radiation pattern when single or different types of cross loop configurations, listed in Table I were used in the optimization. The radiation pattern was calculated using array theory given by the following equation [21]:

(5) Fig. 10. Radiation pattern of the dual-band, 1.2 m reflectarray.

marginally degraded sidelobe performance at the extreme upper band frequencies. V. RECEIVE BAND The most challenging part is the design of Rx-band elements. This is due to the requirement of broad bandwidth for Rx-band, which is from 11.4–12.8 GHz (11.6 %). Fulfilment of this challenging requirement calls for application of an optimization technique, which was unnecessary for the Tx-band design. Different classes of double-cross loop elements with variable length (L) (cf., Fig. 4) were used for designing the reflectarray at Rx-band. These different loop elements were generated by , loop separation and cross changing the line width (e.g., Table I). These set of loops form the search width space for the selection of the elements according to the criteria outlined in the Section II. In practice, the objective function introduced in (4) is tested within the search space and the element with the minimum objective function is selected as the optimum element from the point of view of bandwidth performance. Fig. 11 shows the phase of reflected wave versus loop for the double-cross loop element when length for different cross widths (w). Changing the parameters of the cell element generates different slope values. All the simulations were done in EMPIRE XCcel [17] using a waveguide simulator to emulate the periodic boundary condition.

where center,

is the distance from reflectarray element to array is the distance between feed and reflectarray center, is the feed pattern, and are the transmit and receive element patterns, respectively, is the direction of main beam, and is the compensation phase generated by reflectarray element which was calculated in EMPIRE XCcel [17] for each element configuration set in a periodic lattice. The cross loop forms the pool of loop elements that populate the selection space based on different widths, . In fact, the first 16 loop elements have the same cross loop width ( mm) and the width values of the other two classes of loop elements (25 each) are mm and mm. for the center As noted in Section II, the value of for the edge element is selected in such a way that for the rest of the elements. Reelements and flectarrays were designed when the selection pool is composed of a single type of element or 66 types of elements. Radiation patterns were calculated for each case using array theory. The simulated results are shown in Fig. 12. Comparison between Fig. 12(a) and (b) demonstrates significant improvements of radiation pattern characteristics as the selection pool is enlarged. Fig. 13 shows a histogram of the cross loop elements that are selected in the design of the reflectarray when 66 different cross loop configurations, as tabulated in Table I, were used in the optimization. It is evident in this figure that element numbers 16, 41, and 66 were used the most in this design. These curves and gap with cross widths of 3.5 have same line width mm, 4 mm, and 4.5 mm respectively. Inspection of the phase

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Fig. 14. Calculated radiation pattern for a 1.2 m reflectarray with positive 1'=1f for the elements at the edge of reflectarray.

Fig. 12. Calculated radiation pattern for the 1.2 m reflectarray for different d g cross loop configurations in Table I. (a) one cross loop, d 0:2 mm, w = 3:5 mm and (b) 66 different cross loop configurations (see Table I).

=

=

=

Fig. 15. The simulation setup in HFSS to evaluate the bandwidth of reflectarray.

Fig. 13. A histogram of number of times each cross loop type in Table I is used in the design of the reflectarray.

versus cross loop length of these elements reveals their broadband nature. Another reflectarray with positive dispersion phase for the elements at the edge of reflectarray was designed and radiation patterns of this reflectarray are shown in Fig. 14. Rapid decline of gain for the extreme frequencies is evident as compared to the same parameter for the previous design, which was designed based on negative dispersion phase for all reflectarray elements.

The large number of elements (20000 total, 10000 elements for each band), which are implemented in the 120 cm reflectarray prohibits simulation of the whole structure using commercial software. On the other hand, it is a very difficult task to capture the intricacies involved in large reflectarrays that employ such cell elements as multi-loop in any dedicated computer software. For large size reflectarrays, the question of bandwidth should be addressed prior to fabrication. In the following, an approximate method is outlined to find a reliable estimate of the bandwidth of reflectarray using commercial software such as HFSS [19]. The method is based on close examination of the elements on a center row/column of the reflectarray as shown in Fig. 15 ( -axis). The central row is defined to be located at the intersection of the reflectarray plane and the plane that is defined by the normal to the reflectarray and the focal point (shown in Fig. 15). Reflectarray bandwidth can be estimated by careful consideration of the scattering characteristics of the single row when it is illuminated by the appropriate excitation. In this simulation, the single row/column is illuminated by an oblique angle plane and ). The direction of this plane wave is wave ( the same as the direction of the reflectarray main beam. The incident plane wave should be collimated at the focal point of the

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Fig. 16. Calculated nearfield in HFSS on line 1 of Fig. 15 for (a) non-optimized and (b) optimized reflectarrays.

reflectarray. Because of the bandwidth limitation of the reflectarray, the maximum field at the focal point was changed as the frequency of the plane wave excitation swept across the band. In other words, the variation of the field strength at the focal point is an indication of the operating bandwidth of the structure. Therefore, the field is monitored on a line perpendicular (line 1) or parallel (line 2) to the reflectarray going through the focal point as shown in Fig. 15. Depending on the state of polarization, a perfect electric conductor (PEC) or a perfect magnetic conductor (PMC) is imposed at the two sides of this single row to emulate the condition of an infinite, 1-D periodic structure composed of a single column. The reflectarrays with optimized and non-optimized elements were simulated using this setup in HFSS [19] and the field on line 1 and line 2 are shown in Figs. 16 and 17. It is evident from these figures that the maximum field intensity is observed at the mm and mm). As the frequency focal point ( is shifted from the center frequency, the field intensity on both line 1 and line 2 drops faster for the non-optimized as compared to the optimized elements, which testifies to the power of the optimization to improve the bandwidth. VI. MEASUREMENT RESULTS Having obtained confidence in the optimization method using the estimation that was described in the previous section, a 1.2 m dual-band reflectarray with optimized double cross open loop elements for the receive band and double square open loop elements for the transmit band was designed and fabricated. A view of this reflectarray is shown in Fig. 18. The reflectarray is designed on a single-layer dielectric material with permittivity and thickness of mm. The reflectarray of

Fig. 17. Calculated nearfield in HFSS on line 2 of Fig. 15 for (a) non-optimized and (b) optimized reflectarrays.

Fig. 18. A view of dual-band 120 cm reflectarray.

is offset-fed with feed location of cm, cm and mm. The reflectarray consists of 9 small panels of 40 cm 40 cm as described earlier. The radiation pattern of this reflectarray was measured in a compact range at the Communications Research Centre Canada (CRC) and the result is shown in Fig. 19 for the Rx-band center

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VII. CONCLUSION

Fig. 19. Measured radiation pattern for 1.2 m reflectarray at f

= 12

GHz.

The design and fabrication process of a dual-band 1.2 m reflectarray was presented in this paper. This reflectarray was designed for two frequency bands: 11.4 –12.8 GHz for receive and 13.7–14.5 GHz for transmit. An optimization technique was used to minimize the adverse effect of frequency dispersion on the level of gain at the receive band. Different classes of double cross open loop elements were utilized in the design of the elements for the receive band and double square open loops were used for the transmit band. The bandwidth of reflectarray at receive band was improved significantly by using the optimization method. A method was introduced to verify the bandwidth performance of the reflectarray using HFSS and the results of this simulation showed a significant improvement in bandwidth performance of the reflectarray in the receive band. The reflectarray consisted of 9 panels of 40 cm 40 cm that were assembled in an array of 3 3 panels to realize the whole reflectarray. The measurement results showed that the reflectarray meets the ITU specifications at both receive and transmit bands and the measured gain for both receive and transmit are comparable with the measured gain of a conventional reflector of the same size.

REFERENCES

Fig. 20. Measured radiation pattern (H-plane) for three different frequencies of 11, 12, and 12.8 GHz.

frequency of 12.0 GHz. A maximum gain of 40.6 dBi, which is equivalent to 50% efficiency, with sidelobe level below dB for H-plane and dB for E-plane were measured for dB. Similarity this antenna. The cross-pol. level is below of the shape of co-pol. and cross-pol. raises the possibility of misalignment of feed as the main cause of the rather high crosspol. level. Fig. 20 shows the H-plane radiation pattern for this reflectarray at three different frequencies of 11.4, 12, and 12.8 GHz (12% bandwidth). The pattern is quite stable for all these frequencies and gain drops less than 1 dB and side lobe level stays dB within the frequency band. The measured gainbelow bandwidth is better than 12% for this antenna, which shows a significant improvement as compared to conventional singlelayer reflectarrays with same size (3% [15]). The performance of this reflectarray at transmit band was explained in Section III. As it was shown in Fig. 10, a good performance in terms of bandwidth and radiation pattern was also achieved for the transmit band.

[1] D. M. Pozar, S. D. Targonski, and H. D. Syrigos, “Design of millimeter wave microstrip reflectarray,” IEEE Trans. Antennas Propag., vol. 45, no. 2, pp. 286–295, Feb. 1997. [2] J. Shaker, M. R. Chaharmir, M. Cuhaci, and A. Ittipiboon, “Reflectarray research at the Communications Research Centre Canada,” IEEE Antennas Mag., vol. 50, no. 4, pp. 31–52, Aug. 2008. [3] D. M. Pozar, “Bandwidth of reflectarray,” Electron. Lett., vol. 39, no. 21, pp. 1490–1491, Oct. 2003. [4] J. A. Encinar, “Design of two-layer printed reflectarrays using patches of variable size,” IEEE Trans. Antennas Propag., vol. 49, pp. 1403–1410, 2001. [5] H. Deguchi, K. Mayumi, M. Tsuji, and T. Nishimura, “Broadband single-layer triple-resonance microstrip reflectarray antennas,” in Proc. EuMA 2009, Rome, Italy, pp. 29–32. [6] D. M. Pozar, “Wideband reflectarrays using artificial impedance surfaces,” Electron. Lett., vol. 43, no. 3, pp. 148–149, Feb. 2007. [7] M. R. Chaharmir, J. Shaker, M. Cuhaci, and A. Ittipiboon, “Wideband reflectarray research at the Communications Research Centre Canada,” ANTEM, submitted for publication. [8] H. Li, B. Z. Wang, and P. Du, “Novel broadband reflectarray antenna with windmill-shaped elements for millimeter-wave application,” Int. J. Infrared Millimeter Waves, Mar. 339–44, 2007. [9] M. R. Chaharmir, J. Shaker, M. Cuhaci, and A. Ittipiboon, “Broadband reflectarray antenna with double cross loops,” Electron. Lett., vol. 42, no. 2, pp. 65–66, Jan. 2006. [10] J. Encinar and J. A. Zornoza, “Broadband design of a three-layer printed reflectarray,” IEEE Trans. Antennas Propag., vol. 51, no. 7, pp. 1662–1664, July 2003. [11] L. Marnat, R. Loison, R. Gillard, D. Bresciani, and H. Legay, “Optimization strategies for dual polarized reflectarrays,” presented at the 30th ESA Antenna Workshop, The Netherlands, 2008. [12] M. R. Chaharmir, J. Shaker, and H. Legay, “Broadband design of a single layer large reflectarray using multi cross loop elements,” presented at the ESA 31st Antenna Workshop, The Netherlands, 2009. [13] F. Yang, Y. Kim, J. Huang, and A. Elsherbeni, “A single-layer triband reflectarray antenna design,” in Proc. IEEE Int. Conf. Antennas. Propag., 2007, pp. 5307–5310. [14] M. Zawadzki and J. Huang, “A dual-band reflectarray for X- and ka-bands,” in Proc. PIERS Symp., Honolulu, HI, Oct. 2003. [15] M. E. Bialkowski, “Bandwidth considerations for a microstrip reflectarray,” PIER 2008, vol. 3, pp. 173–187.

CHAHARMIR et al.: DESIGN OF BROADBAND, SINGLE LAYER DUAL-BAND LARGE REFLECTARRAY

[16] M. R. Chaharmir, J. Shaker, and H. Legay, “Broadband design of a single layer large reflectarray using multi cross loop elements,” IEEE Trans. Antennas Propag., vol. 57, no. 10, pp. 3363–3366, Oct. 2009. [17] “IMST EMPIRE XCcel 3D EM simulation tools,” [Online]. Available: http://www.empire.de [18] B. A. Munk, Frequency Selective Surfaces: Theory and Design. New York: Wiley, 2000. [19] “Ansoft HFSS,” “The 3D, electromagnetic, finite-element simulation tools for high-frequency design,” [Online]. Available: http://www.ansoft.com [20] M. R. Chaharmir, J. Shaker, M. Cuhaci, and A. Ittipiboon, “A broadband reflectarray antenna with double square rings,” Microw. Opt. Technol. Lett., vol. 48, no. 7, pp. 1317–1320, Jul. 2006. [21] J. Huang and J. A. Encinar, Reflectarray Antennas. Piscataway, NJ: IEEE Press, 2008.

Mohammad Reza Chaharmir received the B.Sc. degree (with honors) in electrical engineering from K.N. Toosi University of Technology, Tehran, Iran, in 1993, the M.Sc. degree in electrical engineering from Amir Kabir University of Technology, Tehran, in 1996, and the Ph.D. degree in electrical engineering from the University of Manitoba, Winnipeg, MB, Canada, in 2004. He has been a Research Scientist at the Communications Research Centre (CRC), Ottawa, ON, Canada, since 2005. He has also been an Adjunct Professor at Concordia University, Montreal, Canada, since 2005. His research interests and activities include periodic structures, reflectarray antennas, FSS, bandgap photonic, metamaterials and antenna beam scanning.

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Jafar Shaker received the B.Sc. degree in electrical engineering from Iran University of Science and Technology, Tehran and the Ph.D. degree from the University of Manitoba, Winnipeg, MB, Canada, in 1987 and 1995, respectively. He has been a Research Scientist at the Communications Research Centre, Ottawa, ON, Canada, since 1996. He has also been an Adjunct Professor at Carleton University, Ottawa, since 1999. His areas of interest include periodic structures, reflectarray, FSS, quasi-optical techniques, and application of optical concepts in microwave and antenna engineering.

Nicolas Gagnon received the B.A.Sc. (summa cum laude) and M.A.Sc. degrees in electrical engineering from the University of Ottawa, ON, Canada, in 2000 and 2002, respectively, where he is been working toward the Ph.D. degree. Since 2001, he has been a Research Engineer in the Advanced Antenna Technology Lab at the Communications Research Centre Canada, Ottawa. His research interests include quasi-optics, permittivity measurement, microwave holography and microwave antennas. Mr. Gagnon is a licensed professional engineer in the province of Québec, Canada, and a member of the Ordre des ingénieurs du Québec.

David Lee graduated from Algonquin College in electrical engineering technology, Ottawa, Ontario, Canada. From 1981–2000, he was RF group leader responsible for passive and active microwave antenna measurements in the David Florida Laboratory at the Canadian Space Agency. He joined the Communications Research Centre in 2000 as the Head of the Antenna Test Facility, in the Advanced Antenna Technology Group. He is currently establishing a new compact range facility capable of 2–100 GHz measurements. His research interest includes novel low cost antennas for wireless and other antenna designs. He assists graduate students at various universities with antenna prototype development and testing, and is a co-inventor on a patent for an ultra-wideband antenna.

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Near Field Focusing Using Phase Conjugating Impedance Loaded Wire Lens Oleksandr Malyuskin, Member, IEEE, and Vincent Fusco, Fellow, IEEE

Abstract—The properties of a lumped loaded wire array as a means for near field focusing using phase conjugation is studied. The constructive role of phase conjugation in the near field image formation is justified both analytically and numerically. The generation of phase conjugated energy and how this is influenced by lumped impedance loading of the wires constituting the lens is discussed. In particular it is shown that inductive loading of the constituent lens wire elements is essential for subwavelength focusing since this leads to the creation of a phase conjugated near field predominantly determined by a convolution of the array current distribution with the real part of the Greens function which oscillates at a subwavelength scale. The characteristic resolution of the lens 7 in terms of the full width at half maximum is shown to be 4 for two dipole sources at for a single source and better than 10 source-lens separation distance. Index Terms—Array, near field, phase conjugation, subwavelength imaging.

I. INTRODUCTION

S

UB-DIFFRACTION near field imaging has attracted major interest recently due to its potential applications in biomedical diagnostics, remote sensing, microscopy and lithography, etc. [1], [2]. In general to achieve near field subwavelength resolution of a source or multiple sources an imaging device has to collect the evanescent field of the source(s) and transfer it to the image plane with some amplification in order to compensate for fast near field decay away from the source. Recently several techniques have been used for subwavelength imaging including left-handed metamaterial superlens [2], [3], wire grid lens [4], photonic crystal slabs [5] and dielectric layers [6]. The common feature of these devices is that they can support electromagnetic waves with wavenumbers larger than the wavenumber of free space. When such a lens is positioned in a close proximity to a source(s) to be imaged in free space, the evanescent field of the source excites corresponding electromagnetic wave modes in the imaging device which transfer the “subwavelength” information stored in the evanescent field of the source to the image plane. At the same time the transmitted field can be amplified inside the lens due to stimulation of certain resonance conditions depending on the

Manuscript received September 24, 2009; revised February 16, 2010; accepted March 20, 2010. Date of publication June 14, 2010; date of current version September 03, 2010. This work was supported in part by the Northern Ireland Strengthening all Island Mobile Wireless Futures Program and in part by the U.K. Engineering and Physical Research Council under Grants EP/D045835/1 and EP/01707X1. The authors are with the Institute of Electronics Communications and Information Technology, Queens University Belfast, Queens Island, Belfast BT3 9DT, Ireland (e-mail: [email protected]). Digital Object Identifier 10.1109/TAP.2010.2052571

material and geometry of the lens [2], [5], [6]. Particularly in the case of a left-handed Veselago-Pendry lens [2] this condition relates the refraction index and effective relative permittivity and permeability of the lens material, , which gives rise to growing backward waves in a left-handed slab [2], [7]. In this process the energy is extracted from the source or re-distributed between the enhanced and suppressed parts of the electromagnetic wave spectrum [6]. The resonant nature of evanescent wave amplification imposes very stringent design requirements suggesting that practical implementation of this type of lens would be difficult since even small losses being amplified at resonance can deteriorate lens performance very severely. In addition, since all practically realizable materials exhibit dispersion the condition can be realized only in for very narrowband operation [2], [3]. A physical implementation of the Veselago-Pendry lens has been reported recently based on the multilayered left-handed transmission line structure [2], [3], [7]. In this paper we propose a different concept utilizing a phase conjugating (PC) lens based on a finite nonlinearly loaded [8] wire array operating at microwave frequencies. Unlike the left-handed lens a PC lens does not support backward waves: the near field of a source is reconstructed in the image plane due to scattering by the lens constituent wire elements and by constructive interference caused by phase conjugation action. The PC field transferred to the image plane can be amplified due the extraction of the energy from a pump wave spatially applied to the PC lens through the action of signal-pump wave mixing on the lumped nonlinear element embedded within the wires of the lens. The subwavelength image resolution properties of the PC lens proposed here are due to array current distribution resonance acting in harmony with constructive interference due to phase conjugation. Acting in concert these effects enhance the convolution of the array current density with the real part of the Greens function which is fast varying in the vicinity of the source (image) while concurrently suppressing the convolution of the current density with the imaginary part (slowly varying). The details of this mechanism are discussed in Sections III and IV. The unique feature of the microwave PC lens is that it can be composed using a finite number of loaded wire elements which are loaded with standard linear and non-linear lumped components. Additionally the lens operating frequency can be controlled by changing the frequency of the pump source and wire element impedance loading component values. Phase conjugation techniques have previously been used in optics and acoustics for far field source localization [9], however only recently has it been suggested that phase conjugation or time reversal can be used for the sub-diffraction near field focusing in free space [10]–[12]. In this paper we analyze the role of phase conjugation in the process of near field imaging

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MALYUSKIN AND FUSCO: NEAR FIELD FOCUSING USING PHASE CONJUGATING IMPEDANCE LOADED WIRE LENS

of a single or multiple Hertzian dipole sources and propose a simple PC lens architecture for use at microwave frequencies. In order to get a better insight into PC lens operation we consider the properties of an “ideal” PC surface [12] composed from point-like uncoupled dipole transceivers along with the properties of an impedance loaded wire lens. We show that for a Hertzian dipole source located in free space “ideal” PC lens phase conjugation cannot alone result in subwavelength localization in the quasistatic near field region ). In the Fresnel (with dominating inverse cubic terms bezone of the near field when inverse quadratic terms come significant, phase conjugation plays a positive role in focusing process ensuring constructive interference of the image near field. Therefore for the “ideal” PC lens the positive contribution of phase conjugation in near field subwavelength resolution is limited by the Fresnel zone only. The situation is different in the case of a PC lens composed of finite length wire elements. Here a Hertzian dipole source induces currents along the array antenna elements (which are less or about half wavelength) such that the quasistatic and Fresnel regions are now “coupled” by the array wire currents. Constructive interference caused by phase conjugation can now result in subwavelength image field confinement in both the quasistatic and Fresnel near field regions. Mutual coupling between the antenna elements increases the effective aperture of the PC lens across the array, i.e., in the transversal direction and along the wire elements thus making possible near field image confinement due to the constructive interference caused by simultaneous activation of phase conjugation and array current resonance. II. STATEMENT OF THE PROBLEM The wire PC lens is shown in Fig. 1. The lens is formed by a finite array of wires into which are inserted lumped linear and nonlinear loads. The lens is excited by a monochromatic signal excited Hertzian dipole(s)

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Fig. 1. Lens Geometry. The loaded wire array is illuminated by a field due an imaged Hertzian source/sources and a pump wave. Below the structure geometry is an expanded view of a typical element load.

Here, is the phase conjugated voltage across the th is nonlinear device terminals, and the difference phase the phase due to pump and signal wave mixing [8]. of the PC wave is determined by the difThe frequency ference for the quadratic nonlinearity or by in the case of a cubic nonlinearity. The voltage amplitudes depend both on the current voltage characteristic of the nonlinear device and on the array element impedance loading. The PC voltages (3) excite current distributions along the wire elements which generate the PC field (4) with amplitude

(1) with real valued amplitude vector and positioned in the vicinity of the lens in the point . The array is also pumped by a monochromatic plane wave (or another Hertzian dipole source acting as a pump) (2) at frequency to produce two wave mixing at the nonlinear elements [8]. This mixing results in a generation of a voltage with a conjugated phase across each terminal of each nonlinear device in the lens. The voltage drop across the th terminal depends on the order of nonlinearity [8], namely (3a) for a second order nonlinear device (3b) for a third order nonlinear device, and so on.

(5) In (5) the Helmholtz operator is given by , i.e., it is assumed that all wires are y-oriented; is a free space Greens function; is the free space wave number at the frequency of a phase conjuis the distance between the integragated wave; tion and observation points; is the current distribution along the th wire due to the PC voltage drops (3). The PC field (5) intensity distribution forms the image of the dipole . This image formation and its source in the image plane properties are now studied. In order to do this we calculate the PC field (5) using the combined time-frequency domain analysis strategy outlined in [8]. Here as the first step the nonlinear circuit problem is solved at each nonlinear terminal array in the time domain using Fourier

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transformed frequency domain inputs obtained for the linear part of each antenna element in the array environment as seen across the nonlinear device terminals. At the second step we invert the phase of the Fourier derived time sequence (3) and the transform it back into frequency domain. After this we calculate the array wire current distributions and generated PC field using a classical frequency domain MoM approach. For this last step the commercial FEKO MoM solver [13] is used to calculate the PC field distribution. III. PC LENS OPERATION: FREQUENCY DOMAIN ANALYSIS In this section the image formation properties of the PC lens is analyzed. In order to obtain a better understanding of the role of phase conjugation in subwavelength imaging the near field of the Hertzian dipole is analyzed first. It is shown that the lens resolution defined in terms of the field intensity profile full width at half amplitude maximum (FWHM) substantially depends on the region of the near field—quasistatic (with dominating cubic inverse distance terms) or Fresnel (with dominating cubic and quadratic inverse distance terms). We note that phase conjugation acts to invert the sign of the imaginary part of the field which results in a positive role in the imaging process in the Fresnel zone, where the imaginary component of the near field is the same order of magnitude as the real part. In the quasistatic region the real component of the field produced by real valued Hertzian dipole is several orders of magnitude larger than the imaginary component so phase conjugation does not assist in the field focusing process unless there is coupling between quasistatic and Fresnel zones mediated by, for example, the wire elements from which an actual array might be composed. These near field region dependent properties of a PC lens are now demonstrated by the simulation of the dipole field imaging by a “perfect” PC lens [12]. The perfect PC lens is composed of point-like dipole Hertzian transceivers. Next through analysis of the case of a lump loaded resonant wire array we show that phase conjugation has to be augmented with properly controlled array mutual coupling in order to produce a subwavelength image of a dipole source. A. Near Field of a Hertzian Dipole Source and Ideal PC Mirror The field generated by a Hertzian point-like dipole can be written in the form [14] (6) is defined as where the Helmholtz vectorial operator is a dipole vectorial amplitude. Application of the Helmholtz operator in (6) to the free space Green’s function leads to highly oscillatory behavior of both the real and imaginary component of the field in the vicinity of the source. If we consider a y-oriented dipole then

(7) Here, the oscillation rate of the real part of the near field is much higher than that of the imaginary part, Fig. 2. Fig. 2(a) shows the y-component of the field distribution in

Fig. 2. The y-component of the Hertzian dipole near field. (a) Field distribution in the transversal plane xy for the distance from source =10. (b) FWHM, dotted line, and ratio of real to imaginary part of the field, solid line, as a function of distance from the source in the xy plane at the line y = 0.

the transversal xy plane for and distance from the source , where is the wavelength at the frequency of dipole field radiation. It can be seen that in vicinity close to the source subwavelength information is dominantly encoded into the real part of the dipole field. Fig. 2(b) displays the dependence of the FWHM of the dipole field amplitude as a function of distance from the source along with the ratio of real and imaginary components. This graph shows that phase conjugation will influence image resolution when since phase conjugation inverts the sign of the imaginary part leaving the real part of the field intact. It can be concluded from Fig. 2 that subwavelength resolution through the use of an “ideal” PC lens [12] is enhanced due to phase conjugation only in the Fresnel zone of the near field since in quasistatic region the real component of the field dominates over the imaginary component. To illustrate this feature we consider the dipole source near field imaging by a “perfect” PC lens composed of point-like co-aligned dipole transceivers whose amplitudes are proportional to the complex conjugated incident dipole field (8) where for the simplicity we consider y-oriented dipole transceivers, is a radius vector of the element located in a node of a spatial two-dimensional array, is a constant. The

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B. Impedance Loaded Wire PC Lens

Fig. 3. The y-component of a Hertzian dipole image near field at the focal line y = 0 in the plane z = 0:1 . Solid line: source field at the line y = 0 in the plane z = 0 (without array); dotted line: image field due to PC lens; dashed line: transmitted field due to array without phase conjugation.

generated PC field can be written according to (6) in the form of a superposition of all fields re-radiated by the dipole transceivers (9) where . Fig. 3 shows the image field at generated by a finite PC lens composed of an 8 by 8 rectangular array of point like dipole transceivers separated by in the x and y directions. The array is positioned in the xy plane symmetrically with respect to the z axis. In Fig. 3 the field generated by a PC array is shown along with the field generated by the same array of non-PC dipole transceivers. To illustrate image transfer properties of the phase conjugating array we also compute the field of the dipole source at , without an array of transceivers present. It can be seen that in the quasistatic near field region the intensity field distribution has approximately the same focal width for PC and non-PC arrays. This can also be shown analytically by taking into account (8) and (9) and neglecting all field terms except for the quasistatic ones. In this case the PC field and ordinary scattered fields can be respectively written as (10a) (10b) where

are real valued amplitudes and is the quasi-static Green’s function for free space. In a quasistatic approximation the focal width of the field distributions (10) is the same since . Fig. 3 demonstrates that in the Fresnel zone constructive interference caused by phase conjugation results in field focusing while a non-PC array produces a divergent field pattern. The comparison of the transferred by the PC array image at with the field of the dipole at , i.e., at the same source-observation plane separation demonstrates that the image is transferred without distortion, i.e., no compression or de-focusing.

Consider now the near field focusing properties of a one-dimensional array comprised of loaded wire elements as shown in Fig. 1. Unlike the “ideal” lens conjugating a dipole field at every point of a lens, the PC wire array performs phase conjugation in a set of sampling points corresponding to the spatial locations of the nonlinear elements. The field is thus integrated over the array aperture since the array coupling influences current distribution in each wire. Therefore in this case the quasistatic, Fresnel and propagation zone fields are coupled by way of the array current distributions. This fact can offer certain advantages in practical lens implementation particularly, since inductive loading enables opportunity for enhancement of wire current distributions (this will be discussed in the following section) and also allows coupling of the real and imaginary parts of the Greens function and current distribution in a manner favorable for achieving subwavelength image confinement. To illustrate these points further consider array current distributions in the “transmission” or “generation” regime, i.e., the current distributions generated by voltage “generators” (3). The image field amplitude will be determined by a convolution (5) of the array current density with the electric field Greens’ function (obtained after applying the Helmholtz operator to the free space Greens function [14]) which has fast varying (at suband slowly varying wavelength scales in the near field) real imaginary part in the vicinity of a source [cf. Fig. 2(a)]. In what follows we consider only the large y component of the field which in the case of the y directed wire array dominates . over the other field components, i.e., To understand better the role of the array resonance we calculate the current distributions for the one-dimensional 9 1-element PC array composed of quarter-wavelength wires loaded with pairs of parallel LC loads with pF and nH with series 1 parasitic resistance inserted mid-point at each element [15] and also the current distributions for the same 9 element array but loaded with pairs of 1 loads included into each wire symmetrically with respect to the nonlinear device. The parallel LC load forces the array current distribution to be resonant at around 1.5 GHz. A purely resistively loaded array would operate well below resonance. Fig. 4(a) shows the normalized current distribution along the centre wire element for the parallel LC loaded case; Fig. 4(b) displays the normalized current distribution along a central element in the resistively loaded array. In both cases the array is illuminated by a Hertzian dipole operating at 1.5 GHz and located at position and the array is pumped by a plane wave at 3.0 GHz. It can be seen that the current density for the first case obeys the condition while for the resistively loaded array . The convolution (5) can be written in the form

(11) It can be seen from this expression that the field in the vicinity of a focal point will be oscillating at the subwavelength scale provided the condition is satisfied.

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(11)] resulting in the near field convergence to form the focal spot. These two mechanisms of phase conjugated current generation work in unison to produce subwavelength confined near field image. IV. NUMERICAL RESULTS A. Imaging Properties of an Impedance Loaded Wire PC Lens

Fig. 4. Real and imaginary parts of the “phase conjugated” current along the central wire element in the PC array excited by the dipole located at (0; 0; =10). The array consists of 9 quarter-wavelength wires separated by =10. (a) Parallel LC loaded array, C = 1 pF, L = 6:2 nF series parasitic resistance 1 ; (b) 1 resistively loaded array.

0

This is because the fast oscillating, in the vicinity of the focal spot , convolution term , is enhanced with respect to slowly varying term . If the imaginary part of the current density is large, , then the slowly varying term is not small with respect to the fast oscillating term and thus the oscillation rate of the field given by the sum of fast and slow varying terms (11) will be reduced in the vicinity of the focal spot, thus the resolution of the lens will deteriorate. It should be noted that the mentioned resonance condition is fulfilled for the array elements close to the source, since the real part of the field is dominating in the vicinity of the source only, Fig. 2. In the case of array elements far from the source location this condition is not critical because the fast oscillating real part of the Greens function decays quite quickly away from the source. The contribution from these remote array elements is positive dominantly due to phase conjugation ensuring field convergence. This is further illustrated in Fig. 7 which shows the field distributions for the inductively and resistively loaded PC arrays. Thus array resonance ensures that the subwavelength oscillating part of the image field is enhanced with simultaneous suppression of the slow varying part of the image field. At the same time phase conjugation enables proper phase conditions across the whole array aperture [since there is a summation over all array elements in

A numerical study of lens performance has been conducted at the frequency of the signal (imaged) field 1.5 GHz with pump plane wave normally incident on the array at 3.0 GHz. Fig. 5 shows the image of a single Hertzian dipole located at . The array is formed by 11 1 quarter-wavelength wires each loaded with pairs of identical LC parallel lumped loads with capacitance 1 pF and inductance 6.2 nH. This ensures current resonance concurrently at the signal (1.5 GHz) frequency and at the doubled frequency (3 GHz to optimize the effectiveness of pumping at the doubled frequency through the use of a quadratic nonlinearity). The resistance of each lumped component was chosen to be 1 [15]. Fig. 5 and demonstrates the image formation by the array at spacings between wire elements. It can be seen that some image intensity amplification due to the extraction of the energy from the pump wave is possible. The performance for denser arrays in terms of image intensity amplification and side lobe reduction deteriorates. This is believed to be due to the distortion of the resonant condition for the current density, namely a denser array has a higher capacitive component associated with the linear part of the array self-impedance, thus the terminal current amplitudes are reduced as compared to the case of a sparser array with tuned to resonance. Side lobe levels are increased in due to the smaller size of the denser array. the case Fig. 5 shows the degree of resolution of a single source at separation between the source and array that can be achieved is . Fig. 5(b) and (c) illustrate 2D E field magnitude distributions which show that source imaging is possible not only on but in the whole transverse plane, approxithe focal line mately with the same resolution in x and y directions. The field of the PC lens is compared with the source field without the to show the image array at the same separation distance transmission properties. Unlike the ideal lens, Fig. 3, the interference in the array plane results in the appearance of side lobes and nulls of the field intensity, Fig. 5(a), however the FWHM of the image field is approximately the same as the FWHM of the source field at the same separation and the image shape is . preserved in the vicinity of the maximum, Fig. 6 illustrates subwavelength imaging for two dipole . The separation between the array sources separated by and the sources is . The array consists of 17 1 wire spacing between them, selected so as to elements with reduce side lobe levels. The same level of image intensity amplification as in Fig. 5(a) is observed. For clarity Fig. 6(a) shows normalized field distributions. Here we compute the (at the array plane) field distribution of two sources at (at the image plane) without array to illustrate and at the image transmission properties. Namely it can be seen that the lens can improve the resolution due to mutual coupling

MALYUSKIN AND FUSCO: NEAR FIELD FOCUSING USING PHASE CONJUGATING IMPEDANCE LOADED WIRE LENS

Fig. 5. The y-component of a Hertzian dipole near field. (a) Un-normalized 1D source and image field distribution at the focal line y = 0 in the z = =10 plane; (b) 2D distribution of the source field in the xy plane, z = 0, in the absence of the array; (c) 2D distribution of the image field in the xy plane, z = =10.

acting in a favorable manner (cf. Section III.B)—the depth of the minimum between the image field peaks is increased as , so the sources are compared to the field distribution at better resolvable, Fig. 6(a). Secondly, the comparison of the with the source field at the same plane image field at shows that two sources are not resolvable at all without PC lens. Fig. 7 demonstrates the effect of loading on the imaging properties of the PC lens. As was shown in the previous section the array resonance condition is crucial for near field imaging

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Fig. 6. The y-component of two Hertzian dipoles near field in the transversal xy plane. (a) Normalized 1D source and image field distribution at the focal line y = 0; (b) 2D distribution of the source field in the absence of the array at the plane z = 0; (c) 2D distribution of the image field at the plane z = =10.

with subwavelength resolution. In Fig. 7 we compare the situation when the 9 1 element quarter-wavelength wire array is loaded with pairs of parallel LC (1 pF, 6.2 nH) loads, resonance case, and with a 1 resistively loaded 9 1 element array of quarter-wavelength wires, operating off resonance, and finally with a 9 1 element array of half-wavelengths wires loaded with 1 resistors to produce a low quality resonance. The array as for Fig. 4 simulations. is excited by a dipole at It can be seen that the resistively loaded array cannot perform subwavelength imaging at all. This is due to the above mentioned fact of slow oscillation of the field due to large imaginary

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Fig. 7. The y-component of a Hertzian dipole image near field at the focal line y = 0 at the plane z = =10. Solid line: high quality resonance array; dashed line: low quality resonance array; dotted line: non-resonant array imaging.

part of the array current density on the elements in the vicinity of the focal spot. These numerical results demonstrate that the resolution of the wire PC lens is determined only by the separation between the source and array. In the case of a single dipole the resolution of the lens characterized by its FWHM will be the same as FWHM of a source field at the array plane, i.e., in principal there is no fundamental upper limit on the resolution of a PC wire lens operating in resonance. In the case of two dipoles resolution depends on both the separation between the sources and also on the separation between the sources and the array plane. Mutual coupling between the array elements can play a positive role by increasing the depths of the minimum between the two peaks of the image field, Fig. 6(a) thus making multiple sources better resolvable, at the same time mutual coupling between the sources reduces the usable separation between source plane and image plane. B. Comparison With Wire Grating Lenses In this section, we compare the imaging properties of the above PC lens composed of 17 1 wire elements with inter-element spacings and the wire grating structure considered in [4]. First we reproduce the results in [4] now using the FEKO solver with excellent agreement. Next in order to confirm the considerations of Section III.B of the present paper we calculate the current distribution along the wire element in a 129 1 element grating comprised of 30 cm long, 8 m radius wires separated by 2 mm [4] at 1.67 GHz. The chosen wire element is located opposite to one of the dipole sources with its centre at . The grating is illuminated by two sources with separation between them and separation between these sources and the array plane. The current distribution for the arrangement is shown in Fig. 8. It can be seen that the real part of the current distribution dominates the imaginary one, so that subwavelength imaging occurs due to the mechanism explained in Section III, namely due to the suppression of the convolution of the current density with the imaginary part of the Greens function. It should be noted that the high quality resonance of the current in this grating is due to the extended length of the

Fig. 8. Current distribution along the wire of the passive wire grid structure in [4] used for imaging of two dipole sources located in the near field of the grid, grid-source plane separation is 0:1.

(at 1.67 GHz) from which it is constructed. The wires, quality of the resonance would deteriorate in a sparser array with so that resolution would deteriorate. This shorter wires effect of resolution deterioration is supported by simulations not presented here for the brevity’s sake. Thus the effect of subwavelength resolution observed in [4] is due to the suppression of the slowly varying part of the convolution of the Greens function with current density and it does not involve wavefront re-focusing due to phase conjugation. As a consequence of this the grating lens resolution will significantly deteriorate when the source-grating separation is increased due to the fact that the fast varying part of the Greens function becomes the same order of magnitude as the slowly varying part (with simultaneous reduction of the oscillation rate) and there is no wavefront negative refraction (constructive interference) due to phase conjugation. To illustrate this, we compare the imaging properties of a 17 1 wire PC lens and the above considered grating when illuminated by two dipole sources. Consider the from each other situation when the sources are separated by from the lens. Fig. 9(a) displays in the cross range and by (symmetric the field intensity profiles at the plane to the source position with respect to the lens plane). It can be seen that PC lens produces an image with minor distortions, two peaks of the image field coincident with the positions of the dipole sources. At the same time the field transmitted through grating experiences outgoing behavior (the wavefront does not converge since there is no phase conjugation present) leading peaks separation (cf. Fig. 4 from [4]). Additionally to the minimum between peaks is reduced due to the fast varying Greens function attenuation with the distance. It is interesting to , Fig. 9(b)—here, the compare the field distribution at field distribution transmitted through the grating is close to the field distribution of two dipole sources at the same separation , but the field produced by a PC lens is distorted. distance This distortion is due to two reasons: first, the PC lens creates an image with minimal distortions in the symmetric, with re. Secondly, spect to the source plane position, i.e., at the wire PC lens is rather sparse, so the maxima of the field in Fig. 9(b) correspond to the positions of the wire elements. The small central peak in Fig. 9(b) is due to mutual coupling which

MALYUSKIN AND FUSCO: NEAR FIELD FOCUSING USING PHASE CONJUGATING IMPEDANCE LOADED WIRE LENS

Fig. 9. Imaging of two sources by a PC lens and a wire grating [4]. (a) Field distribution at the focal line y = 0 in the z = =10 plane; (b) Field distribution along the line y = 0 at z = =20 plane. Solid line: source filed distribution without array; dotted line: image field due to PC lens; dashed line: field transmitted through the grating.

is producing negative effect (artifact) at but results in ! enhanced resolution at the image plane at It is interesting to note the wire grating can only produce an when the source-lens image in its near field vicinity separation becomes large (but the lens is still positioned in the source near field Fresnel zone [4]) while PC lens operates for any source-lens separation distance. To show this we model the in across-theimaging of two dipole sources separated by range direction and located at separation from the lens. Fig. 10(a) shows the field produced by a PC lens at different image-lens separation distances. In this case it can be seen that the PC lens produces the image with two peaks corresponding to the dipole sources’ across-the-range positions. The wire grating produces a distinguishable image of two sources only in its near . vicinity at C. Forward Transmitted Field of PC Lens Without Pump Wave Consider the field forward transmitted by the 17 1 array with loading described above when no pump wave present. Strictly speaking, in this situation the lens cannot be referred to as a PC lens since no PC wave is produced. In this Section the role of wave mixing and phase conjugation in the subwavelength image formation is demonstrated. First, it can be shown for that in general the conditions for the currents the PC currents and

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Fig. 10. Imaging of two sources by a PC lens and a wire grating [4]. (a) Field distribution at the focal line y = 0 due to PC lens for various lens-image plane separations and (b) transmitted through the grating field distribution along the line y = 0 for various lens-image plane separations. Solid line: Lens-image separation z = =20; dashed line: z = =10; dotted line:z = =6.

Fig. 11. Forward transmitted field due to two dipole sources separated by =4 in across-the-range direction and by =10 from the 17 1 array. Solid line: the source field at z = 0 without the array; dotted line: forward transmitted field at z = =20; dashed line: forward transmitted field at z = =10.

2

in the “receive mode” induced by a signal wave cannot be satisfied simultaneously. Secondly, since no phase conjugation occurs the array generates outgoing wavefront with no constructive interference at the image plane. To illustrate this we calculate the transmission of the field due to two dipole sources in the cross range and located from the separated by array. It can be seen that the forward transmitted wave, Fig. 11, has a single beam pattern so that at the image plane it is impossible to distinguish exciting sources.

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Fig. 13. Conversion efficiency of the PC array excited by a Hertzian source with amplitude 1 Am at 1.5 GHz and pumped by a plane wave at 3.0 GHz.

2

Fig. 12. (a) Current distribution along the central wire element in 5 1 element array environment at 1.5 GHz. (b) The dependence of the terminal current amplitude on frequency for the central wire element in a quarter-wavelength wire array. The array is excited by a dipole source located at =10 from it, where  corresponds to frequency 1.5 GHz.

D. Practical Design Considerations It was shown in the previous Section that inductive loading enables one to improve the imaging capabilities of the PC lens. Loading is also important for achieving gain (or at least reducing PC conversion loss) in the mixing process at the nonlinear device terminals. Fig. 12 demonstrates wire current amplitude enhancement due to inductive loading of a quarter wavelength central wire in a 5 1 element array environment. Here the wires are separated by in the x direction; the array is excited by a , dipole source (with amplitude 1 mAm) located at where corresponds to frequency 1.5 GHz. It can be seen that the current amplitude in the parallel LC loaded quarter-wavelength wire is two times larger than the current amplitude in an unloaded half-wavelength antenna element. The capacitance 1 pF and inductance 6.2 nH values selected here ensure inductive behavior of LC load at 1.5 GHz. Another interesting property of this loading is that it ensures dual band resonant frequencies at 1.5 GHz and at GHz, Fig. 12(b). This feature is essential for optimal extraction of pumping energy necessary for achieving best possible PC convergence gain in the case of a square law nonlinear device. Fig. 13 shows the theoretical PC conversion efficiency as a function of both the power of the pump wave and nonlinear device bias voltage. In this graph for

simulation purposes we approximated the current voltage characteristics of a HSMS-282X Schottky diode [16] with ideality factor 1.08 by a polynomial series relating terminal current and applied voltage [8]. The effect of saturation is not taken into account which in practice can limit the output conjugated power [17]. In Fig. 13 the conversion efficiency is defined as the ratio of the PC voltage amplitude to the un-conjugated signal voltage amplitude across the terminals of the central wire element in the array. The dipole source amplitude is 1 Am, the separation from the array is ( is a wavelength at 1.5 GHz). From Fig. 13 it can be seen that the PC field can be amplified provided mW/m and the the power of the pump wave is sufficient, diode is not in the saturation regime. It is interesting to investigate a possible effect of the nonlinear load type [18] on the PC lens imaging properties. Particularly when the PC power is created by mixing on the nonlinear resistive element like, e.g., a diode or diode pair the major negative effect caused by the nonlinear element is the additional ohmic loss. This effect can be very severe [17] if the position of the operating point is not in the optimal region of the i-v curve. Particularly, for a single diode with quadratic type nonlinearity the operating point should be within the square law region. To verify numerically the degrading effect of the loss we calculate the differential resistance of the parallel pair of HSMS-282X Schottky – V. diodes [16] in the range of forward voltages In this range the typical differential resistance of a diode pair to 40 . Fig. 14 demonstrates the FWHM of an varies from from the PC lens image of a single dipole source located at (the lens parameters are the same as for Fig. 7). It can be seen that the resistance of the nonlinear device does not prohibit subwavelength imaging provided the loss is not unduly high. The requirement of low loss posses limitations on the dynamic range of the pump and signal wave since the operating point can only – V range. So, in general to be located within optimal achieve high PC output power with low loss (and therefore to allow PC lens to image with high quality) the nonlinear diode has to support large forward currents for moderate forward voltages i.e., it has to possess i–v curve with low differential resistance characteristic across the square law region.

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Fig. 14. Effect of the differential resistance of the nonlinear diode pair on the image quality.

V. CONCLUSION In this paper, the operation of an impedance loaded phase conjugating wire array as a means for near field focusing was studied for the first time. We have shown both analytically and numerically the constructive role of phase conjugation in near field image formation. It has been shown that array inductive loading is essential for subwavelength focusing since it leads to the creation of a phase conjugated near field predominantly determined by a convolution of the array current distribution with the real part of the Greens function which oscillates at a subwavelength scale. The near-field characteristic resolution of a finite 17 1 wire lens in terms of the full width at half maxfor a single source and better imum is predicted to be for two dipole sources at source-lens separation than distance. ACKNOWLEDGMENT The authors are grateful to the Reviewers whose valuable and helpful comments and suggestions allowed them to improve the original manuscript. REFERENCES [1] K. P. Gaikovich, “Subsurface near-field scanning tomography,” Phys. Rev. Lett., vol. 98, pp. 183902–, May 2007. [2] A. K. Iyer and G. V. Eleftheriades, “Free-space imaging beyond the diffraction limit using a Veselago-Pendry transmission-line metamaterial superlens,” IEEE Trans. Antennas Propag., vol. 57, no. 6, pp. 1720–1727, June 2009. [3] P. Alitalo and S. Tretyakov, “Subwavelength resolution with three-dimensional isotropic transmission-line lenses,” Metamaterials, vol. 1, pp. 81–88, 2007. [4] G. Fedorov, S. I. Maslovski, A. V. Dorofeenko, A. P. Vinogradov, I. A. Ryzhikov, and S. A. Tretyakov, “Subwavelength imaging: Resolution enhancement using metal wire gratings,” Phys. Rev. B, vol. 73, pp. 035409–, 2006. [5] Z. Tang, H. Zhang, R. Peng, Y. Ye, C. Zhao, S. Wen, and D. Fan, “Subwavelength imaging by a dielectric-tube photonic crystal,” J. Opt. A: Pure Appl. Opt., vol. 8, pp. 831–834, 2006. [6] M. Tsang and D. Psaltis, “Theory of resonantly enhanced near-field imaging,” Opt. Express, vol. 15, no. 19, pp. 11959–11970, 2007.

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[7] T. Andrade, A. Grbic, and G. V. Eleftheriades, “Growing evanescent waves in continuous transmission-line grid media,” IEEE Microw. Wireless Compon. Lett., vol. 15, no. 2, pp. 131–133, Feb. 2005. [8] O. Malyuskin, V. Fusco, and A. Schuchinsky, “Microwave phase conjugation using nonlinearly loaded wire arrays,” IEEE Trans. Antennas Propag., vol. 54, no. 1, pp. 192–203, Jan. 2006. [9] M. Fink, “Time reversal of ultrasonic fields,” IEEE Trans. Ultrason. Ferroelect. Freq. Control, vol. 39, no. 5, pp. 555–566, Sept. 1992. [10] S. Maslovski and S. Tretyakov, “Phase conjugation and perfect lensing,” J. Appl. Phys., vol. 94, no. 7, pp. 4241–4243, Oct. 2003. [11] O. Malyuskin, V. Fusco, and A. Schuchinsky, “Phase conjugating wire FSS lens,” IEEE Trans. Antennas Propag., vol. 54, no. 5, pp. 1399–1404, 2006. [12] J. de Rosny and M. Fink, “Focusing properties of near-field time reversal,” Phys. Rev. A, vol. 76, pp. 065801–, 2007. [13] FEKO Suite. [Online]. Available: http://www.feko.info [14] H. Chen, “Theory of electromagnetic waves,” in A Coordinate Free Approach. New York: McGraw-Hill, 1983. [15] Farnell Catalogue, [Online]. Available: http://uk.farnell.com/ [Online]. Available: http://www.farnell.com/datasheets/357047.pdf [Online]. Available: http://www.avx.com/docs/Catalogs/useries.pdf [16] HSMS282x Surface Mount RF Schottky Barrier Diodes Data Sheet, Avago Technologies Ltd, Jun. 2006. [17] V. Fusco, A. Munir, and O. Malyuskin, “Characterization of microwave phase conjugate signal generation using nonlinearly loaded wire frequency selective surface (FSS),” IET Microw. Antennas Propag., vol. 3, no. 5, pp. 834–842, Aug. 2009. [18] O. Malyuskin and V. Fusco, “The effect of nonlinear load type on phase conjugation production in double periodic lump loaded wire arrays,” in Proc. Loughborough Antennas Propag. Conf., Apr. 11–12, 2006, pp. 333–336. Oleksandr Malyuskin (M’04) received the M.Sc. degree in radiophysics and electronics and the Ph.D. degree in electrical engineering from Kharkiv National University, Ukraine, in 1997 and 2001 respectively. He joined the Institute of Electronics, Communications and Information Technology, Queens University Belfast, in March 2004 as a Postdoctoral Research Fellow involved in the development of novel composite materials for advanced EM applications. His research interests include analytic and numerical methods in electromagnetic wave theory, characterization and application of complex and nonlinear materials, antenna arrays and time reversal techniques.

Vincent Fusco (S’82–M82–SM’96–F’04) received the Bachelors degree (1st class honors) in electrical and electronic engineering, the Ph.D. degree in microwave electronics, and the D.Sc. degree, for his work on advanced front end architectures with enhanced functionality, from Queens University of Belfast (QUB), Belfast, Northern Ireland, in 1979, 1982, and 2000, respectively. His research interests include nonlinear microwave circuit design, and active and passive antenna techniques. He is the Technical Director of the High Frequency Laboratories, Queens University of Belfast, and is also Director of the International Centre for Research for System on Chip and Advanced MicroWireless Integration, SoCaM. He has published over 400 scientific papers in major journals and international conferences, and is the author of two textbooks. He holds several patents on active and retrodirective antennas and has contributed invited chapters to books in the fields of active antenna design and EM field computation. Prof. Fusco is a Fellow of the Royal Academy of Engineering and a Member of the Royal Irish Academy. In 1986, he was awarded a British Telecommunications Fellowship and 1997 he was awarded the NI Engineering Federation Trophy for outstanding industrially relevant research.

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Electromagnetic Coupling Reduction in High-Profile Monopole Antennas Using Single-Negative Magnetic Metamaterials for MIMO Applications Mohammed M. Bait-Suwailam, Graduate Student Member, IEEE, Muhammed Said Boybay, Member, IEEE, and Omar M. Ramahi, Fellow, IEEE

Abstract—Single-negative magnetic metamaterials are used in order to reduce mutual coupling between high-profile antennas used in multiple-input multiple-output systems. The magnetic permeability of the developed single-negative inclusions have negative effective response over a specific frequency band. The inclusions considered here are composed of broadside coupled split-ring resonators. The single-negative magnetic inclusions are inserted between closely-spaced high-profile monopole antenna elements. It is shown that mutual coupling between the antenna elements can be reduced significantly by incorporating such magnetic inclusions. Effective response of the constitutive parameters of the developed magnetic inclusions are incorporated within the numerical models. Good agreement is obtained between the experimental and numerical results. Index Terms—Artificial magnetic materials, metamaterial, monopole antennas, multiple-input multiple-output (MIMO), mutual coupling.

I. INTRODUCTION

D

ECORRELATING multiple antenna elements when placed in a small platform is very important in order to improve the performance and capacity of an antenna system compared to a single-input single-output (SISO) system [1]. in order Usually antenna elements need to be spaced by to have suitable isolation and low correlation between the elements. However, degradation would result upon placing the antenna elements in close proximity, due to near-field effects, diffraction from finite-ground planes, and strong inductive and capacitive coupling between the elements [2]–[4]. Therefore the performance of antenna arrays or multiple-input multiple-output (MIMO) systems can be degraded when the antenna elements are in close proximity. In many outdoor and indoor wireless communication environments, there are many obstacles and scatterers, like buildings, mobile terminals, and offices. A problem that is encountered in such environments is multipath fading. This fading phe-

Manuscript received July 17, 2009; revised February 03, 2010; accepted March 20, 2010. Date of publication June 14, 2010; date of current version September 03, 2010. This work was supported by in part by the Sultan Qaboos University of Oman, Research in Motion Inc., and in part by the National Science and Engineering Research Council of Canada under the NSERC/RIM Industrial Research Chair and Discovery Programs. The authors are with the University of Waterloo, Department of Electrical and Computer Engineering, Waterloo, ON N2L 3G1, Canada. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TAP.2010.2052560

nomenon limits the performance and capacity of the antenna system. One of the ways to combat that multipath fading is to use multiple antennas at either transmit, receive, or both ends. In MIMO systems, more than two antennas are often employed. Thus, the correlation between any two antennas within the array is often required and needs to be kept as low as possible for better performance of the MIMO antenna system. Compactness and low-weight have become a highly desirable feature in an antennas’ design. As such, reduction of electromagnetic coupling or interference between the containing antenna elements becomes a challenging design task. Mutual coupling is a common problem in the antenna and electromagnetic interference (EMI) communities. It significantly affects most types of antenna arrays. The study of the mutual coupling problem started several decades ago, and several research efforts have been devoted to combat the mutual coupling between coupled antennas, not just from antenna engineers, but also from other disciplines such as communications where multiple antennas are frequently encountered, like in MIMO systems. Anderson et al. in his work [5] introduced the possibility of connecting a lossless network between the input ports and the antenna ports, such that no coupling between antennas is encountered. It was shown that antenna mutual impedances should be purely reactive at the resonance in order to realize a decoupling network and hence isolate the antenna elements when placed close to each others. Other methods have also been suggested in [6], [7], where transmission lines are used as antenna decouplers. Although the capacitive decouplers work well, they are inherently narrowband, and limited by the antenna bandwidth. An alternate way of reducing the electromagnetic coupling between radiating and/or receiving antenna elements sharing a common ground plane or chassis is to introduce resonant defects or slits in the ground plane [8]–[10]. By proper choice of dimensions, the slits resonate and can trap some of the energy between the radiating elements. Another strategy to mitigate the coupling between radiating antennas is to use electromagnetic band-gap (EBG) structures [11]. EBG structures were used extensively in mutual coupling reduction in planar and low-profile antennas [12], [13]. Another mechanism proposed previously to decorrelate (i.e., isolate) highly-coupled monopole antenna elements is by using 180 hybrid couplers [7], [14], [15]. The method is based on the mode-decomposition network, in which a multi-port network is inserted between the antennas and their driving ports.

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Ferrer et al. introduced the idea of using capacitively loaded loop (CLL) magnetic resonators in order to decorrelate two monopole antennas [16]. Although the coupling had been reduced in [16], the antenna elements were not well-matched. In [17], split-ring resonator (SRR) magnetic inclusions were used to reduce the coupling between closely-spaced monopole antennas. Higher suppression of mutual coupling was achieved in [17] in comparison to [16]. In this work, single-negative magnetic (MNG) metamaterials are developed in order to efficiently suppress the electromagnetic coupling between closely-spaced high-profile monopole antenna elements. One way of realizing MNG metamaterials is to use SRRs [18], [19]. Once these inclusions are excited using proper polarization, an induced electric current develops on the inclusions. If a large number of inclusions are arranged either periodically or aperiodically, the inclusions behave as magnetic dipole arrays. Those dipole elements result in having negative , over a certain frequency band. This effective permeability in turn prevents the existence of real propagating modes within the MNG metamaterials. Thus, it is plausible that a MNG metamaterials layer can block electromagnetic energy radiated by one antenna element from being transmitted to a nearby antenna element within an array system. This implies that the ensemble of resonators, comprising the MNG layer, act as a decoupling layer. The mutual coupling and envelope correlation between two monopole antennas, separated by an MNG layer, are investigated. This paper is organized as follows. Section II gives a conspectus of the theory and motivation behind using single-negative magnetic metamaterials as antenna decoupler. The design methodology for the magnetic materials considered in this work is also discussed with emphasis on the numerical characterization of the magnetic metamaterials. Experimental and numerical setups are presented and discussed in Section III. Section IV presents the results obtained from both the numerical and experimental setups. Moreover, an experimental analysis and investigation on the effectiveness of the developed magnetic materials as antennas decoupler is also presented. Conclusion and summary are given in Section V.

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Fig. 1. (a) Schematic model for the coupling path with the two antenna system and (b) its equivalent network model.

here the “coupling path” term, as shown in Fig. 1(a), in order to account for the mutual coupling between the antennas and the current path through the displacement current. That current path is also expected to strongly couple the antenna elements, and within which a magnetic field exists around the path between the antennas. This coupling path is indeed critical in high-profile antennas. Therefore, mitigating it through the use of an appropriate synthesis technique or introducing a decoupling network is desirable in many applications. Let us consider highly-coupled high-profile antennas in freespace. For simplicity, two antenna elements are considered in this analysis. The model comprising the two antennas with the coupling path, as shown in Fig. 1(a), is analyzed systematically in terms of scattering parameters for ease of analysis. Then, we show that the magnetic resonators indeed work as a decoupling network, in which the mutual impedance should be purely reactive at the resonance frequency in order to decouple the antenna at resonance.) Such a condition is elements (i.e., necessary for the existence of a decoupling network. This necessary condition had been discussed and verified in [5], [6] and [20]. Fig. 1 shows the two antenna elements as a two-port linear network with the following scattering parameters (1) represents the coupling path between the two where elements, clearly designated in Fig. 1(a). Let us assume that the two coupled antennas are lossless, reciprocal, matched and have ), then (1) becomes poor isolation (i.e., (2)

II. SINGLE-NEGATIVE MAGNETIC METAMATERIALS AS ANTENNA DECOUPLER When mounting closely-spaced high-profile monopole antenna arrays, degradation in impedance matching, field pattern, and strong mutual coupling become a performance challenge. Although the impedance can be tuned and/or optimized, the mutual coupling still remains as a bottleneck that deteriorates the performance of the antenna system. Due to the nature of the current distribution on monopole antennas, a magnetic field circulates around the antennas, leading to radiation into free-space, and possibly to nearby elements. A discussion on mutual coupling effects between linear antenna elements can be found in [2]. Displacement current is one of the contributors to the strong mutual coupling in antenna arrays. Such a current can exist in many types of matter, even in free-space. To have more physical insights into that kind of current, consider having two coupled antennas and spatially spaced in free-space. We introduce

Obviously what we need in order to efficiently decouple the anto tenna elements is to have high-isolation between them, be zero, which is an ideal case at resonance. It follows from (2) , should be rethat the antenna mutual impedances active, and thus all the mutual impedances should ideally be reactive. Although this might not be intuitive, it will be motivated and validated with antenna mutual impedance results. Note that the condition holds quite often at a single resonant frequency, but nonetheless, it could be satisfied over a frequency band depending on the designed decoupling network [5]. Generally, natural materials are characterized by constitutive parameters: the electrical permittivity , which is related to the response of a material to an electric field and the magnetic permeability , which gives the response of the material to a magnetic field. At microwave frequencies, and are both positive for natural materials, which can be termed double-positive (DPS) materials.

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Fig. 2. The developed single-negative magnetic metamaterials based on the (BC-SRRs): (a) Split-ring resonator (SRR) unit cell with its dimensions, (b) waveguide structure used for the characterization of MNG metamaterials. Note that -field points in y-direction, -field is in z-direction, and the propagation is x-direction.

E

H

An interesting phenomenon of strong relevance to the wide range of problems where electromagnetic interference is of concern, is the elimination of propagation when enhanced magnetic structures are employed. In such a scenario, transmission of electromagnetic energy would cease since purely evanescent waves (i.e., no real energy flow) exist within the magnetic decoupling layer. In this work, the decoupling layer has a complex with a negative real part effective magnetic permeability, above the enhanced resonance and positive real part below the resonance. In [21]–[23], several types of MNG metamaterial designs were discussed. In this work, without loss of generality, we consider one of the popular types, namely the broadside coupled rectangular split-ring resonators (BC-SRRs). Fig. 2(a) shows a unit cell of the developed artificial magnetic inclusion. A unit cell of the BC-SRR metamaterial is designed in order to decouple the antenna system while at the same time maintain low correlation between the antenna elements. Initial design dimensions of the SRR inclusion unit-cell were estimated numerically using the characterization model that will be discussed later. Next, the optimized dimensions were obtained such that the inclusion resonance takes place at the middle of the frequency band of interest. The SRR rings considered here have with strip width of 1 mm. equal sides of lengths The rings with opposite cut openings are etched on the sides , of a dielectric substrate (Rogers RO4350, ) having a thickness of 0.762 mm. The cut gaps within the metallic rings is 1 mm. The size of the dielectric substrate, , [see Fig. 2(a)] is 16 mm, which is much less than the operating wavelength at a frequency of 1.24 GHz. The SRR rings are made . of copper with a thickness of 20 The characterization and retrieval of MNG metamaterials are considered next. The model adopted in our work is based on the retrieval extraction method reported in [24]. Basically, one has to compute the scattering parameters of a unit cell SRR inclusion, from which the effective refractive index and impedance Z are first computed. The effective permittivity and permeability are then calculated from and . In order to numerically characterize the SRR inclusions, an air-filled waveguide with a unit cell positioned at the center of the waveguide is used, as shown in Fig. 2(b). Notice that the cell is positioned such that the incident magnetic field is perpendicular to the inclusion’s trace (or surface). The model mimics a transverse electromagnetic mode in both ports [see Fig. 2(b)], with top and bottom sides of the air-filled waveguide assigned

Fig. 3. Scattering parameters of a MNG unit cell inclusion extracted from the waveguide structure shown in Fig. 2(b).

Fig. 4. Effective response of the MNG unit cell constitutive parameters, extracted using the retrieval method in [24].

as perfect electric conducting walls, while its sides as perfect magnetic walls. and , comFig. 3 shows the scattering parameters, puted using two commercially available full-wave simulation tools (Ansoft HFSS [25], and CST Microwave Studio [26]). is below 20 dB at Clearly, the transmission coefficient, resonance. That dip in the transmission coefficient is attributed to the magnetic resonance nature of the developed inclusions when a magnetic field impinges normally to the inclusions axis. As such, the energy is sustained within the inclusions and results in no transmission at the enhanced magnetic resonance. The extracted real and imaginary parts of the effective electric permittivity and magnetic permeability of the magnetic resonators are shown in Fig. 4. As mentioned earlier, the antenna mutual impedance should be purely reactive at resonance with its real part being nearly zero at resonance. In order to show that condition, a numerical model comprising two monopole antennas with the single-negative magnetic decoupling network is made (see Fig. 5). The two antenna system with and without magnetic inclusions are compared. Fig. 6(a) shows the reactive part of the computed mutual , between the two monopoles with and without impedance, the magnetic decoupler layer. Around the resonance of the decoupling network, the reactive part is inductive, while it is capacitive over the antenna frequency band for the air case. . Fig. 6(b) shows the real part of the mutual impedance It is noticed that the computed resistances do not turn out to be exactly zero at resonance. Those losses are mainly due to the losses within the MNG decoupling network. It is of interest to note that the necessity condition in [5] was provided particularly for lossless decoupling networks. The decoupling

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III. EXPERIMENTAL AND NUMERICAL SETUPS

Fig. 5. Lateral view of the two-monopole antennas with SRR inclusions. Dis. The tances are given in terms of an operational wavelength  plastic support is not shown for clarity purposes.

= 240 mm

Fig. 6. Computed mutual impedance, Z , between the two monopole antennas with and without the MNG decoupling network: (a) reactive part and (b) resistive part.

Fig. 7. Fabricated monopole antenna system with the MNG metamaterial. Note that one monopole antenna is visible and another antenna element is behind the MNG layer.

network presented here is based on magnetic resonators, which are lossy and inherently narrowband [27]–[29].

Fig. 5 shows the schematic of two monopole antennas separated by a distance of , where is the wavelength corresponding to the resonant frequency of the separate monopole antennas. The two antennas have been designed to operate at a frequency of 1.24 GHz. A finite copper ground plane of size is used. Stacks of MNG inclusions, as designed and discussed in Section II, are aligned vertically between the two monopole antennas. In this work, 4 SRR inclusion pairs are etched on both sides of the dielectric substrate. The periodicity of the magnetic inclusions is an important parameter in the design of such inclusions, and it needs to be much smaller than the operating wavelength. The periodicity, or separation distance between each strip of the developed magnetic inclusions (see at the Fig. 5), corresponds to an electrical thickness of resonance frequency. The developed MNG inclusions have high permeability values below the resonance frequency. Those high permeability values enhance the inclusions resonance frequency and sustain much of the induced magnetic field within the MNG layer. The model setup for the monopole antennas, shown in Fig. 5, was fabricated using two brass rods of length 57 mm and diameter of 1.3 mm, soldered to 50 coaxial (SMA) connectors. Fig. 7 shows the fabricated model with the MNG metamaterials. Fig. 8 shows the reflection coefficient of the antenna , obtained using an HP8722ES VNA, and Fig. 9 system, shows the mutual coupling, , between the two antenna elements. A two-antenna system with no spacer (air case) is used as a reference for comparison purposes. Another case when placing a PEC screen between the antenna elements is considered for completeness, although it seems very intuitive from a PEC screen to reflect back incident waves. In order to sustain the SRR inclusions in a vertical position, a plastic support , ) has been used. The inclusions layer ( were sandwiched within the plastic holder with a uniform gap spacing between the MNG strips of 16 mm (see Fig. 7). Note that the spacing between the SRR inclusions corresponds to the spacing used in the characterization model of the MNG unit cell in Fig. 2(b). The scattering parameters have been computed using Ansoft HFSS and compared with measurements. Due to computational memory constraints, the effective response of the magnetic inclusions (see Section II and Fig. 4) is used in order to mimic the response of the magnetic inclusions. The artificial magnetic structures are in general inherently dispersive and anisotropic. The MNG materials considered in this work are based on the BC-SRRs [19]. Such inclusions provide enhanced permeability only in the direction normal to the inclusions plane ( -direction in Fig. 5), and enhanced permittivity in the directions tangent to the plane ( - and -directions in Fig. 5). In this work, the orientation of the magnetic inclusions is assumed in -plane, as shown in Fig. 5. In such a case, the effective permeability and permittivity of the magnetic structures can take the following tensor forms, respectively

(3)

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(4) represents the averaged permittivity between where the host medium ( with a slab thickness of ) and air gaps between successive MNG strips with an air-gap thickness of — ). ( It is instructive to note that within the numerical models, effective response of the constitutive parameters need to be carefully oriented. In more details, the effective permeability in the directions correspond to ( , 1, 1), while the effective permittivity response corresponds to in respectively, as can be seen from (3) and (4). IV. RESULTS A. Scattering Parameters By placing the MNG inclusions between the antenna elehas been reduced by almost 25 ments, the mutual coupling dB at the resonance frequency, while at the same time maintaining good impedance match for the two-antenna system. The high values below resonance of the MNG inclusions, see Fig. 4, have contributed to the mutual coupling suppres, starts to drop sion, where the transmission coefficient, below 10 dB around 1.17 GHz. Moreover, the negative values above resonance have stronger influence on the mutual coupling suppression. This is attributed to the existence of evanescent fields within the negative region of the magnetic inclusions (i.e., above resonance), which blocks the EM energy from being transmitted from one antenna element to another. A (below 40 dB) was noticed at a frequency sizeable dip in of 1.22 GHz. We note here that the antennas without magnetic inclusions (air case) were not well-matched due to the strong mutual coupling between the two monopole antennas. Good agreement between the numerical results and experimental ones can be seen. The modeling of the effective response of the developed MNG inclusions, rather than modeling the real structure shows its effectiveness from both computational time and memory requirements. The mutual coupling suppression level achieved as a result of using the BC-SRRs inclusions is higher than the suppression level presented in [16], especially at the antennas’ resonance. Most interestingly, however, is that unlike [16], the antennas in this work are well matched at the operating frequency despite the severe limitation placed on their separation distance. (The antennas were separated by a , and in another case . In terms distance of only of the operating wavelength, the separation distances between the antennas considered here were relatively smaller than the given in [16].) antennas separation distance of The field generated by antennas can be considered as a superposition of evanescent and propagating waves. The interaction between antennas is a combination of the effects of these plane wave components. In order to eliminate the coupling, the propagating waves and the evanescent components with low decay constants must be suppressed. To analyze the relevant evanescent spectrum, we assume that coupling due to the evanescent discomponents that decay more than 10 times within a

tance can be ignored. Therefore the evanescent fields that satare ignored, where is the compoisfy nent of the wave vector (see Fig. 5). Using dispersion relation and the assumption stated above, it can be deduced that the components that cause the interaction between the antenna elements are both the evanescent and propagating waves with . As a result the minimum spatial wavelength in the plane to be suppressed is . Since the periodicity of the developed SNG (i.e., magnetic metamaterial inclusions is smaller than ), the SNG layer can be assumed as an effective hoaround mogenized medium for these components. B. Envelope Correlation Next, the performance of antenna arrays applicable to MIMO systems is studied. In a rich scattering multipath environment, the correlation between the antenna elements can be expressed using far-field components [4], mutual impedances between the antenna elements [30], [31], or directly from the scattering parameters measured at the ports [32]. Under the assumption of uniform incident waves and good impedance matching, the envelope correlation can be calculated from the scattering parameters much more readily than from the far-field patterns. In this work, the use of scattering parameters is incorporated in the envelope correlation computation and compared with that using far-field method [4]. of a two antenna system using The envelope correlation the far field method [4] can be calculated using

(5)

represents the field radiation pattern of the anwhere tenna system when port is excited and all other ports are terminated in a matched 50 load [32], and is the Hermitian product. The envelope correlation based on the scattering matrix can be calculated using [32], [33] (6) In the case of a 2 2 MIMO system correlation between antenna element as

and

, the envelope is given

(7) for the antenna system with the The envelope correlation MNG inclusions is computed using (6) and compared with the far field formula in (5). Results presented in Fig. 10 show comparison with the case without spacers between the antennas. Good agreement between the envelope correlation computed using (6) and that obtained using the far field method in (5) can be seen for the air case. The computed envelope correlation was above 0.3 in average.

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Fig. 8. Magnitude of S for the monopole antenna system with and without the MNG metamaterial slab.

Fig. 9. Magnitude of S for the monopole antenna system with and without the MNG metamaterial slab.

Fig. 10. Envelope correlation,  , for the monopole antenna system with and without MNG inclusions.

The assessment of envelope correlation using (6) is more suitable for lossless cases (i.e., no lossy decoupling networks between the antennas) rather than to use the Far-field method (5). This is because the scattering parameters formulation is more cost effective and can be obtained from a simple measurement of scattering parameters instead of using the far-field radiation pattern, which is a time-consuming process. The presence of the artificial magnetic medium between the antennas introduces energy dissipation which can be accounted for if a three-port network model is conceived for the system at hand (in such model, the third port will be terminated with a resistive network to account for the losses.) Therefore, since the coupling between the parameter, two antennas is diminished as measured by the the 3-port S-parameter model used for calculating the correlation coefficient, while not fully descriptive of the energy transfer

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between the two antennas, is more relevant to analyzing the system presented in this work. From Fig. 10, the envelope correlation results using (6) for the MNG case shows low correlation between the antenna elements below 0.2 over the antennas frequency band as compared to the air case. The correlation then starts to increase after 1.3 GHz, which corresponds to diminishing of the mutual coupling suppression when using the developed magnetic inclusions (see Fig. 9). We emphasize here that the increase in envelope correlation beyond 1.3 GHz will result in non-orthogonal radiation patterns. Nonetheless, the 1.3 GHz is at the edge of the operational band of the two-monopole antenna system. The envelope correlation results obtained using (5) show that the antenna elements are well-decorrelated below 0.1 for frequencies up to 1.25 GHz where losses of the magnetic inclusions are inherently pronounced above 1.25 GHz. An important conclusion based on the assessment of the envelope correlation between antennas is that the scattering matrix based formula is inaccurate, especially in situations when lossy decoupling networks are placed between the coupled antenna elements, which is simply because the evaluation of correlation based on the scattering parameters do not account for the antennas efficiency. Similar observations were reported in [33]. Although the difference between envelope correlation calculations is attributed to the electromagnetic loss of the MNG material, Figs. 4 and 10 show that the deviation between envelope correlation calculations correspond to the frequencies where the loss tangent of the MNG material is low. This counter intuitive observation is explained as follows. The first thing to note is that the decay and energy dissipation relation in the case of a regular double positive lossy material is different than the relation in the case of a single negative material. Therefore, a straight forward relation between the imaginary part of the and the electromagnetic loss within the negative material that states “the higher the imaginary part, the higher the loss” is not correct in all cases. Basically, the decay within MNG material is a result of the high negative value of the real part of the . When the real part of is highly negative, the field is suppressed faster and the field would not penetrate to the MNG material. Therefore, the amount of the field within a slab with highly negative real is not as much as the amount of the field within a MNG material with negative closer to zero. As a result, even if the imaginary part is higher for highly negative MNG materials, they do not dissipate as much energy as MNG materials which have a negative closer to zero. This behavior is also affected by the thickness of the slab and the mode, direction and evanescence of the incident field. This phenomenon is described in Fig. 11, where the electric field intensity is plotted within the MNG material at different frequencies. Although the imaginary part is lower at higher frequencies, since the field penetrates more, it is possible to lose more energy. Note that for the presented plot, it is assumed that the incident field is a TEM plane wave. In addition, the total power consumed within the metamaterial layer (using effective medium parameters) was calculated using CST Microwave Studio and presented in Fig. 12. The power consumption is higher at higher frequencies although the imaginary part of the permeability is lower.

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Fig. 11. Computed electric field intensity within the MNG material at several frequencies.

Fig. 14. Computed gain pattern for the two monopoles with magnetic inclu), (b) H-plane (yz -cut, ). sions at 1.2 GHz (a) E-plane (yz -cut,

= 90

Fig. 12. Computed Power Loss within the MNG layer using CST Microwave Studio.

Fig. 13. Computed gain pattern for the two monopoles with and without ), (b) magnetic inclusions at 1.22 GHz (a) E-plane (yz -cut,  H-plane(xy -cut, ).

= 90

= 90

C. Far-Field Results Far-field radiation patterns for the monopole antennas with and without the MNG metamaterial are numerically computed using Ansoft HFSS. In the numerical simulation, one antenna was connected to a 50 coaxial (SMA) connector while the other element is terminated with a 50 load. Fig. 13 shows the far-field pattern for the two antennas with and without the magnetic inclusions. The computed results [see Fig. 13(a)] show that

= 90

the use of MNG inclusions enhances the antennas’ potential to steer or concentrate energy into a more specified direction, thus increasing the gain in specific directions, whereas the counterpart antenna system (i.e., antennas without SRRs) yield the typical donut shape. For the resonant frequency of 1.22 GHz, the gain has increased from 4.2 dB for the air case to 5.6 dB for the case when SRR magnetic inclusions were used between the two at the resonance frequency. antennas. We also notice a dip in ) for Fig. 13(b) shows the gain in the H-plane (xy-plane, the aforementioned cases. It is observed that the MNG inclusions help in achieving quasi-orthogonal patterns and reducing the back radiation in comparison to the air case. This feature of achieving orthogonal or quasi-orthogonal patterns is desirable in order to maintain low correlation between antenna elements. As there is a trade-off between mutual coupling suppression and attained envelope correlation when incorporating the magnetic inclusions, the two antenna system, when used for MIMO applications, can still operate at a frequency of 1.2 GHz where high and low suppression level for mutual coupling envelope correlation below 0.1 were achieved. Fig. 14 shows the far-field patterns for the two antenna elements with MNG inclusions at frequency of 1.2 GHz. The antenna system achieve quasi-orthogonal patterns when using the magnetic inclusions. Due to the nature of the magnetic resonators losses, the radiation efficiency of the antenna system with magnetic inclusions layer dropped to 60% at the SRR’s resonance of 1.24 GHz. Despite the encountered losses, the gain has been enhanced when using the magnetic inclusions at a frequency of 1.2 and 1.22 GHz where the radiation efficiency was almost 93% and 80% respectively. D. MNG Decoupler Effectiveness The effectiveness of the MNG as an antenna decoupler is experimentally investigated. Parametric analysis based on varying the number of MNG strips is considered. Results are

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Fig. 15. Parametric study for the measured mutual coupling between the monopole antenna elements when MNG strips are varied.

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load. The HFSS full-wave solver is terminated with a 50 used in this context. Two normalized separation distances of and 0.125 are shown for two antenna elements with the developed MNG inclusions and compared with air case (no spacers). By placing the MNG metamaterials between the two antennas, much of the radiated energy is blocked and no transmission of energy is observed within such materials. The strength of the coupling path can be seen for the case of no spacers between the antenna elements, due to the strong mutual interaction between the antennas. The MNG layer effectively reduced the mutual coupling between the antennas and mitigated the displacement current and as such the coupling path effect diminished. V. CONCLUSION

Fig. 16. Snapshots of the H-field in the transverse plane (i.e. yz -plane) for the monopole antenna system with: (a) MNG metamaterials (d= = 0:1), (b) MNG metamaterials (d= = 0:125), and (c) without any spacers (d= = 0:125). Note that a maximum H-field strength of 1 A/m is used within the snapshot plots.

shown in Fig. 15. It is observed that by inserting 2 strips of the MNG metamaterials, the effectiveness of such materials in suppressing the mutual coupling is diminished. However, when using 8 strips, a minimum of 44 dB suppression was achieved, and the 10 strips case is as illustrated before and shown in Fig. 9. A case study was also conducted to investigate the effects on the envelope correlation between the antennas when varying the number of MNG strips from 2 to 12 at the antennas resonant frequency. Although it is not shown, it was observed that the use of 8 MNG strips is sufficient to achieve low correlation between the antenna elements, below 0.25. Fig. 16 illustrates how the displacement current is mitigated using the developed single-negative magnetic materials. In order to show the effectiveness of the developed MNG inclusions, one of the antennas is fed while the other element is

Mutual coupling between closely-spaced high-profile monopole antennas was investigated with particular focus on multiple-input multiple-output (MIMO) systems. Guidelines for the design and analysis of single-negative magnetic metamaterials as an antenna decoupler were discussed in detail. The metamaterials constructed in this work have high negative effective magnetic response. Effectiveness of the magnetic inclusions was experimentally investigated with emphasis on the effect of the number of MNG strips inserted between closely-spaced monopole antenna elements. The magnetic inclusions show their effectiveness in terms of reducing the mutual coupling and their shielding effectiveness in suppressing the displacement current. Thus the MNG layer is an efficient magnetic shielding wall that can be advantageous in antenna applications and EMI problems. Numerical and experimental results show that more than 20 dB reduction in mutual coupling between antenna elements was achieved. Moreover, good impedance matching can be achieved when using the MNG inclusions, unlike the case without MNG inclusions. An interesting added advantage when using the MNG metamaterials is the ability to increase the directivity, which can be useful for point-to-point communications. The envelope correlation between high-profile monopole antenna elements was computed and assessed using scattering parameters formulation and far-field radiation pattern method. It is shown that the correlation based on the far-field pattern is more accurate than the correlation based on scattering parameters. REFERENCES [1] G. J. Foschini and M. J. Gans, “On limits of wireless communications in a fading environment when using multiple antennas,” Wireless Personal Commun., vol. 6, no. 3, pp. 311–335, 1998. [2] C. A. Balanis, Antenna Theory Analysis and Design. Hoboken, NJ: Wiley, 2005. [3] B. Bhattacharyya, “Input resistances of horizontal electric and vertical magnetic dipoles over a homogeneous ground,” IEEE Trans. Antennas Propag., vol. 11, no. 3, pp. 261–266, May 1963. [4] R. Vaughan and J. Andersen, “Antenna diversity in mobile communications,” IEEE Trans. Veh. Technol., vol. 36, no. 4, pp. 149–172, Nov. 1987. [5] J. Andersen and H. Rasmussen, “Decoupling and descattering networks for antennas,” IEEE Trans. Antennas Propag., vol. 24, no. 6, pp. 841–846, Nov. 1976. [6] S.-C. Chen, Y.-S. Wang, and S.-J. Chung, “A decoupling technique for increasing the port isolation between two strongly coupled antennas,” IEEE Trans. Antennas Propag., vol. 56, no. 12, pp. 3650–3658, Dec. 2008.

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[7] S. Dossche, S. Blanch, and J. Romeu, “Three different ways to decorrelate two closely spaced monopoles for MIMO applications,” in Proc. IEEE/ACES Int. Conf. on Wireless Communications and Applied Computational Electromagnetics, Apr. 2005, pp. 849–852. [8] T. Kokkinos, E. Liakou, and A. Feresidis, “Decoupling antenna elements of PIFA arrays on handheld devices,” Electron. Lett., vol. 44, no. 25, pp. 1442–1444, 2008, 4. [9] C.-Y. Chiu, C.-H. Cheng, R. Murch, and C. Rowell, “Reduction of mutual coupling between closely-packed antenna elements,” IEEE Trans. Antennas Propag., vol. 55, no. 6, Jun. 2007. [10] I. Kim, C. W. Jung, Y. Kim, and Y. E. Kim, “Low-profile wideband MIMO antenna with suppressing mutual coupling between two antenans,” Microwave Opt. Tech. Lett., vol. 50, no. 5, pp. 1336–1339, March 2008. [11] D. Sievenpiper, L. Zhang, R. Broas, N. Alexopolous, and E. Yablonovitch, “High-impedance electromagnetic surfaces with a forbidden frequency band,” IEEE Trans. Microw. Theory Tech., vol. 47, no. 11, pp. 2059–2074, Nov. 1999. [12] F. Yang and Y. Rahmat-Samii, “Microstrip antennas integrated with electromagnetic band-gap (EBG) structures: A low mutual coupling design for array applications,” IEEE Trans. Antennas Propag., vol. 51, no. 10, pp. 2936–2946, Oct. 2003. [13] M. F. Abedin and M. Ali, “Reducing the mutual-coupling between the elements of a printed dipole array using planar EBG structures,” in Proc. IEEE AP-S Int. Symp. Antennas Propag., Jul. 2005, pp. 598–601. [14] T.-I. Lee and Y. Wang, “Mode-based information channels in closely coupled dipole pairs,” IEEE Trans. Antennas Propag., vol. 56, no. 12, pp. 3804–3811, Dec. 2008. [15] C. Volmer, J. Weber, R. Stephan, K. Blau, and M. Hein, “An eigen-analysis of compact antenna arrays and its application to port decoupling,” IEEE Trans. Antennas Propag., vol. 56, no. 2, pp. 360–370, Feb. 2008. [16] P. J. Ferrer, J. M. Gonzalez-Arbesu, and J. Romeu, “Decorrelation of two closely spaced antennas with a metamaterial AMC surface,” Microw. Opt. Tech. Letts., vol. 50, no. 5, pp. 1414–1417, May 2008. [17] M. M. Bait-Suwailam, M. S. Boybay, and O. M. Ramahi, “Mutual coupling reduction in MIMO antennas using artificial magnetic materias,” in Proc. 13th Int. Symp. on Antenna Technology and Applied Electromagnetics (ANTEM/URSI), Feb. 2009, pp. 1–4. [18] J. Pendry, A. Holden, D. Robbins, and W. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microw. Theory Tech., vol. 47, no. 11, pp. 2075–2084, Nov. 1999. [19] R. Marques, F. Medina, and R. Rafii-El-Idrissi, “Role of bianisotropy in negative permeability and left-handed metamaterials,” Phys. Rev. B, vol. 65, pp. 144440–144446, 2002. [20] W. Wasylkiwskyj and W. Kahn, “Theory of mutual coupling among minimum-scattering antennas,” IEEE Trans. Antennas Propag., vol. 18, no. 2, pp. 204–216, Mar. 1970. [21] D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “A composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett., vol. 84, pp. 4184–4187, May 2000. [22] S. Maslovski, P. Ikonen, I. Kolmakov, S. Tretyakov, and M. Kaunisto, “Artificial magnetic materials based on the new magnetic particle: Metasolenoid,” Progr. Electromagn. Res., vol. 54, pp. 61–81, 2005. [23] A. Erentok, P. Luljak, and R. Ziolkowski, “Characterization of a volumetric metamaterial realization of an artificial magnetic conductor for antenna applications,” IEEE Trans. Antennas Propag., vol. 53, no. 1, pp. 160–172, Jan. 2005. [24] X. Chen, T. M. Grzegorczyk, B.-I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E, vol. 70, no. 1, pp. 016 608.1–016 608.7, Jul. 2004. [25] Ansoft HFSS [Online]. Available: http://www.ansoft.com [26] CST Microwave Studio [Online]. Available: http://www.cst.com [27] K. Aydin, I. Bulu, K. Guven, M. Kafesaki, C. M. Soukoulis, and E. Ozbay, “Investigation of magnetic resonances for different split-ring resonator parameters and designs,” New J. Phys., vol. 7, p. 168, 2005. [28] X. Q. Lin and T. J. Cui, “Controlling the bandwidth of split ring resonators,” IEEE Microw. Wireless Comp. Lett., vol. 18, no. 4, pp. 245–247, Apr. 2008. [29] R. Marques, F. Mesa, J. Martel, and F. Medina, “Comparative analysis of edge- and broadside- coupled split ring resonators for metamaterial design—Theory and experiments,” IEEE Trans. Antennas Propag., vol. 51, no. 10, pp. 2572–2581, Oct. 2003. [30] A. Derneryd and G. Kristensson, “Antenna signal correlation and its relation to the impedance matrix,” Electron. Lett., vol. 40, no. 7, pp. 401–402, Apr. 2004.

[31] H. Hui and H. S. Lui, “Expression of correlation coefficient for two omindirectional antennas using conventional mutual impedances,” Electron. Lett., vol. 44, no. 20, pp. 1177–1178, Sep. 2008. [32] S. Blanch, J. Romeu, and I. Corbella, “Exact representation of antenna system diversity performance from input parameter description,” Electron. Lett., vol. 39, no. 9, pp. 705–707, May 2003. [33] J. Thaysen and K. Jakobsen, “Envelope correlation in (N, N) MIMO antenna array from scattering parameters,” Microw. Opt. Tech. Letts., vol. 48, no. 5, pp. 832–834, May 2006.

Mohammed M. Bait-Suwailam (S’98) received the B.E. degree from Sultan Qaboos University, Muscat, Oman, in 2001 and the M.A.Sc. degree from Dalhousie University, Halifax, Nova Scotia, in 2004, both in electrical and computer engineering. He is currently working toward the Ph.D. degree at the University of Waterloo, Waterloo, ON, Canada. In 2001, he was appointed as a Lecturer at Sultan Qaboos University, where he was involved with teaching, academic advising and research. From 2002 to 2004, he was a teaching assistant at Dalhousie University, while pursing his masters degree. His research interests include electromagnetic bandgap (EBG) structures, metamaterials for EMI reduction in antenna systems, computational electromagnetics and EMI/EMC applications. Mr. Bait-Suwailam is the recipient of two scholarships from the Sultan Qaboos University. Bait-Suwailam is an IEEE student member since 1998.

Muhammed Said Boybay (S’07–M’09) received the B.S. degree in electrical and electronics engineering from Bilkent University, Turkey, in 2004 and the Ph.D. degree in electrical and computer engineering from the University of Waterloo, Waterloo, ON, Canada, in 2009. From 2004 to 2009, he was a research and teaching assistant in the Mechanical and Mechatronics Engineering, and Electrical and Computer Engineering Departments of the University of Waterloo. Currently, he is a Postdoctoral Fellow in the Department of Electrical and Computer Engineering, University of Waterloo. His research interests include double and single negative materials, near field imaging, electrically small resonators, electromagnetic bandgap structures and EMI/EMC applications.

Omar M. Ramahi (F’09) received the B.S. degree in mathematics and electrical and computer engineering (summa cum laude) from Oregon State University, Corvallis and the M.S. and Ph.D. degrees in electrical and computer engineering from the University of Illinois at Urbana-Champaign. From 1990 to 1993, he held a visiting fellowship position at the University of Illinois at Urbana-Champaign. From 1993 to 2000, he worked at Digital Equipment Corporation (presently, HP), where he was a member of the alpha server product development group. In 2000, he joined the faculty of the James Clark School of Engineering at the University of Maryland at College Park as an Assistant Professor and later as a tenured Associate Professor. At Maryland he was also a faculty member of the CALCE Electronic Products and Systems Center. Presently, he is a Professor in the Electrical and Computer Engineering Department and holds the NSERC/RIM Industrial Research Associate Chair, University of Waterloo, Ontario, Canada. He holds cross appointments with the Department of Mechanical and Mechatronics Engineering and the Department of Physics and Astronomy. He has been a consultant to several companies and was a co-founder of EMS-PLUS, LLC and Applied Electromagnetic Technology, LLC. He has authored and coauthored over 240 journal and conference papers. He is a coauthor of the book EMI/EMC Computational Modeling Handbook, 2nd Ed. (Springer-Verlag, 2001). Dr. Ramahi serves as an Associate Editor for the IEEE TRANSACTIONS ON ADVANCED PACKAGING and as the IEEE EMC Society Distinguished Lecturer.

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Diffraction by a Planar Metamaterial Junction With PEC Backing Gianluca Gennarelli and Giovanni Riccio, Member, IEEE

Abstract—A uniform asymptotic solution is proposed for solving the local diffraction problem arising from the presence of a discontinuity in planar metamaterial structures. In particular, a junction formed by double-positive/double-negative material layers on a perfect electric conductor ground plane is considered in the case of incident plane waves. The diffracted field is obtained by using a physical optics approximation of the electric and magnetic surface currents in the radiation integral and by performing a uniform asymptotic evaluation of this last. The resulting expression contains the geometrical optics response of the structure and the transition function of the uniform theory of diffraction. The accuracy of the proposed solution is well assessed by comparisons with a commercial tool based on the finite element method. Index Terms—Diffraction, double-positive/double-negative material junction, perfect electric conductor backing, uniform asymptotic physical optics solution.

I. INTRODUCTION HIS manuscript deals with the local diffraction problem originated by a plane wave impinging on a planar junction formed by lossy double-positive (DPS)/double-negative (DNG) material layers with a perfect electric conductor (PEC) backing (see Fig. 1). Its solution represents the key to very important applications involving DNG metamaterials (MTMs) based structures and devices, such as modern antenna systems to be mounted on civil or military vehicles. Moreover, the MTMs coating of their otherwise metallic surfaces may be used for controlling their radar cross section. DNG MTMs have negative permittivity and permeability simultaneously (or negative refractive index), so that waves propagate with antiparallel phase and group velocities unlike DPS materials. They can be manufactured by embedding small inclusions in host media (volumetric DNG MTMs) or by connecting inhomogeneities to host surfaces (planar DNG MTMs) for obtaining electromagnetic properties not generally found in nature, and this justifies the interest on them [1]–[3]. Note that the losses increase the difficulties in both design and applications of modern DNG MTMs [4]–[6]. Numerical methods can be used to solve scattering problems concerning DNG MTMs (see [7]–[10] as references), but they become very poorly convergent and inefficient when

T

Manuscript received December 16, 2009; revised February 25, 2010; accepted March 20, 2010. Date of publication June 14, 2010; date of current version September 03, 2010. The authors are with the Department of Electrical and Information Engineering, University of Salerno, 84084 Fisciano (SA), Italy (e-mail: riccio@diiie. unisa.it). Digital Object Identifier 10.1109/TAP.2010.2052581

Fig. 1. Geometry of the problem.

considering structures large in terms of the wavelength. At high frequencies, such problems are not easy to solve from the analytical standpoint and most of studies available in literature are mainly focused on the ray-oriented framework of Geometrical Optics (GO). On the other hand, the important effects originated by truncation or discontinuity of the structure cannot be ignored for an accurate solution of the problem, so that it becomes very important to extend GO to the geometrical theory of diffraction (GTD) framework including the diffracted rays. In this context, a uniform geometrical theory of diffraction (UTD) for predicting the radiation by sources near thin planar DPS/DNG material discontinuities can be found in [11]. It has been obtained via a partially heuristic spectral synthesis approach and recovers the proper local plane wave Fresnel’s reflection and transmission coefficients and surface wave constants of the DPS/DNG material. In addition, a uniform asymptotic physical optics (UAPO) solution has been recently proposed by the authors for determining the field diffracted by the edge of a lossless, isotropic and homogeneous DNG MTM layer in the case of plane waves at skew incidence [12]. It is expressed in terms of the GO response of the structure and the UTD transition function [13], and gives accurate results. Moreover, it is easy to handle and apply. The peculiarities of the UAPO-based approach suggest working in this context for solving the problem here tackled. The starting point is that of considering the radiation integral with a PO approximation of the electric and magnetic surface currents in the integrand. Due to the linearity of the problem and its analytical formulation, each layer forming the junction contributes to the scattered field separately. A useful approximation and a uniform asymptotic evaluation of the resulting integral allow one to derive the UAPO solution for the field diffracted by the edge of each layer with a PEC backing. The

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final expression is in closed form and given in a useful matrix notation, so that it is simple to identify the diffraction matrix related to the whole structure. Comparisons with Comsol Multiphysics results are used to assess the accuracy of the proposed UAPO-based approach. II. GO RESPONSE OF THE STRUCTURE A thin lossy, isotropic and homogeneous layer with thickness is placed on a PEC ground plane and illuminated by a linearly polarized plane wave. It is characterized by and , where and are the free-space permittivity and permeability, respectively, and the sign is relevant to the DPS (DNG) material. The GO response of the structure can be conveniently evaluated by considering the local ray-fixed reference systems shown in Fig. 2. Accordingly, the reflected field can be expressed as

(1) wherein and denote the incident and reflected field components parallel and perpendicular to the ordinary plane of incidence. As well-known, the elements of the reflection matrix can be determined by considering the equivalent transmission lines (ETLs) circuit, so obtaining

Fig. 2. Ray-fixed co-ordinate systems in the incidence plane.

III. UAPO DIFFRACTION MATRIX A useful reference co-ordinate system is fixed with the -axis directed along the discontinuity and the -axis on the illumi, nated DPS layer. The incidence direction is specified by where the angle is a measure of the skewness with respect to the discontinuity and the angle gives the aperture of the discontinuity-fixed plane of incidence with respect to the DPS layer (see Fig. 1). The observation direction is specified by in a similar way. The starting point for determining the diffracted field is to and magconsider a PO approximation for the electric surface currents due to the incident field. The field netic generated by such currents can be expressed by means of the well-known radiation integral in the far-field approximation

(2) is the free-space impedance and is the angle between If the unit vector normal to the illuminated surface and the incidence direction, the ETL characteristic impedances related to the free-space surrounding the structure are given by and . The ETL input impedances concerning the grounded layer can be so determined

(3) where

where

,

is the (3

(10) 3) identity matrix,

, and denote the observation and source points, respectively, and is the unit vector from the radiating element at to the observation point. According to (10), each layer forming the junction contributes to the scattered . field separately, so that , the electric and magnetic PO surWith reference to face currents can be expressed in terms of the GO response of the structure as follows:

(4) (5)

(6)

(11)

(7) (8) (9) in which

is the free-space propagation constant.

(12) in which are the coordinates of the integration point on the surface, and .

GENNARELLI AND RICCIO: DIFFRACTION BY A PLANAR METAMATERIAL JUNCTION WITH PEC BACKING

In order to evaluate the edge diffraction confined to the , it is possible to approximate Keller’s cone for which by , which is the unit vector in the diffraction direction. Accordingly, it is possible to write

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in the high frequency approximation (see [16] for reference). The resulting diffraction term is

(13) (18) wherein in which is the UTD transition function [13], and the idenand are used on the diffraction tities cone. The above result defines the UAPO diffracted field to be added to the GO field, and the matrix formulation (13) can be rewritten as

(14)

and the explicit expression of the matrix the Appendix. Accounting for

(19)

is reported in so that the UAPO solution for the 2 is

(15) it results in

2 diffraction matrix

(20) for obtaining the The same approach can be applied to 2 diffraction matrix . AcUAPO solution for the 2 cordingly, the UAPO diffraction matrix related to the discontinuity is given by (21)

(16)

where

where is the zeroth order Hankel function of the second kind. A useful integral representation of such a function [14] and application of the Sommerfeld-Maliuzhinets inversion formula [15] give

(22) The matrix can be determined by following an approach similar to that used for .

(17)

wherein is the integration path in the complex -plane shown in Fig. 3. The integral in (17) can be reduced to a typical diffraction integral and evaluated by using the steepest descent method

IV. NUMERICAL TESTS The effectiveness of the proposed UAPO solution is here proved by means of numerical tests. If is the free-space wavelength, the junction is characterized by the following , , for what conparameters: , , cerns the DPS layer, and

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Fig. 3. Integration path in the complex -plane.

Fig. 4.

E

Fig. 5. -component of the total field. Incident field: Incidence direction: , .

= 50

-component of the GO and UAPO fields. Incident field: E

= 1. Incidence direction: = 50 ,  = 70

.

= 1,

with reference to the DNG MTM layer. The . circular observation path here considered has radius Figures from 4 to 7 refer to an incident plane wave propa, and having , gating in the direction . As expected, the - and -components of the GO field exhibit a discontinuity at the reflection boundary , whereas the UAPO diffracted field is significant in the vicinity of such a boundary (see Figs. 4 and 6) and guarantees the continuity of the total field as shown in Figs. 5 and 7. Accordingly, the UAPO diffracted field fulfils expectations. Moreover, its accuracy is assessed by performing numerical simulations and comparisons with the RF module of Comsol Multiphysics, a commercial solver based on the proven finite element method. Excellent agreements relevant to normal incidence directions far from the grazing one are reported in Figs. 8–10. When the incidence direction is close to the grazing one, the agreement is not so good (see Fig. 11) because of the well-known limitations of the PO approach and the increased importance of the surface waves neglected in the proposed solution. V. CONCLUSION A UAPO solution for the local diffraction problem due to a discontinuity in planar metamaterial structures has been derived in this work. It possesses the same ease of handling of other solutions in the UTD framework and has the inherent advantage of

Fig. 6.

E

= 70

E

= 1, E = 1.

-component of the GO and UAPO fields. Incident field: E

= 1. Incidence direction: = 50 ,  = 70

.

Fig. 7. -component of the total field. Incident field: Incidence direction: , .

= 50

= 70

E

= 1,

= 1, E = 1.

providing the diffraction coefficients from the knowledge of the reflection coefficients. It is computationally efficient and very accurate in the case of incidence directions far from the grazing one. The well-known drawbacks of the PO approach and the increased importance of the surface waves reduce the accuracy of the UAPO solution for incidence directions close to the grazing one.

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Fig. 8. Amplitude (dB) of the -component of the total field. Incident field: E ,E . Incidence direction:  .

Fig. 10. Amplitude (dB) of the -component of the total field. Incident field: ,E . Incidence direction:  . E

Fig. 9. Amplitude (dB) of the -component of the total field. Incident field: ,E . Incidence direction:  . E

Fig. 11. Amplitude (dB) of the -component of the total field. Incident field: . ,E . Incidence direction:  E

=1

=0

=0

=1

= 45

= 45

APPENDIX The matrix

can be expressed as follows:

=1

=1

=0

= 120

=0

=5

relates the base to dence direction and, at last

in the plane normal to the inci-

where

is the transformation matrix for the edge to ray-fixed coordinate system components

is the transformation matrix relating the base

, to ,

Note that the matrices and sions of the PO surface currents.

originate from the expres-

REFERENCES [1] N. Engheta and R. W. Ziolkowski, “A positive future for double-negative metamaterials,” IEEE Trans. Microwave Theory Tech., vol. 53, pp. 1535–1556, 2005.

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[2] N. Engheta and R. W. Ziolkowski, Metamaterials: Physics and Engineering Explorations. Hoboken: Wiley-Interscience, 2006. [3] C. Caloz and T. Itoh, Electromagnetic Metamaterials: Transmission Line Theory and Microwave Applications. Hoboken: Wiley-Interscience, 2006. [4] S. Zhang, W. Fan, K. J. Malloy, S. R. J. Brueck, N. C. Panoiu, and R. M. Osgood, “Demonstration of metal-dielectric negative-index metamaterials with improved performance at optical frequencies,” J. Opt. Soc. Am. B, vol. 23, pp. 434–438, 2006. [5] A. Alù, A. Salandrino, and N. Engheta, “Negative effective permeability and left-handed materials at optical frequencies,” Opt Express, vol. 14, pp. 1557–1567, 2006. [6] A. G. Kussow, A. Akyurtlu, A. Semichaevsky, and N. Angkaw-based negative refraction index metamaterial at isittpan, “ visible frequencies: Theoretical analysis,” Phys Rev B, vol. 76, pp. 195123:1–195123:7, 2007. [7] C. D. Moss, T. M. Grzegorczyk, Y. Zhang, and J. A. Kong, “Numerical studies of left handed metamaterials,” Progr. Electromagn. Res., vol. 35, pp. 315–334, 2002. [8] R. W. Ziolkowski, “Pulsed and CW gaussian beam interactions with double negative metamaterial slabs,” Optics Express, vol. 11, no. 7, pp. 662–681, April 2003. [9] P. P. M. So, H. Du, and W. J. R. Hoefer, “Modeling of metamaterials with negative refractive index using 2D-shunt and 3D-SCN TLM networks,” IEEE Trans. Microwave Theory Tech., vol. 53, pp. 1496–1505, 2005. [10] Y. Shi and C. H. Liang, “Analysis of the double-negative materials using multi-domain pseudospectral time-domain algorithm,” Progr. Electromagn. Res., vol. 51, pp. 153–165, 2005. [11] T. Lertwiriyaprapa, P. H. Pathak, and J. L. Volakis, “A UTD for predicting fields of sources near or on thin planar positive/negative material discontinuities,” Radio Sci., vol. 42, p. RS6S18, 2007. [12] G. Gennarelli and G. Riccio, “A UAPO-based solution for the scattering by a lossless double-negative metamaterial slab,” Progr. Electromagn. Res., vol. 8, pp. 207–220, 2009. [13] R. G. Kouyoumjian and P. H. Pathak, “A uniform geometrical theory of diffraction for an edge in a perfectly conducting surface,” Proc. IEEE, vol. 62, pp. 1448–1461, 1974. [14] P. C. Clemmow, The Plane Wave Spectrum Representation of Electromagnetics Fields, ser. IEEE/OUP Series on Electromagnetics wave theory. Piscataway: IEEE, 1996.

MgBB

[15] G. D. Maliuzhinets, “Inversion formula for the Sommerfeld integral,” Sov. Phys. Dokl., vol. 3, pp. 52–56, 1958. [16] T. B. A. Senior and J. L. Volakis, Approximate Boundary Conditions in Electromagnetics, ser. IEE Electromagnetic Waves Series. London: Inst. Elect. Eng., 1995.

Gianluca Gennarelli was born in Avellino, Italy, in 1981. He received the Laurea degree (cum laude) in electronic engineering and the Ph.D. degree in information engineering from the University of Salerno, Italy, in 2006 and 2010, respectively. Since 2006, he has been with the Applied Electromagnetics Research Group, University of Salerno, where he is currently a research fellow. His research interests include diffraction problems, near field—far field transformation techniques and numerical methods in electromagnetics.

Giovanni Riccio received the Laurea degree in electronic engineering from the University of Salerno, Italy. From 1995 to 2001, he was an Assistant Professor with the Engineering Faculty at the University of Salerno, where he is currently an Associate Professor of electromagnetics. His research activity concerns nonredundant sampling representations of electromagnetic fields, near field—far field transformation techniques, radar cross section of corner reflectors, wave scattering from penetrable and impenetrable structures. He is an author/coauthor of about 220 scientific papers, mainly in international journals and conference proceedings. He served as an Editor of the Journal of Electromagnetic Waves and Applications and Progress in Electromagnetics Research Journals. Prof. Riccio is a Member of the IEEE Society and Fellow of the Electromagnetics Academy.

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Sub-Wavelength Elliptical Patch Antenna Loaded With -Negative Metamaterials Pai Yen Chen, Student Member, IEEE, and Andrea Alù, Member, IEEE

Abstract—Following our recent findings on the possibility of squeezing the resonant dimensions of circular patch antennas by using negative-permeability loadings, here we theoretically and numerically analyze sub-wavelength elliptical patch antennas partially loaded with magnetic metamaterials. First, we formulate a general theory for inhomogeneously loaded subwavelength elliptical patch antennas, deriving a closed-form solution for the modes supported by this geometry in the long wavelength limit. Our theory proves that their resonant size may be in principle squeezed to any arbitrarily small dimension, provided that the properties of the loading metamaterial are properly tailored. Then, we highlight several advantages offered by the elliptical shape: two orthogonal modes may be independently excited within a subwavelength volume, providing large flexibility in the design, and more degrees of freedom compared to the circular geometry. In particular, the odd mode is shown to provide better gain than the circular case, due to larger aperture efficiency. Full-wave simulations, considering a finite ground plane, realistic feed and the influence of metamaterial loss, prove that the elliptical geometry presents great potentials for a variety of electrically small low-profile antenna applications. Index Terms—Electrically small antennas, metamaterials, miniaturized antennas, patch antennas.

I. INTRODUCTION HE current demand and interest for compact antennas with good efficiency and gain is relevant in a variety of telecommunication and space applications [1], [2]. In particular, patch antennas are widely used for their low profile and cost, combined with easy design and technology. In order to squeeze the transverse dimension of patch antennas, typically high permittivity dielectrics, such as ceramic-oxide materials [3]–[5], are employed as host substrate. However, their employment raises some intrinsic problems, such as difficulty in impedance matching, or the excitation of surface waves that could lower the radiation efficiency and deteriorate the radiation pattern [4], [5]. To date, many alternative techniques have been proposed, such as the use of magnetodielectric substrates and metasurfaces, which have the advantage of improving the impedance bandwidth properties [6]–[8]. Volakis and his group

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Manuscript received November 09, 2009; revised January 27, 2010; accepted March 19, 2010. Date of publication June 14, 2010; date of current version September 03, 2010. The authors are with the Department of Electrical and Computer Engineering, University of Texas at Austin, Austin, 78713 TX USA (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TAP.2010.2052578

also proposed the use of textured engineered materials [9] and magnetic photonic crystals [10], [11], as another promising venue to achieve patch antenna miniaturization. With today’s rapid progress in artificial surface and material technology, more degrees of freedom are available for antenna miniaturization without heavily sacrificing impedance matching, gain, bandwidth, efficiency and front-to-back ratio. Of particular interest, artificially engineered metamaterials are composed of electrically small inclusions that may tailor the material’s effective permittivity and permeability with positive, near zero, or negative values. Applications of double negative (DNG) or single negative (SNG) metamaterials have been extensively studied in the miniaturization of subwavelength cavities [12], waveguides [13], scatterers and antennas [14]–[17], in which a filling ratio factor, rather than the total volume, determines their resonance frequency. At the interface between materials with oppositely signed permittivity and/or permeability, a local compact plasmonic resonance may arise, squeezing the dimensions of resonant components, in principle arbitrarily [18]. Applied to patch radiators, in the recent past we have demonstrated that a circular patch antenna partially filled with a -negative (MNG) metamaterial substrate may have its resonant dimension arbitrarily squeezed, without significantly worsening its radiation properties and efficiency [14], [16]. Compared to other techniques to shrink the patch size, the advantage of this inhomogeneous metamaterial filling resides in the arbitrary choice of the resonance frequency, as long as negative effective permeability is achievable at that frequency. Although this technique indeed represents a promising solution to squeeze the resonant dimensions of patch antennas, the circular geometry presents some drawbacks, mainly represented by the limited modes of operation with significant efficiency and by the non-uniform excitation of the dominant mode around the patch, which is reflected in a lower-than-optimal value of aperture efficiency, and ultimately gain. Inspired by these limits, in the following we explore the possibility of using an elliptical metamaterial patch, in order to improve the aperture efficiency and, at the same time, increase the degrees of freedom and improve the gain performance of this electrically small radiator. We show that, indeed, more degrees of freedom will be available in the design, as the eccentricity (or the length of the two principle axes) and the feed position will play a major role in the overall radiation properties. Moreover, we show how, despite its subwavelength dimension, an elliptical resonant patch may support two orthogonal modes, of which the odd one supports a magnetic current aperture effectively larger than the one of a circular patch with same area, leading to an overall increase in gain and aperture efficiency. Even reducing

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the structure. In such cavity, Maxwell’s equations reduce to the following set of equations in elliptical coordinates:

Fig. 1. Geometry of an elliptical patch antenna in the elliptical coordinates; it is partially loaded by an MNG metamaterial core surrounded by a DPS shell.

the overall area of radiation, but increasing its eccentricity, our results show that an elliptical patch may provide analogous radiation performance as a much larger rectangular or circular patch. II. CAVITY MODEL: RESONANT FREQUENCIES AND RADIATION PROPERTIES Fig. 1 illustrates the geometry under consideration, i.e., an elliptical patch antenna partially filled by a concentric elliptical metamaterial core substrate, surrounded by air, with permittivity and permeability . The antenna is loaded by a grounded inhomogeneous substrate with thickness , which is composed of a regular double-positive (DPS) dielectric shell with permitand a metamaterial core with pertivity and permeability and permeability , in general dispersive mittivity with frequency, which may assume negative real parts (an notation is adopted throughout the paper). The substrate is effectively constituted by two confocal elliptical cylinders. The semi-major and semi-minor axes of the metamaterial core are denoted by and , respectively, and and define the surrounding DPS shell, whose outer boundary coincides with the patch perimeter. The geometry is embedded in a suitable elliptical reference system, with coordinates and , related to the Cartesian coordinates by:

(1) , and is the semi-focal length. It follows that the eccentricity of the metallic patch: . When approaches zero, the limit of a circular patch is obtained. On the other hand, approaches unity, a very narrow and thin ellipwhen tical shape is obtained. We may also define a filling ratio as the volume of the metamaterial core divided by the overall volume underneath . the patch Assuming that the thickness of the dielectric substrate is much smaller than the wavelength (low-profile), a standard cavity model [19], [20] may be applied to approximately calculate the patch resonant frequencies, closing the metallic . It is clear that this patch with a magnetic wall at approximation neglects the radiation loss at the edges of the patch, which effectively produce the antenna radiation, but this model may well approximate the relevant resonant features of where

(2) The corresponding elliptical wave equation solution is available in various books [21] and the field distribution in the two regions of the cavity may be expanded in terms of elliptical wave functions as:

(3) is the radial wave number, , where and are the even and odd radial Mathieu function of the th kind, respectively [22], and is the order of the an(even) and (odd), gular Mathieu functions which determine the azimuthal variation along [22]. In the most general dynamic case there is no closed-form dispersion relation for the modes supported by this cavity in the , since the angular case of inhomogeneous filling Mathieu functions are not orthogonal for different values of . This implies that the boundary conditions at the intermay be matched only by the entire summations in face (3), in the general case, making the analytical solution difficultly obtainable. The only possibility that the angular field variations may match separately at this interface for each angular order is that the two filling materials are isorefractive, i.e., . However, since we are interested here in squeezing the resonant dimensions of the cavity, we can safely assume that in such subwavelength scenario the two materials have indeed similar , even when , angular wave numbers is very small. In this case, the problem is equivalent since to the one of an elliptical cavity filled by isorefractive materials, for which the dispersion relation may be expressed, after some algebra, in terms of the -th order radial Mathieu functions [22], [23]. For the -th order even and odd mode the dispersion relation reads in this case (see (4) at the bottom of the next page). Assuming that the dielectric shell and the metamaterial

CHEN AND ALÙ: SUB-WAVELENGTH ELLIPTICAL PATCH ANTENNA LOADED WITH -NEGATIVE METAMATERIALS

core are subwavelength, we can then calculate the quasi-static , which after lengthy limit of (4) for algebraic manipulations of the series expansions of the radial Mathieu functions may be interestingly simplified into the following quasi-static expressions: azimuthally-symmetric mode

(5) th even mode

(6)

th odd mode

(7)

These quasi-static formulas are particularly interesting, since they simply relate the required ratio of permittivities or permeabilities to the geometrical parameters of the patch, depending on the mode of interest. They have been written explicitly both for the radial coordinates of the patch and for its filling factor or geometrical parameters. Except for the , all the fundamental azimuthally-symmetric mode with are split into even and odd other higher order modes distributions. When the geometry collapses to the circular patch , ), these equations are consistent ( with [14], and even and odd modes are degenerate. Eqs. (5)–(7) represent a very interesting closed-form result, that generalizes [14] to the elliptical geometry. They imply that, by employing two oppositely-signed materials with appropriate filling ratio and permittivities or permeabilities, it is in principle possible to select the desired angular variation of the resonant mode of an elliptical patch, and arbitrarily select its resonance frequency, independent on the total size of the patch. Although

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these equations do not depend explicitly on frequency, their frequency variations are implicitly embedded in the required frequency dispersion of the negative parameters involved. In fact, it may be proven that for passive materials the required permittivity dispersion necessarily implies that the bandwidth of operation will fall within Chu’s fundamental limit [23]. We have assumed here that the core material ( , ) is composed by a metamaterial with the required negative values, but in principle a metamaterial shell may fit equally well the requirements of (5)–(7). A metamaterial core has been chosen here for convenience of fabrication and integration of the feeding probe. As expected, and similar to the circular case, the azimuthally symmetric mode is dominated by the electric properties of the substrate in the quasi-static limit, implying that (5) depends only on the permittivity contrast in the substrate. On the other hand, the higher-order modes depend on the magnetic properties, and therefore on the permeability values in this quasi-static limit. The relevance of only one constitutive parameter in this quasi-static limit is a further proof that the isorefractive assumption may be legitimate in this long wavelength limit. Moreover, and the fact that in the quasi-static limit the dependence on is canceled out in (5)–(7) confirms their general validity, also when , or , are arbitrary, respectively in (5) or (6), (7). In order to numerically validate the use of (5)–(7) in the general case, and have a glimpse on what they actually imply in terms of patch design, Fig. 2(a) and (b) show the dependencies and on the eccentricity of an elliptical patch for of the mode and for the higher-order modes, respectively; and , here the filling ratio is fixed at in both regions. The which implies values of smaller than curves in Fig. 2 have been calculated using the full-wave exact dispersion relation of the elliptical cavity model (3), and compared with the solutions of (4) and (5)–(7), for different values of substrate permeability and permittivity. We have verified that the approximation in these equations hold extremely well in this subwavelength limit (for clarity, the approximate curves are not reported in Fig. 2, since they overlap with the plotted ones). For the azimuthally-symmetric mode (Fig. 2(a)) the ratio of permittivities is not influenced by a change in eccentricity, consistent with (5), since it depends only on the filling ratio. For higher-order modes (Fig. 2(b)), on the other hand, as expectable the odd and even mode dispersion becomes more and more distinct as the eccentricity increases. In particular, the odd modes require stronger contrast between permeabilities for a larger eccentricity, whereas the even modes require a smaller one. In the case of a subwavelength rectangular patch, we have shown [14] how the azimuthally-symmetric mode is not ex-

(4)

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H =0 =1 =2 = 0 425

=1 =1

Fig. 3. Tangential magnetic field  distributions for: (a) the n mode of a circular patch antenna; and (b) n , (c) n , odd mode, (d) n , even mode, (e) n , odd mode, and (f) n , even mode, for a subwavelength : . elliptical patch antenna with e

=2

=0

Fig. 2. Variation of (a) the permittivity ratio for n the mode and (b) the permeability ratio for higher-order modes with the eccentricity of an elliptical : . The results are obtained from the rigorous patch with filling ratio dynamic formulation of the modes supported by this geometry, assuming a .  = , which implies q