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Low-profile microstrip end-fire antennas based on metamaterial substrates Ahmadi, Masoud 2018

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Low-Profile Microstrip End-FireAntennas Based on MetamaterialSubstratesbyMasoud AhmadiA THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF APPLIED SCIENCEinTHE COLLEGE OF GRADUATE STUDIES(Electrical Engineering)THE UNIVERSITY OF BRITISH COLUMBIA(Okanagan)January 2018© Masoud Ahmadi, 2018The undersigned certify that they have read, and recommend to the College of GraduateStudies for acceptance, a thesis entitled: Low-Profile Microstrip End-Fire Anten-nas Based on Metamaterial Substrates submitted by Masoud Ahmadi in partialfulfillment of the requirements of the degree of Master of Applied ScienceDr. Lo¨ıc Markley, School of EngineeringSupervisorDr. Thomas Johnson, School of EngineeringSupervisory Committee MemberDr. Jonathan Holzman, School of EngineeringSupervisory Committee MemberDr. Kasun N. Hewage, School of EngineeringExternal ExamineriiAbstractThe development of microstrip technology has introduced a range of revolutionaryantenna designs that provide a low-cost, easily integrable antenna in a low-profile, planarform factor. Typical microstrip antennas have either a broadside or an omnidirectionalradiation pattern. This study investigates the design of a low-profile end-fire microstripantenna based on the use of metamaterial substrates.A 900 MHz dipole antenna is placed above two types of high impedance surfaces (HIS):a single-layer HIS and a double-layer HIS. The patches forming the HIS were designed toproduce a radiation pattern with main lobes as close to 90◦ from normal as possible. Oursimulation results show that a single-layer HIS design with thickness of 0.06λ0 and lengthand width of 1.1λ0 by 1.1λ0 has a main lobe at 56◦ from normal and an efficiency of 28%.A double-layer HIS design with a thickness of 0.03λ0, a length of 1.1λ0, and a width of2.15λ0 produces a main lobe at 40◦ from normal with an efficiency of 50%.In order to produce a radiation pattern closer to end-fire, we propose a compact mi-crostrip patch antenna that uses a negative permittivity substrate to achieve an end-fireradiation pattern. The antenna is designed to operate at X-band frequencies and has afootprint of 42 mm2. Loading a narrow patch with a negative permittivity substrate in-troduces an effective inductance that resonates with the strong fringing capacitance of thepatch. The electric field is vertically polarized and nearly uniform across the patch withnegative permittivity ensuring a uniform phase distribution. This introduces nulls in thetransverse direction that improve the directivity of the antenna. The negative permittivitysubstrate is implemented using a thin-wire medium with four vias spread across the patch.The fabricated antenna is matched using a quarter-wavelength transformer to 50 Ω at 10.8GHz with a peak return loss of 30 dB and a peak directivity of 11.3 dBi. The operatingfrequency appears between two parallel resonances and has a 10-dB impedance bandwidthof 4%. The efficiency is simulated to be approximately 85%.iiiLay SummaryMetals are lossy and extremely reflective. Any radiated energy directed towards metallicsurfaces will undergo reflection, the presence of nearby metals can significantly alter theoverall radiation properties of an antenna. In many applications in vehicular, aviation,and tracking systems, metals are commonly used as ground planes for different typesof antennas. This thesis explores the design of a low-profile antenna against an infinitemetallic ground plane that is capable of radiating along the ground plane (end-fire). Typicalantennas against the ground plane are either large or not able to radiate along that plane.Our study shows that it is possible to design a low-profile end-fire microstrip antenna byusing a metamaterial-based substrate. Our final antenna design uses a negative permittivitysubstrate at 10 GHz and has a total thickness of 0.05 λ0.ivPrefaceThis work has been done under the guidance of Dr. Lo¨ıc Markley at the School ofEngineering in The University of British Columbia.Portions of my thesis have been presented at the following conference:− “End-Fire Microstrip Antenna with Negative Permittivity Substrate,” IEEE Interna-tional Symposium on Antennas and Propagation and North American Radio ScienceMeeting in San Diego, USA, June, 2017.Additionally, a manuscript is currently being prepared that contains the content foundin Chapter 4.vTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvDedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .xviiChapter 1: Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Antenna Radiation Pattern . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.1.1 Isotropic Pattern . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.1.2 Directional Pattern . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.1.3 Omnidirectional Pattern . . . . . . . . . . . . . . . . . . . . . . . . . 31.2 Antennas Against Metallic Objects . . . . . . . . . . . . . . . . . . . . . . . 31.3 End-Fire Antennas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.4 Thesis Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7Chapter 2: A High Impedance Surface (HIS) for RFID Chip DetectionApplications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.1 Use of Ground Planes in Race Timing Systems . . . . . . . . . . . . . . . . 102.2 High Impedance Surface (HIS) . . . . . . . . . . . . . . . . . . . . . . . . . 122.2.1 Equivalent Inductance and Capacitance . . . . . . . . . . . . . . . . 132.2.2 Reflection Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.2.3 Interdigitated HIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.2.4 Two-Layer HIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21viTABLE OF CONTENTS2.3 HIS Based Dipole Against an Infinite Ground Plane . . . . . . . . . . . . . 222.3.1 Two-Layer Profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222.3.2 Three-Layer Profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282.3.3 HIS Magnetic Dipole . . . . . . . . . . . . . . . . . . . . . . . . . . . 312.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34Chapter 3: End-Fire Radiation From Rectangular Patch Antennas . . . . . 353.1 Basic Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363.2 Theory of Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373.3 Cavity Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373.3.1 TM Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373.3.2 Equivalent Magnetic Current Densities . . . . . . . . . . . . . . . . . 403.3.3 Radiated Fields in the Far-Field . . . . . . . . . . . . . . . . . . . . 413.4 End-Fire Patch Antenna . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433.4.1 Finite Ground Plane and Substrate . . . . . . . . . . . . . . . . . . . 493.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51Chapter 4: End-Fire Microstrip Antenna with Negative Permittivity Sub-strate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 524.1 Resonance of a Negative Permittivity Substrate in the Patch Antenna . . . 534.1.1 Antenna Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . 544.2 Characteristics of the Negative Permittivity Substrate Patch . . . . . . . . 584.3 Physical Antenna Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 634.3.1 Negative Permittivity Material . . . . . . . . . . . . . . . . . . . . . 634.3.2 Electromagnetic Properties . . . . . . . . . . . . . . . . . . . . . . . 664.3.3 Finite Ground Plane and Substrate . . . . . . . . . . . . . . . . . . . 684.3.4 Final Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 694.3.5 Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 714.4 Experimental Verification . . . . . . . . . . . . . . . . . . . . . . . . . . . . 734.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76Chapter 5: Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 775.1 Summary of Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 775.2 Contributions and Limitations . . . . . . . . . . . . . . . . . . . . . . . . . 785.3 Future Directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81viiList of TablesTable 2.1 Parameter values of an HIS at the frequency of 900 MHz taken from[1] as a starting point for later characterization . . . . . . . . . . . . 15Table 2.2 The resonant frequency and bandwidth of the HIS for different thick-nesses. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16Table 2.3 The resonant frequency and bandwidth of the HIS with different ma-terials. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17Table 2.4 Dielectric constant and loss tangent of the substrate materials for HIScharacterization are listed. Rogers RT/Duriod 5880 has the lowestpermittivity and loss tangent. FR-4 has the highest dielectric constant. 17Table 2.5 Parameters of the interdigitated HIS . . . . . . . . . . . . . . . . . . 18Table 2.6 Parameter values of a two-layer HIS that resonates at the frequencyof 900 MHz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21Table 3.1 The optimal parameters in the MPA that results in an end-fire pattern. 46Table 4.1 Parameter sweep ranges for MPA characterization. . . . . . . . . . . 55Table 4.2 Optimal antenna design parameters. . . . . . . . . . . . . . . . . . . 58Table 4.3 Final values of the via spacing and their radius to achieve a negativepermittivity of approximately r = -2.2. . . . . . . . . . . . . . . . . 65Table 4.4 Final antenna dimensions. . . . . . . . . . . . . . . . . . . . . . . . . 70viiiList of FiguresFigure 1.1 The transmitter and receiver that Hertz used in his wireless experi-ment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2Figure 1.2 Directional and omnidirectional patterns in (a) and (b). . . . . . . . 3Figure 1.3 A wire antenna placed close to a vehicle body as a part of itsAM/FM radio system in (a) [2]. Receiving and transmitting an-tennas mounted on an airplane. Antennas play an important role inaviation [3]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4Figure 1.4 A monopole antenna and its omni-directional radiation pattern [4]. 4Figure 1.5 (a) a microstrip patch antenna with a broadside radiation patternis shown in [5]. (b) a slot antenna generates an omni-directionalradiation pattern [6]. . . . . . . . . . . . . . . . . . . . . . . . . . . 5Figure 1.6 The Yugi-Uda antenna and its uni-directional end-fire radiation pat-tern [7]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6Figure 1.7 An example of an end-fire radiation pattern with the main lobedirected toward the ground plane located in the XY plane. . . . . . 7Figure 2.1 An HIS shown in (a) is comprised of arrays of vias and patches.These protrusions look like mushrooms jutting out of the bottomplane; thus, the structure is also referred to as mushroom-type HIS[8]. (b) shows the slot antenna currently in use as a magnetic dipoleagainst earth, which leads to an omnidirectional radiation pattern. . 11Figure 2.2 At the resonant frequency, the equivalent circuit model of the HISsimplifies to a parallel LC resonator. . . . . . . . . . . . . . . . . . 12Figure 2.3 The capacitance and inductance in the HIS originates from the fring-ing electric field between the neighboring patches, and the currentflowing from the metallic plates to the bottom sheet through thevias [8]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13Figure 2.4 Reflection phase of the design described in Table 2.1 versus frequencyfor different substrate thicknesses. . . . . . . . . . . . . . . . . . . . 15Figure 2.5 Reflection phase versus frequency for various r and constant thick-ness of 13 mm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16ixLIST OF FIGURESFigure 2.6 Geometry of the interdigitated capacitor (a) and two-layer patchHIS (b). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18Figure 2.7 Placing fingers on each side of the patches creates meandering gapsin an HIS as shown in (a) and (b), and provides more capacitance.The length and width of each finger, and the gap between themdetermines how much capacitance is added to the structure. . . . . 19Figure 2.8 Reflection phase of the interdigitated HIS described in Table 2.5. . . 19Figure 2.9 A row of patches consisting of n unit cells shown in (a) is usedto test surface wave suppression for the interdigitated HIS wherelumped-ports are used at the input and output and its correspondingtransmission coefficient (S21) is depicted in (b). . . . . . . . . . . . 20Figure 2.10 Reflection phase of the two-layer HIS described in Table 2.6 versusfrequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21Figure 2.11 A 0.48λ0 dipole is placed above an HIS with one layer of patchesforming an overall two-layer antenna profile. The HIS has the length(LH) of 1.1λ0 , width (WH) of 1.1λ0, and thickness of 0.04 λ0 and isseparated from the the antenna by a dielectric layer with thicknessof 0.02 λ0 (6.7 mm). The dipole feed aligns with the center of theHIS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23Figure 2.12 Normalized E and H plane radiation patterns of the HIS-based dipoledepicted in Figure 2.11 at the resonant frequency of 935 MHz in (a)and (b) show that, due to the infinite PEC ground plane, thereis no in-plane radiation. The maximum directivity of the antennais 9 dBi. The half-power beamwidth (HPBW), which is the anglebetween the half-power points of the main lobe, when referenced tothe peak radiated power of the main lobe, is 80◦. The return lossand input impedance displayed in (c) and (d) demonstrate that atthe resonant frequency the antenna input impedance is 34 Ω. . . . . 24Figure 2.13 (a) and (b) show the efficiency, the angle of maximum direction(θmax), and maximum directivity versus HIS patch width. (c) and(d) depict variations of LD and W that lead to non-broadside radi-ation patterns. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25Figure 2.14 The graded HIS includes patches with variant width. . . . . . . . . 26Figure 2.15 Normalized E and H plane radiation patterns of the graded HIS-based dipole antenna depicted in Figure 2.15(a) at the resonantfrequency of 840 MHz in (a) and (b) show that there is still noin-plane radiation. The maximum directivity is 8.3 dBi. HPBW ofthe antenna is 90◦, which is in good agreement with the maximumdirectivity decrease compared to the original design. The return lossand input impedance are displayed in (c) and (d). At the resonantfrequency the antenna input impedance is 58 Ω. . . . . . . . . . . . 27xLIST OF FIGURESFigure 2.16 Half-wavelength dipole placed above a two-layer HIS forming anoverall three-layer antenna profile. . . . . . . . . . . . . . . . . . . . 28Figure 2.17 Normalized E and H plane radiation patterns of the three-layer HISbased dipole depicted in Figure 2.16 against an infinite PEC groundplane, at the resonant frequency of 858 MHz, are shown in (a) and(b), respectively. The direction of maximum radiation and maxi-mum directivity are 30◦ and 8.3 dBi. The return loss and inputimpedance in (c) and (d) demonstrate that the antenna resistanceat the resonant frequency is 41 Ω. The 10-dB impedance bandwidthand radiation efficiency are 0.5% and 92%, respectively. . . . . . . . 29Figure 2.18 (a) and (b) show the efficiency, angle of maximum direction, andmaximum directivity associated with a design in which the dipolelength is 0.48λ0, the length and width of the HIS are 1.2λ0 and2.15λ0, and the patch width is swept from 0.07λ0 to 0.11λ0. . . . . 30Figure 2.19 Geometry of the proposed HIS dipole in (a). (b), (c), and (d) showthe electric current density of the structure when fed from threedifferent positions: center-bottom side (A), center-right side (B),and the center of the middle via (C), respectively. . . . . . . . . . . 31Figure 2.20 Normalized E and H plane radiation patterns at the frequency of920 MHz in (a) and (b) show that in design A and B the proposedstructure is broadside, but design C results in an end-fire radiationpattern. The maximum directivity of 6.5, 5.7, and 6 dBi are achievedfor design A, B, and C, respectively. . . . . . . . . . . . . . . . . . . 32Figure 2.21 The resistance, reactance, and return loss of the proposed structuresin (a), (b), and (c) reveal that all the designs are resonant. Thereactance in design A sharply crosses through zero at the frequencyof 950 MHz. The resonant resistance is higher than 400 Ω leadingto a high reflection coefficient. The simulated efficiency at 950 MHzis 2%. Design B resonates at 913 MHz with resistance of 22 Ω,efficiency of 4%, and 10-dB impedance bandwidth of 0.25%. At theresonant frequency of 922 MHz, design C has input impedance of40 Ω, efficiency of 4.5%, and bandwidth of 0.64%. All three designssuffer from poor efficiency. . . . . . . . . . . . . . . . . . . . . . . . 33Figure 3.1 Photograph of a fabricated rectangular patch antenna [9]. . . . . . . 36Figure 3.2 Microstrip patch antenna geometry [10]. . . . . . . . . . . . . . . . 36Figure 3.3 The cavity model is based on the assumption that the substrate islimited to the patch edges and the ground plane is infinitely large. . 38Figure 3.4 Image theory is used to account for the presence of the infinite PECplane. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40xiLIST OF FIGURESFigure 3.5 The dominant mode electric field distribution and equivalent chargedensities at radiating (y = −l/2 and y = l/2) and non-radiatingedges (z = −W/2 and z = W/2). . . . . . . . . . . . . . . . . . . . . 41Figure 3.6 Normalized E and H plane radiation patterns are plotted in (a) basedon Equation 3.16 and 3.17 where r = 2.2, k0h = 0.15, W = 0.3λ0,and leff = 0.3λ0. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43Figure 3.7 The cavity model simplifies an MPA to a two-element array. Twopossible radiation patterns are shown, using an array of two Hertziandipoles is shown: end-fire where dipoles are out-of-phase and sepa-rated by λ0/2 in (a) and broadside where the distance between theelements is still λ0/2 but they are in-phase in (b). As shown in thenormalized radiation pattern of the end-fire array (c), the maximumradiation is directing toward the array axis (Z) and there are nullsalong the other two axes. The broadside array the radiates max-imally normal to the array axis (Y) and has nulls along X and Zaxes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44Figure 3.8 The electric fields and equivalent current densities on the radiating(left) and non-radiating (right) edges of for an MPA, which has anend-fire radiation pattern. . . . . . . . . . . . . . . . . . . . . . . . . 45Figure 3.9 Two modes of operation that results in end-fire radiation pattern [11]. 46Figure 3.10 Geometry of patch simulated in COMSOL Multiphysics . . . . . . . 46Figure 3.11 The vertical electric on the patch in the XY plane and magneticof the tangential magnetic field on the ZY and ZX sidewalls areshown (a), (b), and (c), respectively. . . . . . . . . . . . . . . . . . . 47Figure 3.12 The reflection coefficient and input impedance of the design de-scribed in Table 3.1 with respect to frequency . . . . . . . . . . . . 48Figure 3.13 Normalized radiation patterns in the XY and Y Z planes at thefrequency of 9.4 GHz show that the maximum radiation occurs alongthe Y axis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48Figure 3.14 The geometry of the end-fire patch antenna is displayed when afinite PEC plane and a substrate, which is extended to the edge ofthe ground plane. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49Figure 3.15 Impact of finite ground plane on the antenna, characterized by theelevation angle of main lobes from XY plane (a), maximum direc-tivity (b) and input impedance (c). . . . . . . . . . . . . . . . . . . 50Figure 4.1 (a) geometry of the optimized patch and (b) equivalent circuit of it. 54Figure 4.2 The variety of patch feed configurations studied. . . . . . . . . . . . 55xiiLIST OF FIGURESFigure 4.3 Directivity in dBi along different axes with respect to the patchlength (Lp) and width (Wp) is shown in terms of free-space wave-length. In (a), (b), and (c), r is -2.2 and (d), (e), and (f) are forthat of -3. Regions in which antenna resistance lies within the rangeof 30 to 96 Ω are depicted with black arrows. . . . . . . . . . . . . . 57Figure 4.4 Return loss and input impedance of the patch antenna with lp =0.05λ0, Wp = 1.5λ0, h = 0.05λ0, and r = −2.2 designed at 10 GHz.The frequency of 10 GHz, where the resistance and reactance of theantenna are 58 and 24 Ω, is close to the resonant frequency of 9.5GHz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60Figure 4.5 The electric field distribution of the theoretical antenna design. . . 61Figure 4.6 Radiation mechanism in the negative permittivity substrate patch. . 62Figure 4.7 Normalized far-field radiation pattern in E and H planes, at thefrequency of 10 GHz for the patch antenna described in Table 4.2.The antenna substrate is limited to the edges of the top conductorand an infinite ground plane. Since the phase across the patch isuniform, every point on the patch can be paired with another pointalong the Y axis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62Figure 4.8 Thin-wire array structure is known as one of the simplest realizationsof a media with a negative permittivity [12]. . . . . . . . . . . . . . 64Figure 4.9 Thin-wire transmission-line equivalent circuit [12]. . . . . . . . . . . 64Figure 4.10 The implementation of the negative permittivity substrate in thepatch using four vias. . . . . . . . . . . . . . . . . . . . . . . . . . . 66Figure 4.11 The simulated return loss and input impedance of the physical an-tenna design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66Figure 4.12 The vertical electric field distribution of the physical antenna design 67Figure 4.13 Normalized far-field radiation pattern in E and H planes, simulatedat the frequency of 10 GHz for the patch antenna that has four thinwires to produce a negative permittivity. . . . . . . . . . . . . . . . 67Figure 4.14 The elevation angle of the antenna main lobes from the XY plane,maximum directivity, and input impedance at the frequency of 10GHz are shown in (a), (b), and (c), respectively. . . . . . . . . . . . 69Figure 4.15 Final antenna design. . . . . . . . . . . . . . . . . . . . . . . . . . . 70Figure 4.16 Normalized E and H plane radiation patterns with a finite and in-finite ground plane, simulated at the frequency of 10.8 GHz, areshown in (a) and (b). . . . . . . . . . . . . . . . . . . . . . . . . . . 71Figure 4.17 Simulated resistance, reactance, and reflection coefficient in (a) and(b) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71Figure 4.18 Simulated reflection coefficient of the antenna for different via radii. 72Figure 4.19 The efficiency, maximum directivity, resistance and reactance of theend-fire patch versus substrate thickness. . . . . . . . . . . . . . . . 73xiiiLIST OF FIGURESFigure 4.20 The final antenna design is fabricated using PCB technology, as pre-sented in (a). The simulated and measured return loss, resistance,and reactance of the antenna are shown in (a), (b), and (c). . . . . 74Figure 4.21 The far-field measurement setup is displayed in (a) and (b). Thereare two stations: the transmitter and the receiver. While the trans-mitter station rotates, the receiver is stationary. A mount andsemi-rigid coaxial cable are used to stabilize the antenna during themeasurement. Simulated and measure E plane co-polarization andcross-polarization directivity in dBi at the frequency of 10.8 GHzare shown in (c). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75xivAcknowledgementsIt was certainly the blessing of God to be surrounded by many wonderful peoplethroughout my studies. I would first like to express my deep appreciation to my supervisor,Dr. Lo¨ıc Markley, for his direction, expertise, and continued support throughout all of myresearch. His leadership and accountability, as well as his constant expression of faith inmy capabilities, has both strengthened my confidence in myself as an engineer, as well asdeepened my respect for him as a mentor in this profession. It has been a privilege workingalongside Dr. Markley, and I can attest that I would not be where I am today without hisintentional, vested interest in my personal and professional development. I consider myselfextremely lucky to be one of his students that grows through his commendable personality,high standards, and great brilliance. I would also like to express my thanks to Dr. ThomasJohnson and Dr. Jonathan Holzman for their significant feedback and valuable discussionsas well as their constructive suggestions that aided the precision of my research. Specialthanks to Dr. Bruce Veidt for his great contribution to the antenna far-field measurementsat Dominion Radio Astrophysical Observatory antenna chamber.I would like to thank all my skilled and talented colleagues and fellow researchers. Ithas been a pleasure working collaboratively with Connor Badowich, Nibirh Jawad, ImanAghanejad, Mohammed Al-Shakhs, Ali Maleki, and Suzanne Campbell. Because of thesewonderful individuals, I have gained a deeper understanding of what it truly means to bepart of a team. Special thanks to Asif Al Noor for his guidance and counsel, not onlyas my previous colleague but as my friend also. I wish him all the best in his futureendeavors. A debt of gratitude is owed to Megan Wylie for her never-ending support andcompanionship. I am also grateful for her great assistance in proofreading and editing ofmy thesis and other project reports. Thanks for believing in me and being present duringtimes of hardship. I owe you a big one, “Dear Dude”.On a more personal note, my deepest thanks and appreciation to my amazing mother,Sarah, for pushing me to be the best I can be. Her endless love, unselfish and enduring, issomething that no one can fully explain. It is made of deep devotion, sacrifice and pain,and I will be forever indebted for her presence, kindness, and patience in my life. Abundantgratitude must go to my fantastic brother, Saeed, for his phenomenal support, not onlyduring the pursuit of this goal but also through my entire life. Steady, protective, andwatchful, he is one of my true heroes. Special thanks to my father, Majid, and my brother,Hamid, for their continuous love and long-distance support. I am also thankful to my aunt,Mahin, and uncle, Ali, for their love and encouragement.xvAcknowledgementsI would like to thank my dear friends Ekene Iloabachie, Dr. Vojteˇch Kapras, KathyWalraven, Peter O’Brien, Joshie Fisher, and Bill Pittman for their ongoing friendship andencouragement. Thanks must also go out to Jeff Beech, Brady Bloomer, Rachel Clowater,and Timothy William Beck for being accommodating and keeping me on my feet. A finalword of thanks to Selah, Mosey, and Hypu who stood by me through the good times andbad.xviDedicationTo the memory of my grandmother, Khanum-Taj Golchin,who would be extremely proud of meTo my mother, Sarah Qanei,my biggest blessing and my greatest fanxviiChapter 1IntroductionElectromagnetic radiation refers to electromagnetic waves that propagate through space(usually free-space) over a distance carrying electric and magnetic radiant energy. Asa key element in wireless communication systems, radiation solely depends on devicescalled antennas—metallic structures which transmit and receive electromagnetic waves ina particular direction. Antennas can serve as transmitters which emit energy taken froma source through space by creating travelling electromagnetic waves. The radiated energyis then detected and absorbed by another antenna as a receiver.The first antenna was built by German physicist Heinrich Rudolf Hertz in 1887 [13].His transmitter, known as a dipole resonator was comprised of a pair of wires and twoconducting balls. A simple loop with two identical balls was used as the receiver, asdepicted in Figure 1.1. In a series of highly-sensitive experiments, Hertz was able to provethe existence of electromagnetic waves. He demonstrated this by using a variable voltagesource to power his transmitter antenna; when the voltage reached a certain value, a sparkwas generated at the gap between the two conducting balls. Then by adjusting the gap inthe loop antenna, he was able to receive a similar spark in the receiver.Hertz could not have anticipated the importance his radiowave experiments would haveon wireless radio communication. Over the next decade, these “radio waves” (initially re-ferred to as “Hertzian Waves”) enabled the wireless technology to embark on a revolution-ary journey. In 1901, Italian inventor Guglielmo Marconi developed a transatlantic radiotransmission method. Marconi was able to receive data transmissions from Poldhu Pointin England to a receiving station in St. John’s, Newfoundland in Canada [13]. His deviceattracted a lot of attention and led to the development of wireless technology in the 20thcentury, as it demonstrated the effectiveness of this system to transmit radio signals overgreat distances. Because Marconi mainly used monopole antennas in both the transmitterand receiving apparatus, monopole antennas are also known as Marconi antennas. Afterhis initial experiments, he went on to establish worldwide affiliated companies, includingthe very well-known Wireless Telegraph and Signal Company [14].Antenna technology has become a critical component of wireless communication, par-ticularly used in applications such as cellular phones, satellite communication, aircraft,radio frequency identification, radio broadcast, radar, radiometry, imaging, and microwaveovens.An antenna is characterized by its radiation properties: input impedance, radiationpattern, bandwidth, and efficiency. A transmitter should be capable of collecting the11.1. Antenna Radiation PatternFigure 1.1: The transmitter and receiver that Hertz used in his wireless experiment.maximum available power from the source, efficiently generating radio waves over a certainfrequency range, and sending the energy toward the direction of the receiver. A well-designed receiver antenna absorbs the transmitted energy efficiently and delivers it toother components of the system.1.1 Antenna Radiation PatternThe radiation pattern of an antenna shows the directional (angular) distribution of itsradiated energy in the far-field. Antennas are categorized into three types based on theirradiation patterns: isotropic, directional, and omnidirectional.1.1.1 Isotropic PatternAn isotropic antenna distributes its energy evenly in all directions. Though physicallynon-realizable, it is used as a mathematical reference to describe how directive an actualantenna is. In other words, the directivity of any actual antenna is compared to theisotropic radiator (commonly described in terms of dBi, where i stands for isotropic).1.1.2 Directional PatternA directional antenna transmits and/or receives waves more significantly in some direc-tions than others. There are two commonly-known directional patterns: broadside, whichhas its maximum radiation normal to the antenna plane, and end-fire, whose main lobe isparallel to that plane. Microstrip patch antennas, Yagi-Uda antennas, leaky-wave anten-nas, helical antennas, parabolic antennas, and Vivaldi antennas (Figure 1.2(a)) are types21.2. Antennas Against Metallic Objectsof directional radiators. This group of antennas is widely used in vehicular technology,mobile and satellite communications, astronomical imaging, and detection systems.1.1.3 Omnidirectional PatternOmnidirectional antennas are isotropic in one single plane and directional in anotherplane. Dipole antennas (see Figure 1.2(b)), slot antennas, monopole antennas, biconi-cal antennas, discone antennas, folded unipole antennas, and planar inverted F antennas(PIFAs) are some examples of omnidirectional radiators.(a) Vivaldi Antenna [15] (b) Dipole Antenna [11]Figure 1.2: Directional and omnidirectional patterns in (a) and (b).1.2 Antennas Against Metallic ObjectsAntennas have been placed around metallic objects for many applications in vehicularand aviation systems, as seen in Figure 1.3. Metals are lossy and extremely reflective. Sinceany radiated energy directed towards metallic surfaces will undergo reflection, the presenceof nearby metals can significantly alter the overall radiation properties of an antenna.Metals are commonly used as ground planes for different types of antennas. A monopoleantenna is formed when a wire antenna is mounted vertically against a conductive groundplane. The most common form is the quarter-wavelength monopole, which has an omni-directional pattern with maximum radiation along the ground plane (see Figure 1.4). Theoverall height of the antenna is λ0/4 at the operating frequency so the antenna is notlow-profile. Another example of an antenna with a ground plane is a microstrip patchantenna. It has two parallel conducting plates separated by a dielectric layer. The lowerconductor forms a ground plane for the upper patch, as depicted in Figure 1.5(b). Theantenna is typically designed to have its maximum radiation normal to the ground plane.31.2. Antennas Against Metallic Objects(a) (b)Figure 1.3: A wire antenna placed close to a vehicle body as a part of its AM/FM radiosystem in (a) [2]. Receiving and transmitting antennas mounted on an airplane. Antennasplay an important role in aviation [3].Slot antennas are another type of antennas that are placed against an infinite ground planeto produce an omni-directional radiation pattern. A slot antenna consists of a metallic flatplate, with slots cut out and acts as a magnetic dipole. The antenna is capable of radiatingnot only along the ground plane but also normal to it (Figure 1.5(b)). In order to excitethe slot mode, a cavity must be placed under the ground plane, thereby increasing thethickness of the antenna.Figure 1.4: A monopole antenna and its omni-directional radiation pattern [4].41.3. End-Fire Antennas(a) (b)Figure 1.5: (a) a microstrip patch antenna with a broadside radiation pattern is shown in[5]. (b) a slot antenna generates an omni-directional radiation pattern [6].1.3 End-Fire AntennasThe Yagi-Uda antenna is a popular uni-directional end-fire radiator. It is a lineararray of dipoles, commonly half-wavelength, with one element driven directly, and the restexcited by near-field coupling. The longest element (pictured on the far left in Figure1.6) serves as a reflector; waves propagating toward the reflector interfere destructively,resulting in no backward radiation. The forward beam is formed by the directors, as aresult of constructive interference. A Yagi-Uda antenna can have a gain of up to 20 dBi,depending on the number of elements used and the spacing between them; more directivedesigns require more elements [16]. The Yagi-Uda antenna is best known for its use asterrestrial home TV antenna [11][16], but its relatively high gain and simple structure alsomake it applicable for radars [17], long-distance communication by broadcasting stationsand radio amateurs [18], and point-to-point fixed communication [19].With modern-day wireless communication devices becoming increasingly small andlight, the demand for compact planar antenna designs is greater than ever. The end-fire pattern of a Yagi-Uda antenna is realized by using an array requiring significant space;most have 8 to 14 dipoles, with a total length of approximately 6λ0 (where λ0 is thefree-space wavelength at the operating frequency) [11]. The antenna characteristics suchas gain, input impedance, efficiency, maximum sidelobe level (SLL), and backlobe level(BLL) are extremely sensitive to design parameters.The Vivaldi antenna (shown in Figure 1.2(a)) is another uni-directional end-fire an-tenna. Its planar structure can be easily fabricated using standard printed circuit board(PCB) technology. It has constant radiation characteristics over a wide frequency band.These properties are widely used in remote sensing [20], radar imaging applications [21],and ultra wide band (UWB) wireless communication systems [22]. The Vivaldi antenna51.3. End-Fire Antennas,Figure 1.6: The Yugi-Uda antenna and its uni-directional end-fire radiation pattern [7].typically has a gain of 5 dBi so it is not popular in high-directivity applications. Given anarrowband application, there are other types of antennas with a higher gain.Over the past decade, scientists have been focusing on new planar antenna designs withend-fire patterns. R. Suga et al. achieved an end-fire antenna package using an open-endedpost-wall waveguide at the frequency of 60 GHz [23]. The antenna is designed with thetotal size of 0.96λ0 × 1.3λ0 × 0.2λ0 and is used for a wireless file-transfer link. This designsuffers from a low directivity of 2.2 dBi. The same authors in [24] reported another planarantenna that achieves a higher gain of 6 dBi at the same frequency but at the price ofhaving larger dimensions of 1.74λ0 × 1.3λ0 × 0.2λ0. Both designs have not only large sizebut also complicated structures. Recently, a planar quasi Yagi-Uda antenna for millimeter-wave applications was presented [25]. The antenna has a three-layer structure with a totalthickness of 1.93 mm (0.23λ0), length of 12.2 mm (1.5λ0), and width of 11 mm (1.30λ0)at 36 GHz. The peak realized gain is approximately 8 dBi. The proposed structure is notcompact, and also has a very complicated structure. A structure with two back-to-back12-element YagiUda antennas was proposed to produce an bi-directional end-fire radiation[26]. The antenna with 24 elements has a total length of 4λ0 and a peak gain of 9.25 dBi. L.Liu et al. [27] proposed a bi-directional end-fire array consisting of six meander-line-basedfolded dipole elements that has a peak gain of 8 dBi.Much effort has been devoted to designing planar end-fire antennas at extremely highfrequencies (30 to 300 GHz), where the corresponding wavelengths (1 to 10 mm) are withinthe fabrication range of PCB printing technology. There are several designs that usedifferent array configurations, to accomplish an end-fire pattern but still result in largeand complex structures [28][29][30]. Aforementioned antennas may not radiate at end-firewhen they are placed against an infinite ground plane.61.4. Thesis Organization,Figure 1.7: An example of an end-fire radiation pattern with the main lobe directed towardthe ground plane located in the XY plane.The principle motivation of this research was to design a low-profile antenna against aninfinite metallic ground plane capable of radiating along the ground plane. This descriptionfor the radiation pattern of interest is not limited to a specific type. The antenna couldhave any of the radiation patterns shown in Figures 1.4, 1.5(b), and 1.7; as long as thereis radiation toward the ground plane. Hereafter, we refer to this type of radiation patternas “end-fire” in this thesis. The research objective of this thesis was to achieve an antennaprofile with a total thickness of less than 3 mm that can be fabricated using PCB technology.1.4 Thesis OrganizationThis thesis aims to investigate two antenna configurations: high impedance surface(HIS)-based dipoles and microstrip patch antennas. Both are planar and simple to fabri-cate. While an HIS dipole has an omnidirectional pattern, a patch antenna is typically abroadside radiator. However, our research shows that it is possible to design an end-fireHIS-based dipole and end-fire patch antenna. In order to report the necessary backgroundand the important aspects of each design, this thesis is divided into two main sections withfive chapters. A brief summary of each chapter content is as follows:− Chapter 2 focuses on the design of a very low-profile HIS-based dipole placed over aninfinite ground plane for RFID detection purposes in race timing. Basic propertiessuch as the reflection phase, equivalent circuit model, and resonant frequency of theHIS are discussed. The impact of the infinite ground plane on the antenna patternis investigated to address the need for an end-fire structure. This is followed by ademonstration of modifications that can be applied to the original design (such asrectangular and graded HIS, and magnetic dipole) to potentially enable an end-firepattern.− Chapter 3 is devoted to the design and analysis of a microstrip patch antenna (MPA).71.4. Thesis OrganizationBasic properties (such as geometry, current distribution, radiation pattern, and inputimpedance), as well as the patch antenna cavity model are studied. The chapter willconclude with details on designing a bi-directional end-fire microstrip patch antennaby exciting a higher-order mode in the cavity, as well as a demonstration that theground plane size significantly impacts the radiation characteristics of the proposedantenna.− Chapter 4 explores an alternative design to the model outlined in Chapter 3 to achievean end-fire radiation pattern without the need to excite a higher-order mode in theantenna. In this design, with a negative permittivity substrate, the directivity ofthe bi-directional antenna is greatly improved, along with a slight increase in theimpedance bandwidth, while maintaining a low-profile structure.− Finally, Chapter 5 summarizes the thesis, states the conclusions, and presents ideasfor future work.8Chapter 2A High Impedance Surface (HIS)for RFID Chip DetectionApplicationsScientists are constantly searching for efficient and affordable methods to improve an-tenna radiation characteristics while still achieving a low-profile structure. One testedmethod is the utilization of a metallic ground plane, known as “perfect electric conductor”(PEC). A PEC serving as a reflector directs antenna radiation to one hemisphere, produc-ing an increase in gain of 3 dB. One must be cautious, however, as when a parallel dipoleis placed very close to a metal sheet, an opposite image current is induced by the reflectorwhich then cancels out the current in the antenna. In other words, fields from these twoopposite currents interact with each other destructively, ultimately resulting in very poorradiation efficiency. Improved radiation performance can be obtained by including a λ0/4distance between the radiating element and the ground plane.Metallic surfaces, such as the ones that form ground planes, are known to supportthe propagation of surface waves [31][32][33]. Electromagnetic waves are bound along ametal-dielectric interface through their interaction with the free electrons in the metal.These are referred to as “surface plasmons” at optical frequencies and “surface currents”in the microwave range [34]. These surface waves do not impact radiation patterns as longas they do not radiate into surrounding space. If the conductor is smooth and flat, thesurface waves will not couple to plane waves. However, they start radiating if scattered bybends, edges, corners, discontinuities, or surface texture. Surface waves appear in manysituations when antennas are used. If an antenna is placed close to a ground plane, it willnot only radiate plane waves into surrounding space, but it will also induce currents thatpropagate along the sheet. On an infinite metallic ground plane, the surface currents onlyresult in a slight decrease in radiation efficiency. The ground plane is always of finite size,and these currents radiate when they reach an edge or corner. Radiation of surface currentshas destructive interference on the antenna performance; examples of these include loweringthe efficiency of a single antenna, multi-path interference, unwanted coupling when usingmultiple antennas, and forming ripples in the radiation pattern.By applying a special periodicity to a metallic sheet, one can change its interactionwith propagating electromagnetic waves [35]. The periodic structure is comprised of ar-rays of metallic protrusions on a conducting flat sheet (shown in Fig. 2.1(a)). They can92.1. Use of Ground Planes in Race Timing Systemsbe visualized as a two-dimensional lattice of mushrooms jutting out of the solid lower con-ducting sheet. This structure is commonly referred to as electromagnetic band gap (EBG)structure because it exhibits a forbidden frequency band. In contrast to normal conduc-tors, the tangential magnetic field on the periodic surface is small leading to high surfaceimpedance. It is therefore also known as a high impedance surface (HIS). These surfacesare simple enough to be fabricated using PCB technology.The HIS is made of continuous metal and conducts DC currents, however, AC currentsare not supported on its surface within a forbidden frequency band [8]. This behaviour issimilar to that of a perfect magnetic conductor (PMC). This property makes these surfacesattractive for a variety of applications. Y. Qian et al. [36] used an HIS in a microstrippatch antenna to suppress surface waves and achieved an improvement in the antennabandwidth and gain. HISs have also been utilized to lower the mutual coupling of antennaarrays [37][38][39].The reflection phase of an HIS is one of its distinguishable properties and can bemeasured as the phase of the reflected electric field normalized to the phase of the incidentelectric field at the reflecting surface. A PEC or PMC (which does not exist in nature)is known to have a 180◦ and 0◦ reflection phase, respectively. As a consequence, in thecase of a wire antenna lying flat against a PMC, the induced image current is in-phaserather than out-of-phase to the antenna current. The HIS reflection phase is a continuousfunction of frequency which varies from 180◦ to -180◦. It therefore satisfies the PMC-likecondition over a certain frequency band [40]. In theory, at the frequency that the reflectionphase crosses through 0◦, a dipole can be placed very close to the HIS ground plane, andstill produces an omnidirectional radiation pattern.There are two related operational bands for an HIS and a wire antenna placed aboveit. The first is where the HIS suppresses surface waves and behaves as a PMC, called thesurface-wave-frequency bandgap. The second, termed as the input-match frequency band,is where antenna return loss is low. The frequency band where the reflection phase of theEBG surface is between 45◦ and 135◦ is where these two bands overlap [1].2.1 Use of Ground Planes in Race Timing SystemsOne of the specific applications of using a PEC ground plane for an antenna is race-timing systems. In order to determine the winner, athletic races require to store theprecise start and finish time of every athlete. This is particularly troublesome and error-prone task for large races in which hundreds of athletes may cross the start or finish linein a few seconds. Electronic product code generation 2 (EPC GEN2) passive RFID tagsare the most common tool for collecting start and finish times with the RFID tags beingplaced on the back of the runners bibs. Low-profile antenna mats are designed to be placedacross a road with the expectation that runners will run across them. Currently availablemat-based antennas use slot antennas (see Figure 2.1(b)) as a magnetic dipole against the102.1. Use of Ground Planes in Race Timing Systemsground, to produce an omnidirectional radiation pattern and cover the entire start or finishline. These antenna mats are very robust and consequentially very expensive and heavy.(a) (b)Figure 2.1: An HIS shown in (a) is comprised of arrays of vias and patches. These pro-trusions look like mushrooms jutting out of the bottom plane; thus, the structure is alsoreferred to as mushroom-type HIS [8]. (b) shows the slot antenna currently in use as amagnetic dipole against earth, which leads to an omnidirectional radiation pattern.Based on the image theory, the alternative is to place an electric dipole above an HIS(PMC), which results in a similar omnidirectional radiation pattern. However, a significantchallenge arises when the presence of the ground (which acts like an electric ground plane)beneath the antenna is considered. The in-plane (end-fire) radiation that was previouslyformed by a typical HIS-based dipole with an omnidirectional pattern is no longer achieved.The objective of this chapter is to design a low-profile end-fire HIS-based antenna placedagainst the ground that can be integrated into a low-cost, thin, lightweight mat for easydeployment. The operational frequency is 900 MHz, which lies within the RFID frequencyrange of 860 to 970 MHz.At the operating frequency, the free-space wavelength is 333 mm. Current slot antennasused in race-timing systems are typically 25 mm thick. It is desired to design an antennaprofile with a total thickness of less than 3 mm, which can then be fabricated using PCBtechnology.In this chapter, first the theory behind the HIS operation is studied. Following this,the equivalent circuit model is briefly discussed. An HIS-based dipole is placed against aninfinite PEC plane to understand its radiation characteristics. Finally, modified designsshall be presented that could possibly result in an end-fire radiation pattern. It is shown112.2. High Impedance Surface (HIS)that obtaining a thin antenna profile with the desired characteristics is limited by the HISdimensions.2.2 High Impedance Surface (HIS)The electromagnetic properties of the HIS structure can be described using a simplelumped-element equivalent circuit, which includes capacitance (C) and inductance (L).The use of lumped-element equivalent circuit to describe electromagnetic properties of thestructures is valid as long as the wavelength is much longer than the size of the individualfeatures. These surfaces are modeled as a network of parallel LC resonators that canbe simplified to an equivalent parallel LC circuit as seen in Figure 2.2. At the resonantfrequency, the parallel LC circuit has high impedance that can be used to model the HIS.Figure 2.2: At the resonant frequency, the equivalent circuit model of the HIS simplifies toa parallel LC resonator.Currents are induced in the patches (they are also referred to as metallic plates) be-cause of the interaction of the HIS with the incident electromagnetic waves. The voltagegenerated between the metallic sheet at the bottom and the HIS surface gathers charges onthe edges of the plates. Due to this alternating voltage, charges are forced to flow towardthe ground planes through the vias.122.2. High Impedance Surface (HIS)Figure 2.3: The capacitance and inductance in the HIS originates from the fringing electricfield between the neighboring patches, and the current flowing from the metallic plates tothe bottom sheet through the vias [8].2.2.1 Equivalent Inductance and CapacitanceThe capacitance of the model shown in Figure 2.2 originates from the fringing fieldbetween the edges of neighboring patches as shown in Figure 2.3. Sievenpiper derived thiscapacitance between the two plates using conformal mapping [35] as followsC =W (1 + 2)picosh-1(2Wg+ 1)(2.1)where W is the patch width, g is the gap between patches, 2 is the material surroundingthe structure, and 1 is the substrate permittivity.The inductance in the HIS originates from the current flowing through the inductiveloops that are comprised of the metallic plates, the PEC ground, and the vias (see Figure2.3). The total inductance of the structure is given by [35]L = µt (2.2)where µ is the substrate permeability and t is the substrate thickness. Based on this linearrelation, t plays a significant rule in the inductance of the structure.The surface impedance of the HIS is equal to that of the parallel LC resonant circuit,which is governed byZ =jωL√1− ω2LC (2.3)where C and L are the HIS total capacitance and inductance given by Equation 2.1 and2.2, respectively. This impedance is inductive at high frequencies, and capacitive at lowfrequencies. At the resonant frequency, the impedance acts like an open circuit. This shows132.2. High Impedance Surface (HIS)that the use of the equivalent circuit model to describe the high impedance property inthese electromagnetic structures is valid. Using Equation 2.3, The resonant frequency ofthe parallel LC resonator, and thus the HIS is given byω =1√LC(2.4)2.2.2 Reflection PhaseThe following section leads to further investigation of how the reflection phase of theHIS correlates to its high impedance, and thus the suppression of surface waves. Standingwaves are formed when electromagnetic waves normally impinge on an HIS. The reflectionphase is the phase difference between the incident and reflected traveling waves. Assumingthat the HIS is in the XY plane and a time-harmonic plane wave is propagating along theZ axis, the impedance of free-space is equal toη =EiHi=ErHr(2.5)The surface impedance of the HIS is given byZs =ExHy(2.6)and the reflection phase is defined byψ = Im{ln(EiEr)}(2.7)Using the free-space and HIS impedance in Equation 2.5 and 2.6, the reflection phase issimplified toψ = Im{ln(Zs − ηZs + η)}(2.8)When the reflection phase is 0◦, Zs has a high value, which results in suppression ofsurface waves. The reflection phase of ±pi are associated with low values of Zs where theHIS acts as a normal PEC surface.The reflection phase is a function of the HIS parameters: the patch width (W ), gapbetween the neighboring patches (g), thickness (t), and substrate dielectric constant (r).Changing any parameter in a way that increases the total capacitance, such as decreasingg or the total inductance, will lower the resonant frequency. The design corresponding tothe values listed in Table 2.1 that resonates at the frequency of 900 MHz and provides agood initial design to use for the structure characterization.Since the only restriction in our design is the thickness of the overall antenna, it is crucial142.2. High Impedance Surface (HIS)Parameter ValueW 40 mm (0.12λ0)g 6.67 mm (0.02λ0)r 1.6 mm (0.005λ0)t 13.3 mm (0.04λ0)r 2.2Table 2.1: Parameter values of an HIS at the frequency of 900 MHz taken from [1] as astarting point for later characterizationto realize the impact of changing the thickness on the resonant frequency and bandwidthof the HIS. The frequency band where the reflection phase lies between 45◦ and 135◦ isused as a reference for the bandwidth as given byBW = 2× f45◦ − f135◦f135◦ + f45◦× 100 (2.9)where f45◦ and f135◦ are the frequencies in which the reflection phase passes through 45◦and 135◦, respectively. Figure 2.4 shows the reflection phase of the HIS (in Table 2.1)versus frequency for different thicknesses. The substrate thickness has a linear relationshipwith the total inductance; its variation significantly changes the resonant frequency. It isobserved in Table 2.2 that as t decreases, the bandwidth of the structure also decreasesbut the resonant frequency increases.0.10.5 11.5 22.5 3−180−90090180Frequency (GHz)Reflectionphase(◦)t = 13 mmt = 10 mmt = 7 mmt = 2 mmFigure 2.4: Reflection phase of the design described in Table 2.1 versus frequency fordifferent substrate thicknesses.152.2. High Impedance Surface (HIS)The impact of changing the HIS substrate material on the reflection phase is shown inFigure 2.5. The dielectric substrates chosen are associated with actual materials, as shownin Table 2.4. As predicted by Equation 2.1, as the substrate permittivity increases, the totalcapacitance is boosted, and consequently the resonant frequency is lowered (see Table 2.3).Additionally, the bandwidth of the structure decreases as the dielectric constant reacheshigher values. There is a trade-off between the bandwidth and the resonant frequency; thehigher the permittivity, the lower the resonant frequency, and the narrower the bandwidth.Thickness (mm) Resonant Frequency (GHz) Bandwidth (%)13 1.36 4810 1.54 317 1.74 242 2.25 3Table 2.2: The resonant frequency and bandwidth of the HIS for different thicknesses.In an HIS with a 2 mm (or less) thick substrate, using a lower permittivity of 2.2 maycompensate for narrow reflection phase bandwidth. This design may resonate at a higherfrequency than 900 MHz, which can be fixed by adjusting the patch width or the gapsize. Using a material with dielectric constant of 2.2 is of interest since it corresponds toRogers Duroid 5880 with a very low loss tangent of 0.0009 in Table 2.4. FR-4 materialwith relative permittivity of 4.4 and loss tangent of 0.02, may also be of interest dueto its cheapest fabrication process, however, its higher permittivity leads to a narrowerbandwidth and it has very high losses.0.10.5 11.5 22.5 3−180−90090180Frequency (GHz)ReflectionPhase(◦) r = 2.2r = 2.95r = 4.4r = 6.35r = 10.3Figure 2.5: Reflection phase versus frequency for various r and constant thickness of 13mm.162.2. High Impedance Surface (HIS)Dielectric Constant (r) Resonant Frequency (GHz) Bandwidth (%)2.2 1.36 482.95 1.225 324.4 1.05 276.35 0.905 2410.3 0.72 20Table 2.3: The resonant frequency and bandwidth of the HIS with different materials.Substrate Material Dielectric Constant Loss TangentRogers RT/Duroid 5880 2.2 0.0009Rogers RT/Duroid 6002 2.94 0.0012FR-4 4.4 0.02Rogers 3006 6.15 0.0025Rogers 3010 10.3 0.0035Table 2.4: Dielectric constant and loss tangent of the substrate materials for HIS charac-terization are listed. Rogers RT/Duriod 5880 has the lowest permittivity and loss tangent.FR-4 has the highest dielectric constant.The lack of inductance in a thin (2 mm thick) HIS leads to a higher resonant frequencythan 900 MHz. The resonant frequency decreases if more capacitance is provided. Thereare several ways to add more capacitance to the structure. If the straight gap betweenthe metallic plates turns into a meandering line, extra capacitance is produced from thefringing field between the interdigitated fingers (see Figure 2.6(a)). This excess capacitancefor the HIS depends on the length (Lf) and width (Wf) of each finger, as well as the gapbetween the fingers (g). Using a two-layer-patch structure, where two layers of metallicplates are separated by a thin substrate layer, as depicted in Figure 2.6(b), also increasesthe capacitance. The total capacitance in this configuration originates primarily from theparallel-plate capacitance between the metallic plates rather then the fringing capacitancebetween the neighboring patches in the first and second layer.172.2. High Impedance Surface (HIS)(a) (b)Figure 2.6: Geometry of the interdigitated capacitor (a) and two-layer patch HIS (b).2.2.3 Interdigitated HISThe fringing capacitance in the interdigitated HIS is a function of the gap between thefingers (g), and their width (Wf) and length (Lf) (Figure 2.7). The capacitance increasesas the gap size decreases. Manufacturing tolerances may dictate the smallest repeatablegap. Reducing Wf, in general, lowers the effective capacitance. Increasing Lf increases thecapacitance. For the purpose of reducing the total thickness of the HIS to the range ofinterest and using FR-4 as the substrate, g, Wf, Lf, and W (shown in Figure 2.7(b)) aredesigned to lower the resonant frequency to 900 MHz as listed in the table below.Parameter ValueLf 4.5 mm (0.013λ0)Wf 150 um (0.0004λ0)g 150 um (0.0004λ0)W 27.2 mm (0.08λ0)t 1.6 mm (0.04λ0)r 4.4Table 2.5: Parameters of the interdigitated HIS182.2. High Impedance Surface (HIS)(a) (b)Figure 2.7: Placing fingers on each side of the patches creates meandering gaps in an HIS asshown in (a) and (b), and provides more capacitance. The length and width of each finger,and the gap between them determines how much capacitance is added to the structure.The reflection phase of the design described in Table 2.5 is shown in Figure 2.8. Theresonant frequency is at 915 MHz and the bandwidth of the design is 7.5%. A set of unitcells comprised of a row with n patches, as displayed in Figure 2.9(a), is used to verifywhether the interdigitated HIS is capable of suppressing surface waves or not. The powertransferred from the input to the output port, referred to as the transmission coefficient(S21), versus frequency for a various number of patches, is depicted in Figure 2.9(b).Increasing the number of patches results in lower transmission, particularly around theoperational frequency. Despite using a limited number of patches to mimic an ideal HIS,a rough estimate on the cutoff frequency of the structure can be made.0.10.5 11.5 22.5−180−90090180Frequency (GHz)ReflectionPhase(◦ )Figure 2.8: Reflection phase of the interdigitated HIS described in Table 2.5.192.2. High Impedance Surface (HIS)(a)0.5 11.5 2−100−80−60−40−200Frequency (GHz)S21(dB)n = 3n = 5n = 7(b)Figure 2.9: A row of patches consisting of n unit cells shown in (a) is used to test surfacewave suppression for the interdigitated HIS where lumped-ports are used at the input andoutput and its corresponding transmission coefficient (S21) is depicted in (b).Although the bandwidth of the interdigitated design is more than that of the one-layerHIS with thickness of 2 mm (listed in Table 2.2). There are more than 40 fingers oneach side of each patch, making the analysis and the full-wave simulation time-consuming.Furthermore, the gap-to-patch width-ratio (g/W ) is 0.005, decreasing the coupling of anincident wave to the resonant mode.202.2. High Impedance Surface (HIS)2.2.4 Two-Layer HISAdding another layer of metallic planes on top of the HIS metallic plates increases thetotal capacitance (see Figure 2.6(b)). In this configuration, in addition to the fringing ca-pacitance between the neighboring plates, the parallel plate capacitance appears betweenthe patches placed against each other. The thickness of the second layer, t2, is a new pa-rameter, which can be adjusted to get the desired resonance frequency; for low resonancefrequencies, this thickness is chosen to be small to boost the total capacitance. The reflec-tion phase for a two-layer HIS with the parameters listed in Table 2.6, is plotted in Figure2.10.Parameter ValueW 31 mm (0.09λ0)r 1.6 mm (0.005λ0)g 1 mm (0.003λ0)t1 1 mm (0.003λ0)t2 0.6 mm (0.002λ0)r 4.4Table 2.6: Parameter values of a two-layer HIS that resonates at the frequency of 900 MHz.0.10.5 11.5 22.5−180−90090180Frequency (GHz)ReflectionPhase(◦)Figure 2.10: Reflection phase of the two-layer HIS described in Table 2.6 versus frequencyThe new surface has a bandwidth of 4.8%, which is small compared to that of theinterdigitated HIS. The gap-to-patch-width ratio is 0.032, which is six times greater thanthat of the interdigitated HIS. Since there are no fingers and the gap between the patchesis greater than that of the interdigitated HIS, the computational process is faster. This212.3. HIS Based Dipole Against an Infinite Ground Planemakes the two-layer design preferable. More details are provided about this type of HISlater in this chapter.2.3 HIS Based Dipole Against an Infinite Ground PlaneIn this section, the radiation properties including the input impedance and radiationpattern of the HIS based dipole antenna over an infinite ground plane are studied. Initially,a half-wavelength dipole is placed against the one-layer patch HIS described in Table 2.1.It is shown that due to the existence of the infinite ground plane, the antenna does nothave in-plane radiation. Changes to the HIS dimensions and the use of different patchwidths are applied to the antenna profile to possibly achieve an end-fire radiation pattern.The operation of the dipole on the two-layer HIS and its modified versions are also ex-plored. Finally a design is explored where the dipole and the HIS are combined to forma “HIS dipole”. All the simulations in this section are performed using advance designsystem (ADS) momentum. Momentum is a 3D planar electromagnetic simulator that usesfrequency-domain method of moments (MoM).MoM is a generic method which is based on the work of R. F. Harrington in the 1960swho applied weighted residuals and variational calculus to electromagnetic field problems.Maxwell’s equations are transformed into integral equations and then discretized. In thismethod the electric and magnetic fields are expressed as a combination of a vector and ascalar potential. The unknowns are the electric and magnetic surface currents flowing inthe planar structure [41].2.3.1 Two-Layer ProfileThe HIS is placed in the XY plane with 8 unit cells along each axis (64 in total), witha 0.48 λ0 dipole operating at 900 MHz placed above it. The antenna is aligned with theX axis and is separated from the HIS surface by a 0.02 λ0 (7 mm) thick layer of RogersDuroid 5880 as seen in the figure below. The desired distance between the antenna andthe HIS (t3) is less than 1 mm, which consequently results in the overall antenna thicknessof less than 3 mm. A comprehensive study of the impedance, bandwidth, and efficiency ofa dipole against an HIS reveals that as the antenna gets closer to the HIS, the radiationefficiency decreases [42][43].The primary objective in this study is to prove that the structure is capable of produc-ing an end-fire radiation pattern. If successful in achieving such a structure, the overallthickness of the structure can be reduced. An initial distance of approximately 7 mm isselected, causing the overall thickness of the antenna to reach approximately 20 mm.222.3. HIS Based Dipole Against an Infinite Ground PlaneFigure 2.11: A 0.48λ0 dipole is placed above an HIS with one layer of patches forming anoverall two-layer antenna profile. The HIS has the length (LH) of 1.1λ0 , width (WH) of1.1λ0, and thickness of 0.04 λ0 and is separated from the the antenna by a dielectric layerwith thickness of 0.02 λ0 (6.7 mm). The dipole feed aligns with the center of the HIS.The input impedance and return loss shown in Figure 2.12(c) and 2.12(d) demonstratethat the structure resonates at the frequency of 935 MHz, which is slightly higher thanpredicted. At this resonant frequency, the antenna resistance is 34 Ω. The 10-dB impedancebandwidth is 6%. The antenna efficiency, which is the ratio of the radiated power by theantenna relative to its power delivered (PradPin ), is simulated to be 75%.232.3. HIS Based Dipole Against an Infinite Ground Plane0◦30◦60◦90◦120◦150◦180◦210◦240◦270◦300◦330◦00.20.40.60.81zx(a)0◦30◦60◦90◦120◦150◦180◦210◦240◦270◦300◦330◦00.20.40.60.81zy(b)0.80.85 0.90.95 11.05−30−20−100Frequency (GHz)S11(dB)(c)0.80.85 0.90.95 11.05−400−2000200400Frequency (GHz)InputImpedance(Ω) ResistanceReactance(d)Figure 2.12: Normalized E and H plane radiation patterns of the HIS-based dipole depictedin Figure 2.11 at the resonant frequency of 935 MHz in (a) and (b) show that, due to theinfinite PEC ground plane, there is no in-plane radiation. The maximum directivity of theantenna is 9 dBi. The half-power beamwidth (HPBW), which is the angle between thehalf-power points of the main lobe, when referenced to the peak radiated power of the mainlobe, is 80◦. The return loss and input impedance displayed in (c) and (d) demonstratethat at the resonant frequency the antenna input impedance is 34 Ω.The infinite ground plane forces the tangential electric field to be zero at far-field,meaning that there is no in-plane radiation for the antenna. This can be observed in theradiation pattern of the structure plotted in Figure 2.12(a) and 2.12(b). The in-plane nullsdo not disappear because of the PEC plane at the bottom. Efforts are devoted to pushing242.3. HIS Based Dipole Against an Infinite Ground Planethe main lobe as close as possible to the XY plane; this can be interpreted as tryingto increase the angle of maximum radiation denoted by θmax (with the Z axis), from 0◦obtained in the previous design, to nearly 90◦.For the purpose of having a better understanding of the antenna, characterization isrequired. Varying the patch width (WP) and the dipole length (LD) can potentially identifya design with the maximum possible value for θmax.0.060.070.090.1050.120.1350.18020406080100Patch Width (λ0)Efficiency(%)0306090θ max(◦)(a)0.060.070.090.1050.120.1350.180246810Patch Width (λ0)MaximumDirectivity(dBi)(b)0.35 0.40.45 0.50.55 0.6020406080100Dipole Length (λ0)Efficiency(%)W = 0.096λ00306090θ max(◦)W = 0.01λ0(c)0.35 0.40.45 0.50.55 0.6024681012Dipole Length (λ0)MaximumDirectivity(dBi)W = 0.096λ0W = 0.1λ0(d)Figure 2.13: (a) and (b) show the efficiency, the angle of maximum direction (θmax), andmaximum directivity versus HIS patch width. (c) and (d) depict variations of LD and Wthat lead to non-broadside radiation patterns.The patch width varies from 0.06λ0 (20 mm) to 0.18λ0 (60 mm), while other dimensionsof the structure including the length of the dipole (0.5λ0), gap (0.02λ0), and size of the HIS252.3. HIS Based Dipole Against an Infinite Ground Plane(1.1λ0) are kept constant. Figure 2.13(a) shows that the direction of maximum radiationmoves toward the Y axis, where W is between 0.09λ0 (30 mm) and 0.105λ0 (35 mm);θmax is respectively 56◦ and 34◦. At these patch widths, the maximum directivity, plottedin Figure 2.13(b), is comparable to those points with θmax of zero; this means that thedipole does not radiate normal to the antenna plane. However, these end-fire-like radiationpatterns are limited by a very low efficiency (Figure 2.13(a)).The variation of the dipole length (LD), from 0.35λ0 to 0.55λ0 with a step of 0.05λ0,along with that of the patch width with the aforementioned range, have been performed topossibly recognize an efficient design with an in-plane radiation pattern. The simulationresults show that no matter what value is chosen for LD, for all the values of the patchwidth, θmax is nearly zero, except for when the patch width is between 0.09λ0 to 1.05λ0. Es-sentially, there is trade-off between the efficiency and angle of maximum radiation; greaterwidths lead to higher efficiency but lower θmax.The trade-off between the efficiency, direction of maximum radiation, and input matchof the dipole is used to consider a surface that contains patches with variant widths. This iscalled the graded HIS. The geometry of the proposed structure, provided in Figure 2.14, hasplates with widths of 0.105λ0 for the purpose of moving the direction of radiation patterntoward the XY plane, 0.12λ0 and 0.18λ0 for input match and efficiency considerations,respectively.Figure 2.14: The graded HIS includes patches with variant width.262.3. HIS Based Dipole Against an Infinite Ground Plane0◦30◦60◦90◦120◦150◦180◦210◦240◦270◦300◦330◦00.20.40.60.81zx(a)0◦30◦60◦90◦120◦150◦180◦210◦240◦270◦300◦330◦00.20.40.60.81zy(b)0.75 0.80.85 0.90.95−30−20−100Frequency (GHz)S11(dB)(c)0.75 0.80.85 0.90.95−300−200−1000100200300400Frequency (GHz)InputImpedance(Ω) ResistanceReactance(d)Figure 2.15: Normalized E and H plane radiation patterns of the graded HIS-based dipoleantenna depicted in Figure 2.15(a) at the resonant frequency of 840 MHz in (a) and (b)show that there is still no in-plane radiation. The maximum directivity is 8.3 dBi. HPBWof the antenna is 90◦, which is in good agreement with the maximum directivity decreasecompared to the original design. The return loss and input impedance are displayed in (c)and (d). At the resonant frequency the antenna input impedance is 58 Ω.The radiation pattern plotted in Figure 2.15(a) and 2.15(b) is still broadside with nullsalong the X and Y axes. The maximum directivity has decreased to 8.3 dBi, directionof maximum radiation has increased to 5◦, and HPBW has risen to 90◦ compared to theoriginal design.The antenna is matched to 50 Ω at the frequency of 840 MHz with a 10-dB impedancebandwidth of 4% and efficiency of 75%. The decrease in the resonant frequency comparedto the original design, is predicted, since the total capacitance and inductance is changed272.3. HIS Based Dipole Against an Infinite Ground Planeby using different widths.The HIS surface is mostly comprised of patches with width of 0.12 λ0 beneath thedipole; they have been more effective on the radiation characteristics. While the efficiencyis greater than 70% and the resonant input impedance is 58 Ω, nonetheless, its broadsidepattern makes it not applicable for our purposes. The limited dimensions of the HIScompared to the ground cause the in-plane (in the XY plane) nulls. Varying its length(LH) and width (WH) may be beneficial to achieve radiation at end-fire. Since there is anull along the X axis because of the dipole orientation, LH is kept constant at 1.1λ0. WH of1.1λ0, 1.38λ0, and 1.66λ0 are selected. Our simulation results show that while maintainingan efficient operation, the maximum radiation is still pointing nearly normal to the antennaplane.2.3.2 Three-Layer ProfileA half-wavelength dipole is placed above the HIS described in Table 2.6 using a 0.02λ0 (6.7 mm) thick layer of FR-4 (with permittivity of 4.4 and loss tangent of 0.02) as aspacer, as seen in the figure below. The first layer of HIS patches has the total length andwidth of 1.1λ0. The second layer has slightly smaller total length and width of 1.08λ0.Figure 2.16: Half-wavelength dipole placed above a two-layer HIS forming an overall three-layer antenna profile.282.3. HIS Based Dipole Against an Infinite Ground Plane0◦30◦60◦90◦120◦150◦180◦210◦240◦270◦300◦330◦00.20.40.60.81zx(a)0◦30◦60◦90◦120◦150◦180◦210◦240◦270◦300◦330◦00.20.40.60.81zy(b)0.840.850.860.870.880.89−30−20−100Frequency (GHz)S11(dB)(c)0.840.850.860.870.880.89−1000100200300Frequency (GHz)InputImpedance(Ω) ResistanceReactance(d)Figure 2.17: Normalized E and H plane radiation patterns of the three-layer HIS baseddipole depicted in Figure 2.16 against an infinite PEC ground plane, at the resonant fre-quency of 858 MHz, are shown in (a) and (b), respectively. The direction of maximum radi-ation and maximum directivity are 30◦ and 8.3 dBi. The return loss and input impedancein (c) and (d) demonstrate that the antenna resistance at the resonant frequency is 41 Ω.The 10-dB impedance bandwidth and radiation efficiency are 0.5% and 92%, respectively.The radiation pattern of the design at the resonant frequency of 858 MHz is plottedin Figure 2.17(a) and 2.17(a). There are still nulls along the X and Y axes. However,the direction of maximum radiation has increased by approximately 30◦ compared to theoriginal two-layer design shown in Figure 2.11. The maximum directivity and HPBW are8.3 dBi and 103◦, respectively.292.3. HIS Based Dipole Against an Infinite Ground PlaneThe input impedance and return loss shown in Figure 2.17(c) and 2.17(d) demonstratethat the dipole input impedance at the resonant frequency is 41 Ω. The 10-dB impedancebandwidth is 0.5%. This is lower than the previous designs as predicted by in the HISreflection phase plotted in Figure 2.10. The antenna efficiency is 92% at the resonantfrequency.Since the capacitance originates primarily from the parallel patches, the HIS interactswith the antenna differently from the HIS with one layer of patches. Sweeps over the patchwidth and HIS length (LH) are performed to characterize the structure. The width ofall the patches varies from 0.07λ0 to 0.11λ0. While the width of the HIS (WH) is keptconstant at 1.1λ0, its length changes from 1.1λ0 to 2.15λ0, where the end value of thisrange is limited to our available computational memory. Our simulation results show thatfor patch widths of 0.088λ0 and 0.097λ0, θmax is 40◦ and 32◦, respectively.0.070.080.0880.0970.109020406080100Patch Width (λ0)Efficiency(%)0306090θmax(◦)(a)0.070.080.0880.0970.109024681012Patch Width (λ0)MaximumDirectivity(dBi)(b)Figure 2.18: (a) and (b) show the efficiency, angle of maximum direction, and maximumdirectivity associated with a design in which the dipole length is 0.48λ0, the length andwidth of the HIS are 1.2λ0 and 2.15λ0, and the patch width is swept from 0.07λ0 to 0.11λ0.The efficiency and direction of maximum radiation of the structure versus the patchwidth are shown in Figure 2.18. θmax is 40◦ when the patch width is 0.088λ0. The sidelobelevel (SLL) of the antenna is -30 dB meaning that there is no radiation normal to theantenna plane. This is consistent with fact that the maximum directivity of 8.3 dBi at thiswidth (see Figure 2.18(b)) is close to that of those designs with θmax of zero (broadsideradiation pattern). The radiation efficiency is 51%. For only an increase of 10◦ in thedirection of maximum radiation, the efficiency decreased more than 40% compared to theoriginal design depicted in Figure 2.16; this is not a reasonable compromise.302.3. HIS Based Dipole Against an Infinite Ground Plane2.3.3 HIS Magnetic DipoleOur initial objective was to place a dipole against an HIS as a PMC surface to producean omnidirectional radiation pattern. The limited dimensions of the HIS compared to theground prevented us from reaching such a goal. The alternative is when a magnetic dipoleis placed against the ground to generate the same omnidirectional pattern.In this section, we study the possibility of using the HIS as a magnetic dipole abovean infinite PEC ground plane. An HIS as a PMC-like structure supports magnetic surfacecurrents that can radiate into surrounding space. The proposed structure that uses theHIS directly as an antenna rather than a ground plane is seen in Figure 2.19(a). Thereis a three-unit cell-HIS which is designed to form a 0.48λ0 magnetic dipole resonatingat the frequency of 900 MHz. Each patch is 0.16λ0 wide on a 2 mm thick RT/Duroid5880 substrate, connected to the solid ground plane by the vias with radius of 0.005λ0;neighboring patches are separated by 0.02λ0.(a) (b) A(c) B (d) CFigure 2.19: Geometry of the proposed HIS dipole in (a). (b), (c), and (d) show the electriccurrent density of the structure when fed from three different positions: center-bottom side(A), center-right side (B), and the center of the middle via (C), respectively.Three points are chosen to feed the antenna: A, B, and C. These three feed pointscorrespond to antenna designs A, B, and C. Each feed creates a different current density312.3. HIS Based Dipole Against an Infinite Ground Planedistribution on the metallic plates (2.19(b), 2.19(c), and 2.19(d)). Despite having a limitednumber of patches, the suppression of surface currents is observed in all configurations.In terms of far-field performance depicted in Figure 2.20(a) and 2.20(b), there is adifference between A and B, and C. While A and B have their maximum radiation alongthe Z axis (broadside), C has its maximum directivity very close to the XY plane andhas a null normal to the antenna plane. None of the designs behaves as an ideal magneticdipole. On the other hand, in C, since the via in the middle is being directly fed, it carriesa strong current, which plays a significant contribution to its radiation. Near-field couplinginduces currents in the other two vias, resulting in a three-element parasitic array. Withthe existence of the ground plane, each element is serving as a monopole based on theE and H plane radiation patterns in Figure 2.20(a) and 2.20(b). This configuration canbe interpreted as a Yagi-Uda antenna where the reflector spacing and dimensions are nottuned to block waves from the back side of the structure. The current on the patchesdecays quickly toward the edges, and due to the effect of the ground plane, does not havemuch contribution to the radiation.0◦30◦60◦90◦120◦150◦180◦210◦240◦270◦300◦330◦00.20.40.60.81ABCzx(a)0◦30◦60◦90◦120◦150◦180◦210◦240◦270◦300◦330◦00.20.40.60.81ABCzy(b)Figure 2.20: Normalized E and H plane radiation patterns at the frequency of 920 MHz in(a) and (b) show that in design A and B the proposed structure is broadside, but designC results in an end-fire radiation pattern. The maximum directivity of 6.5, 5.7, and 6 dBiare achieved for design A, B, and C, respectively.322.3. HIS Based Dipole Against an Infinite Ground Plane0.80.85 0.90.95 1050100150200Frequency (GHz)Resistance(Ω)ABC(a)0.80.85 0.90.95 1−400−2000200400Frequency (GHz)Reactance(Ω)ABC(b)0.80.85 0.90.95 1−30−20−100Frequency (GHz)S11(dB)ABC(c)Figure 2.21: The resistance, reactance, and return loss of the proposed structures in (a),(b), and (c) reveal that all the designs are resonant. The reactance in design A sharplycrosses through zero at the frequency of 950 MHz. The resonant resistance is higher than400 Ω leading to a high reflection coefficient. The simulated efficiency at 950 MHz is2%. Design B resonates at 913 MHz with resistance of 22 Ω, efficiency of 4%, and 10-dBimpedance bandwidth of 0.25%. At the resonant frequency of 922 MHz, design C has inputimpedance of 40 Ω, efficiency of 4.5%, and bandwidth of 0.64%. All three designs sufferfrom poor efficiency.The reflection coefficient and input impedance of all designs are depicted in Figure2.21. All configurations resonate at approximately 900 MHz. The antenna resistance atthe resonant frequency for design A and B is very far from 50 Ω leading to a a highreflection coefficient. Design C’s resonant impedance is 40 Ω at a very narrow frequencyband. Despite achieving the desired radiation pattern in design C, the simulation results332.4. Summaryshow that the efficiency is very low (less than 5%). This poor efficiency can be attributedto the strong currents in the lossy conductive posts.2.4 SummaryThe possibility of using a thin HIS-based dipole for RFID detection systems in racetiming has been investigated. When the antenna is placed against earth, which is modeledas an infinite PEC ground plane, the in-plane radiation disappears. A variety of modifica-tions have been applied to the HIS plane such as changing its dimensions, placing differentsize patches, and adding an extra layer of substrate and metallic plates (two-layer HIS),to direct the maximum radiation toward the antenna plane. It has been shown that thosedesigns with an end-fire-like radiating pattern suffer from poor efficiency or a narrow band-width. Finally, a row of three HIS unit cells is used as a magnetic dipole. The structurehas the desired radiation pattern at approximately 900 MHz, but similar to earlier designs,has poor efficiency. The study on the HIS magnetic dipole has been very limited. Only aset of three patches on a thin substrate has been investigated. There is no variation on thepatch width, substrate thickness, substrate dielectric constant, via radius, or gap betweenthe neighboring patches. More research is required to investigate the proposed antenna inmore detail.34Chapter 3End-Fire Radiation FromRectangular Patch AntennasA microstrip patch antenna (MPA) is one of the most common types of antenna designsused in today’s wireless communication systems, mainly because of its low cost and easyintegrability into different surfaces. As a low-profile structure, the MPA is a preferredantenna choice for applications used in vehicular technology and mobile communications;it has also gained popularity because it is lightweight and extremely easy to construct.These advantages, however, are accompanied by some drawbacks; the MPA has typicallyan efficiency of less than 80% and a narrow impedance bandwidth.Grieg and Englemann described a microstrip transmission-line for the first time in1953 [44]. In the same year, the initial concept of the MPA was proposed by Deschampsand Sichak in their popular publication “Microstrip Microwave Antennas” [45]. In theirresearch, a microstrip transmission line was used in a planar horn radiator, and theirstructure had the same configuration as the microstrip patch antenna we know of today.Patch antennas were commonplace in the mid-1970s; Munson, Byron and Howell presentedpractical aspects of microstrip antenna fabrication, as shown see Figure 3.1 [9][46]. By thelate 1970s, a microstrip antenna with stacked patches has been proposed to provide anincreased the impedance bandwidth [47]. The transmission-line model and the cavity modelwere also introduced at this point, providing more accurate predictions of the antennaimpedance response and resonant frequencies. [48] [49]. The use of patch antennas in arrayswas further explored, leading to the the development of phased arrays in the 1980s [50]. Bythe 1990s, bandwidth enhancement techniques were investigated in more detail. Impedancebandwidth increased up to 67% by using an aperture-coupled stacked patch [51] and patchantennas with multiple frequency bands were introduced [52]. Many efforts were devotedto reducing the size of the patch conductor for the purpose of antenna miniaturization.After the turn of this century, patch antennas were integrated into artificial electromagneticstructures to enhance bandwidth and efficiency, total antennae size reduction, and improvethe overall radiation performance [36] [53] [54].This chapter outlines basic characteristics of the microstrip patch antenna, including anoverview of the patch geometry and typical design parameters. One of the most commonmethods of analysis, the cavity model is investigate. Finally, the possibility of achievingan end-fire radiation pattern in an MPA is studied using the cavity model. The radiationcharacteristics of the end-fire MPA are investigated, in terms of efficiency, input impedance,353.1. Basic PropertiesFigure 3.1: Photograph of a fabricated rectangular patch antenna [9].radiation pattern, and directivity.3.1 Basic PropertiesFigure 3.2 depicts the typical configuration of a rectangular patch antenna. It consistsof two parallel conducting plates separated by a dielectric layer. The lower conductorforms a ground plane for the upper strip, which is called the patch. The patch antenna isa resonant structure in which its resonant frequency is governed by its parameters, whichinclude width (W ), length (l), dielectric constant (r) and thickness (h) of the substrate,and feed type.Figure 3.2: Microstrip patch antenna geometry [10].The bandwidth of patch antennas is typically less than 5%. Bandwidth is primarily363.2. Theory of Operationdetermined by the thickness of the substrate and its material properties [55]. Substrateswith low dielectric constants are desirable, since they have been shown to result in abroader bandwidth and a greater efficiency [56]. As the substrate thickness increases,the bandwidth broadens, however, surface waves start propagating along the metal andsubstrate interface. These waves radiate into space when they reach bends, corners, orany other discontinuities. This introduces ripples in the radiation pattern and ultimatelyresults in decreased directivity.Microstrip patch antenna efficiency depends on substrate thickness and conduction anddielectric losses. Materials with a low dielectric constant typically have lower losses andprovide a higher efficiency at the expense of requiring a larger structure. Although a thickersubstrate increases the efficiency, however, it also may excite surface waves.3.2 Theory of OperationIn order to describe the operation of the rectangular patch antenna, various models havebeen reported. The “cavity model” has been widely used. The cavity model employs waveequations, as well as boundary conditions, to predict the radiation characteristics. It treatsthe patch antenna as a magnetic cavity that radiates energy at its resonant frequencies.Despite needing more numerical computation, the cavity model is able to provide manyphysical insights.3.3 Cavity ModelOne of the most popular methods used to predict the performance of the MPA isthe cavity model, which treats the radiator as a dielectric-loaded cavity [11]. This modeldetermines the electromagnetic field distribution by treating the patch as a cavity boundedby two PECs above and below the patch and four PMC side walls. The perfect magneticwalls model the open circuit condition along the edges of the patch (where the current iszero). However, the open-ended edges do not act as a perfect open circuit.The tangential magnetic fields on the PMC sidewalls vanish leaving the magnetic fieldis normal to the side walls. The electric field in the cavity is nearly normal to the PECplanes (Ex) because the substrate thickness is electrically small (h << λ0) which in turnreduces the fringing fields. The modes supported within the patch cavity are therefore allTM modes.3.3.1 TM ModesThe cavity model is analyzed based on the assumption that the dielectric substratedoes not extend beyond the edges of the patch and the ground plane is of infinite extent,as seen in Figure 3.7. The wave equation for the magnetic vector potential (Ax) is used to373.3. Cavity Modelrealize the possible field configurations within the patch, where Ax is time harmonic withangular frequency of ω.∇2Ax + k2Ax = 0 (3.1)Once Ax is determined, the electric and magnetic fields can be calculated using the equa-tions below [57]Figure 3.3: The cavity model is based on the assumption that the substrate is limited tothe patch edges and the ground plane is infinitely large.Ex = −j 1ωµ(∂2∂2x+ k2)Ax (3.2a)Hx = 0 (3.2b)Ey = −j 1ωµ∂2Ax∂x∂y(3.2c)Hy =1µ∂Ax∂z(3.2d)Ez = −j 1ωµ∂2Ax∂x∂z(3.2e)Hz =1µ∂Ax∂y(3.2f)Simplified expressions for different components of electromagnetic field modes can beobtained by using boundary conditions. Ez and Ey are zero on the top and bottom PECplanes while Hz is zero on the two sidewalls at y = −l/2 and y = l/2 and Hy on the othertwo sidewalls of z = −W/2 and z = W/2.383.3. Cavity ModelEx = −jk2 − k2xωµAnpm cos(kxx) cos(2kyy) cos(2kzz) (3.3a)Ey = −jkxkyωµAnpm sin(kxx) sin(2kyy) cos(2kzz) (3.3b)Ez = −jkxkzωµAnpm sin(kxx) cos(2kyy) sin(2kzz) (3.3c)Hx = 0 (3.3d)Hy = −kzµAnpm cos(kxx) cos(2kyy) sin(2kzz) (3.3e)Hz =kyµAnpm cos(kxx) sin(2kyy) cos(2kzz) (3.3f)wherekx =npihn = 0, 1, 2, ... (3.4a)ky =ppilp = 0, 1, 2, ... (3.4b)kz =mpiWm = 0, 1, 2, ... (3.4c)(3.4d)Anpm is the amplitude coefficient of each mnp mode, and kx, ky, and kz are components ofthe wavenumber, which must satisfyk2x + k2y + k2z = k2 = ω2µ (3.5a)(npih)2+(ppil)2+(mpiW)2= ω2µ (3.5b)The resonance frequencies for the cavity can be found byfnpm =12pi√µ√(npih)2+(ppil)2+(mpiW)2(3.6)The mode with the lowest resonant frequency is referred to as the dominant mode.Assuming l >> h, W >> h, and l > W , the dominant mode is the TM010 whose resonantfrequency is given byf010 =12l√µ(3.7)393.3. Cavity Model3.3.2 Equivalent Magnetic Current DensitiesThe principle of field equivalence for apertures is used to describe the radiation perfor-mance of an MPA from the cavity model. Within this model, the patch antenna consistsof an upper and lower PEC boundary surrounded by four PMC sidewalls. The side wallsact as apertures that can be represented by equivalent electric current densities Js andequivalent magnetic current densities Ms given byJs = nˆ× ~Ha (3.8)Ms = −nˆ× ~Ea (3.9)Ea and Ha are the electric and magnetic fields at the slots, respectively, and nˆ is theunit normal vector to the apertures. There is no equivalent electric current density at theslots because the magnetic field is nearly zero. The effect of the ground plane is taken intoaccount by doubling the magnetic current densities using image theory (Figure 3.4). Thereare two pairs of parallel current densities forming a pair of two-element arrays.(a) (b)Figure 3.4: Image theory is used to account for the presence of the infinite PEC plane.When the dominant mode is considered kx = 0, ky =2pil = ω√µ,and kz = 0, and theelectromagnetic fields in Equation 3.3 are reduced toEx = −jωA010 cos(2pily)= E0 cos(2pily)(3.10a)Hz =2piµlA010 sin(2pily)= H0 sin(2pily)(3.10b)Ey = Ez = Hx = Hy = 0 (3.10c)403.3. Cavity ModelThe electric field and current density distribution on the sidewalls for the dominant modeare depicted in Figure 3.5. Using the electric field expression in Equation 3.10 for theslots located at y = −l/2 and y = l/2, the equivalent current densities are uniform (Ms =jωA010). The varying electric fields on the apertures at z = −W/2 and z = W/2 produceopposite equivalent current densities at each slot that cancel each other out in the far-field;consequently, these two slots are referred to as the non-radiating edges. The two radiatingslots are separated by a distance of l and form a two-element array. As previously statedin the transmission line model, to excite the dominant mode in the cavity, the l must beapproximately λg/2.Figure 3.5: The dominant mode electric field distribution and equivalent charge densitiesat radiating (y = −l/2 and y = l/2) and non-radiating edges (z = −W/2 and z = W/2).3.3.3 Radiated Fields in the Far-FieldRadiating slots in the cavity are analyzed using a combination of aperture theory andarray theory. Using the equivalent current density of E0 on each radiating slot and thecoordinate system shown in Figure 3.9, the electric field in the far-field is given by413.3. Cavity ModelEr = Eθ = 0 (3.11a)Eφ = +jk0WE0h2pire−jk0r[sin θsin(Z)Zsin(X)X](3.11b)whereZ =k0W2sin θ cosφ (3.12a)X =k0h2cos θ (3.12b)Patch antennas are typically designed with k0h 1, which simplifies Equation 3.11b toEφ ' +jE0hpire−jk0r[sin θsin(Wk02 cos θ)cos θ](3.13)The array factor of the two antennas with the same magnitude and phase, separated bythe effective distance of leff isAF = 2 cos(k0leff2sin θ sinφ)(3.14)By multiplying the far-field electric field of each slot by the array factor, the total electricfield is obtained as followsEφ ' +j2E0hpire−jk0r[sin θsin(Wk02 cos θ)cos θ][cos(k0leff2sin θ sinφ)](3.15)For the E plane of the MPA (the XY plane), where θ = 90◦, 0◦ ≤ φ ≤ 90◦ and270◦ ≤ φ ≤ 360◦, the radiated field is reduced toEφ ' +jWk0E0hpire−jk0r[sin(hk02 cosφ)hk02 cosφ][cos(k0leff2sinφ)](3.16)For the H plane (the XZ plane) where φ = 0◦ and 0◦ ≤ θ ≤ 180◦, the radiated field isgiven byEφ ' +jWk0E0hpire−jk0r[sin θsin(hk02 sin θ)sin(Wk02 cos θ)(hk02 sin θ)(Wk02 cos θ) ] (3.17)In-phase radiating current densities, or magnetic dipoles, not only generate nulls along theaxis they are pointing to, the Z axis, but also cancel each other out along the Y axis.Figure 3.6 illustrates the radiation patterns in the principal E and H planes for a typical423.4. End-Fire Patch Antennabroadside radiating patch antenna.(a) (b)Figure 3.6: Normalized E and H plane radiation patterns are plotted in (a) based onEquation 3.16 and 3.17 where r = 2.2, k0h = 0.15, W = 0.3λ0, and leff = 0.3λ0.3.4 End-Fire Patch AntennaIs it possible to obtain an end-fire radiation pattern with the patch antenna? Thisquestion can be answered by referring to the cavity model, which simplifies the antenna toa two-element array. The distance between the two radiating slots, as well as their phasedifference, determine the type of radiation pattern achieved. Figure 3.7 illustrates two ofthe possible radiation patterns with a two-element array of Herzian dipoles. In the end-fireradiation pattern in Figure 3.7(c), the two elements are out-of-phase and separated byλ0/2, which results in the far-field cancellation along the X and Y axes, whereas the samearray with in-phase elements leads to nulls along the Z and Y axes (Figure 3.7(b)) and3.7(d)). The only challenge in achieving an effective end-fire patch antenna is to excite theout-of-phase current densities on the radiating apertures. We can therefore conclude thatit is possible to design an end-fire radiation pattern based on array theory.An end-fire patch antenna is possible if the magnetic current densities on the radiatingedges reflect the radiation the two-element array demonstrated in Figure 3.7(b). A par-ticular mode must be excited in the cavity to induce out-of-phase current densities on theradiating apertures. Based on Equation 3.9, in order to excite this particular mode in theMPA, the radiating slots must be separated by λg (guided wavelength) as shown in Figure3.13. On the other hand, the distance of λ0/2 between the radiating edges is necessary forfar-field considerations (see Figure 3.13). The design of a patch antenna satisfying boththese conditions is possible by choosing an appropriate dielectric.433.4. End-Fire Patch Antenna(a) (b)(c) (d)Figure 3.7: The cavity model simplifies an MPA to a two-element array. Two possibleradiation patterns are shown, using an array of two Hertzian dipoles is shown: end-firewhere dipoles are out-of-phase and separated by λ0/2 in (a) and broadside where thedistance between the elements is still λ0/2 but they are in-phase in (b). As shown in thenormalized radiation pattern of the end-fire array (c), the maximum radiation is directingtoward the array axis (Z) and there are nulls along the other two axes. The broadsidearray the radiates maximally normal to the array axis (Y) and has nulls along X and Zaxes.443.4. End-Fire Patch AntennaFigure 3.8: The electric fields and equivalent current densities on the radiating (left) andnon-radiating (right) edges of for an MPA, which has an end-fire radiation pattern.The relationship between the free-space and guided wavelength for a substrate with therelative permittivity and permeability of r and µr isλg =uf(3.18a)c =1√µ=1√0µ0√rµr(3.18b)λg =1f√0µ0√rµr=λ0√rµr(3.18c)Most materials are non-magnetic, or µr = 1; therefore, Equation 3.18c reduces toλg =λ0√r(3.19)Using the above equations, setting the substrate dielectric constant to 4 satisfies the far-field and electromagnetic field considerations previously stated. The radiating aperturesare separated by λg, which corresponds to λ0/2. Since either length or width of the patchcan be λg (or λ0/2 ), there are two possible modes for the cavity: TM020 and TM002, asshown in Figure 3.9. To consider the input match and the maximum directivity in thedesign, optimization is required. Following the cavity model, the patch and its substrateare placed over an infinite ground plane. The patch, in the XY plane, is fed from thecenter of its width (see Figure 3.9). COMSOL Multiphysics is used to find the optimalvalues of l, W, and r at the frequency of 10 GHz.453.4. End-Fire Patch Antenna(a) TM002 (b) TM020Figure 3.9: Two modes of operation that results in end-fire radiation pattern [11].(a) Top view (b) Side viewFigure 3.10: Geometry of patch simulated in COMSOL MultiphysicsParameter Valuel 7.5 mm (0.26λ0, 0.56λg)W 14.8 mm (0.48λ0, 1.01λg)h 1.5 mm (0.05λ0, 0.11λg))r 4.6Table 3.1: The optimal parameters in the MPA that results in an end-fire pattern.The TM002 mode is excited by setting the MPA parameters to the values listed in theabove table. The simulated vertical electric field (Ez) and magnitude of the tangentialmagnetic field to the side walls in the ZY and ZX planes (|Ht|) are shown in Figure3.11. There is good agreement between the theory and simulation results. As predicted bythe cavity model, the magnitude of the magnetic field on the sidewalls is small while the463.4. End-Fire Patch Antennamagnitude of the electric field is large..(a) Ez in the XY plane (b) Ht in the ZY plane(c) Ht in the ZX planeFigure 3.11: The vertical electric on the patch in the XY plane and magnetic of the tan-gential magnetic field on the ZY and ZX sidewalls are shown (a), (b), and (c), respectively.The reflection coefficient, resistance, and reactance of the MPA is shown in Figure 3.12for a 50 Ω system. The cavity resonates at the frequency of 9.8 GHz. This slight reductionin the resonant frequency (200 MHz) is related to the fringing effect, which is characterizedby a width extension (∆W ). The width of the patch is nearly λg meaning that the effectivewidth (Wef = W +2∆W ) is greater than λg, which consequently results in a lower resonantfrequency. At the resonant frequency, the antenna resistance is approximately 230 Ω thatleads to a return loss of 3.87 dB. The peak return loss is 9.6 dB which occurs at thefrequency of approximately 9.4 GHz, where the antenna input impedance is 93+j20.473.4. End-Fire Patch Antenna88.5 99.5 1010.5 1111.5 12−20−15−10−50Frequency (GHz)S11(dB)(a)88.5 99.5 1010.5 1111.5 12−200−1000100200300Frequency (GHz)Zin(Ω)ResistanceReactance(b)Figure 3.12: The reflection coefficient and input impedance of the design described in Table3.1 with respect to frequencyThe radiation patterns of the MPA at the frequency of 9.4 GHz in the XY and Y Zplanes in Figure 3.13, confirm the far-field cancellation along the X and Z axes due to theout-of-phase magnetic current densities on the radiating edges. The maximum directivityis 6 dBi and the half-power beamwdith (HPBW), which is the angle between the half-powerpoints of the antenna main lobe, is 85◦.(a) (b)Figure 3.13: Normalized radiation patterns in the XY and Y Z planes at the frequency of9.4 GHz show that the maximum radiation occurs along the Y axis.The efficiency of the antenna is calculated when a lossy dielectric material and lossyconductors are used. The permittivity required for this design is 4.6, as outlined in Table3.1. FR-4 with a dielectric constant of 4.4 is chosen. FR-4 is cost-efficient but has a high-483.4. End-Fire Patch Antennaloss material with a loss tangent of 0.02. Copper has been used for the patch and groundplane. The simulated antenna efficiency is 55%.3.4.1 Finite Ground Plane and SubstrateIn order to produce a realizable design, the ground plane must be truncated. To simplifythe fabrication process, the dielectric was extended to the edges of the ground plane. Thisalso provides a substrate for the patch feed network.Our simulation results show that varying Ws significantly affects the radiation proper-ties. In contrast, changing (Ls) has negligible impacts on the antenna performance. Thisoccurs due of the placement of a null along the width of the patch, which is the X axis.In our simulation (Ls) is kept constant at 0.4λ0. As Ws increases, the main lobes of theantenna start moving toward the Z axis, normal the antenna plane (Z axis). This can becharacterized by an increase in the main lobe elevation angle denoted by θmax, which isdefined as the angle between the direction of maximum radiation and the XY plane.Figure 3.14: The geometry of the end-fire patch antenna is displayed when a finite PECplane and a substrate, which is extended to the edge of the ground plane.493.4. End-Fire Patch Antenna0.5 11.5 2 3 4 5 6020406080100Patch Width (λ0)Efficiency(%)0306090θmax(◦)(a)00.5 1 2 3 4 5 60246810Ws (λ0)MaximumDirectivity(dBi)(b)00.5 1 2 3 4 5 6−20020406080100Ws (λ0)Zin(Ω)ResistanceReactance(c)Figure 3.15: Impact of finite ground plane on the antenna, characterized by the elevationangle of main lobes from XY plane (a), maximum directivity (b) and input impedance (c).The efficiency, main lobe elevation angle (θmax), maximum directivity, and input impedanceof the antenna are plotted in Figure 3.15 with respect to the ground plane width. Themaximum efficiency occurs at a width of λ0, at which point, θmax is approximately 60◦,and the radiation pattern can no longer be considered end-fire. As the width goes beyondλ0, the main lobes start pointing closer to the ground and directivity increases. The inputimpedance does not change significantly for widths beyond λ0. The width of 5λ0 leads toθmax of less than 30◦, directivity of 7.3 dBi, input impedance of 28+j3 Ω, and radiationefficiency of 62%.503.5. Summary3.5 SummaryThe radiation mechanism of the patch antenna has been presented in this Chapterthrough a detailed investigation of a common radiation model. In the cavity model, theMPA is treated as a dielectric-loaded cavity with two PEC planes at the top and bottomand four PMC sidewalls. The wave equations and the boundary conditions are used todetermine the resonant frequencies of the modes allowed to propagate within the cavity.The far-field electromagnetic fields radiated from the fundamental mode of the patchantenna have a peak at broadside. By exciting a higher mode in the cavity, such as theTM002 mode or the TM020 mode, an end-fire radiation pattern can be achieved. At thesemodes, the equivalent current densities on the radiating edges are out-of-phase, whichresult in in-plane radiation. Successfully exciting these modes requires permittivity ofapproximately 4, and width or length of λ0/2. The maximum directivity, input impedance,and efficiency are 6 dBi, 89+j20 Ω, and 51%, respectively, where the patch is placed on aninfinite ground plane. A finite ground plane with length of 0.4λ0 and width of 5λ0 leadsto an antenna with maximum directivity of 7.3 dBi, input impedance of 28+j3 Ω, andefficiency of 62%.51Chapter 4End-Fire Microstrip Antenna withNegative Permittivity SubstrateMetamaterials have drawn some interest in recent years with regards to manipulatingelectromagnetic waves. These engineered materials possess properties beyond those ofconventional materials and are typically designed with repeating patterns of metals anddielectrics. Their precise shape, size, and geometry provide many useful features, such ascloaking, beam shifting, beam splitting, blocking, and bending waves.Throughout the last decade, metamaterials have been characterized on the basis ofrelative permittivity and permeability. Two common classes of metamaterials are the sin-gle negative materials (SNG) with either a negative r or a negative µr and the doublenegative materials (DNG), which posses both negative permittivity and permeability [58].Metamaterial-based antennas use metamaterials either to enhance antenna radiation ca-pabilities or to realize new capacities that are impossible or difficult to obtain with regularmaterials. Ziolkowski et al. [53] reviewed the low efficiency levels in electrically-smallantennas, such as Herzian dipoles and short center-fed monopoles. Their findings demon-strated that a negative permittivity metamaterial shell significantly improves the radiatedpower by creating an electrically-small resonant structure. Enoch et al. [54] showed thatthe radiation directivity of a source significantly increases by using a slab of metamaterialwith negative permittivity as a host medium. Zhu et al. [59] and Dong et al. [60] effec-tively added two resonant frequencies to a planar monopole and slot antenna by employingsingle-cell metamaterial loading.By incorporating SNG metamaterials, microstrip patch antennas achieve a miniaturizedstructure, as well as overall improvements in the radiation characteristics. Bilotti et al.[61] theoretically analyzed sub-wavelength patch antennas with inhomogeneous substratesand presented a miniaturized circular patch antenna partially loaded with a negative µmetamatrial with a broadside radiation pattern. Studies have explored embedding blocksof SNG materials in the host medium of a rectangular patch antenna to achieve multipleresonant frequencies and an improvement in the radiation efficiency [62] [63]. Park et al.[64] proposed an epsilon negative zeroth-order resonator antenna with an omnidirectionalradiation pattern; a “negative epsilon meta-structured transmission line” around its zero-order resonance was used as a radiator.In this chapter, we present an MPA that employs a negative permittivity substrate toachieve a bi-directional end-fire radiation pattern around its zeroth-order resonance. We524.1. Resonance of a Negative Permittivity Substrate in the Patch Antennademonstrate that, when a narrow patch with a negative permittivity substrate is loadedbetween the patch and the ground plane, an effective inductance resonates with the strongfringing capacitance. This inductance appears when the capacitor (formed by the patchand the ground) is loaded with a negative permittivity substrate; the structure beginsresonating with this effective inductance, coupling electromagnetic energy into free-space.The electric field is vertically polarized and nearly uniform across the patch with negativepermittivity, ensuring a uniform phase distribution. This inductance appears when thecapacitor formed by the patch and the ground is loaded with the substrate that takeson a negative value. The electric field is vertically polarized and nearly uniform acrossthe patch, with negative permittivity ensuring a uniform phase distribution. Our resultshave shown that an end-fire radiation pattern is possible when we applied electromagneticdistribution in the patch; optimization was then performed to determine ideal patch param-eters. We investigated the radiation characteristics of the negative permittivity substrateMPA, including the resonant frequency, input impedance, and radiation pattern. This isfollowed by a description of the physical realization of the design, with a main focus onthe implementation of the SNG substrate. Additionally, we reported the impact of theground plane dimensions on the antenna radiation characteristics and provide a sensitivityanalysis. Finally, the antenna input impedance and radiation patterns are measured anda comparison between the simulation and measurement is provided.4.1 Resonance of a Negative Permittivity Substrate in thePatch AntennaThe electric field does not vanish abruptly on the open-ended edges, but extends beyondthe patch. This stored energy outside the patch is characterized by fringing capacitance(Cf), which is a function of the substrate thickness (h) and the dimensions of the patch(lp and Wp). Loading a patch with a negative permittivity substrate produces an effectiveinductance (Ls). This inductance appears when the capacitor formed between the patchand the ground plane is loaded with a negative permittivity substrate, as shown in Figure4.1). This effective inductance resonates with the fringing capacitance between the patchand the ground plane.534.1. Resonance of a Negative Permittivity Substrate in the Patch Antenna(a)(b)Figure 4.1: (a) geometry of the optimized patch and (b) equivalent circuit of it.4.1.1 Antenna OptimizationIn order to realize an end-fire pattern, the MPA was characterized in terms of thesubstrate relative permittivity (r), length (lp) and width (Wp) of the patch, and feedconfiguration. The dielectric constant was varied from -0.5 to -8. Wp and lp were changedfrom 0.05λ0 to 1.5λ0 at the frequency of 10 GHz. Four feed configurations were used: twosingle-feed configurations and two double-feed configurations. The patch was excited fromthe corner or the center of its width, for the single feed configurations (see Figure 4.2).A phase difference of 0◦ or 180◦ was applied across a pair of corner feeds for the double-feed configuration (Figure 4.2). Non-magnetic materials were investigated. The substratethickness of 1.5 mm is chosen since it was within the fabrication range of PCB printingtechnology; the corresponding electrical thickness is 0.05λ0. Table 4.1 displays more detailsfor each parameter sweep range.The top conductor is placed over an infinite ground plane, and the lossless substrateis limited to the edges of the top conductor, as displayed in Figure 4.1. Antenna charac-teristics including the directivity and resistance at each point of the parameter space arecomputed using COMSOL Multiphysics.544.1. Resonance of a Negative Permittivity Substrate in the Patch AntennaParameter Start Step Stoplp 0.05 λ0 0.05 λ0 1.5 λ0Wp 0.05 λ0 0.05 λ0 1.5 λ0r -0.5 -0.8 -8Table 4.1: Parameter sweep ranges for MPA characterization.The antenna directivity (D) is a function of θ and φ. The directivity along the X(θ = 90◦ and φ = 0◦), Y (θ = 90◦ and φ = 90◦), and Z (θ = 0◦) axes, denoted by Dx,Dy, and Dz, respectively, were used to represent the total antenna radiation pattern. Thisprovided a quick and efficient method to evaluate a range of patterns and classify patternsinto categories of interest or non-interest. For instance, broadside patterns were identifiedby a dominant Dz and end-fire patterns were identified when either Dx or Dy proved tohold the greatest value.Figure 4.2: The variety of patch feed configurations studied.In order to transfer power into the antenna to be radiated, its input impedance must bematched to the interconnecting transmission line and other associated equipment with thestandard impedance of 50 Ω. This can be described in terms of the reflection coefficient,which is given byΓin =Zin − Z0Zin + Z0(4.1)where Z0 is the standard impedance of 50 Ω. The reflection coefficient (or S11) is typicallyexpressed in dB and is referred to as the return loss (RL = −20 log(|Γin|)). A return loss of10 dB corresponds to 90 % of power transfer into the antenna and is typically used to define554.1. Resonance of a Negative Permittivity Substrate in the Patch Antennaan acceptable match. This corresponds to an input impedance between approximately 26to 96 Ω. Low input resistance can lead to low efficiency, which is expressed bye =RrRr +Rl(4.2)where Rl is the radiation resistance and Rl is the loss resistance due to conductor anddielectric losses. The lower limit of the antenna input resistance was chosen to be 30 Ω.Our simulation results show that in the parameter space described in Table 4.1, an end-fire radiation pattern can be realized when one feed is used and the substrate permittivityto the patch is between -2 and -3. Figure 4.3 shows the directivity in dBi along the X, Y ,and Z axes with respect to the length and width of the patch for dielectric constant of -3(Figure 4.3(a), 4.3(b), and 4.3(c)) and -2.2 (Figure 4.3(d), 4.3(e), and 4.3(f)). Large bluepoints represent points in which Dx is greater than Dy and Dz by 15 dB. Additionally, atthese points, Dx is at least 5 dBi. At small points, Dx is greater than Dy and Dz by 10 dBand Dx is greater than 0 dBi. These figures also contain information about the radiationresistance using black lines. Regions specified by arrows are where Rr lies within the rangeof interest (30 to 95 Ω). Large points within the impedance range that provide smallerdimensions are preferred. The small area within the red circle on the left side of Figure4.3(a) meets the requirements. However, this area is very close the the lower limit of lp,which indicates a potential for a design with a smaller length that may result in a similar,or even better, performance. The radiation pattern cannot be categorized as an end-firebased on only three points. Consequently, as there is no data for the directivity along the−X axis, even within the specified area (Figure 4.3(a)), it is unclear whether the radiationis uni- or bi-directional end-fire. Thus, further investigation and optimization are criticalaround the desired region.564.1. Resonance of a Negative Permittivity Substrate in the Patch Antenna(a) Dx (b) Dy (c) Dz(d) Dx (e) Dy (f) DzFigure 4.3: Directivity in dBi along different axes with respect to the patch length (Lp)and width (Wp) is shown in terms of free-space wavelength. In (a), (b), and (c), r is -2.2and (d), (e), and (f) are for that of -3. Regions in which antenna resistance lies within therange of 30 to 96 Ω are depicted with black arrows.A second set of sweeps is executed to find optimal parameter values to achieve maximumdirectivity along the X axis. Finer steps have been chosen for relative permittivity (-0.2),length, and width of the patch (0.025 λ0). A starting point of 0.025λ0 has been chosen forthe patch length; smaller values may cause fabrication issues.The directivity along the negative X and Y axes are also included to provide a moreprecise estimate of the antenna radiation pattern. The simulation results show that adesign with lp of 0.05 λ0 (1.5 mm), width of 0.9λ0 (26 mm), and dielectric constant of -2.2results in a bi-directional end-fire radiation pattern with a maximum directivity of 7 dBialong the X axis and an input impedance of 58 + j24 Ω. More details about the antenna574.2. Characteristics of the Negative Permittivity Substrate Patchdesign are provided in Table 4.2.Parameter Value Parameter Valuelp 1.5 mm (0.05 λ0) D-x 6.75 (dBi)Wp 27 mm(0.9λ0) Dy -17.2 (dBi)h 1.5 mm (0.05λ0) D-y -16 (dBi)r -2.2 Dz -21 (dBi)Dx 7 (dBi) Zin 58+j24 (Ω)Table 4.2: Optimal antenna design parameters.4.2 Characteristics of the Negative Permittivity SubstratePatchIn this section, the fringing capacitance and effective inductance are first calculatedusing Gauss’s law. The electric field distribution, input impedance, and radiation patternat the resonant frequency are also studied. In addition to the vertical electric field betweenthe ground plane and the top conductor, which is characterized by a parallel-plate capacitor,an electric field extends beyond the patch, producing fringing capacitance. Due to thesmall dimensions of the patch and substrate thickness, the fringing capacitance is quitecomparable to the parallel-plate capacitance. The vertical electric field residing withinthe substrate with a negative permittivity substrate introduces effective inductance in thestructure which, along with the strong fringing capacitance, forms a resonant radiator.COMSOL Multiphysics was used to calculate the fringing capacitance and the effectiveinductance. In the simulation, two conductive plates with the same length and width asthe patch of (l = 0.05λ0 and W = 0.9λ0) were separated by a distance of h = 0.05λ0. Theconductive plates were air-filled. The simulation domain containing the structure was aconductive box with an assigned voltage of 0 V . One plate was charged to a potential of0.5 V while the other was charged to a potential -0.5 V. To avoid having strong capacitancebetween the plates and their domain, the box had length of 3λ0, width of 5λ0, and heightof 7λ0. The charge density can be obtained in terms of the normal electric field using theboundary conditions on metalsEn =ρs0(4.3)The total charge can be calculated by integrating the charge density over the surface ofone of the plates, as given byQT =∫ρsdS (4.4)584.2. Characteristics of the Negative Permittivity Substrate PatchSubstituting Equation 4.3 into Equation 4.4 leads toQT =∫En0dS (4.5a)The total charge is simulated to be 5.84 × 10−13 C. The total capacitance relates to thetotal charge withCT = QT∆V (4.6)where ∆V is the voltage difference between the conductive plates. Due to the potentialdifference of 1 V between the plates, the total capacitance simplifies toCT = QT (4.7)The total capacitance includes the fringing capacitance (Cf) and the parallel-plate capaci-tance (Cpp). Using the parallel-plate capacitance formula governed byCpp =0lWh(4.8)Cpp is calculated to be 2.38×10−13 F . The fringing capacitance is obtained by subtractingthe total capacitance from Cpp as followsCf = CT − Cpp (4.9)The fringing capacitance is 3.46 × 10−13 F . The impedance of a parallel-plate capacitorwith a negative permittivity dielectric material at the frequency of 10 GHz is used tocalculate the effective inductance of LsCs =r0lWh(4.10a)ZCs =1jωCs(4.10b)ZLs = jωLs (4.10c)Ls =ZCsjω(4.10d)Substituting the negative permittivity of the substrate (r=-2.2) and the patch dimensionsin Equation 4.10a leads to Cs of −5.236 × 10−13 F . The corresponding impedance ofthe capacitance with a negative permittivity is j30.4 Ω according to Equation 4.10b. Thiscapacitance acts as an effective inductance (Ls), which is 4.82×10−10 H, based on Equation594.2. Characteristics of the Negative Permittivity Substrate Patch4.10d. The resonant frequency of the structure in this model is then calculated to befr =12pi√LsCf(4.11)Full-wave simulation is used to determine the resonant frequency of the antenna listedin Table 4.2. The simulated return loss and input impedance are shown in Figure 4.4 forthe frequency band of 8 to 12 GHz. Over this wide band of frequencies, the resistance staysconstant at approximately 50 Ω. The reactance crosses zero at three frequencies of 9.5,10.9, and 11.5 GHz. The calculated resonant frequency of our antenna model, presentedin Equation 4.2 is 12.3 GHz, which matches with our simulations results.88.5 99.5 1010.5 1111.5 12−50−40−30−20−100Frequency (GHz)S11(dB)(a)88.5 99.5 1010.5 1111.5 12−100−50050100150200Frequency (GHz)InputImpedance(Ω) ResistanceReactance(b)Figure 4.4: Return loss and input impedance of the patch antenna with lp = 0.05λ0,Wp = 1.5λ0, h = 0.05λ0, and r = −2.2 designed at 10 GHz. The frequency of 10 GHz,where the resistance and reactance of the antenna are 58 and 24 Ω, is close to the resonantfrequency of 9.5 GHz.In our simulation, the substrate permittivity has a constant value of (r)=-2.2 for thewhole frequency band. This is not realistic, since the constitutive parameters of a materialwhether natural or artificial is a frequency-dependent function; therefore, the physicaland theoretical antenna designs are not expected to have the same impedance response.The simulated electric field distribution of the patch antenna (shown in Figure 4.5(c))is vertically polarized and nearly uniform across the patch, with negative permittivityensuring a uniform phase distribution (as illustrated in Figures 4.5(a) and 4.5(b)). Thechange of both the magnitude and phase of the vertical electric across the patch is lessthan 10%.604.2. Characteristics of the Negative Permittivity Substrate Patch(a) |Ez| (b) Phase of Ez(c) |Ex| (d) |Ey|Figure 4.5: The electric field distribution of the theoretical antenna design.The magnitude of the X and Y components of the electric field on the edges of theantenna are shown in Figure 4.5(c) and 4.5(d), respectively. The strength of the fringingfield is comparable to that of the vertical electric field beneath the patch. This phenomenonwas also highlighted in earlier sections, showing that the fringing capacitance was greaterthan the parallel-plate capacitance between the patch and the ground plane.Our studies confirm that uniform electric field distribution on the patch results in anend-fire radiation pattern. The antenna has a null at broadside; an additional null wasplaced in the transverse direction (Y axis) by setting the width of the patch to approxi-mately one wavelength. The antenna substrate is limited to the edges of the top conductorand an infinite ground plane. Since the phase and magnitude of the vertical electric fieldis nearly uniform, every point on the patch can be paired with another out-of-phase pointalong the Y axis and forms a two-element array (see Figure 4.6). The entire patch consistsof an infinite number of two-element arrays; due to the distance of 0.5λ0 between eachelement in the array, the maximum radiation occurs along the X axis and there is no614.2. Characteristics of the Negative Permittivity Substrate Patchradiation in the transverse direction (Y axis), as demonstrated in Figure 4.5(b).Figure 4.6: Radiation mechanism in the negative permittivity substrate patch.0◦30◦60◦90◦120◦150◦180◦210◦240◦270◦300◦330◦00.20.40.60.81zx(a) E plane0◦30◦60◦90◦120◦150◦180◦210◦240◦270◦300◦330◦00.20.40.60.81xy(b) H planeFigure 4.7: Normalized far-field radiation pattern in E and H planes, at the frequency of10 GHz for the patch antenna described in Table 4.2. The antenna substrate is limited tothe edges of the top conductor and an infinite ground plane. Since the phase across thepatch is uniform, every point on the patch can be paired with another point along the Yaxis.624.3. Physical Antenna Design4.3 Physical Antenna DesignSome components of the design need to be addressed when building a prototype. Asubstrate with a negative relative permittivity requires physical implementation. To matchthe antenna input impedance to 50 Ω, a matching network may be required. The substrateshould also extend beyond the patch to the ground plane edges in order to avoid fabricationcomplexity.This section first outlines the design procedure of creating a negative permittivitymedium, then investigates the impacts of a finite substrate and ground plane on the antennaradiation performance. Finally, the sensitivity analysis is explored and the experimentalverification of the final design is presented.4.3.1 Negative Permittivity MaterialElectric dipole moments that are aligned opposite to the applied electric field generatea negative permittivity medium. The imposed electric field of these dipoles reduces thetotal electric flux density until it points anti-parallel to the applied field. This behavior isobserved both in ionized gas plasmas and in the free electrons of metals. Below a certainfrequency in which a balance exists between the particle inertia and electrostatic forces,the effective relative permittivity of such particles is negative. For typical metals, thisfrequency (referred to as “plasma frequency”) is very high (above the infra-red regime),meaning that the permittivity at microwave frequencies is extremely negative.In 1996, Pendry et al. [65] investigated the thin-wire array using plasmonic analysis,and discovered that for such a medium, the plasma frequency can be reduced to microwavefrequencies.When metals are illuminated by electromagnetic radiation, free electrons form an effec-tive plasma, which can be represented by Drude model. In this model, the permittivity is acontinuous function of frequency that increases from negative infinity to the host mediumpermittivity, and crosses zero at the plasma frequency (ωp). The dielectric behaviour ismodeled by = 0r(1− ω2pω2)(4.12)The plasma frequency of typical metals is in the optical frequency range. For example,fp of gold, silver and copper are 2068 THz, 2321 THz, and 1914 THz, respectively [66] [67][68]. At microwave frequencies, it is negative and very large.Structures with a negative permittivity require a negative net shunt susceptance. Thiscan be achieved through the addition of a shunt inductor to the transmission-line modelwith sufficient susceptance to surpass the integral capacitance of the host medium. One ofthe simplest realizations of a medium outside a cut-off waveguide is an array of thin wireswhich is aligned with the electric field perpendicular to the direction of the propagation.These were first introduced as rod media in 1953 by Brown [69], also shown in 1962 by634.3. Physical Antenna DesignRotman [70] to have a plasma-like behavior with an abnormally low plasma frequency.Further research on the thin-wire structure was conducted by Pendry et al. [65] usingplasmonic theory, and additionally studied by Wu et al. [71] using transmission-line theoryto arrive at the same dispersive response.Figure 4.8: Thin-wire array structure is known as one of the simplest realizations of amedia with a negative permittivity [12].If a plane wave is examined as it travels through an infinite array of thin-wires, withthe electric field oriented along the wire axes, image theory and transmission-line analysisallows this scenario to be modeled as a parallel-plate waveguide loaded with shunt wires.In the transmission-line model representing a unit-cell of length ∆z, the host mediumwill be assigned to a series inductor with a value of µ0∆z and a shunt capacitor of value0r∆z. The wires add a further inductance of L′zayax/∆z where L′z is the per-unit-lengthinductance of a single wire (Figure 4.7).Figure 4.9: Thin-wire transmission-line equivalent circuit [12].The total admittance of the shunt branch is converted to an effective  [12]. = 0r − 1ω2L′zayax= 0r(1− ω2pω2)(4.13)whereω2p =10rL′zayax(4.14)644.3. Physical Antenna DesignThe only parameter that has not been directly related to the geometry is the inductanceof the thin wires. Wu et al. [71] discuss the situation where the lattice spacing is notisotropic and redefine the inductance by the parallel combination of the X axis and Y axisinductancesL′z =µ0pi[ln(axr)‖ ln(ayr)](4.15)Solving Equation 4.12 for plasma frequency results inω2p = ω2(1− 0r)(4.16)Rogers Duroid 5880 (r = 2.2 and loss tangent of 0.0009) was chosen as a host medium.Substituting the frequency of operation, relative permittivity of the host medium, as wellas that of the desired material ((=-2.20) into Equation 4.16 leads to the plasma frequencyof ω2p = 2× ω2 = 2× 1020 (rad/s)2.From Equation 4.16, the required inductance (per length) in terms of the wire spacingand the plasma frequency is obtained asL′z =10rω2payax(4.17)Equations 4.16 and 4.17 assume an isotropic negative permittivity material. However,the necessary SNG metamaterial for the proper antenna operation is limited to the edgesof the patch in the XY plane, and to the height of the top conductor along the Z axis.Therefore, a limited number of the wires is used to approximately generate the requirednegative permittivity. The number of wires, their radius, and spacing between them mustbe found to achieve the same performance as the antenna design described in Table 4.2.ANSYS HFSS optimization tool was used to determine optimal values for the unknowns.The figures of merit in the optimization process are the input impedance, electromagneticfield distribution, and radiation pattern. A summary of our simulation results are displayedin Table 4.1. The physical implementation of the negative permittivity substrate is shownin Figure 4.10.Length Physical (mm) Electrical (λ0)ay 8.7 0.29ax 1.5 0.05r 0.26 0.008Table 4.3: Final values of the via spacing and their radius to achieve a negative permittivityof approximately r = -2.2.654.3. Physical Antenna DesignFigure 4.10: The implementation of the negative permittivity substrate in the patch usingfour vias.4.3.2 Electromagnetic PropertiesThe input impedance of the final antenna design on an infinite ground plane is shownin Figure 4.11. At the frequency of 10 GHz, the input impedance is 30+j52 Ω and matcheswith the simulation results of the theoretical design in Figure 4.4. The antenna resonatesat the frequency 9.8 GHz with the resistance of 34 Ω. The thin-wire array medium has anarrow bandwidth (typically less than 5%); therefore, the input impedance of the physicaland theoretical designs do not match at every single frequency. The operating frequencyappears between two parallel resonances and has a 10-dB impedance bandwidth of 2.8%.88.5 99.5 1010.5 1111.5 12−30−25−20−15−10−50Frequency (GHz)S11(dB)(a)88.5 99.5 1010.5 1111.5 12−100−50050100150200Frequency (GHz)InputImpedance(Ω)ResistanceReactance(b)Figure 4.11: The simulated return loss and input impedance of the physical antenna design.The magnitude and phase of the electric field of the patch with the thin-wire array isshown in Figure 4.12. The vertical electric field is nearly uniform across the patch. Thereis good agreement between the vertical electric field distribution of the physical antennaand that of the theoretical design displayed in Figures 4.5(a) and 4.5(b).664.3. Physical Antenna Design(a) |Ez| (b) Phase of EzFigure 4.12: The vertical electric field distribution of the physical antenna designThe E and H plane radiation patterns of the physical design at 10 GHz are shown in thefigure below. There is a null at broadside and a null along the Y axis and the maximumdirection of radiation is along the X axis. The radiation pattern of the design is similar tothat of the theoretical design. The directivity along the X and −X is 6.5 dBi and 6.3 dBi,respectively.0◦30◦60◦90◦120◦150◦180◦210◦240◦270◦300◦330◦00.20.40.60.81zx(a) E plane0◦30◦60◦90◦120◦150◦180◦210◦240◦270◦300◦330◦00.20.40.60.81xy(b) H planeFigure 4.13: Normalized far-field radiation pattern in E and H planes, simulated at thefrequency of 10 GHz for the patch antenna that has four thin wires to produce a negativepermittivity.Similarities in the input impedance, electric field distribution, and radiation pattern674.3. Physical Antenna Designbetween the both designs show that the effective permittivity of the substrate is approxi-mately -2.2.4.3.3 Finite Ground Plane and SubstrateSimilar to the end-fire patch antenna studied in Chapter 3, the infinite ground plane atthe bottom of the structure must be excluded from the antenna design and the substrateshould extend beyond the edges of the patch. The ground plane and the substrate havethe same length (Ls) and width (Ws). The antenna has a null along the Y axis; thus, Wshas negligible effects on the radiation characteristics. In contrast, Ls significantly affectsthe antenna radiation. As Ls increases, the main lobes of the antenna start moving fromthe XY plane toward the Z axis. This is characterized by an elevation angle (θd) from theXY plane, which is plotted with respect to the ground plane length in Figure 4.14(a). Forlengths of less than 0.5λ0, the lobes are pointing toward the X axis. As Ls goes beyond0.5λ0, θd increases. Maximum θd of approximately 60◦ occurs at the length of λ0. Atthis point, the radiation pattern is no longer considered as an end-fire. θd decreases as Lsexceeds λ0. At infinity, the elevation angle goes back to 0◦.The maximum directivity of the antenna is shown in Figure 4.14(a). The antenna getsmore directive as Ls increases. At Ls of 4λ0, the maximum directivity is 12.3 dBi. Thedirectivity stays nearly constant for ground plane lengths greater than 4λ0. At infinity, themaximum directivity is 6.5 dBi.The input impedance of the antenna versus Ls is plotted in Figure 4.14(b). The effectsof the ground plane dimensions on the resistance and reactance are negligible.684.3. Physical Antenna Design00.5 1 2 3 4 5 60306090Ls (λ0)ElevationAngle(◦)(a)00.5 1 2 3 4 5 602468101214Ls (λ0)MaximumDirectivity(dBi)(b)00.5 1 2 3 4 5 6−100−50050100Ls (λ0)InputImpedance(Ω)ResistanceReactance(c)Figure 4.14: The elevation angle of the antenna main lobes from the XY plane, maximumdirectivity, and input impedance at the frequency of 10 GHz are shown in (a), (b), and (c),respectively.Ls and Ws of respectively 1.5λ0 of 2.8λ0 are selected, where the elevation angle isapproximately 30◦ and the maximum directivity is 12.3 dBi.4.3.4 Final DesignThe final design of our antenna on a 1.5 mm thick Rogers Duroid 5880 substrate isshown in Figure 4.15. A vertical array of four thin wires produces an effective negativepermittivity beneath the patch. The input impedance of 34 Ω at the resonance is matchedto 50 Ω using a 40 Ω quarter-wavelength transformer. Assuming a substrate r of 2.2, the694.3. Physical Antenna Designwidth of the microstrip transformer is 6.4 mm. To avoid connecting the transformer to thepatch, a 1 mm transmission line is used as a buffer. This minimizes the coupling betweenthe thin-wire medium and the wide quarter-wavelength transmission-line section. Finalvalues of the parameters shown in Figure 4.15 are listed in Table 4.4.LengthPhysical(mm)Electrical(λg,λ0)LengthPhysical(mm)Electrical(λg,λ0)lp 1.5 0.08 (0.05) W1 4.8 0.24 (0.16)Wp 27.5 1.38 (0.93) W2 6.4 0.32 (0.21)L1 34.5 1.71 (1.15) h 1.57 0.08 (0.05)L2 4.9 0.24 (0.16) Lv 8.7 0.43 (0.29)L3 1 0.05 (0.34) dv 0.52 0.026 (0.02)Ws 44 2.57 (1.73) Ls 86 4.25 (2.87)Table 4.4: Final antenna dimensions.Figure 4.15: Final antenna design.The normalized electric field radiation pattern for an infinite and finite (2.8λg) groundplane is plotted in Figure 4.16(b). The maximum lobe elevation can be recognized in bothpatterns: for an infinite ground plane, the main lobe points toward the X axis with nullsalong the Z and Y axes. For the design with a finite ground plane the main lobe appearsin the rotated version of the XY plane toward the Z axis by 30◦.704.3. Physical Antenna Design0◦30◦60◦90◦120◦150◦180◦210◦240◦270◦300◦330◦00.20.40.60.81Finite ground planeInfinite ground planezx(a)0◦30◦60◦90◦120◦150◦180◦210◦240◦270◦300◦330◦00.20.40.60.81Finite ground planeInfinite ground planexy(b)Figure 4.16: Normalized E and H plane radiation patterns with a finite and infinite groundplane, simulated at the frequency of 10.8 GHz, are shown in (a) and (b).The reflection coefficient and the input impedance of the antenna is shown in Figure4.17(a) and 4.17(b). The antenna is well-matched to 50 Ω at 10.8 GHz with a peak returnloss over 30 dB. The resonance point appears between two parallel resonances, and has a10-dB impedance bandwidth of 4 %.99.5 1010.5 1111.5 12−100050100200300Frequency (GHz)Imag(Zin)(Ω)ResistanceReactance(a)99.5 1010.5 1111.5 12−50−40−30−20−100Frequency (GHz)S11(dB)(b)Figure 4.17: Simulated resistance, reactance, and reflection coefficient in (a) and (b)4.3.5 Sensitivity AnalysisSensitivity analyses can be performed to measure how much variations in system pa-rameters may affect or vary the outputs of that system. A mathematical model can bedefined to relate the system input parameters to its outputs. A well-designed antennahas minimum sensitivity to variations of its parameters. Our goal is to demonstrate how714.3. Physical Antenna Designthe variation in the substrate thickness and vias’ radii can affect the antenna character-istics. The via radii affect the permittivity of the substrate, which consequently changethe antenna properties. An increase in the height of the substrate in a broadside patchantenna is used to boost the efficiency and bandwidth [56]. However, increasing the heightmay cause unwanted surface waves to appear in the structure, which ultimately lower thepatch efficiency and form ripples in the radiation pattern. Therefore, it is critical to de-termine whether this same phenomenon occurs during an increase of height in the end-firemicrostrip antenna.The reflection coefficient with respect to frequency for different via radii is plotted inFigure 4.19(a). A very small change in the via radius (0.00067λ0) leads to a 1 % changein the resonant frequency. Those designs with smaller radii have a closer resistance to 50Ω at the resonant frequency. The bandwidth of the antenna decreases as the via radiusincreases.9.5 1010.5 1111.5 12−40−30−20−100Frequency (GHz)S11(dB)rv=0.24 mmrv=0.26 mmrv=0.28 mmrv=0.30 mmFigure 4.18: Simulated reflection coefficient of the antenna for different via radii.The efficiency, maximum directivity, resistance, and reactance of the antenna (withoutmatching network) versus the substrate thickness at the frequency of 10.8 GHz is shownin Figure 4.19. As the thickness increases from the 0.5 mm to 1.5 mm, the efficiency andmaximum directivity increases. The peak efficiency, maximum directivity, and resistanceoccur at the thickness of 1.5 mm and are 85%, 11.3 dBi, and 35 Ω, respectively. Thereactance of the antenna is negative for all thicknesses and approaches to zero as thethickness increases. The radiation efficiency has a decrease of 7% at the thickness of 2 mmrelative to the previous point. This shows that similar to a broadside patch antenna, surfacewaves can be excited in the end-fire patch antenna. The effects of unwanted surface wavesalso can be observed in the maximum directivity which is decreased by 1 dBi comparedto that at thickness of 1.5 mm. These results demonstrate that 1.5 mm is an optimalthickness for the negative permittivity substrate patch antenna.724.4. Experimental Verification0.5 11.52.0020406080100Thickness (mm)Efficiency(%)(a)0.5 11.52.0024681012Thickness (mm)MaximumDirectivity(dBi)(b)0.5 11.52.001020304050Thickness (mm)Resistance(Ω)(c)0.5 11.52.0−50−40−30−20−100Thickness (mm)Reactance(Ω)(d)Figure 4.19: The efficiency, maximum directivity, resistance and reactance of the end-firepatch versus substrate thickness.4.4 Experimental VerificationA prototype of the proposed patch antenna with the negative permittivity substratewas fabricated and tested. Four un-plated holes were drilled through a Rogers Duroid 5880double-sided copper clad laminate with the patch etched on the top copper layer. The topand bottom copper are connected together by 24 gauge wires running through the holes.The final PCB design is depicted in Figure 4.20(a).734.4. Experimental Verification(a)9.5 1010.5 1111.5 12−60−50−40−30−20−100Frequency (GHz)S11(dB)SimulatedMeasured(b)99.5 1010.5 1111.5 12050100200300Frequency (GHz)Re(Zin)(Ω)SimulatedMeasured(c)99.5 1010.5 1111.5 12−400−300−200−100050100200300Frequency (GHz)Imag(Zin)(Ω)SimulatedMeasured(d)Figure 4.20: The final antenna design is fabricated using PCB technology, as presented in(a). The simulated and measured return loss, resistance, and reactance of the antenna areshown in (a), (b), and (c).The simulated and measured reflection coefficient, resistance, and reactance displayedin Figures 4.20(b), 4.20(c), and 4.20(d), respectively. The measurement is executed bya PNA-X vector analyzer from Agilent Technologies. The antenna resonates at 10.84GHz with resistance of 48 Ω. The 10-dB impedance bandwidth is 3.8 %, from 10.66 to11 GHz. There is a slight frequency shift between the measured and simulated results.The sensitivity of the antenna to the via radii is high, as shown in Figure 4.19(a). Thisdiscrepancy can be attributed to the limited fabrication tolerances. The via radius in ourdesign is 0.24 mm and hole tolerances provided by vendors are typically ±0.5 mm. Thesimulated efficiency is 85%.744.4. Experimental VerificationThe near-field data obtained by the Orbit/FR acquisition application 959 AntennaAcquisition Module is readily transformed by the near-to-far transformation applicationSpectrumAnalysis (SNF-X) to a complete spherical far-field radiation pattern. The far-field measurement setup is shown in Figures 4.21(a) and 4.21(b). In order to ensure precisemeasurements, the mount is designed to prevent any antenna vibration while the positionerrotates. For more stability, a semi-rigid coaxial cable is feeding the antenna. The receiverantenna is an open-ended waveguide that stays motionless while the positioner rotates.(a) (b)0◦30◦60◦90◦120◦150◦180◦210◦240◦270◦300◦330◦−40−30−20−1001020Measured co-polarizationMeasured cross-polarizationSimulated co-polarizationSimulated cross-polarizationzx(c)Figure 4.21: The far-field measurement setup is displayed in (a) and (b). There are twostations: the transmitter and the receiver. While the transmitter station rotates, thereceiver is stationary. A mount and semi-rigid coaxial cable are used to stabilize theantenna during the measurement. Simulated and measure E plane co-polarization andcross-polarization directivity in dBi at the frequency of 10.8 GHz are shown in (c).754.5. SummaryFigure 4.21 shows the measured and simulated co-polarization and cross-polarizationdirectivity in the E plane at the frequency of 10.8 GHz. There is a significant differencebetween the co- and cross-polarization directivity. Thus, the antenna is linearly polarized,similar to the broadside patch antenna. Due to the ground plane, there is not muchradiation at the lower hemisphere. As sketched in Figure 4.15, the geometry of the antennais not symmetric with respect to the X and Z axes because of the feed network. This canobserved in both the measured and simulated radiation patterns. Dz and D-z are measuredto be -5 and -20 dBi. The measured directivity at the angle of 60◦ and 300 ◦ is 9.1 and10 dBi, respectively. The maximum directivity is simulated and measured to be 11.3 and10.7 dBi, respectively. The side lobe level of the simulated and measured designs areapproximately -9 dB. There is good agreement between the simulated and measured data.Compared to the patch with a regular substrate material studied in Chapter 3, theradiation characteristics have improved by using the negative permittivity substrate. Themaximum directivity has increased by 4.3 dBi. The radiation efficiency has improved by30%. The footprint of the metamaterial based patch is 71% less than that of the regularpatch antenna. Further, the proposed antenna in this Chapter does not depend on aparticular substrate. Any substrate material can be used as the host medium for thethin-wire array.The negative permittivity patch antenna is low-profile and has a simple structure with ahigh directivity compared to the designs in the literature. The antenna radiates maximallytoward two directions (bi-directional). The open-ended post-wall antenna proposed by [23]is uni-directional and has the maximum directivity of 6 dBi, which is approximately half ofwhat we achieved. The structure operates at 60 GHz with thickness of 0.2λ0. For X bandapplications, its thickness is not compatible with PCB standards. The three-layer antennaoperates at the frequency of 36 GHz in [25] has an unidirectional peak directivity of 8 dBi.The thickness of the antenna is 0.23λ0. An increase of approximately 2 dBi is achievedcompared to the two 12-element Yagi-Uda placed back-to-back to produce a bi-directionalend-fire pattern in [26].4.5 SummaryThis Chapter has explored a bi-directional end-fire patch antenna loaded with an SNGmetamaterial. We have demonstrated that the negative permittivity substrate producesan effective inductance between the patch and the ground plane, which resonates with thefringing capacitance of the structure. After performing sweeps over the patch parameters,including the patch length, width and dielectric constant, we chose a design with themaximum directivity and good return loss. The calculation of our proposed model showsthat its resonant frequency is in good agreement with the full-wave simulation results.The antenna fabrication verifies our prediction that it results in an end-fire pattern at thefrequency of 10.8 GHz.76Chapter 5Conclusion5.1 Summary of ResearchThe microstrip patch antenna is one of the most revolutionary antenna designs intoday’s wireless communication systems and is used in most modern-day applications, fromradio and radar transmission, to cellular and satellite communications. In order to keep upwith the significant increase in the demand for compact planar antennas, researchers havegiven much attention to antenna designs capable of producing an end-fire radiation pattern.In Chapter 1, we raised the question of whether a low-profile, bi-directional end-fire patterncan be achieved using microstrip technology. Throughout this thesis, the question has beenaddressed by the use of various substrates, including a high-impedance surface and a singlenegative metamaterial.In the second chapter, we explored the application of an HIS beneath a dipole antennaover an infinite ground plane and addressed the need for a low-profile end-fire antennain race-timing systems. An HIS acting as a PMC surface within a forbidden frequencyband can serve as a ground plane to produce a compact antenna structure with an om-nidirectional radiation pattern. The dipole antenna over the HIS acts as an alternativeto currently available mat-based antennas that typically use a slot antenna as a magneticdipole against a PEC ground plane.We presented two different HIS designs: our single-layer HIS has a thickness of 13.2mm, a resonant frequency of 1.36 GHz, and a bandwidth of 48% (A thicker substrate waschosen to initially prove that the structure is capable of radiating at end-fire). Our seconddesign has two layer of metallic patches which enables us to design a thinner structure.This double-layer HIS design had a total thickness of 1.6 mm with a resonant frequency ofapproximately 900 MHz, and bandwidth of 4.8%.A sweep over the patch width in both structures was performed. Our simulation resultsshow that a single-layer HIS design with thickness of 0.06λ0 and length and width of 1.1λ0and 1.1λ0 has a main lobe at 56◦ from normal and efficiency of 28%. A double-layer HISdesign with thickness of 0.03λ0, length of 1.1λ0, and width of 2.15λ0, produces a main lobeat 40◦ from normal and an efficiency of 50%. We have studied the structure that uses anHIS as a magnetic dipole on top of an infinitely large ground plane. The magnetic dipoleconsists of three HIS cells that are designed to resonate at 900 MHz. The HIS dipole isseparated from the ground plane by 1.6 mm. We presented that a maximum radiation isapproximately 90◦ from normal when the antenna is fed from its surface. The unit cells775.2. Contributions and Limitationsform a three-element array and produce a radiation pattern similar to that of a monopoleantenna. The antenna resonates at 922 MHz with the input impedance of 40 Ω, efficiencyof 4.5%, and bandwidth of 0.64% .In Chapter 3, we focused on the characteristics of microstrip patch antennas. One ofthe most common methods of analysis have been explored: the cavity model. The cavitymodel treats the antenna as a dielectric-loaded cavity surrounded by two PEC planes at thetop and bottom and four PMC sidewalls. The antenna radiation performance is simplifiedto an array of two equivalent magnetic dipoles at the dominant resonant frequency. Thebroadside radiation pattern of the antenna at the dominant mode of TM010 is calculatedusing Maxwell’s equations as well as boundary conditions. We presented that a patchantenna produces an end-fire radiation pattern if a higher mode of TM020 or TM002 getsexcited in the dielectric-loaded cavity using the cavity model. We simulated an end-firepatch antenna with length of 0.26λ0, width of 0.48λ0, and a dielectric constant of 4.6 atthe frequency of 10 GHz; this design supports TM002. The antenna input impedance,maximum directivity, and the direction of maximum radiation were characterized withrespect to the ground plane dimensions. In order to achieve a radiation pattern close toan end-fire, the length and width of the ground plane must be at least 0.4λ0 and 5λ0,respectively. The maximum directivity and radiation efficiency of the final design are 7dBi and 62%.In Chapter 4, we presented the simulated and measured results of a microstrip patchantenna that achieves a bi-directional end-fire radiation pattern without the need to excitea higher-order mode. The antenna consists of a negative permittivity substrate beneaththe patch, which produces an effective inductance between the patch and the ground plane.The fringing capacitance starts resonating with the effective inductance and couples elec-tromagnetic energy into free-space. The substrate is implemented using a vertical array offour thin wires to produce an effective negative permittivity. The currents passing throughthe vias from the top conductor to the ground plane form a four-element antenna array thathas nulls at broadside (the Z axis) and the transverse direction (the Y axis) and radiatesmaximally along the X axis. We investigated the effects of the ground plane dimensionsand discovered that an end-fire radiation pattern is achieved when the ground plane hasthe length 2.87λ0 and width of 1.7λ0. Compared to the existing bi-directional antennas,the proposed antenna has a thickness of 0.05λ0 and a high directivity of 11.3 dBi. Wepresented that there is good agreement between the measured and simulated design. Theantenna resonates at the frequency of 10.8 GHz with a 10-dB impedance bandwidth of 4%.5.2 Contributions and LimitationsThe importance of this study is to show that designing an efficient low-profile antennathat can be placed against an infinite ground plane and radiate along that plane is possible.Our proposed antenna uses a substrate with a negative permittivity to achieve its compact785.3. Future Directionsstructure and has a thickness of only 0.05λ0. The antenna is capable of radiating atend-fire with an efficiency of more than 85% with or without the existence of an infiniteground plane at its bottom. The antenna is designed at 10 GHz and has the thickness 1.5mm at this frequency. It was fabricated using PCB technology. Antennas are frequencyscalable components and can be designed at any frequency. As frequency decreases, thecorresponding wavelength increases. At lower frequencies the antenna thickness is greaterthan 1.5 mm; thus, it may not be possible to fabricate the antenna using PCB.We also focused on designing an HIS-based dipole placed against the ground withradiation at end-fire. It was revealed that placing the maximum radiation along the groundis impossible because of the finite size of the HIS plane in comparison to the infinite groundplane at the bottom of the structure. Attempts were performed to increase the dimensionsof the HIS and push the direction of maximum radiation as close as possible toward theground plane. The limitation of our HIS study was the lack of computational memory forthe purpose of simulating larger HIS planes. Determining how big the HIS plane can be toproduce radiation very close to the ground was impacted by this limitation. The maximumdimension of the HIS was 2.15λ0 in our simulation.5.3 Future DirectionsThere is room for further investigation into placing dipoles on HIS substrates. The ideaof using a graded HIS in the antenna profile was briefly discussed. only one configurationhas been explored, however, there are numerous ways to form a graded HIS. Additionally,the dimensions of the graded HIS were kept constant. A characterization of the graded HISin terms of the patch width and its dimensions may lead to a design with desired radiationcharacteristics.The HIS magnetic dipole in Chapter 2 was also briefly studied. In spite of havinga desired radiation pattern, the structure suffered from a very poor efficiency. Furtherinvestigation on the number of unit cells, thickness, and other parameters related to itsgeometry is required to possibly find a design with an efficient performance.The substrate materials used in the end-fire patch antennas, reported in Chapter 3 and4, are non-magnetic. Using a negative permeability substrate material in a patch antennato achieve radiation at end-fire is another future research direction. Using a substrate witha negative permeability is more difficult than a negative permitivity medium in terms offabrication but it may lead to a more compact antenna design.Our future research also focuses on achieving a uni-directional radiation pattern fromthe bi-directional metamaterial-based patch discussed in Chapter 4. As previously stated,the spacing between the vias are designed in a way that the waves along the X and -X axes have constructive interference casing the antenna to radiate along both directions.There may be a configuration where the vias are spaced unevenly beneath the patch, whichenables waves to have destructive interference along one direction (X or -X); this results795.3. Future Directionsin an uni-directional end-fire antenna design. This idea is inspired by the configurationof Yagi-Uda antennas (discussed in Chapter 1), where there is an element serving as areflector blocking the propagation of waves along the back side of the antenna.80Bibliography[1] F. 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