Patent Publication Number: US-11394121-B2

Title: Nonplanar complementary patch antenna and associated methods

Description:
RELATED APPLICATIONS 
     This application claims priority to U.S. Provisional Patent Application No. 62/754,211, titled “Nonplanar Patch Antenna RF Tag and Associated Methods,” filed Nov. 1, 2018, the entirety of which is incorporated herein by reference. 
    
    
     BACKGROUND 
     Wireless tracking tags, such as those based on ultra-wideband (UWB) radio technology, may be used to track athletes participating in a sporting event in a venue (e.g., a stadium). Tracking tags may similarly be used to track referees, sports equipment (e.g., a football), and other objects used for the sporting event. Each wireless tracking tag periodically transmits a wireless signal that is received by a plurality of receivers located around the venue. Based on the various times at which the wireless signal is received by the plurality of receivers, the position coordinates of the corresponding wireless tracking tag can then be determined via multilateration (e.g., time difference of arrival). 
     SUMMARY OF THE EMBODIMENTS 
     A minimum size and weight of a wireless tracking tag are determined by transmission requirements for its intended use. For example, for wireless tracking tags used to track athletes participating in a sporting event on a playing field, receivers must be placed around the playing field such that they do not interfere with the athletes. Locations of the receivers establish a maximum distance between any wireless tracking tag on the playing field and any of the receivers. This maximum distance, in turn, determines a minimum power with which each tracking tag must periodically transmit its wireless signal, and thus a size of a battery that powers each wireless tracking tag. 
     Some wireless tracking tags use an antenna with a three-dimensional (3D) geometry whose size and structure are obtrusive when configured with athletes and athletic equipment. To protect the antenna, the wireless tracking tags are made mechanically rigid, typically with a hard enclosure. However, this rigidity also makes the enclosure fragile when exposed to bending forces, resulting in breaking rather than flexing. 
     Some wireless tracking tags use a planar microwave patch antenna that produces a radiation pattern biased unidirectionally toward a normal axis of the tracking tag. Although the patch antenna is a two-dimensional structure, the radiation pattern is not ideal when the tracking tag is oriented with its normal axis pointing away from the receivers (e.g., upward when the receivers are located horizontally around the playing field). In this case, most of the power emitted by the tracking tag is lost, and the tracking tag must transmit at a higher power to ensure that its wireless signal is properly received (i.e., with sufficient signal-to-noise ratio). Higher-power transmissions drain the tracking tag&#39;s battery, either limiting its operational lifetime, or requiring a larger battery that makes the tracking tag more obtrusive and prone to damage. 
     Some wireless tracking tags use a “balanced” or “complementary” architecture in which a pair of antenna elements are differentially driven. Advantageously, this architecture eliminates the need for a bulky “balun” (balanced-to-unbalanced converter) that is required when driving a “single-ended” or “unbalanced” antenna. The balun introduces insertion loss that wastes power, thereby reducing transceiver performance and operational range. 
     The present embodiments overcome the above problems with a nonplanar complementary patch antenna that includes an antenna ground plane, a first antenna patch that lies in a first plane forming a first angle with the antenna ground plane, and a second antenna patch that lies in a second plane forming a second angle with the antenna ground plane. Compared to prior-art complementary patch antennas in which the antenna patches are coplanar (i.e., each of the first and second angles is 0°), the radiation pattern produced by the nonplanar complementary patch antenna is advantageously biased away from the normal axis of the tracking tag, and therefore requires less power to communicate with receivers when the tracking tag is oriented with its normal axis pointing away from the receivers. 
     One aspect of the present embodiments includes the realization that there is a tradeoff between a volume enclosed by the nonplanar complementary patch antenna, and the efficiency with which it wirelessly communicates with the receivers. Specifically, as the first and second angles are increased from 0°, the radiation pattern becomes increasing biased away from the normal direction, advantageously improving the efficiency and operability. At the same time, a height of the nonplanar complementary patch antenna increases, thereby increasing its volume. To prevent a nonplanar tracking tag that houses the nonplanar complementary patch antenna from becoming too bulky, it is advantageous to keep the volume (i.e., the height) of the nonplanar complementary patch antenna small. There is a range of the first and second angles within which the efficiency is improved, yet the corresponding increase in volume is negligible. That is, for non-zero first and second angles, the nonplanar complementary patch antenna may still be sufficiently “flat” that the nonplanar tracking tag can be made robust and unobtrusive. 
     In one embodiment, a nonplanar complementary patch antenna includes an antenna ground plane, a first antenna patch in a first plane forming a first angle with the antenna ground plane, and a second antenna patch in a second plane forming a second angle with the antenna ground plane. 
     In another embodiment, a nonplanar complementary patch antenna includes a flexible substrate formed with first and second antenna patches and corresponding first and second balanced feed lines. The flexible substrate is configured for forming around a dielectric material having a geometry to position the first and second antenna patches in first and second planes, respectively, that form first and second angles, respectively, with an antenna ground plane. 
     In another embodiment, a nonplanar tracking tag includes a flexible circuit having a first antenna patch formed at a first end of the flexible circuit, a second antenna patch formed at a second end, opposite the first end, of the flexible circuit, and a transceiver circuit electrically coupled to the first and second antenna patches. The nonplanar tracking tag also includes a battery and a dielectric material having a shape and size to position the first and second antenna patches, when the flexible circuit is wrapped around the dielectric material, in first and second planes, respectively, that form first and second angles, respectively, with an antenna ground plane. 
    
    
     
       BRIEF DESCRIPTION OF THE FIGURES 
         FIG. 1  is a perspective view of a nonplanar tracking tag with a nonplanar complementary patch antenna, in embodiments. 
         FIGS. 2 and 3  are side and plan views, respectively, of the nonplanar complementary patch antenna included in the nonplanar tracking tag of  FIG. 1 , in embodiments. 
         FIG. 4  shows a radiation pattern of the nonplanar complementary patch antenna of  FIG. 2 . 
         FIGS. 5 and 6  are polar plots comparing the radiation pattern of  FIG. 4  with a far-field radiation pattern of a square planar patch antenna, at two polar angles. 
         FIG. 7  is a schematic illustrating example circuitry and functionality of the nonplanar tracking tag of  FIG. 1 , in embodiments. 
         FIG. 8  is a flowchart showing one example method for fabricating the nonplanar tracking tag of  FIGS. 1 and 7 , in embodiments. 
         FIG. 9  is a plan view of a flexible circuit used to fabricate the nonplanar tracking tag of  FIGS. 1 and 7 , according to an embodiment. 
         FIGS. 10-14  are side views of the flexible circuit of  FIG. 9  as manipulated during the fabrication method of  FIG. 8 . 
         FIG. 15  shows two nonplanar tracking tags of  FIGS. 1 and 7  positioned on an American football player. 
         FIGS. 16 and 17  show example propagation of transmissions from nonplanar tracking tags configured with the player of  FIG. 15  on an American football field, in an embodiment. 
     
    
    
     DETAILED DESCRIPTION OF THE EMBODIMENTS 
       FIG. 1  is a perspective view of a nonplanar tracking tag  100  with a nonplanar complementary patch antenna. Nonplanar tracking tag  100  includes two antenna patches  102 ( 1 ),  102 ( 2 ) located on first and second patch panels  104  and  105 , respectively. A base  101  extends in the x-y plane (see right-handed Cartesian coordinate axes  120 ), and is located at the bottom of wireless tracking tag  100  in the z direction (as shown in a cut-away portion  110 ). First and second patch panels  104  and  105  are positioned above base  101  in the z direction, and are angled so that first and second patch panels  104  and  105  are not parallel to base  101 . Patch panels  104 ,  105  each join opposite sides of a top panel  106  that may be parallel to base  101 . Nonplanar tracking tag  100  also has first and second end panels  107  and  108  that are parallel to the x-z plane and connect with base  101 , patch panels  104  and  105 , and top panel  106 . 
     Antenna patches  102 ( 1 ),  102 ( 2 ) and an antenna ground plane cooperate to form the nonplanar complementary patch antenna (see complementary patch antenna  202  in  FIGS. 2 and 3 ). Antenna patches  102 ( 1 ),  102 ( 2 ) are driven by electrical components  112  located inside nonplanar tracking tag  100  and above base  101  (as shown in cut-away portion  110  of  FIG. 1 ). Electrical components  112  receive power from a rechargeable battery  116  that may be charged via an external power connector  114 . 
     Base  101 , patch panels  104  and  105 , end panels  107  and  108 , and top panel  106  may be formed from flexible materials (e.g., a flexible circuit board) and rechargeable battery  116  may be flexible such that nonplanar tracking tag  100  is also flexible. Accordingly, nonplanar tracking tag  100  is less fragile than rigid wireless tracking tags since it accommodates the inevitable bending forces that occur during use by flexing, rather than breaking. Furthermore, size and weight of nonplanar tracking tag  100  is reduced by (1) using a rechargeable battery instead of a larger, heavier, single-use battery, and (2) using low-profile planar antenna patches  102  that are easier to protect as compared to larger 3D antenna structures. Nonplanar tracking tag  100  may also be sealed to prevent the ingress of moisture, allowing nonplanar tracking tag  100  to operate in wet or dirty conditions as well as being washable. 
     The advantages of nonplanar tracking  100  of  FIG. 1  make it ideal for tracking an individual using a UWB real-time location system. Nonplanar tracking tag  100  may be placed unobtrusively on or in athletic equipment and clothing. To facilitate this placement, nonplanar tracking tag  100  may include provision for attachment, such as areas for sewing, loops, button holes, and the like, for inclusion into the pockets of, and/or sewn into, clothing, uniform fabric, and other attire of an individual. An outside surface of base  101  may have an adhesive coating for adhering nonplanar tracking tag  100  to a surface (e.g., sports equipment, helmet, clothing, skin of the athlete). The adhesive may be protected by a removable layer that allows nonplanar tracking tag  100  to be applied using a technique similar to applying an adhesive bandage or small medical dressing for bodily injuries. In another example, nonplanar tracking tag  100  may be configured for attaching to a bicycle to allow a real-time location tracking system to track the movement of the bicycle. In another example, nonplanar tracking tag  100  is configured for attaching to a lanyard and worn like a pendant. 
       FIGS. 2 and 3  are side and plan views, respectively, of nonplanar complementary patch antenna  202  included in nonplanar tracking tag  100  of  FIG. 1 . Nonplanar complementary patch antenna  202  includes antenna patches  102 ( 1 ),  102 ( 2 ), feed lines (see balanced feed lines  705  in  FIG. 7 ), and an antenna ground plane  204  that is parallel to base  101  and positioned beneath antenna patches  102 ( 1 ),  102 ( 2 ) in the z direction. Antenna patches  102 ( 1 ) and  102 ( 2 ) lie in first and second planes that form first and second patch angles  206 ,  207  with the mathematical plane in which antenna ground plane  204  lies. The straight line forming an intersection of the first and second planes may be parallel to antenna ground plane  204  and on the same side of antenna ground plane  204  as antenna patches  102 ( 1 ),  102 ( 2 ). 
     Advantageously, patch angles  206  and  207  may be selected to create a radiation pattern (e.g., see radiation pattern  400  of  FIG. 4 ) with a higher directivity in certain directions and a reduced directivity in other directions. For example, the radiation pattern of nonplanar complementary patch antenna  202  may be configured with greatest directivity in directions where tracking receivers are located relative to the positioning of nonplanar tracking tag  100 , thereby improving the range and/or reducing the power consumption of nonplanar tracking tag  100 . 
       FIG. 4  shows a radiation pattern  400  at 6.5 GHz of nonplanar complementary patch antenna  202  of nonplanar tracking tag  100 .  FIGS. 5 and 6  are polar plots  500 ,  600  comparing radiation pattern  400  with a far-field radiation pattern of a square planar patch antenna, at polar angles of θ=85.26° and θ=75.79°, respectively.  FIGS. 4-6  illustrate how patch angles  206  and  207  may be selected to generate a radiation pattern advantageous for certain wireless tracking applications.  FIGS. 4-6  are best viewed together with the following description. 
     In  FIG. 4 , the orientation of radiation pattern  400  is shown relative to spherical coordinate axes  410 . The origin is at the center of nonplanar tracking tag  100  in the x and y directions, and at the bottom of base  101  in the z direction. Azimuthal angle φ is defined in the x-y plane relative to the positive x axis, and polar angle θ is defined relative to the positive z axis. 
     In  FIGS. 5 and 6 , polar plots  500  and  600  show antenna directivities  510 , in decibels relative to a theoretical isotropic point source, versus azimuthal angles  512 , in degrees. Data points  502  and  602 , shown in  FIGS. 5 and 6  as squares connected by a solid line, correspond to a far-field of radiation pattern  400 , as numerically simulated on a computer. Data points  504  and  604 , shown in  FIGS. 5 and 6  as circles connected by a dashed line, correspond to the square planar patch antenna, wherein a width and length of the square patch each equal one-half of the radiating wavelength, and the square patch lies in the x-y plane. Points  504  and  604  are computed from analytic equations that model the square planar patch antenna as two radiating slots coinciding with two opposing edges of the square patch (the other two opposing edges of the square patch are non-radiating). 
     Patch angles  206  and  207  are configured such that as polar angle θ approaches 90°, nonplanar complementary patch antenna  202  has an increasingly higher directivity along the x-axis (i.e., at φ=0° and 180°) and y-axis (i.e., at φ=90° and 270°) compared to the square planar patch antenna. As shown in  FIG. 5  for θ=85.26°, nonplanar complementary patch antenna  202  has 15 dB higher directivity along the x-axis, and 10 dB higher directivity along the y-axis, compared to the square planar patch antenna. As shown in  FIG. 6  for θ=75.79°, nonplanar complementary patch antenna  202  has 15 dB higher directivity along the x-axis, and 3 dB higher directivity along the y-axis, compared to the square planar patch antenna. 
     Thus, nonplanar tracking tag  100  advantageously projects more radiant intensity towards locations where it may be preferable to place receivers communicating with nonplanar tracking tag  100 . As discussed in more detail below, one example where it may be beneficial to increase power along the x-axis is tracking the locations of players on a rectangular sports field, such as an American football field, wherein the tracking receivers may be placed behind the end zones of the football field (see  FIGS. 15-17 ). By directing more power towards along directions coinciding with receivers, and less power upward to the sky, nonplanar tracking tag  100  advantageously uses less power than a planar patch antenna of the same orientation, and thus may operate over longer distances to the receivers. Alternatively, nonplanar tracking tag  100  may consume less electrical power, thereby allowing for a smaller battery  116  and/or longer operating charge lifetime of battery  116 , as compared to the planar patch antenna of the same orientation. 
     In one embodiment, size, geometry, location, and orientation, of antenna patches  102 ( 1 ) and  102 ( 2 ) relative to antenna ground plane  204  are selected to transmit a wireless UWB signal with a desired radiation pattern (e.g., radiation pattern  400  of  FIG. 4 ) for use in a real-time location system. In the example of  FIG. 1 , antenna patches  102 ( 1 ),  102 ( 2 ) are rectangular with a patch length (in the y direction) longer than a patch width (in the x-z plane of patch panels  104 ,  105 ), and where the patch width is shorter than the widths of patch panels  104 ,  105 . However, antenna patches  102 ( 1 ) and  102 ( 2 ) may have other shapes and sizes without departing from the embodiments herein, such as one or more of regular polygonal (e.g., square), irregular polygonal (e.g., rectangular), circular, and elliptical. In certain embodiments, antenna patches  102 ( 1 ),  102 ( 2 ) have a patch width similar to the widths of patch panels  104 ,  105 . Also, as shown in the example of  FIG. 1 , antenna patches  102 ( 1 ),  102 ( 2 ) may be centered on first and second patch panels  104  and  105 , respectively, in the y direction; however, in other embodiments, antenna patches  102 ( 1 ),  102 ( 2 ) are not centered. In certain embodiments, antenna patches  102 ( 1 ),  102 ( 2 ) are offset from each other in the y direction. 
     In one embodiment, nonplanar tracking tag  100  operates at a frequency between 3.1 and 10.6 GHz, for use with a UWB radio system or a high-data-rate personal area network. In one example, nonplanar tracking tag  100  operates at a frequency of 6.5 GHz. In another embodiment, nonplanar tracking tag  100  operates at a frequency of 2.4 GHz and/or 5.8 GHz, for use with a Wi-Fi wireless local area network. In these embodiments, a patch length and a patch width of antenna patches  102 ( 1 ),  102 ( 2 ) may be chosen according to the frequency and/or a relative dielectric constant of a dielectric material disposed near antenna patches  102 ( 1 ),  102 ( 2 ) (e.g., see shaped dielectric material  1202  of  FIGS. 12 and 13 ). In one example, antenna patches  102 ( 1 ),  102 ( 2 ) are rectangular with the patch length being 19 mm and the patch width being 15 mm. 
     A size, geometry, and location of antenna ground plane  204  may be selected to achieve a radiation pattern (e.g., radiation pattern  400  of  FIG. 4 ) from nonplanar complementary patch antenna  202  suitable for use in a real-time location system. For example, antenna ground plane  204  may be selected to generate fringe electric fields between edges of antenna patches  102 ( 1 ),  102 ( 2 ) and antenna ground plane  204 , and to ensure a high front-to-back ratio (e.g., the ratio of power gain between a front (z&gt;0) and a rear (z&lt;0)), as shown in radiation pattern  400  of  FIG. 4 . In the examples of  FIGS. 2 and 3 , antenna ground plane  204  is rectangular with edges that extend past the edges of antenna patches  102 ( 1 ),  102 ( 2 ). In some embodiments, antenna ground plane  204  is formed as two non-overlapping rectangular segments, each segment having edges that extend past the edges of one of antenna patches  102 ( 1 ),  102 ( 2 ). 
     In the examples of  FIGS. 2 and 3 , antenna ground plane  204  is formed on a top (in the z direction) surface of base  101 . Alternatively, antenna ground plane  204  may be located within or on a bottom surface of base  101 , or formed from a metal housing of rechargeable battery  116 . 
       FIG. 7  is a schematic illustrating example circuitry and functionality of nonplanar tracking tag  100  of  FIG. 1 . Nonplanar complementary patch antenna  202  includes antenna patches  102 ( 1 ) and  102 ( 2 ), antenna ground plane  204 , and balanced feed lines  705 ( 1 ) and  705 ( 2 ) that are driven by a differential output  723  of an RF transceiver circuit  722 . Microcontroller circuit  720  controls RF transceiver circuit  722  to transmit data-encoded signals via nonplanar complementary patch antenna  202 . For example, microcontroller circuit  720  may encode a signal with data identifying (e.g., a serial number or an identification number) nonplanar tracking tag  100  (or a user thereof) to a receiver of the transmitted signal. Microcontroller circuit  720  may include memory for storing the identifying data. In certain embodiments, RF transceiver circuit  722  is implemented with only transmit functionality. 
     Nonplanar complementary patch antenna  202  may also receive wireless signals, wherein differential output  723  of RF transceiver circuit  722  is also a differential input. RF transceiver circuit  722  may decode information from received signals such that microcontroller circuit  720  may respond to, or act according upon, the decoded information. For example, the decoded information may request for nonplanar tracking tag  100  to transmit identifying information. 
     Advantageously, complementary patch antenna  202  has a balanced input that may connect directly to differential output  723  of RF transceiver circuit  722  and does not require a balun. Accordingly, electrical power loss associated with a balun is not incurred, thereby improving transceiver performance and range. 
     Microcontroller circuit  720  and RF transceiver circuit  722  are powered from rechargeable battery  116  that may be recharged via external power connector  114  when connected to an external regulated power source. In certain embodiments, nonplanar tracking tag  100  may include a charging regulator circuit  710  to regulate electrical power received from external power connector  114  to charge rechargeable battery  116  when the external power is unregulated. In one embodiment, charging regulator circuit  710  and external power connector  114  are omitted and rechargeable battery  116  is replaced with a one-time use, long-life, flexible battery. 
       FIG. 8  is a flowchart showing one example method  800  for fabricating nonplanar tracking tag  100  of  FIGS. 1 and 7 .  FIGS. 9-14  show various stages of fabricating nonplanar tracking tag  100  using method  800  of  FIG. 8 .  FIGS. 8-14  are best viewed together with the following description. 
     In a block  802  of method  800 , flexible substrate  902  is fabricated with antenna patches and electrical traces.  FIGS. 9 and 10  are a plan view and side view, respectively, of a flexible substrate  902  formed with one or more layers that include electrically conductive segments (e.g., metal traces, pads, vias) that form antenna patches  102 ( 1 ),  102 ( 2 ), antenna feed lines  705 ( 1 ),  705 ( 2 ), and antenna ground plane  204 . In one example of block  802 , antenna patches  102 ( 1 ),  102 ( 2 ) and antenna feed lines  705 ( 1 ),  705 ( 2 ) are formed on a top surface  905  of flexible substrate  902 , as shown in the example of  FIG. 9 . 
     Flexible substrate  902  may be cross-shaped, with first and second side flaps  914 ,  915 , and first and second end flaps  907 ,  908 , as shown in  FIG. 9 . Flexible substrate  902  may also form (e.g., by cutting, punching, milling, or drilling) an opening  904  for accepting external power connector  114 . Alternatively, external power connector  114  may be formed as a pair of electrically conductive pads on a bottom surface of flexible substrate  902 . 
     In a block  804  of method  800 , electrical components are affixed to the flexible substrate. In one example of block  804 , electrical components  112  are soldered and/or adhered using electrically conductive epoxy to electrically conductive traces  906  on top surface  905  of flexible substrate  902 , as shown in  FIGS. 9 and 10 . In certain embodiments of block  804 , antenna patches  102 ( 1 ),  102 ( 2 ) are not formed on or within flexible substrate  902  in block  802 , and each of antenna patches  102 ( 1 ) and  102 ( 2 ) is formed of a metal plate (e.g., copper) that is connected (e.g., soldered and/or adhered) to pads formed, in block  802 , on top surface  905  of flexible substrate  902 . 
     In a block  806  of method  800 , a battery is electrically affixed to the electrical components. In one example of block  806 , rechargeable battery  116  is adhered to electrical components  112 , as shown in  FIG. 11 . Rechargeable battery  116  may be flat and flexible. In one embodiment, rechargeable battery  116  is a rechargeable lithium polymer battery from BrightVolt, Inc. In certain embodiments, rechargeable battery  116  is encased in metal that serves as ground for electrical components  112  and/or as antenna ground plane  204 . 
     In a block  808  of method  800 , a dielectric material is positioned on top of the battery. In one example of block  808 , a shaped dielectric material  1202  is placed on a top surface of rechargeable battery  116 , as shown in  FIG. 12 . Dielectric material  1202  may be chosen to modify radiation pattern  400  of nonplanar tracking tag  100  for use in a real-time location system, and may be shaped to provide mechanical support to patch panels  104 ,  105  and top panel  106 . 
     In a block  810  of method  800 , sides of the flexible substrate are folded over the dielectric material. In one example of folds  810 , first side flap  914  of flexible substrate  902  is folded in a first folding direction  1310  over dielectric material  1202  to form first patch panel  104 , and second side flap  915  is folded in a second folding direction  1320  over dielectric material  1202  to form second patch panel  105 , as shown in  FIG. 13 . Side flaps  914 ,  915  may also form top panel  106  with a top seam  1330 . As in the examples of  FIGS. 1 and 13 , first and second patch panels  104 ,  105  may have the same width and lie in planes that form the same angle with a plane of base  101 , wherein top panel  106  is (a) parallel to base  101 , and (b) centered with respect to base  101  in the x direction. 
     Antenna feed lines  705 ( 1 ),  705 ( 2 ) may have a constant characteristic impedance, and may be fabricated as microstrip transmission lines, traditional stripline transmission lines, or co-planar waveguides. When antenna feed lines  705 ( 1 ),  705 ( 2 ) are fabricated as microstrip or traditional transmission lines, antenna feed lines  705 ( 1 ),  705 ( 2 ) include a transmission ground plane below and/or above a corresponding signal conductor, wherein a dielectric material separates the transmission ground plane from each signal conductor. For example, signal conductors of antenna feed lines  705 ( 1 ),  705 ( 2 ) may be formed on top surface  905  of flexible substrate  902 , and a transmission ground plane may be placed on a bottom surface of flexible substrate  902 , such that flexible substrate  902  forms the dielectric material separating the transmission ground plane from the signal conductors. In one embodiment, antenna feed lines  705 ( 1 ),  705 ( 2 ) are fabricated as grounded co-planar waveguides. In another embodiment, antenna feed lines  705 ( 1 ),  705 ( 2 ) are fabricated as conventional co-planar waveguides, wherein the transmission ground plane is formed on the same surface of flexible substrate  902  as the signal conductors such that the transmission ground plane lies adjacent to the signal conductors. 
     As will be appreciated by those trained in the art, in block  810  of method  800 , antenna feed lines  705 ( 1 ),  705 ( 2 ) may be folded similarly to side flaps  914 ,  915 , affecting the impedance of antenna feed lines  705 ( 1 ),  705 ( 2 ). In one embodiment, signal transmission along antenna feed lines  705 ( 1 ),  705 ( 2 ) is simulated with a computer (e.g., with three-dimensional finite element analysis) so as to account for the folding, wherein a design of antenna feed lines  705 ( 1 ),  705 ( 2 ) is modified to compensate for the effects of bending of antenna feed lines  705 ( 1 ),  705 ( 2 ). 
     In a block  812  of method  800 , the end panels are formed. In one example of block  812 , first end flap  907  is folded in a first end folding direction  1410  to form first end panel  107 , and second end flap  908  is folded in a second end folding direction  1420  to form second end panel  108 , as shown in  FIG. 14 . After folding, flexible substrate  902  forms a protective enclosure  730  (see  FIG. 7 ) that encases electrical components  112  (including RF transceiver circuit  722 , microcontroller circuit  720 , and charging regulator circuit  710 ), rechargeable battery  116 , antenna patches  102 ( 1 ),  102 ( 2 ), and antenna feed lines  705 ( 1 ),  705 ( 2 ). 
     In another example of block  812 , where end flaps  907  and  908  are omitted from flexible substrate  902  in block  802 , end panels  107  and  108  are formed from a waterproof sealant. In another example of block  812 , end flaps  907  and  908  are formed, in block  802 , with side tabs that may be secured to (e.g., adhered to) edges of side flaps  914 ,  915 , after side flaps  914 ,  915  are wrapped around dielectric material  1202 , to improve integrity and/or sealing of nonplanar tracking tag  100 . Alternatively, side tabs may be formed on side flaps  914  and  915  such that they may be secured to end flaps  907  and  908 . 
     In the example of  FIG. 9 , antenna patches  102 ( 1 ) and  102 ( 2 ) are formed on top surface  905  such that after substrate  902  is folded in block  810 , antenna patches  102 ( 1 ),  102 ( 2 ) are positioned on the inner faces of patch panels  104 ,  105 , as shown in  FIG. 13 . However, antenna patches  102 ( 1 ),  102 ( 2 ) may be formed on or within flexible substrate  902  to be within, or on the outer faces of, first and second patch panels  104 ,  105 , without departing from the scope hereof. 
     In a block  814  of method  800 , seams of the folded flexible substrate are sealed, thereby forming protective enclosure  730  ( FIG. 7 ). For example, top seam  1330  may be sealed by covering and/or filling top seam  1330  with tape, epoxy, thermosetting plastics, silicone rubber (e.g., room-temperature-vulcanizing (RTV) silicone), and the like, to aid sealing and make protective enclosure  730  waterproof. Seams produced where each of patch panels  104 ,  105  meets end panels  107 ,  108  may be sealed in a similar manner. In one embodiment, top seam  1330  and/or other seams are sealed by dielectric material  1202 . In another embodiment, flexible substrate  902  adheres to dielectric material  1202 , sealing top seam  1330 . 
     External power connector  114  is configured to allow charging of rechargeable battery  116  without opening protective enclosure  730 . For example, external power connector  114  may be a waterproof type electrical connector that is permanently sealed within opening  904 , such that nonplanar tracking tag  100  is waterproof irrespective of whether connector  114  is coupled to external power. In another embodiment, external power connector  114  is external to protective enclosure  730 , which is sealed around the electrical connections running between external power connector  114  and charging regulator circuit  710  and/or rechargeable battery  116 . 
     When formed as a pair of electrically conductive pads on a bottom surface of flexible substrate  902 , external power connector  114  is positioned, after folding of flexible substrate  902 , on one of end panels  107 ,  108  or base  101 . Advantageously, electrically conductive pads allow rechargeable battery  116  to be recharged by simply placing nonplanar tracking tag  100  inside of a cradle that connects the pads to the external power source. 
     In some embodiments, a tag width, tag length, and tag height (in the x, y, and z directions, respectively) of nonplanar tracking tag  100  are selected to accommodate sizes, orientations, and positions of electrical components  112 , rechargeable battery  116 , and dielectric material  1202 . In another embodiment, the tag width and tag length of nonplanar tracking tag  100  are selected according to a length and width of antenna ground plane  204 . In another embodiment, the tag width, tag length, and tag height of nonplanar tracking tag  100  are selected such that a size of patch panels  104 ,  105  accommodates the patch length and patch width of antenna patches  102 ( 1 ),  102 ( 2 ). In another embodiment, nonplanar tracking tag  100  has a tag width of 25 mm, a tag length of 50 mm, and a tag height of 6 mm. 
       FIG. 15  shows two nonplanar tracking tags  100 ( 1 ),  100 ( 2 ) of  FIGS. 1 and 7  positioned on an American football player  1500 . Each nonplanar tracking tag  100 ( 1 ),  100 ( 2 ) is positioned on a shoulder of player  1500  and oriented (see orientation references  120 ( 1 ) and  120 ( 2 )) such that the highest directivities are in the forward and backward directions (relative to player  1500 ) when player  1500  stand upright. Thus, less of the transmitted energy is absorbed by the player&#39;s body, since less power is transmitted in that direction, as compared to a conventional UWB omnidirectional antenna. 
       FIGS. 16 and 17  show example propagation of transmissions  1702 ( 1 ) and  1702 ( 2 ) from nonplanar tracking tags  100 ( 1 ) and  100 ( 2 ) configured with the player of  FIG. 15  on an American football field  1600 . Plays on football field  1600  are generally up or down the football field  1600  (e.g., along the x direction, see coordinate axes  120 ), as opposed to across football field  1600  (e.g., along the y direction). Thus, players in general are also facing up and down the length of football field  1600 . As shown in  FIG. 17 , football field  1600  is surrounded by a plurality of receivers  1704  (also known as anchors) that are configured to receive transmissions from nonplanar tracking tags  100 ( 1 ),  100 ( 2 ). The locations of receivers  1704  and received transmissions  1702 ( 1 ),  1702 ( 2 ) are used to determine the location of nonplanar tracking tags  100 ( 1 ),  100 ( 2 ) within the operational area that includes football field  1600 . At least three receivers  1704  are required to receive a particular transmission to enable location of the corresponding nonplanar tracking tag  100 . 
     Transmissions  1702  correspond to radiation pattern  400  of  FIG. 4 , and also illustrate blockage by the body of player  1500 . Positioning and orientation of nonplanar tracking tags  100 ( 1 ),  100 ( 2 ) partially determines the shape of transmissions  1702 ( 1 ),  1702 ( 2 ), and its effectiveness at being received by receivers  1704 . By configuring antenna patches  102 ( 1 ),  102 ( 2 ) such that more power is transmitted in the directions away from the player (e.g., base  101  faces toward a shoulder of player  1500 , and top panel  106  faces away from player  1500 ), less power is absorbed by the player&#39;s body. 
     Positioning and orientation of nonplanar tracking tags  100 ( 1 ),  100 ( 2 ) also partially determines the effectiveness of transmissions  1702 ( 1 ),  1702 ( 2 ) being received by receivers  1704 . Since football field  1600  is longer in the x direction than it is wide in the y direction, more receivers  1704  receive each transmission  1702 ( 1 ),  1702 ( 2 ). 
     The advantages of nonplanar tracking tag  100  may be used to track other players and objects and used with other sports without departing from the scope hereof. Although the embodiments described above and shown in the figures have two antenna patches, further embodiments are envisioned where multiple antenna patches are coupled together in one or both of serial and parallel configurations. 
     Changes may be made in the above methods and systems without departing from the scope hereof. It should thus be noted that the matter contained in the above description or shown in the accompanying drawings should be interpreted as illustrative and not in a limiting sense. The following claims are intended to cover all generic and specific features described herein, as well as all statements of the scope of the present method and system, which, as a matter of language, might be said to fall therebetween. In particular, the following embodiments are specifically contemplated, as well as any combinations of such embodiments that are compatible with one another: 
     (A) A nonplanar complementary patch antenna, including an antenna ground plane; a first antenna patch in a first plane forming a first angle with the antenna ground plane; and a second antenna patch in a second plane forming a second angle with the antenna ground plane. 
     (B) In the nonplanar complementary patch antenna denoted as (A), the antenna ground plane being positioned beneath the first and second antenna patches. 
     (C) In either of the nonplanar complementary patch antennae denoted as (A) or (B), an intersection of the first and second planes being parallel to the antenna ground plane and on the same side of the antenna ground plane as the first and second antenna patches. 
     (D) In any of the nonplanar complementary patch antennae denoted as (A)-(C), the first and second antenna patches having first and second geometries, respectively, selected to generate a radiation pattern for a wirelessly transmitted ultra-wideband (UWB) signal. 
     (E) In any of the nonplanar complementary patch antennae denoted as (A)-(D), the first and second geometries being similar, and the first and second angles being similar. 
     (F) In any of the nonplanar complementary patch antennae denoted as (A)-(E), the first and second geometries being rectangular. 
     (G) A nonplanar complementary patch antenna, including a flexible substrate formed with first and second antenna patches and corresponding first and second balanced feed lines, the flexible substrate being configured for forming around a dielectric material having a geometry to position the first and second antenna patches in first and second planes, respectively, that form first and second angles, respectively, with an antenna ground plane. 
     (H) In the nonplanar complementary patch antenna denoted as (G), the antenna ground plane being positioned beneath the first and second antenna patches. 
     (I) In either of the nonplanar complementary patch antennae denoted as (G) or (H), an intersection of the first and second planes being parallel to the antenna ground plane and on the same side of the antenna ground plane as the first and second antenna patches. 
     (J) In any of the nonplanar complementary patch antenna denoted as (G)-(I), the first and second antenna patches having first and second geometries, respectively, selected to generate a radiation pattern for a wirelessly transmitted UWB signal. 
     (K) In any of the nonplanar complementary patch antenna denoted as (G)-(J), the first and second geometries being similar, and the first and second angles being similar. 
     (L) In any of the nonplanar complementary patch antenna denoted as (G)-(K), the first and second geometries being rectangular. 
     (M) A nonplanar tracking tag, comprising a flexible circuit having: a first antenna patch formed at a first end of the flexible circuit; a second antenna patch formed at a second end, opposite the first end, of the flexible circuit; and a transceiver circuit electrically coupled to the first and second antenna patches; a battery; and a dielectric material having a shape and size to position the first and second antenna patches, when the flexible circuit is wrapped around the dielectric material, in first and second planes, respectively, that form first and second angles, respectively, with an antenna ground plane. 
     (N) In the nonplanar tracking tag denoted as (M), the first and second antenna patches having first and second geometries, respectively, selected to generate a radiation pattern for a wirelessly transmitted UWB signal. 
     (O) In either of the nonplanar tracking tags denoted as (M) or (N), the battery being flexible. 
     (P) In any of the nonplanar tracking tags denoted as (M)-( 0 ), the battery being a rechargeable battery, and the flexible circuit further having a charging regulator circuit electrically connected to the rechargeable battery and an external power connector. 
     (Q) In any of the nonplanar tracking tags denoted as (M)-(P), the battery being enclosed in a metal case, a position and geometry of the battery being chosen such that the metal case serves as the antenna ground plane. 
     (R) In any of the nonplanar tracking tags denoted as (M)-(Q), the flexible circuit further having a microprocessor circuit electrically coupled to the transceiver circuit. 
     (S) In any of the nonplanar tracking tags denoted as (M)-(R), an intersection of the first and second planes being parallel to the antenna ground plane and on the same side of the antenna ground plane as the first and second antenna patches. 
     (T) In any of the nonplanar tracking tags denoted as (M)-(S), wherein seams formed when the flexible circuit is wrapped around the dielectric material are sealed to make the nonplanar tracking tag waterproof.