Patent Publication Number: US-10320085-B1

Title: High efficiency short backfire antenna using anisotropic impedance walls

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application claims the benefit of priority under 35 U.S.C. § 119 from U.S. Provisional Patent Application 62/009,098 filed Jun. 6, 2014, which is incorporated herein by reference in its entirety. 
    
    
     STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT 
     Not applicable 
     FIELD OF THE INVENTION 
     The present invention generally relates to antennas, and more particularly, to a high efficiency short backfire antenna using anisotropic impedance walls or electromagnetically hard walls. 
     BACKGROUND 
     Short backfire antennas (SBFAs) have seen wide use in terrestrial, maritime, and space-based applications due to their high directivity and low profile. Compared to endfire elements such as the Yagi and Helix antennas, the height of the SBFA is approximately ⅛ of Yagi and ⅕ of Helix antennas for the same directivity (e.g., about 15 dBi). One of the simplest and most widely used variations of the SBFA includes a shallow half-cylinder reflector with a 2λ diameter and a 0.25λ high rim. This SBFA is fed by a dipole placed 0.2λ above the center of the back wall of the reflector, and has a 0.4λ sub-reflector placed 0.25λ above the dipole. The polarization can be linear or circular. The measured antenna efficiency of this SBFA is approximately 83.9% (15.2 dBi). One variation of this basic configuration replaces the flat main reflector disc with conical profile, and also adds a small parasitic sub-reflector. This type of antenna has similar efficiency to the above-described SBFA with shallow half-cylinder reflector but with a wider bandwidth. 
     Another variation is an archery target antenna that uses an annular ring around the sub-reflector, allowing the antenna to use a much larger 5λ main reflector at the expense of approximately 46% aperture efficiency. An additional variation employs annular corrugated soft surface walls to improve the directivity over a baseline configuration with straight metal walls. However, both versions exhibited relatively low aperture efficiency. 
     For SBFAs, linear polarization (LP) can be generated by a linearly polarized feed such as a dipole or LP microstrip patch antenna, and circular polarization (CP) may be generated by a circularly polarized feed such as a crossed dipole fed via 90° hybrid, a CP microstrip patch antenna, or a spiral feed. The circular polarization can also be generated by a linearly polarized feed with a planar (spatial) CP polarizer in the aperture such as a meander-line polarizer. 
     SUMMARY 
     In some aspects, a high efficiency short backfire antenna (SBFA) is described. The SBFA includes a cylindrical reflector and a feed structure. The cylindrical reflector is configured to collect or to radiate electromagnetic waves. The cylindrical reflector has a reflector base and a reflector wall. The feed structure is electromagnetically coupled to the cylindrical reflector. The reflector wall includes a dielectric liner formed on an inside surface of the cylindrical reflector, and the dielectric liner is covered with a structured anisotropic impedance surface. 
     In other aspects, a method for providing a high efficiency short backfire antenna (SBFA) includes providing a cylindrical reflector and a feed structure. The cylindrical reflector is configured to collect or to radiate electromagnetic waves, and includes a reflector base and a reflector wall. The feed structure is electromagnetically coupled to the cylindrical reflector. The reflector wall includes an inside liner. The inside liner includes a dielectric material and includes an electromagnetically (EM) hard surface comprising longitudinal strips. 
     In yet other aspects, an antenna array includes a plurality of high efficiency short backfire antenna (SBFA) elements. Each SBFA includes a cylindrical reflector and a feed structure. The cylindrical reflector includes a reflector base and a reflector wall and is configured to collect or to radiate electromagnetic waves. The feed structure is electromagnetically coupled to the cylindrical reflector and is configured to convert collected electromagnetic waves to an induced electrical current or to convert a feed electrical current to electromagnetic waves for transmission by the SBFA. The reflector wall includes a dielectric liner formed on an inside surface of the cylindrical reflector, and the dielectric liner is covered with an anisotropic impedance boundary. 
     The foregoing has outlined rather broadly the features of the present disclosure in order that the detailed description that follows can be better understood. Additional features and advantages of the disclosure will be described hereinafter, which form the subject of the claims. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       For a more complete understanding of the present disclosure, and the advantages thereof, reference is now made to the following descriptions to be taken in conjunction with the accompanying drawings describing specific aspects of the disclosure, wherein: 
         FIG. 1  is a conceptual diagram illustrating a top view and a cross sectional view of a conventional short backfire antenna (SBFA) and top views and a cross sectional views of example high efficiency SBFAs, according to certain aspects of the subject technology. 
         FIG. 2  is a diagram illustrating examples of hard surfaces of a SBFA, according to certain aspects. 
         FIGS. 3A through 3D  are diagrams illustrating examples of SBFAs and corresponding simulated performance results, according to certain aspects. 
         FIGS. 4A through 4E  are diagrams illustrating examples of SBFAs with different feed structures, according to certain aspects. 
         FIGS. 5A through 5E  are diagrams illustrating an example of a SBFA with a dipole-feed structure and corresponding simulated performance results, according to certain aspects. 
         FIG. 6  is a diagram illustrating examples of arrays of SBFA, according to certain aspects of the subject technology. 
         FIGS. 7A through 7C  are diagrams illustrating an example of a hexagonal SBFA array, according to certain aspects of the subject technology. 
         FIG. 8  is a flow diagram illustrating an example of a method for providing a high efficiency SBFA, according to certain aspects. 
     
    
    
     DETAILED DESCRIPTION 
     The detailed description set forth below is intended as a description of various configurations of the subject technology and is not intended to represent the only configurations in which the subject technology can be practiced. The appended drawings are incorporated herein and constitute a part of the detailed description. The detailed description includes specific details for the purpose of providing a thorough understanding of the subject technology. However, it will be clear and apparent to those skilled in the art that the subject technology is not limited to the specific details set forth herein and can be practiced using one or more implementations. In one or more instances, well-known structures and components are shown in block diagram form in order to avoid obscuring the concepts of the subject technology. 
     The present disclosure is directed, in part, to methods and configuration for providing a high efficiency short backfire antenna (SBFA) using anisotropic impedance boundaries or electromagnetically (EM) hard walls. The subject technology increases the aperture efficiency of the SBFA by adding EM hard walls inside the walls of the reflector or cup. The addition of the hard EM walls enables close to uniform aperture field to be supported over the radiating aperture that corresponds to high aperture efficiency and high gain. A circular aperture with strip-loaded hard walls of the subject technology can achieve close to 100% aperture efficiency for a 2 wavelength (λ) aperture, as compared to ˜84% for a conventional short backfire antenna. The hexagonal aperture SBFA elements, when used in array antennas, can offer 10% higher array aperture efficiency than arrays with circular antenna elements due to 100% packaging efficiency of the hexagonal aperture arrays. 
     The subject technology offers a number of advantageous features over the existing SBFAs. For example, an aperture efficiency of a circular short backfire antenna of the subject technology is nearly 0.7 dB higher than the state of-the-art SBFAs over a single frequency band, and about 1 dB in average over the L1 and L2 dual GPS band. With a hexagonal design, an additional 0.42 dB array aperture efficiency can be obtained due to 100% array packaging efficiency when used as an element in an array. Aperture efficiencies above 90% can be achieved with a strip loaded circular or hexagonal cavity walls or with a metamaterial wall liner. An additional advantage of the subject technology over existing SBFAs is low cross-polarization or axial ratio (AR) due to a more uniform aperture distribution with straighter field lines. 
       FIG. 1  is a conceptual diagram illustrating a top view  110  and a cross sectional view  120  of a conventional short backfire antenna (SBFA) and top views  130  and a cross sectional view  140  of example high efficiency SBFAs, according to certain aspects of the subject technology. A top view  110  of the conventional SBFA shows a cylindrical reflector  112  with a circular reflector base and a feed structure  114 . When the SBFA is used as a receiver antenna, the reflector  112  collects the electromagnetic waves (e.g., a radio-frequency (RF) signal) and concentrates the collected electromagnetic waves onto the feed structure  114 . The feed structure  114  converts the power of the collected electromagnetic waves into an electrical signal (e.g., a current) that is transmitted through a transmission line (e.g., a coaxial cable) to a receiver that amplifies and process the electrical signal. On the other hand, when the SBFA is used as a transmitter antenna, the feed structure  114  receives a signal from a transmitter and converts the signal into electromagnetic waves (e.g., an RF signal) that are radiated (transmitted) by the reflector  112 . The cross sectional view  120  shows the reflector  112  having a reflector wall  122  and a reflector base  124  that can be made in a single piece from an electrically conductive material (e.g., a metal such as copper). An example implementation of a feed structure  114  is shown to include a reflector cup  126  and a dipole  128  which are embedded in a dielectric material  125  (e.g., foam) and are coupled through a 90° hybrid coupler (e.g., in the case circular polarization is being radiated) to a transmission line. In one or more implementations, the dielectric material  125  can be an artificial dielectric formed of, for example, a honeycomb structure (e.g., cardboard). For linearly polarized fields no 90° hybrid coupler is needed. A height h 1  of the reflector wall  122  is within a typical range of 0.25-1.5λ where λ is the wavelength of the electromagnetic waves. A diameter D 1  of the reflector base  124  is typically 2λ. 
     The high efficiency SBFA of the subject technology, as shown in top views  130  ( 130 - 1 ,  130 - 2 , and  130 - 3 ) are distinct from the conventional SBFA by addition of a hard (e.g., electromagnetically (EM) hard) surface  144  on a wall of the reflector  135 , or more generally an anisotropic impedance surface. The high efficiency SBFA can be made with a cylindrical reflector of any shape (e.g., shape of the reflector base). The top views  130 - 1 ,  130 - 2 , and  130 - 3  show examples of circular, square, and hexagonal shape reflectors, but could be a multi-section shape where each side section includes a flat surface. In general, a circular aperture offers the highest aperture efficiency of the three configurations. The feed structures  132 ,  134 , and  136  have reflector cups that have the shape of respective reflector bases of the cylindrical reflectors, although it could have circular shape for all three configurations. In some implementations, the feed structures  132 ,  134 , and  136  can be similar to the feed structure of the conventional SBFA and be coupled through a 90° hybrid coupler to a transmission line in the case of circular polarization. In the high efficiency SBFA of the subject technology, the height h 2  of the wall  142  of the cylindrical reflector  135  is within the typical range of 0.25-1.5λ, and is chosen in a performance optimization simulation, as discussed herein. An important performance metric of the SBFA is an aperture efficiency, which can be defined as the directivity of the antenna relative to the ideal directivity D i =4π A/λ 2 , where A is the aperture area. The subject technology optimizes SBFA design parameters such as the height h 2  of the reflector wall  142 , the thickness d of the EM hard surface  144 , the anisotropic wall impedance (or wall metal structure), and the feed position and feed parameters to achieve an optimum aperture efficiency, assuming a diameter (e.g., D 2 , D 3 , and D 4 ) of the reflector base (e.g., within the typical range of 1.8-2.2λ). It is understood that the antenna aperture efficiency (η ap ) is related to the antenna gain (G) by the electrical efficiency including insertion loss and return loss (η E ) of the antenna, which is below 1 for a passive antenna. For example, the antenna gain can be written as: G=D i *η E *η ap , where * denotes multiplication. 
       FIG. 2  is a diagram illustrating examples of hard surfaces  210 ,  220 , and  230 , according to certain aspects of the subject technology. The EM hard surface  144  of  FIG. 1  can be implemented in a number of ways. For example, the EM hard surface  210  is a corrugated hard surface formed by filling grooves  214  of a corrugated metal  212  with a dielectric material, for example, with a permittivity ε r &gt;2 (e.g., alumina). The corrugation of the EM hard surface  210  is formed in the direction of propagation of the electromagnetic waves. The corrugated metal  214  covers the reflector wall  216 . 
     In some embodiments, the EM hard surface can be a strip-loaded surface  220  formed by creating a dielectric layer  224  on a metal surface  222  (e.g., the reflector wall  142  of  FIG. 1 ) and forming strips  226  on the dielectric layer  224 . In some aspects, the strips  226  are formed of an electrically conductive material such as a metal (e.g., copper, aluminum, etc.). The strips  226  are formed in the direction of propagation of the electromagnetic waves. 
     Another example implementation of the EM hard surface  144  of  FIG. 1  is the EM hard surface  230  created by forming a metamaterial including, for example, two layers  234  and  236  of materials with different permittivity (e.g., ε r &gt;2 and ε r &lt;1, respectively) on a metal surface  232  (e.g., the reflector wall  142 ). More detailed analysis of the strip-loaded EM hard surface  220  will be presented herein. 
       FIGS. 3A through 3D  are diagrams illustrating examples of SBFAs  300 A and  300 B and corresponding simulated performance results  300 C and  300 D, according to certain aspects of the subject technology. The SBFA  300 A, shown in  FIG. 3A , is similar to the conventional SPFA  110  of  FIG. 1  and has a crossed-dipole feed structure  310 . The SBFA  300 B, shown in  FIG. 3B , is a high efficiency SPFA similar to the SPFA  130 - 1  of  FIG. 1 , except that in  FIG. 3B , for simplicity, only a dielectric layer  320 , metal strips  322 , and the crossed-dipole feed structure  310  are shown. The simulated performance results  300 C of  FIG. 3C  shows plot  350  and  352  of co-polarization pattern and cross-polarization pattern, respectively, for the SBFA  300 A. The simulated performance results  300 D of  FIG. 3D  shows plot  360  and  362  of co-polarization pattern and cross-polarization pattern, respectively, for the SBFA  300 B. The high efficiency SBFA of  FIG. 3B  is seen to offer considerably higher (˜0.7 dB) directivity and lower peak cross-polarization relative to peak co-polarization (25 dB versus 17 dB) as compared to the conventional SBFA of  FIG. 3A . Further, the aperture efficiency η ap  is seen to have been improved by ˜17 percent, and relative peak cross-polarization by 8 dB. 
       FIGS. 4A through 4E  are diagrams illustrating examples of SBFAs with different feed structures, according to certain aspects of the subject technology. The SPFA shown in the top view  400 A of  FIG. 4A  and the cross-sectional view  400 B of  FIG. 4B  is a circular cylindrical SBFA that uses a dipole feed structure. The dipole feed structure includes dipole elements  420 , which are coupled through a coaxial balun  424 , a matching network element  426  (e.g., a TEM-line λ/4 stub) for high power handling, and a coax connector  428  to a transmission line. The SPFA shown on the top view  400 A is a high efficiency SPFA that uses a hard EM surface  410  implemented as metal features on a dielectric liner with a dielectric constant of, for example, 1.7, but is not limited to this value. It further includes a circular sub-reflector  440  and planar (e.g., meander-line) polarizer  430  that converts the field between linear and circular polarization. The meander-line polarizer  430  offers a desirable RF performance, offering relative cross-polarization within the GPS field-of-view (˜±14°) below −30 dB, and provides support and ESD bleed-off path for the sub-reflector  440 . The meander-line polarizer and dipole feed concept offers an alternative antenna implementation for circularly polarized fields compared to a circularly polarized feed and a 90° hybrid. 
     The high efficiency SPFA  400 C shown in  FIG. 4C  employs a CP patch feed structure  450  using a dual stacked patch feed with balun. Alternatively, a high efficiency SPFA  400 D, as shown in  FIG. 4D , can use a spiral feed structure  460  with a balun. The patch feed  450  and the spiral feed  460  are circularly polarized feeds and can both be optimized for high power handling. The antenna can be optimized to operate, for example, at L1 and L2 GPS bands. Achievable aperture efficiency for the high efficiency SPFA  400 C is over 90% in both L1 and L2 bands. A circular aperture offers even higher aperture efficiency than a hexagonal aperture. 
     The high efficiency SPFA  400 E shown in  FIG. 4E  employs the dual stacked patch feed structure  450 . The reflector  452  and the liner dielectric  454  are similar to the SBFAs described above. The feed structure  450  includes the dual stacked microstrip CP patch (herein after “dual patch”)  480  with a single feed probe, eliminating the need for a 90° hybrid to generate circular polarization. The feed passes through a metal pedestal  484 , which together with a central rod  472  structurally supports the sub-reflector  470 . The central rod  472  also allows for electro-static discharge (ESD) bleed-off for the sub-reflector  470  and for the dual patch  480 , and also acts as a mode suppressor. 
       FIGS. 5A through 5E  are diagrams illustrating an example of a SBFA with a dipole-feed structure  500 A and corresponding simulated performance results  500 B through  500 E, according to certain aspects of the subject technology. The SBFA  500 A of  FIG. 5A , which in addition to a sub-reflector, has a circular ring with an inner diameter rr and width rw, is optimized with the primary metric being the aperture efficiency at efficiencies corresponding to L1 and L2 bands. The SBFA  500 A can also be optimized for minimum weight and height. The hard-walled SBFA can be optimized for several (e.g., three) different aperture diameters mrw, for example, 35.45 cm, 38.10 cm, and 40.64 cm. The optimization of the hard-walled SBFA may use a number of (e.g., seven) optimization variables including dh, srh, ch, srw, rr, rw, ert, as shown in  FIG. 5A . The height of the cavity (ch) may be constrained between 0.2 and 0.52λ L2 . The height of the dipole (dh) may be constrained between 0.15 and 0.4λ L2 . The height of the sub-reflector (srh) is constrained between dh+0.1λ L2  and dh+1.0λ L2 . The variables srw, rr, and rw may be constrained so that there would be no spatial interference between the ring and sub-reflector and with the main reflector wall. Additionally, if rw is less than λ L2 /100, the ring around the sub-reflector may be removed in the simulation. The thickness of the foam wall (e.g., with low index dielectric) can be constrained between 0.2λ L2 /4t and 1.2λ L2 /4t, where λ L2 /4t (t=(ε r 1) 1/2 ) is the asymptotic hard surface value at L2 for large apertures. To keep the weight down, ε r  is kept low for minimum specific density, but not too close to unity to keep the wall thickness reasonably small to operate as the hard surface. 
     The simulated performance results  500 B includes plots  510 ,  512 ,  514 ,  516 ,  518 , and  520  of L1 aperture efficiency (%) versus L2 aperture efficiency (%) for three different diameters (mrw) of hard walled (including metal strips) and metal-walled (conventional) SBFAs, as shown in the legends of the diagram. 
     The simulated performance results  500 C include plots of circularly polarized patterns showing directivity versus frequency plots  530 ,  532 ,  534 , and  536  for a high efficiency SBFA of the subject technology. The plots  530  and  532  correspond to L2 and L1 right-hand circular polarization (RHCP), respectively, and plots  534  and  536  correspond to L2 and L1 left-hand circular polarization (LHCP), respectively. 
     The simulated performance results  500 D include plots of circularly polarized pattern showing directivity versus frequency plots  540 ,  542 ,  544 , and  546  for a conventional SBFA. The plots  540  and  542  correspond to L2 and L1 RHCP, respectively, and plots  544  and  546  correspond to L2 and L1 left-hand circular polarization (LHCP), respectively. A comparison between the plots in  500 C and  500 D shows a significant improvement in directivity and cross-polarization for the subject high efficiency SBFA over the conventional SBFA. 
     The simulated performance results  500 E include aperture efficiency versus frequency plots  550  and  552  for a high efficiency SBFA of the subject technology and a conventional SBFA, respectively. Both SBFAs were optimized for a high directivity at L1 and L2 bands. The substantially higher performance of the high efficiency SBFA of the subject technology as compared to the conventional SBFA is clear from the above discussed simulation results. 
       FIG. 6  is a diagram illustrating examples of arrays  600  and  610  of SBFA, according to certain aspects of the subject technology. In one or more implementations, the high efficiency SBFA of the subject technology may be employed in a variety of array shapes and array configurations. Examples of shapes of the SBFA, as shown above, are circular, square, or hexagonal. The SBFAs of any shape can be employed in an array such as arrays  600  and  610  of  FIG. 6 . The array  600  can be implemented with circular elements  604  or hexagonal elements  602 . However, the array packaging efficiencies are different. For example, with circular elements  604 , the packing efficiency is ˜91%, whereas with the hexagonal elements  602 , 100% packing efficiency is achievable. Similarly, with square elements  612 , an array  610  with 100% packing efficiency can be achieved. For a circular element (e.g.,  604 ) with a radius b, the area is given as bπ 2 , and for a corresponding equivalent hexagonal element (e.g.,  602 ) the area is 2b 2 √3. For the hexagonal array  600  to have approximately the same average scan loss as the square array  610 , a side c of each square element  612  of the array  610  is given as: c=b√2√3. 
       FIGS. 7A through 7C  are diagrams illustrating an example of a hexagonal SBFA array  700 A according to certain aspects of the subject technology. The hexagonal SBFA array  700 A includes a number of hexagonal SFBA elements  710  assembled over a honeycomb structural panel  720 , which includes a conductive face-sheet  722  and serves as the common ground plane of the hexagonal SBFA array  700 A. The honeycomb structural panel  720  offers reduced assembly cost and excellent heat spreading. A more detailed structure of each element of the hexagonal SBFA array  700 A is shown in  FIG. 7B . As shown in  FIG. 7B , each element of the hexagonal SBFA array  700 A includes a feed structure including a patch element assembly  730  and a perforated sub-reflector  740  for reduced weight. The side walls of the hexagonal element are joined with corner post structures  770 , which include card guides that facilitate assembly of the hexagonal element and reduce assembly cost. Each side wall includes a dielectric wall  750  and perforated metal wall  760 , which offers reduced weight. 
     In some implementations, the side walls of the hexagonal element, as shown in  FIG. 7C , may be formed as one of a single sided wall  780  or double-sided wall  785 . The single sided wall includes a perforated metal wall  786 , a dielectric foam  782  on one side of the perforated metal wall  786 , and a polyamide flex circuit  784  designed to provide a hard surface, implemented with strip loading or metamaterial. The double-sided wall  785  comprises the perforated metal wall  786 , the dielectric foam  782  on both sides of a common perforated metal wall  786 , and the polyamide flex circuit  784  covering the dielectric foam  782  from an inside of the hexagonal element  710 . The wall is an anisotropic impedance boundary and the double-sided wall  785  offers reduced weight and recurring cost. 
       FIG. 8  is a flow diagram illustrating an example of a method  800  for providing a high efficiency SBFA, according to certain aspects of the subject technology. According to the method  800 , a cylindrical reflector (e.g.,  135  of  FIG. 1 ) and a feed structure (e.g., any of  132 ,  134 , or  136  of  FIG. 1, 440  of  FIG. 4C or 460  of  FIG. 4D ) are provided ( 810 ). The cylindrical reflector is configured to collect or to radiate electromagnetic waves, and includes a reflector base (e.g.,  124  of  FIG. 1 ) and a reflector wall (e.g.,  122  of  FIG. 1 ) ( 820 ). The feed structure is electromagnetically coupled to the cylindrical reflector. The reflector wall includes an inside liner (e.g.,  144  of  FIG. 1 ). The inside liner includes a dielectric material (e.g.,  320  of  FIG. 3B ) and includes an anisotropic impedance surface or a hard surface (e.g.,  322  of  FIG. 3B ) comprising longitudinal strips. Alternatively, the inside surface may be a metamaterial structure. 
     The description of the subject technology is provided to enable any person skilled in the art to practice the various aspects described herein. While the subject technology has been particularly described with reference to the various figures and aspects, it should be understood that these are for illustration purposes only and should not be taken as limiting the scope of the subject technology. 
     A reference to an element in the singular is not intended to mean “one and only one” unless specifically stated, but rather “one or more.” The term “some” refers to one or more. Underlined and/or italicized headings and subheadings are used for convenience only, do not limit the subject technology, and are not referred to in connection with the interpretation of the description of the subject technology. All structural and functional equivalents to the elements of the various aspects described throughout this disclosure that are known or later come to be known to those of ordinary skill in the art are expressly incorporated herein by reference and intended to be encompassed by the subject technology. Moreover, nothing disclosed herein is intended to be dedicated to the public regardless of whether such disclosure is explicitly recited in the above description. 
     Although the invention has been described with reference to the disclosed aspects, one having ordinary skill in the art will readily appreciate that these aspects are only illustrative of the invention. It should be understood that various modifications can be made without departing from the spirit of the invention. The particular aspects disclosed above are illustrative only, as the present invention may be modified and practiced in different but equivalent manners apparent to those skilled in the art having the benefit of the teachings herein. Furthermore, no limitations are intended to the details of construction or design herein shown, other than as described in the claims below. It is therefore evident that the particular illustrative aspects disclosed above may be altered, combined, or modified and all such variations are considered within the scope and spirit of the present invention. While compositions and methods are described in terms of “comprising,” “containing,” or “including” various components or steps, the compositions and methods can also “consist essentially of” or “consist of” the various components and operations. All numbers and ranges disclosed above can vary by some amount. Whenever a numerical range with a lower limit and an upper limit is disclosed, any number and any subrange falling within the broader range are specifically disclosed. Also, the terms in the claims have their plain, ordinary meaning unless otherwise explicitly and clearly defined by the patentee. If there is any conflict in the usages of a word or term in this specification and one or more patent or other documents that may be incorporated herein by reference, the definitions that are consistent with this specification should be adopted.