Abstract:
An improved system and method for assigning power and ground pins and single ended or differential signal pairs for a ball grid array semiconductor package. In certain embodiments, the system uses a hexagonal pattern where the grid may be represented by a multiplicity of nested hexagonal patterns.

Description:
BACKGROUND OF THE INVENTION 
       [0001]    1. Field of the Invention 
         [0002]    Embodiments of the disclosure relate in general to the field of integrated circuits and, more particularly, to improved electrical connectors for integrated circuit packages comprising ball grid arrays or land grid arrays. 
         [0003]    2. Description of the Related Art 
         [0004]    A ball grid array (BGA) or land grid array (LGA) package offers a number of advantages relative to other, older package types, e.g., quad flat pack (QFP) and pin grid array (PGA), including small size, high input/output (I/O) pin count, improved electrical performance, low profiles, and good yields. These packages can be constructed with a substrate that can be either single or multi-layer. Substrates are fabricated with plastic or ceramic material, electrically conductive traces, and with planes being formed on a surface of each layer of the substrate. The surface of the substrate opposite from the semiconductor die or integrated circuit (IC) contains a plurality of solder balls that are soldered to the pads on a printed circuit board (PCB), thus attaching the package to the board. The semiconductor die is electrically connected to the substrate by either flip-chip (solder bump) interconnect or wire bonding. In both instances, the die is also generally encapsulated by plastic to protect it from the external environment. 
         [0005]    One of the benefits of BGA packaging is the increase of achievable I/O densities compared to older package options. Since BGA packaging places contacts over the entire surface of the chip instead of just around the edges, IC designers can place more I/Os in a given package size while using relatively looser tolerance compared to older peripheral lead types. This offers additional benefits to board designers who are not subsequently constrained to use the fine pitches that are typically necessary for older high-lead count packages. 
         [0006]    BGA packaging brings new challenges to the packaging designers, particularly in high-speed IC applications, where the effects of electromagnetic interference (EMI) become extremely important, and BGA I/O densities exacerbate this problem. Signal integrity is another important issue for packages and boards emerging from high-speed transceivers in high-end FPGAs and ICs. Impedance control is critical for package-to-board transitions connecting signals from layer to layer. 
         [0007]    In view of the foregoing, it would be desirable to provide a high-speed BGA semiconductor device having improved electromagnetic interference (EMI) and signal integrity characteristics. In particular, it would be desirable to provide a hexagonal ball-grid array having improved electrical performance. 
       BRIEF SUMMARY OF THE INVENTION 
       [0008]    Embodiments of the present invention provide an improved system and method for assigning power and ground pins and single ended or differential signal pairs for a ball grid array semiconductor package. Various embodiments of the invention comprise: a) using a hexagonal pattern wherein the grid may be represented by a multiplicity of nested hexagonal patterns; b) for a 4 to 1 signal to power/ground pin ratio, a first horizontal row of pins consists of pins  1  through  8 , and a second horizontal row of pins  9  through  15 , where each pin in the second row is offset (substantially between two pins of the first row above) from the first, row whereby the pin assignment consists of pins  3 ,  8 ,  9 , and  14  used as power/ground pins with the remainder used as signal pins; c) for a 3 to 1 signal to power/ground pin ratio, a first horizontal row of pins consist of pins  1  through  8  and a second horizontal row of pins  9  through  15 , where each pin in the second row is offset (substantially between two pins of the first row above) from the first row, whereby the pin assignment consists of pins  1 ,  5 ,  11 , and  15  used as power/ground pins with the remainder used as signal pins; and d) for a 2 to 1 signal to power/ground pin ratio, a first horizontal row of pins consists of pins  1  through  8  and a second horizontal row of pins  9  through  17 , where each pin in the second row is offset (substantially between two pins of the first row above) from the first row, whereby the pin assignment consists of pins  1 ,  4 ,  7 ,  11 ,  14 , and  17  used as power/ground pins, with the remainder used as signal pins. 
         [0009]    The above, as well as additional purposes, features, and advantages of the present invention will become apparent in the following detailed written description. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0010]    Selected embodiments of the present invention may be understood, and its numerous objects, features and advantages obtained, when the following detailed description is considered in conjunction with the following drawings, in which: 
           [0011]      FIG. 1  is an illustration of a prior art ball grid array, wherein the individual connectors are arranged in a square grid array; 
           [0012]      FIG. 2  is an illustration of a prior art ball grid array, wherein the individual connectors are arranged in a hexagonal pattern; 
           [0013]      FIG. 3  is an illustration of possible configurations for assigning power and ground pins and also various ways to assign differential signal pairs in a ball grid array; 
           [0014]      FIG. 4  is an illustration of a first embodiment for arranging power/ground connectors and signal connectors in a single-ended hexagonal 1:1 ball grid array; 
           [0015]      FIG. 5  is an illustration of a second embodiment for arranging power/ground connectors and signal connectors in a single-ended hexagonal 1:1 ball grid array; 
           [0016]      FIG. 6  is an illustration of a first embodiment for arranging power/ground connectors and signal connectors in a single-ended hexagonal 2:1 ball grid array; 
           [0017]      FIG. 7  is an illustration of a second embodiment for arranging power/ground connectors and signal connectors in a single-ended hexagonal 2:1 ball grid array; 
           [0018]      FIG. 8  is an illustration of a third embodiment for arranging power/ground connectors and signal connectors in a single-ended hexagonal 2:1 ball grid array; 
           [0019]      FIG. 9  is an illustration of a first embodiment for arranging power/ground connectors and signal connectors in a single-ended hexagonal 3:1 ball grid array; 
           [0020]      FIG. 10  is an illustration of a second embodiment for arranging power/ground connectors and signal connectors in a single-ended hexagonal 3:1 ball grid array; 
           [0021]      FIG. 11  is an illustration of a third embodiment for arranging power/ground connectors and signal connectors in a single-ended hexagonal 3:1 ball grid array; 
           [0022]      FIG. 12  is an illustration of a first embodiment for arranging power/ground connectors and signal connectors in a single-ended hexagonal 4:1 ball grid array; 
           [0023]      FIG. 13  is an illustration of a second embodiment for arranging power/ground connectors and signal connectors in a single-ended hexagonal 4:1 ball grid array; 
           [0024]      FIG. 14  is an illustration of a third embodiment for arranging power/ground connectors and signal connectors in a single-ended hexagonal 4:1 ball grid array; 
           [0025]      FIG. 15  is an illustration of a first embodiment for arranging power/ground connectors and differential signal connectors in a hexagonal 4:1 ball grid array; 
           [0026]      FIG. 16  is an illustration of a second embodiment for arranging power/ground connectors and differential signal connectors in a hexagonal 4:1 ball grid array; 
           [0027]      FIG. 17  is an illustration of a third embodiment for arranging power/ground connectors and differential signal connectors in a hexagonal 4:1 ball grid array; 
           [0028]      FIG. 18  is an illustration of a fourth embodiment for arranging power/ground connectors and differential signal connectors in a hexagonal 4:1 ball grid array; 
           [0029]      FIG. 19  is an illustration of a fifth embodiment for arranging power/ground connectors and differential signal connectors in a hexagonal 4:1 ball grid array; 
           [0030]      FIG. 20  is an illustration of an embodiment for arranging power/ground connectors and differential signal connectors in a hexagonal 3:1 ball grid array; and 
           [0031]      FIG. 21  is an illustration of an embodiment for arranging power/ground connectors and signal connectors in a single-ended hexagonal 2:1 ball grid array. 
       
    
    
     DETAILED DESCRIPTION 
       [0032]    A system and method for improving single-ended and differential signal performance in integrated circuits comprising ball grid arrays is disclosed herein. As will be appreciated by one skilled in the art, the present invention may be embodied as a system or a method. 
         [0033]    Embodiments of the invention are described below with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the invention. 
         [0034]      FIG. 1  is an illustration of a prior art ball grid array, wherein the individual connectors are arranged in a square grid array on the outer surface of an integrated circuit  100 . The ball grid array comprises a plurality of individual connectors  104  arranged in a plurality of rows and columns. In most prior art systems, the connection arrays between integrated circuits and the package and the connection arrays between the packages and boards have been configured using square grid arrays such as that shown in  FIG. 1 . Many historical design optimizations that have been implemented to increase electrical performance are based on square grid arrays such as the one shown in  FIG. 1 . 
         [0035]      FIG. 2  is an illustration of a prior art ball grid array, wherein the individual connectors are arranged in a hexagonal pattern on the outer surface of an integrated circuit  100 . The ball grid array comprises a plurality of individual connectors  104  arranged in a plurality of rows and columns, with the individual rows being offset laterally such that individual balls in one row are offset by approximately one half the distance between individual balls in the adjacent row. As can be seen in  FIG. 2 , the individual connectors in the array are arranged in a hexagonal pattern as illustrated by reference numeral  112 . As will be understood by those of skill in the art, hexagonal ball grid arrays make it possible to increase the density of individual signal connectors by approximately 16%. The efficiencies associated with hexagonal ball grid arrays are described in “Efficient Escape Routing for Hexagonal Arrays of Higher Density I/Os,” Rui Shi and Chung-Kuan Cheng, Annual ACM IEEE Design Conference Proceedings, which by this reference is incorporated herein for all purposes. 
         [0036]      FIG. 3  is an illustration of possible configurations for assigning power and ground pins and also is an illustration of various ways to assign differential signal pairs in a ball grid array. The array shown in  FIG. 3  comprises a plurality of rows of power/ground connectors  108   a - c  and a plurality of rows of signal connectors  110   a - d . The individual signal connectors can be paired “transversely,” i.e., along an axis that is transverse to the longitudinal axis of an adjacent row of power/ground connectors, as illustrated by reference numeral  112 . Alternatively, the individual signal connectors can be paired “longitudinally,” i.e., along the longitudinal axis of the row of power/ground connectors, as illustrated by reference numeral  114 . The individual signal connectors can also be paired “diagonally,” as illustrated by reference numeral  116 . As will be illustrated hereinbelow, the choice of the pairing configuration for pairs of signal connectors can result in significantly different electrical performance. 
         [0037]    Various embodiments for configurations of hexagonal arrays with different signal-to-power/ground ratios, e.g., 1:1, 2:1, 3:1, and 4:1 will be discussed hereinbelow. In the analysis of BSM assignments, the Lself is calculated for the various connectors. The mutual inductance from all other signals is also calculated and summed to calculate Lmutual. Since vias usually have an impedance that is lower than the target value, a higher Lself means that a higher impedance is preferred. However, it is difficult to assess the impact of Lself and, therefore, Lself is listed for informational purposes. Lmutual is used for comparison. When vias of different lengths are compared, for the first-order effect, Lmutual can be assumed to be linearly proportional to the via length. 
         [0038]      FIG. 4  is an illustration of a first embodiment for arranging power/ground connectors and signal connectors in a single-ended hexagonal 1:1 ball grid array. In this embodiment, the power/ground connectors and the individual signal connectors are arranged in interleaved rows, wherein a single signal connector is surrounded on each side laterally by a power/ground connector. In this embodiment, the individual power/ground connectors are arranged in diagonal rows as illustrated by reference numeral  120  and the individual signal connectors are arranged in diagonal rows as illustrated by reference numeral  122 . 
         [0039]      FIG. 5  is an illustration of a second embodiment for arranging power/ground connectors and signal connectors in a single-ended hexagonal 1:1 ball grid array. In this embodiment, the power/ground connectors and the individual signal connectors are again arranged in interleaved rows, wherein a single signal connector is surrounded on each side laterally by a power/ground connector. However, the power/ground connectors are configured in zigzagged rows as illustrated by reference numeral  124 , and the individual signal connectors are likewise configured in zigzagged rows as illustrated by reference number  126 . 
         [0040]    Table 1 is a comparison of the Lself and Lmutual for the configurations shown in  FIGS. 4 and 5 : 
         [0000]    
       
         
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 1 
               
             
             
               
                   
               
               
                   
                 Lself 
                 Lmutual 
               
             
          
           
               
                   
                 Max 
                 Min 
                 Max 
                 Min 
               
               
                   
               
               
                 FIG. 4 
                 0 950 
                 0 950 
                 0 414 
                 0 414 
               
               
                 FIG. 5 
                 0 950 
                 0 950 
                 0 429 
                 0 429 
               
               
                   
               
             
          
         
       
     
         [0041]      FIG. 6  is an illustration of a first embodiment for arranging power/ground connectors and signal connectors in a single-ended hexagonal 2:1 ball grid array. In this embodiment, the power/ground connectors and the individual signal connectors are arranged in interleaved rows, wherein a pair of signal connectors is surrounded on each side laterally by a power/ground connector. In this embodiment, the individual power/ground connectors are arranged in diagonal rows as illustrated by reference numeral  130 , and the pairs of signal connectors are arranged in diagonal rows as illustrated by reference numeral  132 . 
         [0042]      FIG. 7  is an illustration of a second embodiment for arranging power/ground connectors and signal connectors in a single-ended hexagonal 2:1 ball grid array. In this embodiment, the power/ground connectors and the individual signal connectors are again arranged in interleaved rows, wherein a pair of signal connectors is surrounded on each side laterally by a power/ground connector. However, the power/ground connectors are configured in zigzagged rows as illustrated by reference numeral  134 , and the pairs of signal connectors are likewise configured in zigzagged rows as illustrated by reference number  136 . 
         [0043]      FIG. 8  is an illustration of a third embodiment for arranging power/ground connectors and signal connectors in a single-ended hexagonal 2:1 ball grid array. In this embodiment, the power/ground connectors and the individual signal connectors are again arranged in interleaved rows, wherein a pair of signal connectors is surrounded on each side laterally by a power/ground connector. However, in this embodiment, the configuration of individual signal connectors and power/ground connectors results in a configuration wherein each power/ground connector is disposed in the center of a group of hexagonally configured signal connectors as illustrated by reference numeral  138 . 
         [0044]    Table 2 is a comparison of the Lself and Lmutual for the configurations shown in  FIGS. 6 ,  7  and  8 : 
         [0000]                                                  TABLE 2                       Lself   Lmutual                Max   Min   Max   Min               FIG.6   1 062   1 062   1 589   1 589       FIG. 7   1 115   1 024   2 013   1 478       FIG. 8   0 983   0 983   0 900   0 900                    
As can be seen from the data in Table 2, the configuration shown in  FIG. 8  provides significantly lower Lself and Lmutual than the configurations shown in  FIGS. 6 and 7 .
 
         [0045]      FIG. 9  is an illustration of a first embodiment for arranging power/ground connectors and signal connectors in a single-ended hexagonal 3:1 ball grid array. In this embodiment, the power/ground connectors and the individual signal connectors are arranged in interleaved rows, wherein three signal connectors are surrounded on each side laterally by a power/ground connector. In this embodiment, the individual power/ground connectors are arranged in diagonal rows as illustrated by reference numeral  140  and the groups of three signal connectors are arranged in diagonal rows as illustrated by reference numeral  142 . 
         [0046]      FIG. 10  is an illustration of a second embodiment for arranging power/ground connectors and signal connectors in a single-ended hexagonal 3:1 ball grid array. In this embodiment, the power/ground connectors and the individual signal connectors are again arranged in interleaved rows, wherein a group of three signal connectors is surrounded on each side laterally by a power/ground connector. The power/ground connectors are configured in zigzagged rows as illustrated by reference numeral  144 , and the groups of three connectors are likewise configured in zigzagged rows as illustrated by reference number  146 . 
         [0047]      FIG. 11  is an illustration of a third embodiment for arranging power/ground connectors and signal connectors in a single-ended hexagonal 3:1 ball grid array. In this embodiment, the power/ground connectors and the individual signal connectors are again arranged in interleaved rows, wherein a group of three signal connectors are surrounded on each side laterally by a power/ground connector. In this embodiment, the configuration of individual signal connectors and power/ground connectors again results in a configuration wherein each power/ground connector is disposed in the center of a group of hexagonally configured signal connectors as illustrated by reference numeral  150 . 
         [0048]    Table 3 is a comparison of the Lself and Lmutual for the configurations shown in  FIGS. 9 ,  10  and  11 : 
         [0000]    
       
         
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 3 
               
             
             
               
                   
               
               
                   
                 Lself 
                 Lmutual 
               
             
          
           
               
                   
                 Max 
                 Min 
                 Max 
                 Min 
               
               
                   
               
               
                 FIG. 9  
                 1 248 
                 1 102 
                 3 900 
                 2 835 
               
               
                 FIG. 10 
                 1 273 
                 1 046 
                 4 465 
                 2 470 
               
               
                 FIG. 11 
                 1 047 
                 1 043 
                 1 729 
                 1 045 
               
               
                   
               
             
          
         
       
     
         [0049]    As can be seen from the data in. Table 3, the configuration shown in  FIG. 11  provides significantly lower Lself and Lmutual than the configurations shown in  FIGS. 9 and 10 . 
         [0050]      FIG. 12  is an illustration of a first embodiment for arranging power/ground Connectors and signal connectors in a single-ended hexagonal 4:1 ball grid array. In this embodiment, the power/ground connectors and the individual signal connectors are arranged in interleaved rows wherein four signal connectors are surrounded on each side laterally by a power/ground connector. In this embodiment, the individual power/ground connectors are arranged in diagonal rows as illustrated by reference numeral  152 , and the groups of four signal connectors are arranged in diagonal rows as illustrated by reference numeral  154 . 
         [0051]      FIG. 13  is an illustration of a second embodiment for arranging power/ground connectors and signal connectors in a single-ended hexagonal 4:1 ball grid array. In this embodiment, the power/ground connectors and the individual signal connectors are again arranged in interleaved rows, wherein a group of four signal connectors are surrounded on each side laterally by a power/ground connector. The power/ground connectors are configured in zigzagged rows as illustrated by reference numeral  144 , and the groups of four connectors are likewise configured in zigzagged rows as illustrated by reference number  146 . 
         [0052]      FIG. 14  is an illustration of a third embodiment for arranging power/ground connectors and signal connectors in a single-ended hexagonal 4:1 ball grid array. In this embodiment, the power/ground connectors and the individual signal connectors are again arranged in interleaved rows, wherein a group of four signal connectors are surrounded on each side laterally by a power/ground connector. In this embodiment, the configuration of individual signal connectors and power/ground connectors again results in a configuration wherein each power/ground connector is disposed in the center of a group of hexagonally configured signal connectors, as illustrated by reference numeral  160 . 
         [0053]    Table 12 is a comparison of the Lself and Lmutual for the configurations shown in  FIGS. 12 ,  13  and  14 : 
         [0000]                                                  TABLE 4                       Lself   Lmutual                Max   Min   Max   Min               FIG. 12   1 332   1 122   6 476   4 069       FIG. 13   1 387   1 056   7 580   3 525       FIG. 14   1 145   1 056   3 078   2 272                    
As can be seen from the data in Table 4, the configuration shown in  FIG. 14  provides significantly lower Lself and Lmutual than the configurations shown in  FIGS. 12 and 13 .
 
         [0054]      FIG. 15  is an illustration of a first embodiment for arranging power/ground connectors and differential signal connectors in a hexagonal 4:1 ball grid array. The signal connectors in the embodiment shown in.  FIG. 15  are arranged in four rows  162 ,  164 ,  166 , and  168 , with the connectors in rows  164  and  168  offset from the corresponding connectors in rows  162  and  166  by approximately half the distance between the respective connectors. The connectors in rows  162  and  164  are diagonally paired with respect to the longitudinal axis of the power/ground connectors in row  170 . Likewise, the connectors in rows  166  and  166  are diagonally paired with respect to the longitudinal axis of the power/ground connectors in row  172 . 
         [0055]      FIG. 16  is an illustration of a second embodiment for arranging power/ground connectors and differential signal connectors in a hexagonal 4:1 ball grid array. In this embodiment, the signal connectors in rows  162 ,  164 ,  166 , and  168  are paired with adjacent signal connectors in an orientation that is parallel to the longitudinal axis of the power connectors in rows  170  and  172 . 
         [0056]      FIG. 17  is an illustration of a third embodiment for arranging power/ground connectors and differential signal conductors in a hexagonal 4:1 ball grid array. In this configuration, the signal connectors are paired in a repeating pattern of the paired signal conductors identified by reference numeral  174 . The pattern is comprised of first and second signal pairs adjacent to and arranged parallel to the longitudinal axis of the power/ground connectors in rows  170  and  172 , respectively. The pattern also includes two sets of paired signal conductors comprising conductors in the inner rows  164  and  166 , with these paired conductors being oriented diagonally with respect to the longitudinal axes of power/ground rows  170  and  172 . 
         [0057]      FIG. 18  is an illustration of a fourth embodiment for arranging power/ground connectors and differential signal connectors in a hexagonal 4:1 ball grid array. In this configuration, the signal connectors are paired in a repeating pattern of the paired signal conductors identified by reference numeral  176 . In this repeating pattern, first and second signal conductors, e.g., conductors  2  and  39 , are paired with adjacent conductors  3  and  4  on power/ground rows  170  and  172 , respectively. The pattern also includes two sets of paired signal conductors from the inner rows  164  and  166 , e.g., paired conductors  13 ,  26  and  14 ,  27 . These pairs are oriented diagonally with respect to the longitudinal axes of power/ground conductor rows  170  and  172 . Finally, the pattern includes two sets of paired signal conductors, with each pair comprising one conductor from an outer row of conductors, e.g., conductors  4  and  40 , and one conductor from an inner row of conductors, e.g., conductors  15  and  28 , respectively. Each of these sets of paired conductors are oriented diagonally with respect to the longitudinal axis of the power/ground rows  170  and  172 . 
         [0058]      FIG. 19  is an illustration of a fifth embodiment for arranging power/ground connectors and differential signal connectors in a hexagonal 4:1 ball grid array. The embodiment shown in  FIG. 19  is comprised of a pattern of paired signal pairs illustrated generally by the signal conductor pairs  178 ,  180 ,  182 , and  184 . Signal conductor pairs  178  and  180  are comprised of signal conductors  67 ,  79  and  69 ,  81 , respectively. Each of these signal conductor pairs are oriented parallel to adjacent power/ground pairs  54 ,  66  and  82 ,  94 , respectively. The pattern also comprises two sets of signal pairs,  182  and  184  that are oriented perpendicular to pairs  178  and  180 . Each of these sets of paired signal conductors comprises one signal conductor, e.g., 55, 93, that is adjacent to a power/ground conductor and one signal conductor, e.g., 68, 80, that is not adjacent to a power/ground conductor. 
         [0059]      FIG. 20  is an illustration of a third embodiment for arranging power/ground connectors and differential signal connectors in a hexagonal 3:1 ball grid array. In this embodiment, the power/ground connectors and the individual signal connectors are again arranged in interleaved rows, wherein a group of three signal connectors is surrounded on each side laterally by a power/ground connector. The power/ground connectors and signal conductors on alternating rows are alternately staggered by one space left or right. The paired signal conductors are arranged in a pattern illustrated by paired signal conductors  190 ,  192 , and  194 . In paired signal conductors  190  and  194 , each of the conductors  18 ,  33  are within one unit space from two power/ground conductors, e.g., 5, 30 or 21, 47. Each of those conductor pairs also has one signal conductor, e.g., conductor  20  or  31 , that is within one unit space from one power conductor, e.g., conductor  21  or  30 . Conductor pair  192  comprises one signal conductor, e.g., conductor  19 , that is two spaces from the nearest conductor and another signal conductor, e.g., conductor  7 , that is more than one unit space from the nearest conductor. 
         [0060]      FIG. 21  is an illustration of a first embodiment for arranging power/ground connectors and signal connectors in a differential hexagonal 2:1 ball grid array. In this embodiment, the power/ground connectors and the individual signal connectors are again arranged in interleaved rows wherein a group of two signal connectors is surrounded on each side laterally by a power/ground connector. The power/ground connectors and signal conductors on alternating rows are alternately staggered by one space left or right. The paired signal conductors are arranged in a pattern illustrated by paired signal conductors  196  and  198 . Each of the signal conductors  1 ,  2 ,  3 ,  5  in the respective sets of paired conductors is within one unit space of a power/ground conductor. 
         [0061]    Tests conducted on the various configurations for power/ground connectors and differential signal connectors in hexagonal arrays as shown in  FIGS. 15-21  indicated that the configurations shown in  FIGS. 19 ,  20  and  21  provided very low relative coupling. For example the configuration for the 4:1 pairing configuration shown in  FIG. 19  provided a relative coupling of 0.56; the 3:1 pairing configuration shown in  FIG. 20  provided a relative coupling of 0.55 and the 2:1 pairing configuration shown in  FIG. 21  provided a relative coupling of 0.36. 
         [0062]    The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. As used herein, the singular forms “a,” “an,” and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms “comprises” and/or “comprising,” when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof. 
         [0063]    The corresponding structures, materials, acts, and equivalents of all means or step plus function elements in the claims below are intended to include any structure, material, or act for performing the function in combination with other claimed elements as specifically claimed. The description of the present invention has been presented for purposes of illustration and description, but is not intended to be exhaustive or limited to the invention in the form disclosed. Many modifications and variations will be apparent to those of skill in the art without departing from the scope and spirit of the invention. The embodiment was chosen and described in order to best explain the principles of the invention and the practical application, and to enable others of skill in the art to understand the invention for various embodiments with various modifications as are suited to the particular use contemplated. 
         [0064]    Having thus described the invention of the present application in detail and by reference to preferred embodiments thereof, it will be apparent that modifications and variations are possible without departing from the scope of the invention defined in the appended claims.