Abstract:
A low height, space efficient, dual band monopole antenna is provided. The antenna includes a first conductive post, a second conductive post and a third conductive post extending between a lower oblong shaped PCB and an upper oblong shaped PCB. A signal is applied to a bottom end of a first conductive post and bottom ends of the remaining two posts are coupled to ground. The top of the first post is connected to the tops of the second and third posts by a serpentine trace which in one embodiment is symmetric and in another embodiment is asymmetric. The asymmetric embodiment achieves improved dual band operation without the need for an impedance matching network.

Description:
FIELD OF THE INVENTION 
     The present disclosure relates generally to antenna systems. 
     BACKGROUND 
     The Very High Frequency (VHF) band which ranges in frequency from 30 to 300 MHz corresponding to wavelengths in the range of 1 to 10 meters is suitable for direct line of sight radio communication including radio links from terrestrial radios to communication satellites. 
     A drawback of the VHF band is that the relatively large wavelengths call for a relatively large antenna. For example a ¼λ monopole sized for the lowest VHF wavelength of 1 meter would be 0.25 meters high and a ¼λ monopole antenna sized for a wavelength of 2 meter (corresponding to an existing satellite communication system) would be 0.5 meters high. Certain satellite communication systems specifically use vertically polarized signals meaning that the antenna, whatever its height, must be arranged vertically. For certain applications space for the antenna is limited and the aforementioned heights are unacceptable. 
     Thus what is needed is a reduced size VHF antenna. 
    
    
     
       BRIEF DESCRIPTION OF THE FIGURES 
       The accompanying figures, where like reference numerals refer to identical or functionally similar elements throughout the separate views and which together with the detailed description below are incorporated in and form part of the specification, serve to further illustrate various embodiments and to explain various principles and advantages all in accordance with the present disclosure. 
         FIG. 1  is a perspective view of an antenna according to a first example described in this disclosure; 
         FIG. 2  is a top view of the antenna shown in  FIG. 1 ; 
         FIG. 3  is a schematic representation of the antenna shown in  FIG. 1 ; 
         FIG. 4  is a schematic of a matching network used in the antenna shown in  FIG. 1 ; 
         FIG. 5  is a first Smith chart showing the performance of the antenna shown in  FIG. 1  without the matching network shown in  FIG. 3 ; 
         FIG. 6  is a second Smith chart showing the performance of the antenna shown in  FIG. 1  with only the series inductor of the matching network shown in  FIG. 3 ; 
         FIG. 7  is a third Smith chart showing the performance of the antenna shown in  FIG. 1  with the complete matching network shown in  FIG. 4 ; 
         FIG. 8  is a return loss plot for the antenna shown in  FIG. 1  without the matching network shown in  FIG. 4 ; 
         FIG. 9  is a return loss plot for the antenna shown in  FIG. 1  with the matching network shown in  FIG. 4 ; 
         FIG. 10  is a perspective view of an antenna according to a second example described in this disclosure; 
         FIG. 11  is a top view of the antenna shown in  FIG. 10 ; 
         FIG. 12  shows a current distribution on the antenna shown in  FIG. 10  at an instant in time for a first mode corresponding to a first frequency of operation; 
         FIG. 13  is a graph including a polar plot of directivity vs elevation angle in a first cut plane for the antenna shown in  FIG. 10  when operating in the first mode; 
         FIG. 14  is a graph including a polar plot of directivity vs elevation angle in a second cut plane for the antenna shown in  FIG. 10  when operating in the first mode; 
         FIG. 15  is a graph including a polar plot of directivity vs azimuth angle in a third cut plane for then antenna shown in  FIG. 10  when operating in the first mode; 
         FIG. 16  shows a current distribution on the antenna shown in  FIG. 10  at an instant in time for a second mode corresponding to a second frequency of operation; 
         FIG. 17  is a graph including a polar plot of directivity vs elevation angle in the first cut plane for the antenna shown in  FIG. 10  when operating in the second mode; 
         FIG. 18  is a graph including a polar plot of directivity vs elevation angle in the second cut plane for the antenna shown in  FIG. 10  when operating in the second mode; 
         FIG. 19  is a graph including a polar plot of directivity vs azimuth angle in a third cut plane for the antenna shown in  FIG. 10  when operating in the second mode; 
         FIG. 20  is a graph including a return loss plot for the antenna shown in  FIG. 10  when positioned in free space; 
         FIG. 21  is a fourth Smith chart showing the performance of the antenna shown in  FIG. 10  when positioned in free space; 
         FIG. 22  is a graph including a return loss plot for the antenna shown in  FIG. 10  when positioned on an extended ground plane; and 
         FIG. 23  is a fifth Smith chart showing the performance of the antenna shown in  FIG. 9  when positioned on an extended ground plane. 
     
    
    
     Skilled artisans will appreciate that elements in the figures are illustrated for simplicity and clarity and have not necessarily been drawn to scale. For example, the dimensions of some of the elements in the figures may be exaggerated relative to other elements to help to improve understanding of embodiments of the present disclosure; however  FIG. 1  and  FIG. 10  are Computer Aided Design (CAD) drawings. 
     DETAILED DESCRIPTION 
       FIG. 1  is a perspective view of an antenna  100  according to a first example discussed herein. The antenna  100  includes a bottom printed circuit board  102  and a top printed circuit board  104  overlying the bottom printed circuit board  102  in spaced relation therefrom. A transceiver circuit (not shown) and impedance matching network  400  ( FIG. 4 ) can be positioned on the bottom printed circuit board  102 . A top view of the top printed circuit board  104  is shown in  FIG. 2 . The top printed circuit board  104  has a length L and a width W which in the embodiment as shown are shared by the bottom board  102  although, alternatively the bottom printed circuit board  102  may have different dimensions. The antenna  100  has a height H which is equal to the spacing between the printed circuit boards  102 ,  104  plus their thickness. 
     A first conductive post  106 , a second conductive post  108  and third conductive post  110  are each connected to both the bottom printed circuit board  102  and the top printed circuit board  104  and extend between the two printed circuit boards  102 ,  104 . The first conductive post  106  includes a first end  112  that is located at the bottom printed circuit board  102 . The first end  112  of the first conductive post  106  serves as a signal coupling port for the antenna  100  and is suitably coupled to the aforementioned transceiver through the aforementioned impedance matching network  400 . A first end  114  of the second conductive post  108  and a first end  116  of the third conductive post  110  are both coupled to a ground  404  ( FIG. 4 ) that is included in the bottom printed circuit board  102  as a metallization layer thereof. 
     A serpentine conductive trace  118  is formed on the top printed circuit board  104 . A second end  120  of the first conductive post  106  is coupled (e.g., connected by solder) to the center  122  of the conductive trace  118 . A second end  124  of the second conductive post  108  is coupled (e.g., connected by solder) to a first end  126  of the serpentine conductive trace  118  that is located at a first corner  128  of the top printed circuit board  104 . A second end  130  of the third conductive post  110  is coupled (e.g., connected by solder) to a second end  132  of the serpentine conductive trace  118  that is located at a second corner  134  of the top printed circuit board  104 . The second corner  134  is diagonally opposite from the first corner  128 . The serpentine conductive trace can be viewed as including two portions (or “runs”) including a first portion  136  that extends from its center  122  to the first end  126  and a second portion  138  that extends from the center  122  to the second end  132 . In the case that the first portion  136  and the second portion  138  are formed from the same metal layer the first portion  136  and the second portion  138  are joined contiguously to each other. It is noted that the geometry of the second portion  138  is obtained by a 180° rotation of the first portion  136  about the position of the first conductive post  106 . The symmetry of the serpentine trace  118  provides for cancellation of the effect of currents flowing in the two portions  136 ,  138  of the serpentine trace  118  such that the radiation of the antenna  100  is dominated by the currents flowing in the three posts  106 ,  108 ,  110 . 
     The top printed circuit board provides an oblong area of a certain of length L and width Win which the serpentine trace  118  is confined. According to certain embodiments in order to achieve high volumetric space compression which may be defined as the wavelength of operation of the antenna divided by the cube root of the volume, the length to width ratio L/W for the area in which the serpentine trace is confined at least 2. In an exemplary embodiment the length L is 0.432 meters, the width W is 0.088 meters the height H is 0.076 meters, and the wavelength of operation is 2.09 meters, so that the volume of the antenna is 0.289e-2 cubic meters, the cube root of the volume is 0.143, and volumetric space compression is 14.6. 
     At least one portion (in the  FIG. 1  embodiment the full length) of the serpentine conductive trace  118  has a width (denoted “tw” in  FIG. 1 ), which according to certain embodiments, in order to improve bandwidth is between 0.05 and 0.1 times the width W of the oblong area in which the serpentine conductive trace  118  is confined. 
     As shown in  FIG. 2 , the first conductive post  106  is centered between the second conductive post  108  and the third conductive post  110 , so that the distance between the second conductive post  108  and the third conductive post  110  is greater than the distance between the first conductive post  106  and the second conductive post  108  and greater than the distance between the first post  106  and the third conductive post  110 . In the interest of symmetry and cancelation of currents in the serpentine trace  118 , the distance between the first conductive post  106  and the second conductive post  108  is preferably within 10% of the distance between the first conductive post  106  and the third conductive post  110 . For example, as shown the aforementioned two distances are equal. 
     The antenna  100  also includes two dielectric, mechanical support posts one of which  140  is visible in  FIG. 1  and the other of which is located at a diagonally opposite corner from the one  140  which is visible in  FIG. 1 . 
     The antenna  100  is shown supported on a lower housing part  142 . An oblong dielectric (e.g., plastic) antenna housing cover (not shown), also known as “radome”, can be fitted onto the lower housing part  142  over the antenna  100 . A second antenna in the form of a patch antenna  144  suitable for receiving Global Positioning Satellite (GPS) signals is supported on the lower housing part  142  adjacent to the antenna  100 . 
     A third printed circuit board  146  is positioned near one end  148  of the antenna  100  facing in the longitudinal (L) direction of the antenna  100 . A Planar Inverted “F” Antenna (PIFA)  150  is formed on the third printed circuit board and is useful for cellular network communications. 
       FIG. 3  is a schematic representation of the antenna  100  shown in  FIG. 1 . According to certain embodiments, the first portion  136  of the serpentine conductive trace  118  and the second portion  138  of the serpentine conductive trace  118  each have an electrical length of about one-half of the wavelength of operation of the antenna  100 . More specifically, in certain embodiments the aforementioned electrical length is between 0.45λ and 0.55 λ, for example in the embodiment shown the electrical length is 0.5λ. When a signal source  302  (e.g., transceiver) is coupled to the first end  112  (signal coupling port) of the first conductive post  106 , currents will be generated in each of conductive posts  106 ,  108 ,  110  that are in phase with each other and thus constructively contribute to monopole-like radiation from the antenna  100 . The currents in the two portions  136 ,  138  of serpentine trace  118  are mirror images of each other and thus their effect in producing radiation cancel. The arrows in  FIG. 3  represent current flow. At the top of  FIG. 3  is a plot of the cosine function. The horizontal double head axis is the zero level for the cosine function. The spatial variation of the current along the serpentine trace  118  is approximated by the cosine function centered at the center  122  of serpentine trace. Thus, the antenna  100  is able to operate with an efficiency comparable to a significantly taller monopole while being able to fit within height constrained spaces. 
       FIG. 4  is a schematic of a matching network  400  used in the antenna shown in  FIG. 1 . The matching network  400  comprises a first signal input terminal  402  and a second (grounded) signal input terminal  404 . The first signal input terminal  402  is coupled through a first (series) inductor  406  to the first end  112  of the first conductive post  106  which serves signal coupling port for the antenna  100 . The first signal input terminal  402  is also coupled through a second (shunt) inductor  408  to ground. 
       FIGS. 5-7  show a series of Smith charts  500 ,  600 , and  700  illustrating the effect of adding the components of the impedance matching network  400  shown in  FIG. 4 . In a Smith chart, the center of the chart represents an ideal case in which there is no signal reflection and the distance from the center indicates the magnitude of the reflection coefficient. 
       FIG. 5  is a first Smith chart  500  showing the performance of the antenna shown in  FIG. 1  without the matching network shown in  FIG. 3 . The first Smith chart  500  includes a first plot  502  of operating point versus frequency. The correspondence of the frequency markers m 5 , m 6 , m 7  and m 8  shown to frequency for  FIG. 5  and also for the Smith charts shown in  FIG. 6  and  FIG. 7  is shown in the table below. 
     
       
         
               
               
               
             
               
               
               
             
           
               
                   
                 TABLE 
               
               
                   
                   
               
               
                   
                 Marker 
                 Frequency (MHz) 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 M5 
                 136.9 
               
               
                   
                 M6 
                 138.0 
               
               
                   
                 M7 
                 150 
               
               
                   
                 M8 
                 148.1 
               
               
                   
                   
               
             
          
         
       
     
     The frequencies of 136.9 MHz and 138 MHz approximately bound a receive band of the commercial Orbcomm™ satellite system and the frequencies 148.1 MHz and 150 MHz approximately bound a transmit band of the commercial Orbcomm™ satellite system. 
     In  FIG. 5  markers m 5 , m 6  and m 7  are overlapping. By way of clarification, markers m 6  and m 5  point to positions outside the loop formed by the Smith chart plot line, while m 7  points to a position inside the plot line loop. Without the matching network, as shown in  FIG. 5  all of the frequency markers are well away from the center of the Smith chart-the position of an ideal impedance match. 
       FIG. 6  is a second Smith chart  600  showing the performance of the antenna  100  shown in  FIG. 1  with only the series inductor  406  of the matching network shown in  FIG. 4 . The second Smith chart  600  includes a second plot  602  of operating point versus frequency. As shown in  FIG. 6  adding the series inductor  406  reduces the maximum distance (magnitude of the reflection coefficient) of the frequency markers from the center of the Smith chart so that the antenna will operate more efficiently. 
       FIG. 7  is a third Smith chart  700  showing the performance of the antenna shown in  FIG. 1  with the complete matching network shown in  FIG. 4 . The third Smith chart  700  includes a third plot  702  of operating point versus frequency. Adding the shunt inductor  408  again reduces the maximum distance of any of the frequency markers from the center of the Smith chart, relative to what is shown in  FIG. 6  in the case that only the series inductor  406  is used. 
       FIGS. 8-9  show return loss plots comparing the performance of the antenna  100  shown in  FIG. 1  with and without the impedance matching network  400  shown in  FIG. 4 .  FIG. 8  is a graph  800  including a return loss plot  802  for the antenna  100  shown in  FIG. 1  without the matching network  400  shown in  FIG. 4  and  FIG. 9  is a graph  900  including a return loss plot  902  for the antenna shown in  FIG. 1  with the matching network shown in  FIG. 4 . Frequency markers m 1 , m 2 , m 3  and m 4  corresponding to the aforementioned frequency bands of the commercial Orbcomm™ satellite system are shown in  FIG. 8  and  FIG. 9 . As shown in  FIG. 8  the return loss at the frequency markers is relatively high up on the graph  800  indicating poorer performance, whereas as shown in  FIG. 9  the return loss has greater magnitude negative values indicating less reflected power and hence improved performance relative to the case shown in  FIG. 8 . 
       FIG. 10  is perspective view of an antenna  1000  according to a second embodiment of the disclosure and  FIG. 11  is a top view of the antenna  1000  shown in  FIG. 10 . The antenna  1000  includes a bottom printed circuit board  1002  and a top printed circuit board  1004 . A first conductive post  1006 , a second conductive post  1008  and a third conductive post  1010  extend between the bottom printed circuit board  1002  and the top printed circuit  1004 . A first end  1012  of the first conductive post  1006 , a first end  1014  of the second conductive post  1008  and a first end  1016  of the third conductive post  1010  are located at the bottom printed circuit board  1002 . The first end  1014  of the second conductive post  1008  and the first end  1016  of the third conductive post  1010  connect to a ground plane layer (not distinctly visible) that is incorporated into the bottom printed circuit board  1002 . The first end  1012  of the first conductive post  1006  serves as a signal coupling port of the antenna  1000 . A second end  1018  of the first conductive post  1006 , a second end  1020  of the second conductive post  1008  and a second end  1022  of the third conductive post  1010  are located at the top printed circuit board  1004 . 
     A serpentine trace  1024  is formed on the top printed circuit board  1004 . As shown, the serpentine trace  1024  includes a first end  1026  that is coupled (e.g., solder connected) to the second end  1020  of the second conductive post  1008 . The serpentine trace  1024  further includes a second end  1028  that is coupled (e.g., solder connected) to the second end  1022  of the third conductive post  1010 . An intermediate point  1030  on the serpentine trace  1024  is connected to the second end  1018  of the first conductive post  1006 . In certain embodiments including the embodiment shown in  FIG. 10 , the intermediate point  1030  does not bisect the serpentine trace  1024  into two parts of equal path length. A first portion  1032  of the serpentine trace  1024  extends between the first end  1026  and the intermediate point  1030  and a second portion  1034  of the serpentine trace  1024  extends between the second end  1028  and the intermediate point  1030 . 
     Most of the length of the serpentine trace  1024  is made up of longitudinal segments  1036  that extend parallel to the length direction of the antenna  1000  (parallel to the X-axis of the coordinate triad shown in  FIG. 10 ). The longitudinal segments  1036  are connected by shorter cross segments  1038 . Another way of describing this is that the x-component of the direction of the path of the serpentine trace  1024  integrated over the path of the serpentine trace is larger than the y-component of the same. In certain embodiments it is preferred that the integrated x-component exceed the integrated y-component by at least a factor of 5. Tuning patches  1040  are located between adjacent longitudinal segments  1036  adjacent two of the cross segments  1038 . These tuning patches can be trimmed in a prototype in order to tune the antenna  1000  by effectively changing the length of the first portion  1032  and the second portion  1034  of the serpentine trace  1024 . 
     The first portion  1032  generally meanders from the intermediate point  1030  toward a back side  1042  (in the perspective of  FIG. 10 ) of the antenna  1000  but has a long cross segment  1044  that crosses along a first end  1046  of top PCB  1004  to a front left corner at which the first end  1026  of the serpentine trace  1024  is located. In this embodiment, this configuration makes the length of the first portion  1032  of the serpentine trace  1024  greater than the length of the second portion  1034 . According to certain embodiments the length of the first portion  1032  of the serpentine trace is larger than the second portion  1034  of the serpentine trace by a factor of between 1.1 and 1.3 inclusive. For example in the embodiment shown in  FIG. 10  the ratio of the lengths of the first portion  1032  to the second portion  1034  is 1.1. If the ratio is too low the second mode discussed below is not obtained and if the ratio is too high the first mode discussed below is lost. This asymmetry is important in establishing a second mode of the antenna that is discussed below with reference to  FIG. 16 . As in the case of the antenna  100 , the serpentine trace  1024  is confined to an oblong area corresponding to the top printed circuit board  1004 . The oblong area has an oblong area width and an oblong area length. According to certain embodiments each of the first portion (run)  1032  of serpentine conductor and the second portion  1034  (run) of serpentine conductor includes at least two segments that span at least 75% of the oblong area length and the first portion (run)  1032  of serpentine conductor includes a segment that spans at least 75% of oblong area width. 
     According to an alternative embodiment, the serpentine trace could be made up primarily of segments that cross the top PCB  1004  in the width (Y-axis) direction which are connected by shorter segments extending in the length (X-axis) direction 
       FIG. 12  shows a current distribution on the antenna shown in  FIG. 10  at an instant in time for a first mode corresponding to a first frequency (e.g., the 137-138 MHz band) of operation. The first mode is similar to the mode of operation of the first antenna  100  which is illustrated in  FIG. 3 . The radiation of the first mode is dominated by current flowing in three conductive posts  1006 ,  1008 ,  1010 , with some contribution by current flowing in the long cross segment  1044 . There is a substantial symmetry cancellation effect among currents flowing in other parts of the serpentine trace  1024 . 
       FIG. 13  is a graph  1300  including a polar plot  1302  of directivity vs elevation angle in the X-Z plane for the antenna  1000  shown in  FIG. 10  when operating in the first mode. The current distribution for the first mode at an instant in time is shown in  FIG. 12 .  FIG. 14  is a graph  1400  including a polar plot  1402  of directivity vs elevation angle in the Y-Z plane for the antenna  1000  shown in  FIG. 10  when operating in the first mode.  FIG. 15  is a graph  1500  including a polar plot  1502  of directivity vs azimuth angle in the X-Y plane for then antenna  1000  shown in  FIG. 10  when operating in the first mode. As illustrated in  FIGS. 13-15  the first mode radiates similarly to a monopole antenna but with the orientation of the monopole tilted by a small angle from vertical. 
       FIG. 16  shows a current distribution on the antenna  1000  shown in  FIG. 10  at an instant in time for a second mode corresponding to a second frequency (e.g., the 148-150 MHz band) of operation. In contrast to the first mode, for the second mode horizontal currents in the serpentine trace  1024  are a more significant contributor to the radiation pattern of the antenna  1000  than the conductive posts  1006 ,  1008 ,  1010 . 
       FIG. 17  is a graph  1700  including a polar plot  1702  of directivity vs elevation angle in the X-Z cut plane for the antenna shown in  FIG. 10  when operating in the second mode.  FIG. 18  is a graph  1800  including a polar plot  1802  of directivity vs elevation angle in the Y-Z cut plane for the antenna shown in  FIG. 10  when operating in the second mode.  FIG. 19  is a graph  1900  including a polar plot  1902  of directivity vs azimuth angle in the X-Y cut plane for then antenna  1000  shown in  FIG. 10  when operating in the second mode. 
       FIG. 20  is a graph  2000  including a return loss plot  2002  for the antenna shown in  FIG. 10  when positioned in free space. The return loss plot  2002  exhibits a first resonance  2004  corresponding to the first mode and a second resonance  2006  corresponding to the second mode.  FIG. 21  is a fourth Smith chart  2100  showing the performance of the antenna shown in  FIG. 10  when positioned in free space. The fourth Smith chart  2100  includes a plot  2102  of operating point versus frequency. 
     In actuality the data shown in  FIGS. 20-21  is for a version of the antenna  1000  that was optimized, by adjusting the length of the serpentine trace  1024 , to perform best when positioned on an extended ground plane rather than free space. The ground plane tends to lower the frequency of operation, so in order to compensate the length of the serpentine trace  1024  is slightly reduced, e.g., by a few millimeters. In practice the large ground plane may take the form of the top of truck or shipping container, for example. 
       FIG. 22  is a graph  2200  including a return loss plot  2202  for the antenna shown in  FIG. 10  when positioned on an extended ground plane. As expected, the return loss plot  2202  also exhibits a first resonance  2204  corresponding to the first mode and a second resonance  2206  corresponding to the second mode. The first resonance  2204  overlaps the aforementioned 137-138 MHz frequency band and the second resonance  2206  overlaps the aforementioned 148-150 MHz frequency band. Comparing this return loss plot  2202  the return loss  902  shown in  FIG. 9  which is for the antenna  100  shown in  FIG. 1  equipped with the impedance matching network  400  shown in  FIG. 4 , it is evident that there is a better return loss for the 137-138 MHz frequency band and that there is a better return loss for the 148-150 MHz frequency band. Moreover the improved return loss is achieved without using matching network  400  which inherently introduces some additional losses into the system. 
       FIG. 23  is a fifth Smith chart  2300  showing the performance of the antenna shown in  FIG. 10  when positioned on the aforementioned extended ground plane. The fifth Smith chart  2300  includes a plot  2302  of operating point versus frequency. Comparing this Smith chart  2300  to the third Smith chart  700  which is for which is for the antenna  100  shown in  FIG. 1  equipped with the impedance matching network  400  shown in  FIG. 4  it is apparent that the frequency markers, as shown in the table presented above which denote the bounds of frequency bands of interest are, on average, significantly closer to the center of the fifth Smith chart  2300  than is the case for the third Smith chart  700 . It is noted that the distance from the center of the Smith chart is indicative of the magnitude of the reflection coefficient from the antenna. Thus both the return loss plot  2202  shown in  FIG. 22  and the fifth Smith chart  2300  demonstrate the improved performance of the antenna  1000  shown in  FIG. 10 . 
     In this document, relational terms such as first and second, top and bottom, and the like may be used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. The terms “comprises,” “comprising,” or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. An element proceeded by “comprises . . . a” does not, without more constraints, preclude the existence of additional identical elements in the process, method, article, or apparatus that comprises the element. 
     In the foregoing specification, specific embodiments of the present disclosure have been described. However, one of ordinary skill in the art appreciates that various modifications and changes can be made without departing from the scope of the present teachings as set forth in the claims below. Accordingly, the specification and figures are to be regarded in an illustrative rather than a restrictive sense, and all such modifications are intended to be included within the scope of present teachings. The benefits, advantages, solutions to problems, and any element(s) that may cause any benefit, advantage, or solution to occur or become more pronounced are not to be construed as a critical, required, or essential features or elements of any or all the claims. The invention is defined solely by the appended claims including any amendments made during the pendency of this application and all equivalents of those claims as issued.