Abstract:
Various examples are provided for fragmented aperture antennas. In one example, a fragmented aperture antenna includes a two-dimensional lattice of conducting elements, where positioning of the conducting elements in adjacent rows are offset based upon a fixed skew angle. In another example, a fragmented aperture antenna includes a two-dimensional lattice comprising a combination of first and second geometric conducting elements, where a second geometric conducting element provides a connection between adjacent sides of diagonally adjacent first geometric conducting elements. In another example, a fragmented aperture antenna includes a two-dimensional lattice of conducting elements having a single common non-rectangular shape, where the conducting elements interleave in a digitated fashion. Diagonally adjacent conducting elements overlap along a portion of adjacent edges of the diagonally adjacent conducting elements.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
       [0001]    This application claims priority to, and the benefit of, co-pending U.S. provisional application entitled “Fragmented Aperture Antennas” having Ser. No. 62/203,316, filed Aug. 10, 2015, which is hereby incorporated by reference in its entirety. 
     
    
     BACKGROUND 
       [0002]    Originally, fragmented aperture antennas were envisioned as a planar surface with a grid of rectangular regions or pixels that are either conducting or non-conducting. A genetic algorithm (GA) and a computational electromagnetic model were used to determine which pixels should be conducting and which should be non-conducting to form an antenna surface suitable for a given use. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0003]    Many aspects of the present disclosure can be better understood with reference to the following drawings. The components in the drawings are not necessarily to scale, emphasis instead being placed upon clearly illustrating the principles of the present disclosure. Moreover, in the drawings, like reference numerals designate corresponding parts throughout the several views. 
           [0004]      FIGS. 1 through 4  illustrate examples fragmented aperture antennas in accordance with various embodiments of the present disclosure. 
           [0005]      FIGS. 5A through 5D  illustrate examples of fragmented aperture antenna designs addressing diagonal touching in accordance with various embodiments of the present disclosure. 
           [0006]      FIGS. 6 through 8  illustrate examples fragmented aperture antenna designs that avoid diagonal touching in accordance with various embodiments of the present disclosure. 
           [0007]      FIG. 9  illustrates an example of fitness score for a traditional mutation algorithm and an adjacency-based mutation algorithm as a function of generation count in accordance with various embodiments of the present disclosure. 
           [0008]      FIG. 10  is a table illustrating a comparison of the traditional mutation algorithm and the adjacency-based mutation algorithm in accordance with various embodiments of the present disclosure. 
           [0009]      FIG. 11  illustrates examples of representative aperture designs based upon the arrangements of  FIG. 6  in accordance with various embodiments of the present disclosure. 
           [0010]      FIGS. 12 and 13  illustrate test results of the representative aperture designs of  FIG. 11  in accordance with various embodiments of the present disclosure. 
           [0011]      FIG. 14  illustrates examples of representative aperture designs based upon the arrangements of  FIG. 7  in accordance with various embodiments of the present disclosure. 
           [0012]      FIGS. 15 and 16  illustrate test results of the representative aperture designs of  FIG. 14  in accordance with various embodiments of the present disclosure. 
       
    
    
     DETAILED DESCRIPTION 
       [0013]    Disclosed herein are various embodiments related to fragmented aperture antennas. Reference will now be made in detail to the description of the embodiments as illustrated in the drawings, wherein like reference numbers indicate like parts throughout the several views. 
         [0014]    The physical shape and size of highly pixelated apertures can been optimized using genetic algorithms (GA) and full-wave computational electromagnetic simulation tools (i.e. FDTD) to best meet desired antenna performance specifications (e.g., gain, bandwidth, polarization, pattern, etc.).  FIG. 1  shows an example of a fragmented aperture antenna including a grid of rectangular pixels  103   a.  Visual inspection of the design shows that the metallic pixels  103  form many connected and disconnected fragments. Hence, the term fragmented aperture antenna has been coined for this class of antennas. The approach illustrated in  FIG. 1  has been successfully used to design novel antennas. This concept can be generalized to conducting or non-conducting parallelogram pixels  103   b  as shown in  FIG. 2 . 
         [0015]    However, the original fragmented design approach suffers from two major deficiencies. First, the placement of pixels  103  on a generalized, rectilinear grid leads to the problem of diagonal touching as illustrated in the top right of  FIGS. 1 and 2 . Pixels  103  that touch diagonally (i.e., diagonal touching  106 ) lead to poor measurement/model agreement. Second, the convergence in the GA stage of the design process is poor for high pixel count (&gt;&gt;100) apertures. 
         [0016]    Diagonal touching  106  is not a problem during the design phase because in the numerical models the diagonally touching  106  of pixels  103  in the antenna are always touching. However, when fabricated using approaches such as printed circuit board etching, the pixels  103  are often disconnected because of over-etching.  FIG. 3  illustrates an example of over-etching  109  that can lead to diagonal touches  106  between conducting regions  103  being disconnected. Disconnecting metal pixels  103  that should be connected within an antenna causes problems with the antenna impedance and gain characteristics. 
         [0017]    In fact, nearly every fragmented aperture antenna design presented in U.S. Pat. No. 6,323,809 suffers from this issue of diagonal touching.  FIG. 4  illustrates examples of diagonal touching  106  in two designs from U.S. Pat. No. 6,323,809. It has been noted that if the pixels  103  have edges parallel to the lattice forming vectors (as in the approaches of  FIGS. 1 and 2 ), then the issue of “diagonal touching”  106  will persist. Various approaches will be presented that have been successfully used to mitigate these diagonal touching issues. 
         [0018]    Mitigation of Diagonal Touching 
         [0019]    One approach utilizes a super-cell approach as illustrated in  FIG. 5A . A super-cell  503  is a collection of smaller areas such as, e.g., a 3 by 3 lattice of the smaller pixels or sub elements  506  as shown in  FIGS. 5A-5D . To avoid diagonal touching  106 , define the conducting region or pixel  509  as covering the 5 sub-elements  506  that defined a plus sign within the super-cell  503 . Hence, the absence of conducting material in the corners of the super-cell  503  prevents any potential for diagonal touching  106 . This successfully allows antennas to be designed and fabricated with a high probability of good correlation between measured and modeled characteristics of the antenna. In this approach, the electrical currents are constrained to flow in only grid conforming directions, which may limit optimization of the antenna designs. 
         [0020]    Another approach includes fabrication of every pixel  103  with an area that is roughly 10% larger than designed, as illustrated in  FIG. 5B . Oversizing the pixels  103  ensures diagonal touching  106  by overlapping with diagonally adjacent pixels  103 . This approach was found to lead to a high percentage of good fabricated antennas. However, this approach leads to the antennas having approximately 10-20% more conductor area than originally designed, which can lead to less than desired antenna characteristics in the fabricated antennas. 
         [0021]    It is worth noting that fabricating the conducting pixels  103  to be 10% smaller, would guarantee the pixels  103  would never diagonally touch  106 , but this would lead to antennas that never have conducting areas larger than one pixel  103 , which would almost never be any good. Also, this would be contrary to the numerical models used in design where the conducting elements  103  always touch when diagonally adjacent. 
         [0022]    Other implementations include a variant of the slightly larger pixel strategy of  FIG. 5B , where a small patch  512  of conducting material or metal is placed at the diagonal touching location as shown in  FIG. 5C . The small patch  512  can be a square as illustrated in  FIG. 5C  or other appropriate geometrical shape. Another implementation is illustrated in  FIG. 5D , where one of the two open pixel locations adjacent to the diagonal touching  106  is coated with conductive material. A random coin flipping process can be used to decide which of the two non-conducting pixel locations to make conducting to fix the diagonal touch  106  as shown in  FIG. 5D . 
         [0023]    Various approaches for avoiding diagonal touching  106  by breaking the dependence of element edges and lattice directions implicit in  FIGS. 1 and 2  will now be discussed. Three approaches for breaking this dependence are presented which can lead to improved fragmented aperture antennas. 
         [0024]    First Approach. In a first approach to improve the fragmented apertures, the location of individual conducting/non-conducting elements can be defined using a second set of directions (or lattice vectors) that are not both parallel with the lattice constants or edges of the conducting regions or pixels  103  as illustrated in  FIG. 6 . In the example of  FIG. 6 , the antenna comprises a lattice of square or rectangular conducting elements  103  where the lattice includes an X degree skewed lattice such that the adjacent conducting regions  103  are offset from each other based on the skew. Edge vectors E 1  and E 2  define the lattice constants with at least one of the lattice vectors V 1  and/or V 2  not being in parallel with E 1  or E 2 . In  FIG. 6 , skewing the lattice vector V 2  has removed the diagonal touching possibility. The skew angle X will be less than 90 degrees, and can be in a range from 75 degrees to 45 degrees, a range from 60 degrees to 45 degrees, or in a range from 70 degrees to 50 degrees. In the examples of  FIG. 11 , the skew angle is about 63 degrees. In some implementations, both lattice vectors V 1  and V 2  may be skewed. 
         [0025]    Second Approach. In a second approach to improve the fragmented apertures, the shapes of fundamental conducting regions and non-conducting regions can alternate such that the conducting elements  703  diagonally touch in a definite manner as illustrated in  FIG. 7 . In the example of  FIG. 7 , the shapes of the two regions comprise an octagon and a diamond. Other combinations of geometric shapes can be chosen such that the pair of shapes tessellate the plane. 
         [0026]    Third Approach. In a third approach to improve the fragmented apertures, the shape of the fundamental conducting regions and non-conducting regions is chosen such that the single shape tessellates the plane and does not touch diagonally.  FIG. 8  shows one example of such a conducting element or pixel  803 , but many other shapes can also be utilized. The shape of the conducting element  803  in  FIG. 8  is a skewed-Z that allows the regions to be interleaved in an interdigitated fashion to cover the plane. 
         [0027]    Mutation Algorithm to Improve Convergence Rate of Fragmented Apertures 
         [0028]    Traditionally, fragmented aperture antennas are designed using evolutionary algorithms like the genetic algorithm of U.S. Pat. No. 6,323,809, which is hereby incorporated by reference in its entirety. One important step in the genetic algorithm is called mutation. In a standard genetic algorithm, mutation is a random process where a small number of genes are changed each generation to help avoid convergence to a suboptimal solution. For a fragmented antenna, mutation makes a few pixels randomly conducting or not in the next population of antennas. Many of these mutations will create only an isolated metal pixel or small hole in metal that will have a very negligible effect on the antenna performance. 
         [0029]    A modified mutation algorithm tailored for fragmented aperture antennas can be introduced to help speed up the convergence of the design process when the number of elements/pixels is high. The goal of the new or modified mutation process is to bias mutation to either increase the size of conducting fragments in empty (or non-conducting) regions or increase the size of holes (or non-conducting areas) in large metal (or conducting) regions. This new mutation process uses an adjacency matrix that describes which conductive elements/pixels are touching each other. The adjacency matrix provides a two-dimensional metric describing which pixels are touching which other adjacent pixels. The adjacency matrix can range from 4 to 8 depending on the lattice type and the definition of touching. 
         [0030]    To demonstrate the efficacy of this adjacency-based mutation strategy, three consecutive design trials were conducted with the traditional mutation algorithm and with the new mutation algorithm.  FIG. 9  illustrates the convergence of the fitness as a function of generation count. The fitness of any generation is the fitness of the best individual. The y-axis shows the average best individual across three trials. The adjacency-based mutation algorithm (curve  903 ) converges to a better score in less generations than the traditional mutation algorithm (curve  906 ). 
         [0031]    As shown in the table in  FIG. 10 , the three trials with the adjacency-based mutation algorithm were each better than the corresponding trial with the traditional mutation algorithm. The values in the table in  FIG. 10  also illustrate that when using an evolutionary algorithm (e.g., the genetic algorithm) to design a fragmented aperture antenna or any electromagnetic device, more than one design trial should be executed because as illustrated in this table, the subsequent designs can be more than a dB better than the first design. 
         [0032]    Examples of Fragmented Aperture Designs 
         [0033]    First Approach. The approach illustrated in  FIG. 6  was used to design a series of fragmented aperture antennas that spanned from 500 MHz to 2.0 GHz. The lattice skew angle, X, was chosen to be tan −1 (2)˜63.435 degrees to give the desired left/right physical symmetry. The square pixels  103  were 10.8 mm on a side and the total aperture area was 25.4 cm×25.4 cm. Four representative aperture designs are shown in  FIG. 11 . Each of the four sample antenna designs are excited at the terminal pair (feed point  1003 ) in the center with a 100 ohm transmission line. As the aperture designs in  FIG. 11  show, none of the physical shapes of the designed antennas suffer from diagonal touching issues. 
         [0034]    The aperture designs (the placement of conducting and non-conducting regions) were performed using a genetic algorithm with adjacency-based mutation. For these designs, the 25.4 cm×25.4 cm area have 663 individual pixels. Enforcing left/right and top/down symmetry, there are 169 degrees of freedom. Hence assigning a single bit to represent the state of each area (1=conducting, 0=non-conducting) yields a 169 bit genetic code. Using a genetic population size of 32 antennas, 100 genetic algorithm generations was typically required to realize one of these sample designs. The genetic algorithm used a finite-difference time-domain (FDTD) numerical model of each antenna to compute return loss and radiation properties for the evolving population of antennas. The genetic algorithm fitness function rewarded good match (return loss better than 15 dB), and as large as possible, broadside realized gain. 
         [0035]      FIG. 12  shows the broadside realized gain of each antenna design, while  FIG. 13  shows the return loss of each antenna. Curve  1203  shows the 0.5-0.8 GHz design, curve  1206  shows the 0.8-12 GHz design, curve  1209  shows the 1.2-1.6 GHz design, and curve  1212  shows the 1.6-2.0 GHz design. The gains are compared with an aperture gain limit (curve  1215 ). Since these apertures have no ground plane, the aperture gain limit for high frequencies is 2π(Area)/λ 2 . As shown in  FIG. 13 , the VSWR of the four designs of  FIG. 11  are below 1.5 across the respective design bands which is consistent with a return loss of better than 15 dB. Curve  1303  shows the 0.5-0.8 GHz design, curve  1306  shows the 0.8-12 GHz design, curve  1309  shows the 1.2-1.6 GHz design, and curve  1312  shows the 1.6-2.0 GHz design. 
         [0036]    Second Approach. The second approach illustrated in  FIG. 7  is also useful for designing antennas. The second approach also supports left/right and top/down symmetry when appropriate. The aperture area was again 25.4 cm×25.4 cm and was excited in the center with a 100 ohm feed. The aperture has 841 shaped pixels. When left/right and top/down symmetry was enforced, the number of degrees of freedom dropped to 221. FIG.  14  shows examples of two designed apertures for the 0.5-0.8 GHz and the 0.8-1.2 GHz bands. The sample antenna designs are excited at the terminal pair (feed point  1003 ) in the center with a 100 ohm transmission line. 
         [0037]      FIG. 15  shows the broadside realized gain of the antenna designs, while  FIG. 16  shows the return loss of the antennas. Curve  1503  shows the 0.5-0.8 GHz design and curve  1506  shows the 0.8-12 GHz design. The gains are compared with an aperture gain limit (curve  1515 ). In  FIG. 16 , curve  1603  shows the 0.5-0.8 GHz design and curve  1606  shows the 0.8-12 GHz design. 
         [0038]    Third Approach. The third approach illustrated in  FIG. 8  is also useful for designing antennas. However, for the design of vertically or Horizontal polarized elements with a broadside beam, the lack of left/right and top/down symmetry in the third approach is a drawback. For cases where the desired beam direction is not broadside or the desired polarization is different, then the pixelated aperture should not have symmetry and the third approach is comparable to the second or first approaches. 
         [0039]    It should be emphasized that the above-described embodiments of the present disclosure are merely possible examples of implementations set forth for a clear understanding of the principles of the disclosure. Many variations and modifications may be made to the above-described embodiment(s) without departing substantially from the spirit and principles of the disclosure. All such modifications and variations are intended to be included herein within the scope of this disclosure and protected by the following claims. 
         [0040]    It should be noted that ratios, concentrations, amounts, and other numerical data may be expressed herein in a range format. It is to be understood that such a range format is used for convenience and brevity, and thus, should be interpreted in a flexible manner to include not only the numerical values explicitly recited as the limits of the range, but also to include all the individual numerical values or sub-ranges encompassed within that range as if each numerical value and sub-range is explicitly recited. To illustrate, a concentration range of “about 0.1% to about 5%” should be interpreted to include not only the explicitly recited concentration of about 0.1 wt % to about 5 wt %, but also include individual concentrations (e.g., 1%, 2%, 3%, and 4%) and the sub-ranges (e.g., 0.5%, 1.1%, 2.2%, 3.3%, and 4.4%) within the indicated range. The term “about” can include traditional rounding according to significant figures of numerical values. In addition, the phrase “about ‘x’ to ‘y’” includes “about ‘x’ to about ‘y’”.