Abstract:
Embodiments of the invention provide a hybrid tee waveguide structure including a first collinear arm having a first waveguide, a second collinear arm having a second waveguide, an H-arm having a third waveguide and including at least one window; and an E-arm having a fourth waveguide and including at least one window, the E-arm oriented perpendicular to the H-arm. The first, second, third and fourth waveguides join at a common junction. The at least one window of the H-arm and the at least one window of the E-arm are proximate the common junction. The at least one window of the H-arm and the at least one window of the E-arm change an impedance of the common junction to reduce reflections in the H-arm and E-arm. The hybrid tee waveguide structure further includes an impedance matching element positioned in the common junction.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
       [0001]    This application claims the benefit of and priority to U.S. Provisional Application Serial No. 61/651,733, entitled “Broadband Folded E-Plane Magic-Tee,” filed on May 25, 2012, and U.S. Provisional Application Ser. No. 61/655,080, entitled “Broadband Folded E-Plane and H-Plane Magic-Tees,” filed on Jun. 4, 2012, the entireties of which are incorporated by reference herein. 
     
    
     RIGHTS OF THE GOVERNMENT 
       [0002]    The invention described herein may be manufactured and used by or for the Government of the Untied States for all governmental purposes without the payment of any royalty. 
     
    
     BACKGROUND OF THE INVENTION 
       [0003]    1. Field of the Invention 
         [0004]    The present invention generally relates to waveguides and, more particularly, hybrid junction waveguides. 
         [0005]    2. Description of the Related Art 
         [0006]    A hybrid-tee waveguide (magic-tee) junction generally includes an intersection of four rectangular waveguides. Two mutually orthogonal waveguide sections, cross-polarized, have their centerlines in the symmetry plane of the waveguide junction. One of the mutually perpendicular waveguides is designated as the E-arm and the other as the H-arm, corresponding to the relation between the longitudinal axes of each waveguide and the electric field vector ({right arrow over (E)}) and the magnetic field vector ({right arrow over (H)}) of the third and fourth waveguide sections. The remaining two waveguides are formed by extending the bifurcation of the E-arm waveguide into the plane of symmetry at the junction mutual to all the waveguides. These two waveguide section are commonly referred to as the collinear arms. The folded E-plane and H-plane configurations may be obtained by bending the collinear arms back so that their centerlines are parallel to that of the E-arm and H-arm, respectively. 
         [0007]    A waveguide hybrid junction fundamentally is an ideally lossless four-port, 180 degree hybrid power splitter. The device is constructed such that the power incident at either the E-arm or H-arm divides equally into the two collinear arms. Energy supplied simultaneously to both the E-and H-arms is distributed between the two collinear arms based on the relative amplitudes and phases of the input signals. Additionally, high isolation is maintained between the E- and H- arms with ideally no energy coupling between the two arms. Conversely, two coherent signals input into the collinear arms will produce their vector sum and difference at the other two H- and E-arms respectively. 
         [0008]    Approaching the ideal performance of the waveguide hybrid junction over an appreciable range of frequencies generally requires specialized impedance matching elements. It is well known that waveguide hybrid junction design depends on exclusively maintaining device symmetry and simultaneously eliminating E- and H-arm signal reflections. In general, impedance matching may be obtained by inserting fundamentally inductive or capacitive based elements in E- and H-arms or the waveguide junction. Previous attempts at compensating the waveguide hybrid junction relied on various configurations of windows and rods to achieve matching across a limited range of frequencies. Additionally, some configurations refrained from any matching elements in pursuit of maximizing power handling capacity and instead relied on waveguide stepped-impedance transformers at the junction. Even with these efforts, contemporary magic tee configurations are generally limited to operating in 10-15 percent of operational waveguide bandwidth. 
         [0009]    Accordingly, there is a need in the art for an improved magic tee configuration giving a broader operating bandwidth. 
       SUMMARY OF THE INVENTION 
       [0010]    Embodiments of the invention provide a hybrid tee waveguide structure including a first collinear arm having a first waveguide, a second collinear arm having a second waveguide, an H-arm having a third waveguide and including at least one window, and an E-arm having a fourth waveguide and including at least one window, the E-arm oriented perpendicular to the H-arm. The first, second, third and fourth waveguides join at a common hybrid junction. The at least one window of the H-arm and the at least one window of the E-arm are proximate the common junction. The windows of the H-arm and the windows of the E-arm change an impedance of the common junction to reduce reflections in the H-arm and E-arm. 
         [0011]    In some embodiments, the hybrid tee waveguide structure of claim  1  further includes an impedance matching element positioned in the common junction and orthogonal to and extending toward the third waveguide. The impedance matching element is offset from a centerline of the E-arm and aligned with a centerline of the H-arm. In some of these embodiments, the impedance matching element includes a plurality of cylinders of different radii tapering toward the third waveguide. In a particular embodiment, the impedance matching element consists of five cylinders. 
         [0012]    In other embodiments, the first and second collinear arms are oriented parallel to each other and parallel to the E-arm. In these embodiments, the hybrid tee waveguide structure further includes a bifurcating wall separating the first and second collinear arms and a stepped ridge profile extending from the bifurcating wall into the third waveguide in the H-arm and the fourth waveguide in the E-arm. 
         [0013]    Some of the embodiments include waveguides having a rectangular cross section. In some specific embodiments, the rectangular cross section has a ratio of 2:1. 
         [0014]    Additional objects, advantages, and novel features of the invention will be set forth in part in the description which follows, and in part will become apparent to those skilled in the art upon examination of the following or may be learned by practice of the invention. The objects and advantages of the invention may be realized and attained by means of the instrumentalities and combinations particularly pointed out in the appended claims. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0015]    The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and, together with a general description of the invention given above, and the detailed description given below, serve to explain the invention. 
           [0016]      FIG. 1  is a perspective view of an exemplary embodiment of a magic-tee utilizing rectangular waveguides; 
           [0017]      FIG. 2  is a perspective cut view along symmetry plane  3 - 3  exposing a waveguide junction of the magic-tee of  FIG. 1 ; 
           [0018]      FIG. 3  is a side view cut along symmetry plane  3 - 3  exposing impedance matching elements in the E- and H-arms of the magic-tee of  FIG. 1 ; 
           [0019]      FIG. 3A  is a detailed view of the impedance matching elements of  FIG. 3  ; 
           [0020]      FIG. 4  is a side view cut along plane  4 - 4  exposing E-arm matching elements of the magic-tee of  FIG. 1 ; 
           [0021]      FIG. 4A  is a detailed view of the matching elements of  FIG. 4 ; 
           [0022]      FIG. 4B  is a detailed view of the stepped cone matching element of  FIG. 4A ; 
           [0023]      FIG. 5  is a top view cut along plane  5 - 5  exposing internal impedance matching elements of the magic-tee of  FIG. 1 ; 
           [0024]      FIG. 5A  is a detailed view of the impedance matching elements of  FIG. 5 ; 
           [0025]      FIG. 5B  is a detailed view of the stepped cone matching element of  FIG. 5A ; 
           [0026]      FIG. 6  is a perspective view of an alternate embodiment of a folded E-plane magic-tee utilizing rectangular waveguides; 
           [0027]      FIG. 7  is a perspective cut view along symmetry plane  8 - 8  exposing a waveguide junction of the magic-tee of  FIG. 6 ; 
           [0028]      FIG. 8  is a side view cut along plane  8 - 8  exposing a multiple stepped ridge profile of the magic-tee of  FIG. 6 ; 
           [0029]      FIG. 8A  is a detailed view of the multiple stepped ridge profile of  FIG. 8 ; 
           [0030]      FIG. 9  is a top view cut along plane  9 - 9  exposing internal matching elements of the magic-tee of  FIG. 6 ; 
           [0031]      FIG. 9A  is a detailed view of the multiple stepped ridge profile of  FIGS. 8 and 9 ; 
           [0032]      FIG. 10  is a front view cut along plane  10 - 10  at a center point of the H-arm exposing inductive iris tuning elements of the magic-tee of  FIG. 6 ; 
           [0033]      FIG. 11  is a perspective view of an alternate embodiment of a folded H-plane magic-tee utilizing rectangular waveguides; 
           [0034]      FIG. 12  is a perspective cut view along symmetry plane  14 - 14  exposing a waveguide junction of the magic-tee of  FIG. 11 ; 
           [0035]      FIG. 13  is a top view cut along plane  13 - 13  exposing internal impedance matching elements of the magic-tee of  FIG. 11 ; 
           [0036]      FIG. 13A  is a detailed view of a cavity of  FIG. 13 ; 
           [0037]      FIG. 13B  is a detailed top view of a quarter of the stepped conducting cone of  FIG. 13 ; 
           [0038]      FIG. 14  is a side view cut along plane  14 - 14  exposing a profile of a stepped conducting cone of the magic-tee of  FIG. 11 ; 
           [0039]      FIG. 15  is a front view cut along plane  15 - 15  exposing a different profile of the stepped conducting code of the magic-tee of  FIG. 11 ; 
       
    
    
       [0040]    It should be understood that the appended drawings are not necessarily to scale, presenting a somewhat simplified representation of various features illustrative of the basic principles of the invention. The specific design features of the sequence of operations as disclosed herein, including, for example, specific dimensions, orientations, locations, and shapes of various illustrated components, will be determined in part by the particular intended application and use environment. Certain features of the illustrated embodiments have been enlarged or distorted relative to others to facilitate visualization and clear understanding. In particular, thin features may be thickened, for example, for clarity or illustration. 
       DETAILED DESCRIPTION OF THE INVENTION 
       [0041]    A magic-tee is a type of 180 degree hybrid junction, four port device which provides a sum and difference of signals from its two input ports at its two output ports. In conventional form, the magic-tee consists of a waveguide E-plane and H-plane junction, placed mutually perpendicular and intersecting to form symmetry about a specified plane. The combined structure is generally called a hybrid-T junction, where two of the arms are mirror images of each other with respect to the place of symmetry, commonly denoted as collinear arms. Additionally, the remaining two arms lie cross-polarized along a centerline of the symmetry plane and are regarded as either the E-arm or H-arm. 
         [0042]    Turning now to the drawings,  FIG. 1  illustrates a magic-tee  20  consistent with embodiments of the invention. Embodiments of the invention improve the operational bandwidth of the magic-tee  20  by maintaining a geometric symmetry about a designated plane and simultaneously minimizing reflections in an H-arm  22  and an E-arm  24 . These two design criteria are met by use of a matching element design to obtain wideband reduction in a return loss of ports  22   a ,  24   a ,  26   a , and  28   a  associated with each arm  22 ,  24 ,  26 , and  28 . An exemplary structure used in the illustrated embodiment of magic-tee  20  includes an off-centered stepped conducting cone  30  coupled to cascaded windows  32 ,  34  along the E- and H-arms  24 ,  22 . Details of the stepped cone  30  may be seen in various orientations in  FIGS. 2 ,  3 ,  3 A,  4 ,  4 A,  4 B,  5 ,  5 A, and  5 B. Dimensions of the stepped cone (C 1 -C 15 ) normalized to a center frequency are set out the Table below: 
         [0000]                                  TABLE 1                   Frequency Normalized Stepped Conducting Cone Dimensions                Cone Dimension   Frequency Normalized Value                       C1   0.338339           C2   0.102958           C3   0.042191           C4   0.056734           C5   0.031865           C6   0.043953           C7   0.017706           C8   0.022935           C9   0.014046            C10   0.096082            C11   0.086139            C12   0.115717            C13   0.129802            C14   0.135681            C15   0.110488                        
In this exemplary embodiment, the stepped conducting cone  30  consists of five steps, though other embodiments may have more or fewer steps.
 
         [0043]    The windows  32 ,  34  along each waveguide arm act as reactive elements, which assist in matching the waveguide impedance to a junction impedance. The windows act as symmetrical diaphragms along both narrow and broad walls of the waveguide to create a series of shut inductive and capacitive elements. The illustrated embodiment contains four windows in the E-arm  24  and the H-arm  22 . Other embodiments may contain more or fewer windows in each of the arms. In other embodiments the number of windows in the E-arm  24  may be greater or fewer than the number of windows in the H-arm  22 . Details of the E-arm  24  and H-arm windows may be seen in various orientations in  FIGS. 2 ,  3 ,  3 A,  4 ,  4 A,  4 B,  5 ,  5 A, and  5 B. Dimensions of these windows normalized to a center frequency are set out the Tables below: 
         [0000]    
       
         
               
             
               
               
               
             
           
               
                 TABLE 2 
               
             
             
               
                   
               
               
                 Frequency Normalized E-arm Window Dimensions 
               
             
          
           
               
                   
                 E-arm Window 
                 Frequency 
               
               
                   
                 Dimensions 
                 Normalized Value 
               
               
                   
                   
               
               
                   
                 E1 
                 0.726043 
               
               
                   
                 E2 
                 0.641772 
               
               
                   
                 E3 
                 0.672371 
               
               
                   
                 E4 
                 0.876502 
               
               
                   
                 E5 
                 0.139228 
               
               
                   
                 E6 
                 0.178407 
               
               
                   
                 E7 
                 0.158510 
               
               
                   
                 E8 
                 0.143679 
               
               
                   
                 E9 
                 0.018818 
               
               
                   
                  E10 
                 0.077777 
               
               
                   
                  E11 
                 0.167139 
               
               
                   
                  E12 
                 0.106604 
               
               
                   
                   
               
             
          
         
       
     
         [0000]                                  TABLE 3                   Frequency Normalized H-arm Window Dimensions                H-arm Window   Frequency           Dimensions   Normalized Value                       H1   0.146173           H2   0.156376           H3   0.080858           H4   0.109517           H5   0.641959           H6   0.767809           H7   0.667616           H8   0.678784           H9   0.169333            H10   0.148981            H11   0.152039            H12   0.164607                        
Overall geometric symmetry is maintained over the cut plane  3 - 3  for all matching elements. Additionally, the four waveguides in arms  22 ,  24 ,  26 , and  28  in the illustrated embodiment are rectangular in cross section with dimensional ratio of approximately 2 to 1, though other embodiments may utilize waveguides having cross sections with alternate ratios, or cross sections that are not rectangular. The exact dimensions of the waveguides in arms  22 ,  24 ,  26 , and  28  may be determined with respect to an excitation frequency such that a fundamental TE 10  mode may propagate in the waveguides. In the illustrated embodiment, the waveguides were designed for an excitation frequency of approximately 10 GHz.
 
         [0044]    The illustrated embodiment was optimized for X-band applications or WR90 waveguide standards (a=0.9 in, b=0.4 in), though other embodiments may be optimized for other applications. The illustrated embodiment was simulated in an electromagnetic simulation software package, such as ANSYS HFSS by Ansys, Inc. of Canonsburg, Pa. The embodiment was optimized utilizing a genetic algorithm with roulette wheel selection and with a crossover rate of 0.9 and mutation rate of 0.15. The algorithm was applied to the dimensions of the stepped conducting cone  30  and the windows along both the E- and H-arms  24 ,  22 . A cost function applied to the genetic algorithm process is defined as: 
         [0000]    
       
         
           
             
               
                 
                   
                     Cost 
                     = 
                     
                       
                         ∑ 
                         
                           i 
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                           N 
                         
                          
                         
                           
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                               max 
                                
                               
                                 [ 
                                 
                                   0 
                                   , 
                                   
                                     
                                       
                                         S 
                                         ii 
                                       
                                        
                                       
                                         ( 
                                         
                                           f 
                                           n 
                                         
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                                     - 
                                     
                                       S 
                                       obj 
                                     
                                   
                                 
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                              
                           
                           2 
                         
                       
                     
                   
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         [0000]    Where S ii (f n ) is a return loss at the i-th waveguide port number at a test frequency f n  (8.2-12.4 GHz for X-band), and S obj  is an objective return loss of −20 dB. The return loss at ports  26   a  and  28   a  are not considered because maintaining symmetrical geometry while simultaneously reducing E- and H-arm  24 ,  22  reflections generally results in a well matched magic-tee. In the illustrated embodiment, the design exhibits a minimum of −20 dB return loss over 100 percent bandwidth at all waveguide ports  22   a ,  24   a ,  26   a , and  28   a.    
         [0045]    In an alternate embodiment,  FIG. 6  illustrates a magic-tee  40  in an E-plane folded configuration. The folded E-Plane magic-tee is a variation of the magic-tee that was developed for microwave applications requiring higher power carrying capacities. This variation of the magic-tee is created by “folding” the opposing arms (for example arms  26  and  28  in  FIG. 1 ) so that they are parallel to the E-arm. In the illustrated embodiment of the magic-tee  40  in  FIG. 6 , parallel, collinear arms  42   a ,  42   b  are separated by a bifurcating wall  44 , which can be seen in  FIG. 7 . The bifurcating wall  44  extends into both the E-arm  46  and H-arm  48  with a stepped ridge profile  50 . An impedance step from a standard waveguide  52  in the E-arm  46  to the stepped ridge profile  50  is gradual with a ridge height increasing with each step until step R 7  with varied lengths for each step. Details of the stepped ridge profile  50  may be seen in various orientations in  FIGS. 7 ,  8 ,  8 A and  9 . Dimensions of the stepped ridge profile normalized to a center frequency are set out the Table below: 
         [0000]                                  TABLE 4                   Frequency Normalized Stepped Ridge Dimensions            Ridge   Frequency   Frequency       Step   Normalized Height   Normalized Width               R1   0.919307   1.076461       R2   0.957734   0.048266       R3   0.785263   0.022290       R4   0.639852   0.164783       R5   0.435898   0.103390       R6   0.468137   0.169384       R7   0.492055   0.048658       R8   0.306490   0.043572       R9   0.118567   0.003504        R10   0.087042   0.016799        R11   0.041295   0.013916        R12   0.027346   0.030970                    
Coupling between the H-arm  48  and the symmetrical, collinear arms  42   a ,  42   b  may be further increased by step reductions in the stepped ridge  50  profile at steps R 1  and R 5 . Additionally, stepped ridge  50  steps R 1  and R 2  effective act to a characteristic impedance of the rectangular waveguide and allow for broadband electric field propagation of a fundamental mode below a cutoff wavelength of the given rectangular waveguide.
 
         [0046]    A frequency normalized thickness T 1  of the bifurcating wall  44  along the stepped ridge  50  is approximately 0.0254 between steps R 1  and R 12 . A thickness T 2  of a remainder of the bifurcating wall  44  is approximately twice the thickness T 1 , though in other embodiments, other wall thickness may also be appropriate for impedance matching. Additionally, other tapered or varying wall structures may also be used in other embodiments. 
         [0047]    Outer solid walls from the E-arm  46  to the parallel, collinear arms  42   a ,  42   b  may be discontinuous, as illustrated in the exemplary embodiment  40 , by cascaded wall steps of the waveguide height in a waterfall configuration. Details of the cascaded wall steps may be seen in various orientations in  FIGS. 9 and 9A . Dimensions of the cascaded wall steps normalized to a center frequency are set out the Table below: 
         [0000]                                                TABLE 5                   Frequency Normalized Cascaded Wall Step Dimensions                Frequency   Frequency       Wall Step   Normalized Depth   Normalized Width                    W1   0.019820   0.068219       W2   0.001680   0.032576       W3   0.021949   0.040768       W4   0.005401   0.008466       W5   0.004724   0.008983       W6   0.003281   0.06913       W7   0.002189   0.034216       W8   0.000938   0.022355       W9   0.001528   0.180520        W10   0.022660   0.011357        W11   0.022248   0.051054        W12   0.019422   0.096117        W13   0.015267131   0.225569                    
The final step WT of approximately 0.015267 (normalized to the center frequency) is held constant and is equivalent to the equivalent waveguide walls of waveguides  54 ,  56  in parallel, collinear arms  42   a ,  42   b . The number of wall steps present may vary as geometrical dimensions scale to negligible proportion for a desired frequency band of operation and as necessitated by manufacturing tolerances. An effect of the waterfall step configuration is to transform an impedance between the E-arm  46  and the collinear arms  42   a ,  42   b  across the waveguide frequency band.
 
         [0048]      FIG. 10  illustrates a cross-section of the H-arm  48  including symmetrical, inductive window cavities  58 ,  60  situated above the stepped ridge profile  50  of the bifurcating wall  44 . The stepped cavities act as an additional impedance transformer and assist in further reducing electric field reflections along the H-arm  48 . Details of the cascaded wall steps may be seen in  FIG. 10A . Dimensions of the cascaded wall steps normalized to a center frequency are set out the Table below: 
         [0000]    
       
         
               
             
               
               
               
             
           
               
                 TABLE 6 
               
             
             
               
                   
               
               
                 Frequency Normalized H-arm Cavity Dimensions 
               
             
          
           
               
                   
                 H-arm Cavity 
                 Frequency 
               
               
                   
                 Dimensions 
                 Normalized Value 
               
               
                   
                   
               
               
                   
                 H41 
                 0.741190 
               
               
                   
                 H42 
                 0.820355 
               
               
                   
                 H43 
                 1.000157 
               
               
                   
                 H44 
                 0.055650 
               
               
                   
                 H45 
                 0.042959 
               
               
                   
                 H46 
                 0.197666 
               
               
                   
                   
               
             
          
         
       
     
         [0049]    Similar to the embodiment illustrated in  FIG. 1 , the waveguides in arms  42   a ,  42   b ,  46 , and  48  in the illustrated embodiment in  FIG. 6  are rectangular in cross section with dimensional ratio of approximately 2 to 1, though other embodiments may utilize waveguides having cross sections with alternate ratios, or cross sections that are not rectangular. The exact dimensions of the waveguides in arms  42   a ,  42   b ,  46  and  48  may be determined with respect to an excitation frequency such that a fundamental TE 10  mode may propagate in the waveguides. In the illustrated embodiment, the waveguides were designed for an excitation frequency of approximately 10 GHz. 
         [0050]    In an alternate embodiment,  FIG. 11  illustrates a magic-tee  70  in an H-plane folded configuration. The folded H-Plane magic-tee is another variation of the magic-tee, which may be obtained by bending collinear arms  72   a ,  72   b  such that their centerlines are parallel to an H-arm  74 . An E-arm  76  is positioned perpendicular to the H-arm  74  and collinear arms  72   a ,  72   b  similar to the embodiments set forth above. A common junction of the collinear, E- and H-arms  72   a ,  72   b ,  74 ,  76  may be bifurcated along a symmetry plane with a protruding common wall  78 , additionally separating waveguides in the collinear arms. This common wall  78  extends partially into a stepped conducting cone  80  as illustrated in  FIGS. 12 ,  13  and  14 . 
         [0051]    As seen in  FIG. 13 , an outer wall  82  is discontinuous including cascaded wall steps with offset cavities. Heights of the cavities in the illustrated embodiment  70  are held constant and equivalent to a height of the waveguide associated with the H-arm  74 . Additional details of the offset cavities may be seen in  FIG. 13A . Dimensions of the offset cavities normalized to a center frequency are set out the Table below: 
         [0000]                                                TABLE 7                   Frequency Normalized H-arm Offset Cavity Dimensions                H-arm Offset               Cavity   Frequency           Dimensions   Normalized Value                            H71   0.476224           H72   0.786804           H73   0.046521           H74   0.550502           H75   0.114952           H76   0.219614           H78   0.042504           H79   0.010418           H80   0.130765           H81   0.074616           H82   0.104736           H83   0.052090           H84   0.039957539                        
Cavities  84  and  86  may be omitted in some embodiments as geometric dimensions scale to negligible proportions for desired operating frequency bands as well as necessitated by manufacturing tolerances. Additionally, in the illustrated embodiment  70 , walls of cavities  88  and  90  partially protrude into the stepped conducting cone  80 .
 
         [0052]    The E-arm  76  includes a symmetrical inductive window taper at a base of the E-arm  76  and flush with a top of the H-arm  74  and collinear arm  72   a ,  72   b  walls. The inductive taper runs the width of the E-arm  76  with additional dimensional values E 71  and E 72  normalized to the center frequency of 0.056045 and 0.121686 respectively. Additionally, as illustrated in  FIG. 14 , the stepped conducting cone  80  is placed offset from a center for the E-arm  76 . This offset distance E 73  is approximately 0.164394 though other offsets for other embodiments may also be used based on operating frequency ranges. 
         [0053]    The stepped conducting cone  80  includes five cylindrical sections with each respective cone radius having a taper expanding from top to bottom with varied heights, similar to the stepped conducting cone  30  in the embodiment  20  set forth above. Dimensions of the stepped conducting cone  80  (C 71 -C 84 ) normalized to a center frequency are set out the Table below: 
         [0000]                                                TABLE 8                   Frequency Normalized Stepped Conducting Cone Dimensions                Cone Dimension   Frequency Normalized Value                            C71   0.084826           C72   0.118274135           C73   0.065163           C74   0.053276009           C75   0.015964           C76   0.022800           C77   0.027981106           C78   0.126389           C79   0.051988           C80   0.201330           C81   0.016586           C82   0.159286                        
In this exemplary embodiment, the stepped conducting cone  30  consists of five cylinders, though other embodiments may have more or fewer cylinders.
 
         [0054]    As with the other embodiments, this illustrated embodiment waveguides with rectangular cross sections with a dimensional ration of approximately 2 to 1. Again the exact dimensions of the waveguides are determined with respect to an excitation frequency such that a fundamental TE 0  mode may propagate the waveguides. The waveguides for all of the described embodiments are constructed from highly conductive materials, such as copper, brass or the like and have some minimum thickness for all outer walls of the waveguides based on an operational frequency and chosen material properties for the embodiment. 
         [0055]    While the present invention has been illustrated by a description of one or more embodiments thereof and while these embodiments have been described in considerable detail, they are not intended to restrict or in any way limit the scope of the appended claims to such detail. Additional advantages and modifications will readily appear to those skilled in the art. The invention in its broader aspects is therefore not limited to the specific details, representative apparatus and method, and illustrative examples shown and described. Accordingly, departures may be made from such details without departing from the scope of the general inventive concept.