Patent Publication Number: US-7724197-B1

Title: Waveguide beam forming lens with per-port power dividers

Description:
This invention was made with Government support under contract FA9453-05-C-0033 awarded by the United States Department of Defense. The Government has certain rights in this invention. 

   FIELD OF THE INVENTION 
   The present invention relates to a parallel plate waveguide beam forming lens, also known as a Rotman lens. In particular the present invention is related to a low loss beam forming lens for use in an antenna system for producing a number of simultaneously existing beams, where the system incorporates a parallel plate lens cavity filled with vacuum, air or other near homogeneous isotropic dielectric for electromagnetic energy propagating in the TE mode. 
   BACKGROUND OF THE INVENTION 
     FIG. 1  shows a prior art Rotman lens  100 , which includes a plurality of equal-length waveguide beam ports  102 - 1  through  102 - n , which couple to parallel plate lens apertures  108 - 1  through  108 - n , respectively. On the opposing side of the parallel plate lens region  114  are a plurality of waveguide apertures  110 - 1  through  110 - m , which are coupled to array port waveguides  104 - 1  through  104 - m  which also incorporate the Rotman W parameters, which are incremental per-port delays added to the array port waveguides. Dummy ports  112 - 1  through  112 - p  and  106 - 1  through  106 - p  couple unusable wave energy which enters from the parallel plate lens region  114  into termination cavities, which minimize wave energy reflected into the parallel plate lens region  114 . The beam forming lens  100  may be used bi-directionally, such that for one exemplar transmit application, waveguide RF from a transmitter (not shown) is applied to a power splitter (not shown) and thereafter to a plurality of waveguides and applied to beam port waveguides  102 - 1  through  102 - n , through lens region  114  and waveguide array ports  104 - 1  through  104 - m  and thereafter to a transmit antenna. In one examplar receive application, incoming antenna energy is coupled to waveguide array ports  104 - 1  through  104 - m , through parallel plate lens region  114 , through waveguide beam ports  102 - 1  through  102 - m , summed (not shown), and delivered to a microwave receiver (not shown). 
   In an embodiment of the prior art such as U.S. Pat. No. 4,490,723, the Rotman lens  100  of  FIG. 1  may be realized using stripline or microstrip conductors, whereby one or more RF conductors are separated by a substrate material having a dielectric constant. Stripline and microstrip transmission lines and lens structures propagate waves in the transverse electromagnetic (TEM) mode. The TEM mode has a phase velocity that is essentially constant with frequency, which results in a formed beam which is largely frequency invariant, which results in the property known as minimum frequency scan, or minimum variation of the formed beam angle with frequency. Prior art U.S. Pat. No. 4,490,723 is one example of this construction. At high operating frequencies, several problems emerge when using stripline or microstrip Rotman lens structures. A first problem is the finite thickness of the dielectric substrate allows the transmission lines formed over the substrate to support higher order wave modes, and the higher order modes propagate at a different phase velocity than the desired TEM mode, thereby causing interference with the desired TEM mode and undesired sidelobes in the radiation pattern. For best performance, the dielectric thickness should be less than 0.1 wavelengths in the dielectric. For example, at an operating frequency of 45.5 Ghz, a wavelength in vacuum is 0.259 inches, which results in a vacuum dielectric thickness of 0.026 inch, and for most substrate dielectrics which have a dielectric constant of approximately 2.2 such as PTFE (PolyTetraFluoroEthylene), a thickness on the order of 0.017 inch, which results in a substrate dielectric structure with undesirably tight feature and etching tolerances. Additionally, many dielectric materials have undesirable mode dependant dielectric constants, and also wave propagation dependant dielectric constants, where in the lens region of a Rotman lens structure, the dielectric constant may depend on the angle of propagation across the planar surface of the lens region. 
   An alternative to fabricating the Rotman Lens  100  in stripline or microstrip structure is to use a closed waveguide with an air or other dielectric, such as U.S. Pat. No. 6,031,501. The advantage of a waveguide structure is the beam and array waveguides and associated lens structures may be significantly larger and easy to machine and manufacture compared to stripline or microstrip structures, however waveguides support TE modes, and cannot support TEM wave modes. Of the TE modes, TE10 is the lowest mode that can propagate in a rectangular waveguide. For the TE10 mode, the phase velocity Vp is: 
   
     
       
         
           Vp 
           = 
           
             c 
             
               
                 1 
                 - 
                 
                   
                     ( 
                     
                       λ 
                       
                         2 
                         ⁢ 
                         
                           W 
                           h 
                         
                       
                     
                     ) 
                   
                   2 
                 
               
             
           
         
       
     
   
   Where: 
   c=velocity of light; 
   λ is the free space wavelength 
   Wh is the height of the waveguide 
   As can be seen from the formula above, Vp is a function of wavelength λ, which introduces a frequency dependant phase delay producing the result known as frequency scan. The effect of wavelength on Vp can be reduced by maximizing Wh, but this also allows higher mode TE waves to propagate through the waveguide. The TE10 mode is supported by a waveguide with a height Wh of λ/2, TE20 is additionally supported by a waveguide with a height Wh of λ, and TE30 mode is additionally supported when the waveguide height Wh is 3λ/2. It is desired to maximize waveguide height Wh in the lens region, thereby reducing frequency dependant phase velocity which causes frequency scan, while also minimizing the higher modes supported as a consequence of increased Wh. Another desirable outcome of increasing the waveguide height Wh is reduced lens insertion loss. 
     FIG. 2  shows the geometry of a Rotman lens including lens parameters, which include the four basic lens parameters α, β, f 1 , γ, where 
   α is the focal angle shown in  FIG. 1 ; 
   β is the focal ratio f 2 /f 1  of  FIG. 1 ; 
   γ is the expansion factor (sin ψ/sin α). 
   As derived by Hansen, the normalized length W=w/f 1  of the waveguide attached to the array element at y=y3 where w is the length of the transmission line to the array port satisfies the following quadratic equation:
 
 aW   2   +bW+c= 0
 
   with coefficients a,b,c defined by: 
   
     
       
         
           
             
               
                 a 
                 = 
                 
                   1 
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                         ( 
                         
                           1 
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                             cos 
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                             ⁢ 
                             α 
                           
                         
                         ) 
                       
                       2 
                     
                   
                   - 
                   
                     
                       ξ 
                       2 
                     
                     
                       β 
                       2 
                     
                   
                 
               
             
           
           
             
               
                 b 
                 = 
                 
                   
                     - 
                     2 
                   
                   + 
                   
                     
                       2 
                       ⁢ 
                       
                         ξ 
                         2 
                       
                     
                     β 
                   
                   + 
                   
                     
                       2 
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                         ( 
                         
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                         cos 
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                         α 
                       
                     
                   
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                         ξ 
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                         sin 
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                       2 
                     
                   
                 
               
             
           
           
             
               
                 c 
                 = 
                 
                   
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                         sin 
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                         ξ 
                         4 
                       
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                         sin 
                         4 
                       
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                           ( 
                           
                             1 
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                               cos 
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                               α 
                             
                           
                           ) 
                         
                         2 
                       
                     
                   
                 
               
             
           
           
             
               
                 
                   with 
                   ⁢ 
                   
                       
                   
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                 = 
                 
                   
                     
                       y 
                       3 
                     
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                     f 
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   Solving for W for each array port results in a per-array port W distance shown as  202 ,  204 ,  206 ,  208 , each of which is computed from the above formulas based on x,y position, and is added to the equal length array port waveguide to arrive at the overall length for each waveguide  104 - 1  through  104 - m  of  FIG. 1 . 
   PRIOR ART 
   U.S. Pat. Nos. 4,490,723 and 3,761,936 describe a Rotman lens of stripline construction, whereby a plurality of array ports is coupled to a plurality of beam ports on opposite sides of a lens region, where all of the components are formed from stripline conductors fabricated on printed circuit boards. 
   U.S. Pat. No. 6,130,653 describes a stripline Rotman lens using trace delay equalization of the inner ports compared to the outer ports. 
   U.S. Pat. No. 5,677,697 describes a system for controlling the beam scan on a Rotman lens using phase heterodyning. 
   U.S. Pat. No. 5,003,315 describes a lens feed transmission line for varying the feed lengths to the ports of a Rotman lens. 
   U.S. Pat. No. 6,031,501 describes a waveguide beam forming lens which includes power dividers and combiners which also provide for λ/2 port aperture spacings. 
   OBJECTS OF THE INVENTION 
   A first object of this invention is a beam forming lens having substantially frequency independent beam pointing angles and low internal losses, the beam forming lens having a plurality of beam ports, each beam port having a power divider for coupling energy from a waveguide to a plurality of beam port apertures and thereafter into a lens region, where the lens region has a waveguide height Wh 2  greater than 1.8 times that of the waveguide height Wh 1 , whereby on the opposite side of the lens region, the power is coupled into a plurality of array ports apertures, the array port apertures coupling power from an adjacent pair of array port apertures into an array port waveguide using an array port combiner and transformer, the beam forming lens also having a plurality of dummy ports coupled to a parallel plate lens region and positioned between the plurality of beam port apertures and array port apertures. 
   A second object of the invention is a parallel plate beam forming lens formed from a first and second plate having a first planar surface therebetween, the first and second plate forming beam port waveguides substantially centered about the common first and second plate planar surface, where a second planar surface is formed opposite the second plate planar surface and adjacent to a third parallel plate, where the first, second, and third plates form a feedthrough waveguide which is coupled to a jog waveguide that is centered about the second planar surface, the jog waveguide thereafter coupled to a beam port divider coupling power through beam divider apertures into a lens region, the opposite side of which is coupled to a plurality of array port apertures which sum power into an array port waveguide. The lens region also has dummy ports positioned between the plurality of beam port apertures and array port apertures. The beam port divider and apertures, lens region, array port dividers and apertures, dummy ports, and array port waveguides are positioned symmetrically about the second and third parallel plate second planar surface, whereas the beam port waveguides are positioned symmetrically about the first and second parallel plate first planar surface. 
   A third object of the invention is an array port power divider/combiner which couples efficiently to a waveguide and produces improved radiation patterns inside of a lens region, the array port power divider/combiner including an array port waveguide input having a first height, an array port divider including a matching region with increasing waveguide height steps to a second height, an array port septum having a resistive surface and the second height, and array port waveguide outputs having a second height. 
   A fourth object of the invention is a beam port power divider/combiner which couples efficiently to a waveguide and produces improved radiation patterns inside of a lens region, the beam port power divider including a beam port waveguide input having a multi-stage divider, the multi-stage divider having a first divider including a first divider waveguide input, a first divider resistive septum, and a pair of first divider outputs, each first divider output coupled to a second divider including a second divider waveguide input, a second divider resistive septum, and a pair of second divider outputs, whereby the second divider outputs have apertures which are adjacent to the parallel plate lens region. 
   A fifth object of the invention is a feedthrough waveguide structure for coupling power from a first waveguide to a second waveguide through an aperture positioned between the first and second waveguide. 
   SUMMARY OF THE INVENTION 
   In a first embodiment of the invention, a waveguide beam forming lens is formed from a first plurality of substantially uniform length beam port waveguides, each of which is coupled to a beam port divider which comprises a first divider including a vertical resistive septum which is coupled to first divider outputs, each first divider output coupled to a second divider including a vertical resistive septum forming a pair of output waveguides leading to the parallel plate lens region. Opposite the beam port waveguides are the array port waveguides which include uniform length waveguides individually modified by the Rotman W values described earlier, each of which are coupled to an array port divider, each array port divider comprising a waveguide height increase forming a transformer, a vertical septum having a resistive surface, and a pair of array port divider output waveguides which terminate into the parallel plate lens region. Dummy ports are placed between the contiguous ports of the array port apertures and contiguous ports of the beam port apertures, and each dummy port comprises a waveguide with height Wh 2  having an aperture leading to the parallel plate lens region which also has a height Wh 2 , the aperture including a termination having a first resistor and a second resistor, each resistor formed from substrate having a surface film of resistive material deposited on one side, the first and second resistors placed substantially parallel to the plates of the parallel plate lens region with separations from each other and the parallel plates so as to attenuate both TE20 and TE10 modes. 
   In a second embodiment of the invention, a beam forming lens comprises a lens region, beam port dividers having a first divider and a pair of second dividers with apertures coupled to the lens region, feedthough and jog waveguides for creating equal-length beam port waveguides, array port dividers having apertures also coupled to the lens region, and array port waveguides for creating equal length beam port waveguides. The structures are formed from a first substantially planar plate, which is placed adjacent to a second plate and having a first substantially planar contact surface, and a third substantially planar plate is placed adjacent to the opposite side of the second plate, thereby creating a second substantially planar surface. The first and second plates are used to form the beam waveguides, and the first, second, and third plates are used to form the feedthrough waveguides. The beam port dividers, lens region, and array port dividers are formed symmetrically about the second planar contact surface. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  is a top view of a prior art Rotman lens microwave device. 
       FIG. 2  shows the geometrical construction constraints of a Rotman lens. 
       FIG. 3  shows a waveguide beam forming lens of the present invention. 
       FIGS. 3A ,  3 B,  3 C,  3 D,  3 E,  3 F,  3 G,  3 H,  3 I and  3 J show various section views of the beam forming lens of  FIG. 3 . 
       FIG. 4A  shows the top view of an array port of  FIG. 3 . 
       FIG. 4B  shows a section view of  FIG. 4A . 
       FIG. 4C  shows a section view of  FIG. 4A . 
       FIG. 4D  shows a detail view of  FIG. 4A . 
       FIG. 5A  shows the top view of a beam port of  FIG. 3 . 
       FIG. 5B  shows a section view of  FIG. 5A . 
       FIG. 5C  shows a section view of  FIG. 5A . 
       FIG. 6A  shows the top view of a dummy port of  FIG. 3 . 
       FIG. 6B  shows a section view of  FIG. 6A . 
       FIG. 6C  shows a section view of  FIG. 6A . 
       FIG. 6D  shows a detail view of  FIG. 6A . 
       FIG. 7  shows a jog feedthrough waveguide. 
       FIGS. 7A ,  7 B,  7 C, and  7 D show various section views of  FIG. 7 . 
   

   DETAILED DESCRIPTION OF THE INVENTION 
   In the discussion of the prior art, an increased waveguide height Wh resulted in reduced phase velocity dependence on frequency, which reduces undesired frequency scan, however this increased waveguide height Wh comes at the expense of introducing higher order modes into the lens and waveguide regions which would share this same Wh dimension. The higher order modes represent power loss and increased sidelobes in the resulting radiation pattern. It is desired to increase Wh to the largest practical value in the lens region to minimize frequency scan and decrease insertion loss while minimizing the generation of higher order modes supported by the increased Wh. In the present invention of  FIG. 3 , the lens region has a Wh 2  dimension which is selected to be just below the TE30 mode cutoff Wh 2 , thereby suppressing TE30 modes. The lens height Wh then supports only TE10 and TE20 modes, and the reflected TE20 modes in the lens region  310  are suppressed via dummy ports  306 , which have a resistive planar film placed in a region which preferentially attenuates TE20 mode compared to TE10 but attenuates both modes. Wh is stepped from a lens height Wh 2  which supports TE10 and TE20 but does not support TE30, down to a height Wh 1  which only supports TE10 in the beam port aperture region and in the array port divider region. Waveguide regions  330  and  336  have a waveguide height Wh 1  which supports only TE10 mode, and the height of the waveguide Wh 2  in the lens region  310  is increased to more than 1.8*Wh 1 . By carefully coupling power from the waveguides  330 ,  336  having Wh 1  to the lens region  310  having larger Wh 2 , and by adding dummy ports with special terminations suitable for attenuation and absorption of TE20 modes, a beam forming lens with reduced frequency scan reduced insertion loss and reduced reflected high-order lens modes can be realized. 
     FIG. 3  shows an embodiment of the waveguide beam forming lens  300  of the present invention, which includes beam ports  316 , each of which is coupled to a beam port waveguide  330  in waveguide region  308 , which is thereafter coupled to a feed-through structure and offset jog waveguide region  312  prior to being fed to beam port divider  304 , as will be discussed later, where the beam port divider  304  comprises a multi-level power divider which separates the incoming waveguide power into four adjacent beam port apertures opening into the parallel plate lens region  310 . On the opposite end of the beam ports  316  and parallel plate lens  310  are array ports  318 , where the array ports  318  each have waveguides  340  which feed into a waveguide path equalizer region  326  having waveguide feedthroughs and jogs, and thereafter into an array port divider  302  which has apertures opening into the lens region  310 . The array port divider  302  comprises a transformer formed from a change in height of the array port waveguide in the z axis (perpendicular to the parallel plates) after which an array port divider provides power to an adjacent pair of array port apertures in the lens region. The beam port divider  304  comprises a first divider which uses a conductive or resistive septum to convert a single first port common to the waveguide into two second ports, where each second port feeds a second divider, and each second divider similarly has a first port and a pair of second ports, where the second divider first port is coupled to the first divider second port, and each second divider second port has an output aperture coupled to the parallel plate lens region. In this manner, each beam port waveguide  330  is coupled to four beam port apertures which are adjacent to each other. The beam forming lens  300  also includes a plurality of dummy ports  306 , which are placed between the continuous series of array port apertures and continuous series of beam port apertures. An additional feature of the lens of  FIG. 3  is that the paths through each beam port waveguide  330  to each beam port divider  304  has as components a wavelength length Lb 1 , a feedthrough and jog waveguide length Lb 2 , and a lens waveguide length Lb 3 , and it is desired to make the sum Lb 1 +Lb 2 +Lb 3  equal across all waveguide regions by varying path length Lb 2 . This is accomplished using a set of serpentine folds and bends (not shown) in feedthrough and jog waveguide region  312 . Similarly, it is desired to form each of the array port waveguides such as  340 ,  338 , and  336  such that the array port waveguide length sum La 1 +La 2 +La 3  is equal across all array ports, and where the per-port incremental waveguide length governed by the Rotman waveguide length (Rotman W) parameter is preferably provided by array port divider  302  structure, or alternatively incorporated into the waveguide  336 ,  338 , or  360  length. 
     FIG. 3I  shows a beam port or array port waveguide with the different TE modes also included for reference. Each TE mode requires an additional lambda/2 in waveguide height Wh, and if the physical dimension of Wh is less than that required to support this particular mode, the mode is fully suppressed and does not propagate. Waveguide  358  has a height Wh 1 , shown in the example as 0.188″ for 45.5 Ghz operation. Since TE10 has a lambda/2 dimension of approximately 0.129″ at 45.5 Ghz, waveguide  358  will only support TE10 mode  352 , and the higher modes TE20  354  and TE30  356  are suppressed.  FIG. 3J  shows the lens region  360 , which has an increased height of Wh 2 , shown as 0.35″ at 45.5 Ghz. This value of Wh 2  is sufficient to support TE10  352  and TE20  354 , but is selected to be inadequate to support TE30. In this manner, the waveguide height Wh is selected to provide support exclusively for TE10. 
     FIGS. 3A through 3H  show various cross section views corresponding to sections A-A through H-H, respectively, of  FIG. 3 , which are intended to show one particular way of fabricating a beam forming lens of the present invention using a top or first plate  324 , a middle or second plate  322 , and a bottom or third plate  320 , each plate being substantially parallel and having a substantially planer first contact surface  323  and a substantially planar second contact surface  321 . The structures of the beam forming lens are positioned such that they may be formed by machining features into each plate, and the structures are completed in form when the plates are placed in contact across the first contact surface  323  and second contact surface  321 , as shown in  FIGS. 3A through 3H .  FIGS. 3A and 3H  show different views of a cross section of the beam port waveguides  330  in region  308  of  FIG. 3 , which are formed symmetrically on the shared first surface  323  of first parallel plate  324  and second parallel plate  322 .  FIG. 3B  shows a cross section view of a feedthrough waveguide  325  formed on first plate  324 , second plate  322 , and third plate  320 , followed by a jog waveguide  327  shown in  FIG. 3H  formed form the second plate  322  and third plate  320  in region  312 , each structure of which enables microwave energy to couple from one nominal z axis position to another with minimum loss and reflection.  FIG. 3C  shows the output of the jog waveguide  334  centered about the second contact surface  321  of the second parallel plate  322  and the third parallel plate  320 . The beam port divider  304  of  FIG. 3H  includes an aperture which couples energy to parallel plate lens region  310  shown in  FIG. 3D , which is formed from the second parallel plate  322  and third parallel plate  320 .  FIG. 3E  shows the outputs of the array port divider/transformer  304  with reduced waveguide  336  height Wh in region  336 .  FIG. 3F  shows the feedthrough waveguides in the region where waveguide paths are used as in the prior art to equalize the waveguide length sum La 1 +La 2 +La 3  of  FIG. 3  by selecting La 2 , and  FIG. 3G  shows the beam port waveguides  340  at the exit point of the beam forming lens structure  300 .  FIG. 3H  follows a section H-H of the structure which follows the waveguide and lens structures continuously for clarity, rather than in planar section.  FIG. 3H  thereby shows the parallel plate construction and z-axis structure for, in sequence, the beam waveguide  308 , feedthrough  325 , jog waveguide  327 , beam port divider  304 , parallel plate lens region  310 , array port divider and transformer  302 , array port jog and feedthrough section  338  including length equalization, and array port waveguide  340 . 
   A single array port divider  302  of  FIG. 3  is shown in detailed top view  FIG. 4A , where the array port waveguide  402  encounters a transformer, or impedance matching network comprising a first transition step height change  408  to Ht and then to a final lens height change Hf  410  in the direction of propagation of waveguide  402 , followed by a separation  416  of a fixed value such as 0.5 inches plus the per-port Rotman W value described in  FIG. 2  and preceding equations. This is followed by resistive septum  404  which couples power into the parallel plate lens region via array port apertures  406  and  414 .  FIG. 4B  shows section A-A of  FIG. 4A , including a transformer where the waveguide  402  has a first height such as Hw of 0.188 inch, a transition height Ht of 0.256 inch, and a final height Hf of 0.35 inch. These heights correspond to best performance for EHF-band microwave TE mode waves in the range of 40 GHz-50 GHz.  FIG. 4C  shows the array port cross section B-B of  FIG. 4A , where the section includes the array port waveguide  402 , step transition  408 , and array port final region  410 .  FIG. 4D  shows additional detail of the resistive septum  404  of  FIGS. 4A and 4B . The resistive septum  404  of  FIG. 4D  is formed from a first substrate  440  with resistive surface  446  interacting with propagating waves and second substrate  442  with resistive surface  448  on the opposite side, also interacting with propagating waves in the waveguide. The septum  404  is fitted into a slot  452  in first divider output waveguide structure  450 . Adjacent to first septum  404  are also shown waveguide  402 , transition step  408 , and final step  410 . 
     FIG. 5A  shows the detail of a beam port such as  304  of  FIG. 3 . Beam port waveguide  502  leads to first divider  504 , which includes a resistive septum  510  fabricated from a first and second substrate, each with a resistive coating placed on opposite surfaces, as was previously described for the array port waveguide. Section D-D of  FIG. 5A , shown in  FIG. 5C  details first divider  504 , which includes a step change from a waveguide height  544  of 0.188 to a final height  542  of 0.375, and the first divider septum  510  also follows this step change in height. Each output from the first divider is coupled to a pair of second dividers, one of which is shown as  506 , and includes an input waveguide of final height, a septum  508  formed from a pair of substrates, each having a resistive surface placed on opposing surfaces, as was described earlier. 
     FIG. 6A  shows a dummy port such as  306  of  FIG. 3 . The dummy port comprises an aperture  612  which is common to the parallel plate lens region  310  of  FIG. 3 , with each aperture having a first resistive wedge  608  and a second resistive wedge  610  placed at approximately ⅓ of the waveguide height from each parallel plate surface. In the preferred mode, the first resistor  608  and second resistor  610  are placed at z-axis heights which result in maximum attenuation for TE20 mode  620  compared to TE10 mode  622 , such as shown at the maximum amplitude points of TE20  620 . This preferential attenuation of TE20 over TE10 may be realized by a separation distance from each resistor to the adjacent lens surface which ranges from ⅛*Wh 2  to ⅓*Wh 2 . The wedges  608  and  610  are supported in place by insulators  602 ,  604 , and  606 . The resistive wedges  608  and  610  are fabricated from a substrate material with a resistive surface applied to one side, as shown in resistive deposition coating  640  applied to wedge  608  and resistive deposition coating  648  applied to wedge  610  of detail  FIG. 6D . 
     FIG. 7  shows a feedthrough  710  and jog  712  used in beam port length equalization region  312  and array port length equalization region  326  of  FIG. 3 . Feedthrough  710  and jog  712  are formed from first plate  324 , second plate  322 , and third plate  320 , as shown in section views of  7 A,  7 B,  7 C, and  7 D. Feedthrough  710  is formed from array port or beam port waveguide  702  with is formed from first plate  324  and second plate  322 . A coupling aperture  704  enables the wave energy to couple from outer waveguide  702  to inner waveguide  706 , which is then provided with a jog waveguide  712  which offsets inner waveguide  706  to a z axis location which is symmetric about the second layer interface between second layer  322  and third layer  320 . The feedthrough aperture  704  has a width Wa which is less than the waveguide width Ww for either the first waveguide  702  or second waveguide  706  located on either side of the feedthrough aperture  704 . Additionally, the first waveguide has a terminus  722  (shown in  FIG. 7A ) which is located more than 2 wavelengths from the aperture  704 , while the second waveguide has a terminus  724  (shown in  FIG. 7C ) which is more than 2 wavelengths from aperture  704  and located on the opposite side of the terminus of the first waveguide. As was described earlier for the beam port waveguides and array port waveguides, the equalization of length and incorporation of Rotman W parameters in the array port waveguides may be accomplished by a series of length-adding serpentine bends  720 .