the following description of the preferred embodiment describes a four - port rectangular te 10 to circular te 01 mode transducer . it is to be clearly understood , however , that this invention comprehends an n - port device . referring now to the drawings , fig1 is a plan view of a four - port rectangular te 10 to circular te 01 mode transducer 10 . transducer 10 is shown divided into sections 1 , 2 and 3 , indicated at 12 , 14 and 16 respectively and is done for purposes of illustration only . fig2 shows section 1 with a cylindrical end 18 and an end 20 wherein the cylinder has been divided into four arms . it is noted that the number of arms is equal to n , the number of ports . fig3 shows section 2 with an end 22 corresponding to end 20 of section 1 and a second end 24 . fig4 shows section 3 with one end 26 corresponding to end 24 of section 2 and an end 28 . end 18 of section 1 is connected to a circular waveguide , not shown , and end 28 is connected to four individual rectangular waveguides , not shown . fig5 shows section aa of fig2 and arrow 30 indicates the electric field pattern . the direction of the arrows indicating the electric field pattern indicates relative polarizations and the length of the arrows indicates relative electric field strength . fig6 shows section bb of fig2 and arrows 32 indicate the electric field patterns . fig7 shows section cc of fig3 and arrows 34 indicate the electric field patterns . similarly fig8 and 10 show sections dd and ee of fig3 and 4 and arrows 36 , 38 and 40 indicate electric field patterns present at each section . section 1 , shown in fig2 transforms the circular te 01 mode , indicated by arrow 30 , fig5 to an intermediate mode , indicated by arrows 32 , fig6 and when n = 4 the intermediate mode is a cross - shaped te 22 + . section 2 , shown in fig3 converts the intermediate mode into n te 10 modes . the n - sided pyramidal structure 42 transitions the intermediate mode into n rectangular te 10 modes . with n = 4 the pyramidal structure has four sides and a square base 44 . the apex 46 of the pyramid is located in the center of the device at approximately the intersection of sections 1 and 2 . at the apex 46 of the pyramidal structure 42 the electric field is nearly zero ( on the axis ) for minimal field perturbation . the outer arc - shaped boundaries , indicated at 48 in fig2 and 6 , of each arm 50 gradually transition to straight waveguide walls , indicated at 52 in fig3 and 9 , along the length of section 2 . the transition is indicated at 49 , fig1 . at the position indicated by cross - section ee , fig3 and 9 , the base 44 of pyramid 42 has divided arms 50 into four spatially independent rectangular waveguides . in section 3 , fig4 the rectangular waveguides continue to separate spatially and at the position indicated by section ff in fig4 and 10 , four standard rectangular waveguides are attached . with n = 8 , for example , eight standard waveguides would be attached at the position indicated by section ff . fig1 - 13 show detailed dimensions at selected cross sections of section 1 shown in fig1 . the dimensions are given in units of free space wavelengths λ o to allow scaling to any frequency of interest . the length 1 o of each section is at least 31 / 3λ o . a nominal length of 31 / 3λ o is applied here as the basis for computing the cross - sectional dimensions . the inner diameter d indicated at 54 in fig1 and 13 of the overmoded circular end 18 of the transducer and the waveguide to be attached is chosen sufficiently small so that the higher order circular te modes ( i . e ., te om , m = 2 , 3 , . . . ) cannot propagate . the diameter d is large enough , however , to provide low signal distortion in the te 01 mode within about ± 7 % of the center frequency . the arms 50 at section bb , fig1 and 13 , have a dimension t indicated at 56 equivalent to the rectangular waveguides to be attached at the other end of the transducer . for the design illustrated herein , conventional approximately &# 34 ; half - height &# 34 ; waveguides are used , for example , wr284 , where t = w / 2 = 0 . 37λ o where w is the waveguide cross section length . fig1 - 18 show the primary design features of section 2 . the most important design details are the dimensions of the pyramidal structure 42 and the transition of the outer walls of arms 50 from arced , indicated at 48 , fig1 , to straight , indicated at 52 , fig1 . the apex 46 , fig1 , of pyramidal structure 42 is situated on the axis of section 2 and has dimensions of s b = 0 . 04λ o on each side indicated at 53 , fig1 , and is rounded to reduce electric field concentration to reduce arcing . in the center of section b &# 39 ; b &# 39 ; the electric field is very small and the introduction of apex 46 will not significantly change the electric field patterns . the side dimension s of the pyramidal structure 42 increases by 0 . 1λ o for each 1 . 0λ o increase in length from section b &# 39 ; b &# 39 ; towards section e &# 39 ; e &# 39 ;. the parameter s is determined at an arbitrary distance 1 2 from section b &# 39 ; b &# 39 ; from the following formula : wherein 1 b &# 39 ; g is indicated in fig1 . similarly , s d , indicated at 60 , fig1 , is calculated as follows : at section e &# 39 ; e &# 39 ;, fig1 and 18 , the cross section of pyramidal structure 42 has increased to the extent that the areas of arms 50 are spatially independent whereby four &# 34 ; half - height &# 34 ; rectangular waveguides emerge , each supporting the te 10 mode . the sides of pyramidal structure 42 at section e &# 39 ; e &# 39 ;, fig1 , are equal to t , as indicated at 62 , fig1 . between section b &# 39 ; b &# 39 ;, fig1 , and section gg , fig1 , the cross section of pyramidal structure 42 increases without a corresponding increase in the diameter d of a circle , indicated at 64 , circumscribing arms 50 . in other words , the side of transverse dimension s of the pyramidal structure 42 gradually increases , in accordance with the above equation , in the direction from cross - section b &# 39 ; b &# 39 ; to cross - section g &# 39 ; g &# 39 ;; while the extending arms 50 remain at a constant cross - section ( compare fig1 and 16 ). at section gg the length w indicated at 66 , fig2 , between pyramidal structure 42 and the straight line connecting the ends of the arced outer wall is w = 0 . 793λ o . the dimension w is the long dimension of the &# 34 ; half - height &# 34 ; conventional waveguide for t = 0 . 374λ o . from section gg to section e &# 39 ; e &# 39 ; each arm 50 is fixed at length w from pyramidal structure 42 , therefore , as the pyramidal side length s increases the transducer cross sectional length ( 2w + s ) correspondingly increases . between section gg and section hh , about 0 . 34λ o in length , the outer wall of each of arms 50 transitions in shape from an arc of the circumscribing circle 64 of diameter d to a straight wall as indicated at 49 , fig1 . fig2 - 24 illustrate the details of the transition in wall shape . fig2 illustrates the outer wall shape at section gg which lies 1 . 18λ o from section b &# 39 ; b &# 39 ;. fig2 illustrates the straight outer wall at section hh which lies 1 . 18λ o + 0 . 34λ o from section b &# 39 ; b &# 39 ;. fig2 illustrates an intermediate section between section gg and section hh wherein the pyramidal side s of structure 42 is equal to s c + 0 . 17λ o and lies 1 . 18λ o + 0 . 17λ o from section b &# 39 ; b &# 39 ;. fig1 - 21 show detail of section 3 , the purpose of which is to gradually separate the rectangular waveguide arms 50 until spacing is sufficient to allow couplers to be attached for connection to conventional waveguides . the length of this section also allows damping of any evanescent modes which might arise in the transition . the variable s is no longer interpreted as the side dimension of the cross section of pyramidal structure 42 but as the separation between the inner walls of coplanar waveguides . the formula for computing s versus length 1 3 from section ee is : therefore , the distance s i , fig2 , is calculated as : it is noted that a standard rectangular waveguide stepped - transform match section may be required in each arm 50 of section 3 to optimally match rectangular waveguides to the transducer . for convenience to the reader the applicable dimensions are reproduced in table i as follows : table i______________________________________1 . sub . o = 31 / 3 λ . sub . o s . sub . b = 0 . 04 λ . sub . o1 . sub . b &# 39 ; g = 1 . 18 λ . sub . o s . sub . c = 0 . 158 λ . sub . o1 . sub . gh = 0 . 34 λ . sub . o s . sub . d = 0 . 192 λ . sub . o1 . sub . he &# 39 ; = 1 . 81 λ . sub . o s . sub . e = 0 . 374 λ . sub . o1 . sub . ee = 1 . 67 λ . sub . o s . sub . i = 0 . 54 λ . sub . o1 . sub . ef = 1 . 67 λ . sub . o s . sub . f = 0 . 707 λ . sub . od = 1 . 78 λ . sub . ow = 0 . 793 λ . sub . ot = 0 . 374 λ . sub . o______________________________________ the above dimensions represent the best mode known at the time of filing the present patent application . while the invention has been described with reference to the accompanying drawings and associated dimensions , it is to be clearly understood that the invention is not to be limited to the particular and specific details shown herein as obvious modifications and dimensional variations may be made by those skilled in the art . the scope of the invention should only be construed within the scope of the following claims .