AN EXPERIMENTAL DUAL POLARIZATION ANTENNA FEED 407 



Appendix II 



DESIGN OF 4-KMC COUPLER 



A round guide size is selected so that no modes are cut-off in the three 

 bands. CoupUng power varies with wavelength as shown in (17) for 

 TEio to TEii° coupling. 



Y = 



(17) 



3.413/? 



)■] 



To maintain the minimum variation across the band, the following re- 

 quirements must be met which were deduced from the coupled wave 

 theory and (17). 



sin (cx)i = sin (cx)2 (18) 



(cx)i _ ^0 



(^ ~ i /i / Xo \' (19) 



V \saisr) 



(cx)i + (c.r)2 = T (20) 



The equations are solved for sin ex (the minimum band edge transfer 

 loss) which for a diameter of 2.10" is 0.5 db. A value of 30 db is chosen 

 for a, (2), as the first approximation. Because the band edge transfer 

 loss is 0.5 db due to frequency variation of coupling, an additional loss 

 of only 0.2 db is allowed for the phase constant difference (/3l° — /8°). 

 It is now necessary to make jS*^ = ^l° , where /3l° is the phase constant 

 of the loaded rectangular guide. Equation (21) gives a theoretical periodic 

 loading formula where L is the spacing between loading elements.^ 



cos 0L°L = A cos (i8°L + *) 



lAHU 



Assume initially that L = -k/^^ . The required susceptance 6o of the ca- 

 pacitive rods can be found experimentally from a loaded test line by 

 varying 6o until the first rejection band covers the 6 kmc band. An 

 iterated process is used to find L because it is dependent on j8° which is 

 the parameter being sought. Measurements indicated that (21) does not 

 predict |8° very accurately and for that reason an experimental adjust- 

 ment of (/3l° - /3°) is desirable. 



The guide dimensions are now known; however, they must be cor- 

 rected for the perturbations of the phase velocities as outlined in the 11- 



