408 THE BELL !^YSTEM TErilXirAL JOURNAL, MARCH 1957 



knic coupler design. A single row of longitudinal coupling slots which 

 are not resonant in the 6- or 11-kmc bands is used. The radius of a round 

 hole ecjuivalent to the slot is obtained as in Appendix I, In' setting 

 ir' = Pf. 



Impedance matching of the coupling array and of the loading elements 

 is accomplished by tapering the amplitude of the end elements as indi- 

 cated b}' a discrimination function of the coupled wave theory. For a 

 5 element series 1 —th —n^ —ui — 1 



^ 'lin, + 1) + n. 



■<" 



47rZ , SttZX , (22) 



1 cos — h cos ^,^ 1 + n-i 



where Z is the spacing between elements. 



The discrimination D is set equal to infinit}^ which permits the de- 

 nominator to be set equal to zero and solved simultaneously for ?h and 

 Ho by using both band edge wave-lengths. Round hole sizes are readily 

 obtained .since the coupling coefficient is directly proportional to the 

 cube of the hole radius from which the necessary equivalent longitudinal 

 slot can be calculated. Susceptance values of the capacitive posts are 

 found from the absolute value of the reflection coefficient which equals 



ho 



REFERENCES 



1. S. E. Miller, Waveguide as a Communication Medium, B.S.T.J., Nov., 1954. 



2. A. T. Corbin and A. S. May, Broadband Horn Reflector Antenna. Bell Labora- 



tories Record. 33, p. 401, Nov.. 1955. 



3. A. P. King, Dominant Wave Transmi.ssion Characteristics of a Multimode 



Round Waveguide, Proc. I.R.E., 40, Aug., 1952. 



4. S. E. ^liller, Coupled Wave Theory and Waveguide Applications, B. S.T.J. , 



Mav, 1954. (See page 681.) 



5. H. A. Bethe, Physical Review, 66, p. 63, 1944. Also Report 43-22, Lumped 



Constants for Small Irises, Mar. 24, 1943; Report 43-26, Formal Theory of 

 Wave Guides of Arbitrary Cross Section, Mar. 16, 1943; and Report 43-27, 

 Theory of Side Windows in Wave Guides, Apr. 4, 1943; from M.I.T. Radia- 

 tion Lab. 



6. X. Marcuvitz, Waveguide Handbook, p. 408, McGraw HiU. 



7. H. Seidel, private communication re: Slab Width Determination and Effects 



on Coupling Parameters in Partial Dielectric Loading. 



8. S. B. Cohn, Determination of Aperture Parameters by Electrolytic Tank Meas- 



urements, Proc. I.R.E., Nov., 1951. 



9. J. C. Slater, Microwave Electronics, p. 183, Van Xostrand. 



