4 



392 THE BELL SYSTEM TECHXIf'AL JOUKXAL, MARCH 1957 



separated one at a time at the antenna end of the arraj'. The 6-kmc bands 

 are separated next and the 11-kmc bands are added or removed at the 

 far end of the array. 



GENERAL OBJECTIVES 



Neghgiblc loss of power should result when coupling TEio° waves 

 to TEu° waves for the six bands concerned.* The 6- and 11-kmc waves of 

 both polarizations must pass through the round guide of the 4-kmc 

 transducers without significant attenuation. Waves in the 11-kmc band 

 must also pass through the circular guide of the 6-kmc transducers 

 without appreciable loss. A good impedance match is desired at all 

 ports. No cross coupling is desired between the orthogonally polarized 

 waves in the round guide. 



FUXDAMEXTAL PROBLEMS EXCOUXTERED 



The frequency-selectivit}^ required to separate various bands in the 

 same polarization can be achieved in a coupled-wave device bj^ either 

 varying the coupling coefficient and/or var\'ing the phase constant, as 

 illustrated by the expression for the amplitude of the selected wave:^ 



E\ = , :„ ==^,,Ax/\^[^-^^^\\cx (1) 



7rTfiiy--it^-(-)'l 



Avhere c = coupling coefficient 



X = length of coupling array 



jS = phase constant 



In the present designs some of the frequency selectivity is in the coupling 

 holes. The greater part of the selecti^'ity is in the design of the phase 

 constants; the\' are made equal in the band to be selected (|(3i — /3o = 0) 

 and ver}^ unequal 



(' 



2c > 



in the frequency bands to be passed. 



The size of the coupling hole must be controlled to avoid coupling hole 

 resonance in any of the three bands that may be present. This problem 

 is especially bothersome in the 4 kmc coupler where signals are present 



* As used in this article, superscripts O and D refer to round and rectang- 

 ular waveguides, respectively. 



