712 THE BELL SYSTEM TECHNICAL JOUKNAL, MAY 1954 



in very broad band mode-selective characteristics, as has been demon- 

 strated. 



The transfer loss characteristics are in general a function of frequency, 

 since the individual coupling holes are somewhat frequency selective. 

 There may be applications wherein less variation in transfer loss as a 

 function of frequency is required. One approach to this problem is to 

 make the coupling holes individually have less coupling variation with 

 frequency; since the total coupling loss between two identical transmis- 

 sion lines is a function only of number of coupling holes and the loss per 

 hole (equations (39) and (40)) constant coupling per hole will produce 

 constant coupling overall. Riblet and Saad have reported on this ap- 

 proach. 



There is another approach to obtaining flat coupling versus frequency 

 despite variations in the coupling per hole, and that is to intentionally 

 create a difference between the phase constants of the two coupled lines. 

 Fig. 17 illustrates the transfer characteristic when the coupled lines have 

 unequal phase constant, and either identical or negligible attenuation 

 constants. Near the maximum for the transferred wave | E2* \ there is a 

 region wherein the transfer loss is independent of coupling strength, and 

 the transfer loss in this flat-loss region is under control of the ratio 

 (iSi — ^2)/c. Hence for a given transfer loss there is an optimum ratio of 

 phase constant difference to coupling strength in order to minimize the 

 overall transfer loss variation. For the distributed coupling case, equa- 

 tions (31) and (32) represent the transferred wave amplitude and show 

 that the transferred wave goes through a maximum as a function of 

 integrated coupling strength ex, when 



/• 



<»^'+„..; + „ w 



The transferred amplitude at this maximum point is 



1 



1/^ 



-^.r^, 



(43) 



4c2 

 The integrated coupling strength at the maximum point is 



Co-'Co = /v^ ^ x ^f^ • K • (44) 



IT 



/^^T^+^ ' 



For the important case of an optimum 3 db transfer loss coupler, E->* 

 is 0.707. Then (^i — l32)/c equals 2 and CoXo equals 7r/2-\/2 from (43) 



