674 



THE BELL SYSTEM TECHNICAL JOURNAL, MAY 1954 



in undesired mode response at the same value of 



L _ LViY- +- 



Ai A2/ \Ai X2 



as for uniform strength couplmgs equally spaced. Fig. 11 shows the latter 

 relation, a very useful yardstick with which to evaluate the extra coupling 

 length required by less ideal but more easily constructed coupling distri- 

 butions. 



An important practical question is "What is the smallest number of 

 point couplings which will satisfy requirements in a given stiuation?", 

 for it is time-consuming and expensive to fabricate the coupUng holes or 

 probes in some circumstances. The large range of possible mode condi- 

 tions and discrimination requirements makes it difficult to give an answ^er 

 in closed form, but the general restrictions involved may be stated. In 

 the case of n equally spaced couplings (of any amplitude taper) the dis- 

 crimination vanishes at d/w = (n — 1). This is illustrated by the dis- 

 crimination plot of Fig. 12. 



Moreover, it is found that equally spaced couplings produce discrimina- 

 tions which are periodic in d/w on the interval (n — 1), and which are 

 symmetrical about O/t = (w — l)/2. 



The implication of the discrimination zero at d/w = (n — 1) is that a 

 large number of point couplings are required to get good directivity and 

 good forward wave discrimination. In the simple case cited above in 

 which L = 20Xo , the O/t value for directivity was shown to be 33.3. 



t 20 





.L 



1 



0123456789 



e 



77 



Fig. 12 — Discrimination for 8 equal-strengtli point couplings equallj^ spaced. 



