278 BELL SYSTEM TECHNICAL JOURNAL 



ratio is unity for an ideally designed selective circuit, and can actually 

 be made to approximate closely to unity with correctly designed band- 

 filters. Formula (14) is believed to have very considerable value in 

 comparing various circuits designed to eliminate interference, and is 

 easily computed graphically when the frequency characteristics of 

 the selective circuit are specified. 



The general propositions dediicihle from ii ina\' be briefiy listed 

 and discussed as follows: 



With a signaling frequencv range -^ - — ' specified, the upper limiting 



Ztt 



value of S ivilh a theoretically ideal selective circuit is , and the 



(a>2 — o)i) 



excellence of the actual circuit is measured by the closeness with 'which 



its figure of merit approaches this limiting value. 



I'ormula (14) for the figure of merit S has been applied to the study 

 of the optimum design of selective circuits and to an analysis of a 

 large number of arrangements designed to eliminate or reduce static 

 interference. The outstanding conclusions from this study may be 

 briefly reviewed and summarized as follows : 



The form of the integrals a and p. taking into account the signaling 

 requirements, shows that the optimum selective circuit, as measured 

 by S, is one which has a constant transfer impedance over the signaling 



frequencv range ^^ — '-, and attenuates as shar[)lv as possible 



currents of all frequencies outside this range. Ncnv this is precisely 

 the ideal to which the band filter, when properly designed and termi- 

 nated, closely approximates, and leads to the inference that the wave 

 filter is the best possible form of selective circuit, as regards random 

 interference. Its superioritv' from the steadv-state viewpoint has, of 

 course, long been known. 



An investigation of the effect of securing extremely high selectivity 

 by means of filters of a large number of sections was matle, and led 

 to the following conclusion: 



In the case of an efficientl>' designed Inmd-tilter, terminated in the 

 proper resistance to substantially eliminate reflection losses, the 

 figure of merit is given to a good approximation by the equation 



5=_J_ __i 



(j>i — W\ 1-|-1/H)M- 



wliere n is the number of filter sections and -^- ^ tlu' transmission 



band. 1 1 follows that the selective figure of merit increases inappreciably 

 with an increase in the number of filter sections beyond 2, and that the 



