800 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1953 



4,000 cycles or below 300 cycles in message channels of supergroups 

 other than Nos. 113 and 114 would fall close to 4,000 cycles in a program 

 circuit where there is high susceptibility to interference. 



2.19 Uncertainties 



In the early stages of system design, firm decisions have to be made 

 on such matters as repeater spacing, bandwidth, and component char- 

 acteristics. These decisions must be based on a detailed signal-to-noise 

 analysis which in turn involves many judgements of repeater perfor- 

 mance parameters, tolerable system requirements and the effects of 

 signal mechanisms on system performance. It would be easy and safe 

 to engineer the system to provide enough signal-to-noise margin to 

 cover the uncertainties in each of these judgements. Conservative en- 

 gineering of this type could easily have justified a repeater spacing of 

 three miles instead of the four miles actually chosen. Instead, an effort 

 was made to estimate a "mid-range" or most probable value for each 

 performance, requirement or mechanism factor entering into the signal- 

 to-noise design. In addition, a "probable" uncertainty was estimated 

 for each critical parameter. This was usually taken as one third of the 

 maximum foreseeable error in the estimate. Finally, these uncertainties 

 in electron tube modulation, realizable feedback, network impedances, 

 channel requirements, interaction laws between signals and a myriad 

 of other factors were all translated by the signal-to-noise analysis into 

 their effect in db on the television channel signal-to-noise performance. 

 On this basis, the "probable" uncertainties were summed on an rss 

 basis to find the "probable" uncertainty in the overall design. Whereas 

 the direct addition of the probable uncertainties gave a figure of about 20 

 db uncertainty in the design, the rss addition indicated about six db 

 uncertainty. It was then argued that during the ensuing years of develop- 

 ment the probability of finding all the judgements to be wrong in the 

 same sense was extremely small. On the other hand it was deemed reason- 

 able to provide enough margin so that there would be perhaps a 75 per 

 cent chance of not exceeding the margin. Six db of margin was therefore 

 provided, half by clear margin and half by having available economically 

 feasible changes in system design such as a decrease in the telephone 

 channel frogging interval. Any further error in judgement would then 

 have to be taken up i)y degrading performance below the desired ob- 

 jectives. As the system design proceeded, the early judgements were 

 changed in considerable measure. Likewise, numerous additional system 

 parameters were introduced. However, at no point in the system plan- 



