BAXD WIDTH A\D TRAXSMISSIOX PERFORMANCE 537 



results illustrate the properties of PCM as a means of converting bandwidth 

 into transmission advantage. 



The PCM-FM entries are taken from the curves of Fig. 16 plotted for 

 noise 12 db down. Curves are also given in Fig. 16 for noise 18 db down. 

 It will be noted that the bandwidths indicated become smaller when the 

 noise is required to be farther down, but that the power requirements become 

 greater because the bandwidth reduction factor is less than the factor multi- 

 plying the r-f signal-to-noise ratio. 



The columns at the right in Tables II and III show the bandwidths which 

 must be employed in order to attain a 60 db signal-to-interference ratio in 

 the presence of one source of interference whose amplitude is just marginal 

 for the type of system concerned. 



Tables IV and \' are prepared from another point of view — that of con- 

 serving bandwidth-^ instead of power. The systems particularly suited for 

 narrow bands such as FDM and PAM-AM have been added to the Ust. 

 The actual minimum bandwidths are, in many cases, determined by engi- 

 neering judgment; smaller values than those tabulated may be possible at 

 the expense of greatly increased power and precision requirements. Thus 

 in the case of PPM-AM we have arbitrarily chosen 40 mc as necessary for 

 1000 4-kc channels. According to our initial postulate the audio signal- 

 to-noise ratio vanishes at 2>2 mc, and indefinitely great signal power would 

 be required as we approach this limit. In PAM-AM we have assumed that 

 pulses in adjacent channels just touch, thereby setting the bandwidth at 

 32 mc. Smaller bandwidths could be used if the pulses were allowed to 

 overlap. This would reduce the allowable duration of the channel gate 

 and deprive the system of some of its tolerance to similar system interference 

 as well as noise. The maximum pulse power required for 100% modulation 

 is tabulated. If instantaneous sampling were used this would be 6 db above 

 the unmodulated pulse power which is, in turn, 38 db above the mean total 

 fluctuation power accumulated in a 32-mc band from 133 spans. We have 

 reduced the value of power thus computed by 1.7 db to allow for a calculated 

 improvement in signal-to-noise ratio obtainable by gating at the channel 

 input with a time function of the same shape as the signal pulse. 



The FM systems listed are of two kinds. The first is a relatively narrow- 

 band type in which advantages such as relative immunity to gain fluctua- 

 tion and amplitude non-linearity are sought with small increment in band- 

 width over AM. Since these objectives are not sufficient in themselves to 

 fix the actual bandwidth needed, an arbitrary additional requirement has 



2« We do not here entertain the idea of using certain exchange methods to permit use of 

 less band width than the conventional minimum of 4 kc per channel, but rather to use 

 modest amounts of additional band width. Appendix III discusses briefly a band reduc- 

 tion principle. 



