BAND U IDTU AND TRANSMISSION PERFORMANCE 581 



its description not 64 values but only 2, the number of possible amplitudes 

 would be 2\ With some of the better transmission circuits in existence, as 

 many as 10 such channels could be multiplexed in the same bandwidth re- 

 quired by one channel, by this adaptation of the PCM method. 



The above considerations show that PCM offers the means of matching 

 the transmission signal to the capabilities of the transmission circuit in order 

 to transmit the maximum amount of information. As has been shown, with 

 microwave telephone systems the economical balance seems to come well 

 over on the wide band side, permitting operation with low transmitted power 

 through relatively strong interference. 



APPENDIX IV 



Supplementary details of derivation of bandwidth-curves 



PPM-AM 



The diagram of Fig. 8 shows that the maximum time deviation is assumed 

 to be 



e = — -T = — - -. (1) 



2Nfr 2Nfr Fb 



The shift in time produced by an interfering voltage of magnitude E„ at the 

 slicing instant is 



At = En/s (2) 



where s is the slope of the signal pulse at the slicing instant. For small noise 

 the slicing instant occurs near half the peak, £, of the pulse and the slope of 

 the assumed sinusoidal pulse (Fig. 6) is : 



Hence 



irFbE 



The signal-to-noise power ratio in the channel is the ratio of mean square 

 values of signal deviation cr and A/. For thermal noise we assume that the 

 root mean square value is one fourth the peak and place the peak at l/\/2 

 times E/2 for marginal operation. We write, therefore, 



En = E/2V2, Afi = i-iEl/T- fIe") /16 (5) 



2 



"~2 C 



" =2 



Vjl -iY^^i"-^ -lY 



2V2A7r fJ 2Fl\2Nfr ) 



^/-^-(w.- 0=^^(4-0 



(6) 



(7) 



