HAM) H //>/// AM) TNAXSMISSIO.X I'l.KiORM A \CE >2S 



and this musl jusL make up for the difiference between the 12 db (or 18 dbj 

 FM wave-to-noise ratio and the pulse-to-noise ratios of 18 db -f 20 log 

 {h — 1) required in the AM case. Substituting values from the curves will 

 show that this is so. 



These curves show a minimum bandwidth for an optimum PCM base. 

 'I'his is to be e.xpectcd since two different rates of exchange Ijetween ])and- 

 width and advantage are involved. One is the advantage growing out of 

 PCM of reduced base while the other is the conventional FM advantage. 

 An analogous situation was found in PPM-FM. 



It is of interest to examine the PCM-FM situation when the FM circuit 

 is as tolerant of noise as the most tolerant AM case, namely when the r-f 

 signal-to-noise ratio is 18 db. The optimum PCM base is octonary and the 

 corresponding minimum bandwidth (as we define it) is actually 20% less 

 than for binary AM. This apparent advantage of PCM-FM is not ob- 

 tained when tolerance to C\V and similar systems is considered. Figure 17, 

 which follows, shows that when allowance is made for a 9 db r-f signal-to- 

 interference ratio (as in binary PCM-AM), the minimum FM bandwidth is 

 greater by about 30% than for binary AM and the optimum base is ternary 

 or quaternary. If the 3 db interference tolerance possible in FM is required, 

 it is obtained, as shown in Fig. 17, with ternary PCM-FM, at a cost of ap- 

 proximately twice the bandwidth required in binary PCM-AM, which has a 

 tolerance of 9 db. We should point out here that binary PCM transmitted 

 by single sideband and detected by a local carrier has a tolerance of 3 db 

 and requires half the bandwidth shown in Fig. 16. PCM-FM requires a 

 bandwidth 3.8 times that of single sideband binary PCM for the same 3 db 

 tolerance. 



Fig. 17 — PCM-FM, CW and Similar System Interference 



In PCM, sequences of several pulses of the same amplitude may occur. 

 The FM signal then consists of a steady frequency. A steady beat frequency 

 persisting for several pulse periods will be produced by CW interference." 

 If this beat frequency is Fh the maximum interfering amplitude will be pro- 

 duced. The amplitude is {Q/P) Fb while the step interval is (3/(b - 1). 

 To confine the interference to a half step (with 3 db margin) requires that 



/3/(6 - 1) ^ 2(Q/P) V2 Fb 



For Q/F = 0.707, 



^^ 2(b - \)Fb 



^* The general solution of the problem of frecjuency error produced by superimposing a 

 sine wave on an unmodulated carrier is given in Appendix II. 



