626 BELL SYSTEM TECHNICAL JOURNAL 



The application of probability theory is evidently indicated as the 

 method of attack. 



Those characteristics of multi-channel amplifiers which are im- 

 portant to the problem will be described first. Then a description 

 will be given of the variables which must be taken into account in com- 

 puting load capacity. Finally, the combined effects of these variables 

 will be determined on a statistical basis to establish the required load 

 capacity as a function of the number of channels in the system. 



Characteristics of the Multi-Channel Amplifier 



At the present time, multi-channel systems of primary interest 

 employ single sideband transmission ; the carrier frequencies are largely 

 suppressed and different amplifiers are used for the two directions of 

 transmission. For such systems negative feedback amplifiers have 

 outstanding advantages, particularly with respect to stability of gain 

 and reduction of modulation effects, and are thus being used almost 

 exclusively in present day multi-channel systems. The following 

 discussion is related particularly to such systems, although many of 

 the calculations are also applicable to less common types. 



At light loads the principal modulation products in a negative 

 feedback amplifier increase approximately as the square or the cube of 

 the fundamental output power. Beyond a certain critical point, 

 however, the modulation increases very rapidly and the total output 

 of the amplifier soon becomes practically worthless for communication 

 purposes. This critical point will be called the "overload" point. 

 For most tube circuits it is either the point at which grid current begins 

 to flow, or that at which plate current cutoff occurs. This point 

 obviously defines the instantaneous load capacity. 



Below the overload point the higher order modulation products 

 are negligible in comparison with second and third order products, 

 and the interference may be regarded as due to the latter sources alone. 

 Beyond the overload point, however, the higher order products become 

 important very rapidly and the resultant disturbances appear in most, 

 if not all, of the channels. With given tubes, the interference below 

 the overload point may be altered by changing the amount of feedback. 

 The interference above the overload point, however, may be little 

 changed in this way because of the rapid loss of feedback as the 

 amplifier overloads. Accordingly, in designing an amplifier, the 

 necessary load capacity may be determined solely by insuring that the 

 output will rarely rise above the overload point, afterwards adjusting 

 the amount of feedback so that the inteference below the overload 

 point will be tolerable. There are thus two problems which may be 



