588 BELL SYSTEM TECHNICAL JOURNAL 



The load capacity requirement has been discussed in a paper by 

 B. D. Holbrook and J. T. Dixon. ^ In the present paper we assume 

 that the principles there developed have been used to fix the maximum 

 load which the amplifier must deliver and proceed with the second 

 phase of the problem — the determination of the modulation require- 

 ments which the amplifier should meet below overload. A secondary 

 objective is to set up simple testing procedures by which the per- 

 formance of the system may be assessed without incurring the com- 

 plications attendant upon loading the system with talkers. One such 

 procedure involves the measurement of distortion products by a 

 current analyzer when sinusoidal waves are impressed upon the system. 

 Another involves the measurement of noise in a narrow frequency band 

 when a band of noise uniformly distributed over the transmission range 

 is impressed upon the system. 



The path followed in reaching these objectives starts in Section (2) 

 with a demonstration of the way in which non-linearity leads to inter- 

 ference in specific cases. Section (3) then considers the magnitudes of 

 typical modulation products and arrives at volume distributions for 

 them, by which the fluctuating character of speech may be taken into 

 account. The basis for treating interchannel modulation as noise is 

 given in (4). Since one of the most convenient testing methods in- 

 volves the use of sine waves the relationship of distortion measured 

 with sine waves to the distortion observed with speech on the system 

 must be set up as in (5). The number of products falling in any single 

 channel is considered in (6) and the average noise in any channel may 

 then be evaluated in (7) with the aid of the results of preceding sections. 

 The effects introduced by multiple centers of distortion in the ampli- 

 fiers of a transmission link are considered in (8). The paper concludes 

 with a discussion of test methods presented in the ninth section. 



2. Interchannel Modulation as a Source of Crosstalk 

 We shall consider specifically a single sideband suppressed-carrier 

 multichannel speech transmission system of the four-wire type al- 

 though much of the treatment is also applicable to other kinds of 

 carrier systems. The carrier frequencies will be assumed to be ad- 

 jacent harmonics of a common base frequency greater than the highest 

 signal frequency. The amplifier characteristic will be assumed to be 

 expressible with sufficient accuracy by means of linear square and 

 cube law terms. That is if ip represents the output current and eg 

 the input voltage we' write 



ip = aieg + 02^/ + cLz^o^- (2-1) 



1 Bell System Technical Journal, Oct. 1939, Vol. 18, pp. 624-644. 



