MULTICHANNEL AMPLIFIERS BELOW OVERLOAD 589 



Multivalued characteristics such as associated with ferromagnetic 

 materials and reactive characteristics in which the coefficients vary 

 with frequency are not included. The mechanism by means of which 

 the characteristic (2.1) gives rise to interchannel interference may be 

 illustrated by assuming that a sinusoidal signal of frequency q radians 

 per second is impressed on the voice frequency channel associated with 

 the carrier frequency mp, where p is the base frequency in radians per 

 second and m is an integer. The resulting wave impressed on the 

 amplifier is of the form 



eg ^ Q cos {mp + g)t, (2.2) 



if upper sidebands are transmitted; the plus sign would be replaced by 

 a minus sign in a system using lower sidebands. Substituting the 

 value of eg given by (2.2) in the characteristic (2.1), we find: 



ip = aiQ cos (mp + q)i + 2^2<2' + 2«2<2^ cos {2mp + 2q)t 



+ iazQ^ cos (mp + q)t + ia^Q^ cos (Smp + 3q)L (2.3) 



Considering the terms which appear in the response (2.3), we note 

 that the first term is the desired amplified signal. The second term 

 is a direct current of trivial importance; if the system contains a trans- 

 former, this component is not transmitted. If q does not exceed p/l, 

 the third term will be received in the channel associated with the 

 carrier frequency 2mp and will there produce a detected frequency 

 twice as great as the original signal frequency. In such a case, it 

 represents interference produced in the 2w/>-channel when the mp- 

 channel is actuated. If q exceeds p/2, the interference falls in the 

 {2m + l)^-channel. The fourth term of (2.3) is received in the 

 w^-channel and represents a non-linearity in intrachannel transmission 

 since its frequency is the same as that of the applied signal but its 

 amplitude is proportional to the cube of the impressed signal amplitude. 

 This term is of trivial interest in the study of transmission quality of 

 individual channels of a well-designed multichannel system and is of 

 no interest in the interference problem with which we are here con- 

 cerned because it is received only in the originating channel. Finally, 

 if q is less than p/3, the fifth term represents interference of frequency 

 3q received in the channel associated with the carrier frequency three 

 times that of the originating channel; if q is greater than p/S, the 

 interference falls in a higher channel. 



Next suppose that a number of carrier channels are simultaneously 

 transmitting signals. By substituting an expression representing the 

 resulting carrier wave, which is a sum of several terms such as (2.2) 

 with different values of Q, m and q, in the amplifier characteristic (2.1), 



