INTERMODULATION INTERFERENCE IN RADIO SYSTEMS 65 



NUMBER OF INTERMODULATION PRODUCTS AND FREQUENCY BAND AF- 

 FECTED 



It is of interest to know how many intermodulation products can be 

 produced by a block of n uniformly spaced channels and where they 

 will fall ^vith respect to the frequency band occupied by the n channels. 



Third Order Products 



When all possible combinations of n uniformly spaced operating 

 channels are activated three at a time, n\n — l)/2 products mil be 

 formed and they vnll lie between A — {n — 1) and A -\- 2{n — 1) where 

 the operating band lies between channels A and A -\- {n — 1). This 

 means that the bandwidth of the intermodulation products is very 

 nearly three times that of the operating channels. The products are 

 sj^mmetrically distributed with respect to the midpoint of the operating 

 band. There will be 



2n^ + 3n' - 2n - 6 



24 



third order products that will fall in the n — 1 channels immediately 

 below the operating band and a like number of products that will fall 

 in the n — 1 channels immediately above the operating band. The 

 remaining products, 



4n^ - 9n' + 2n + 6 

 12 



in number, will fall in the n channels that constitute the operating band. 

 Not all of these products, however, are capable of producing interference 

 since some products of the A + 5 — C type can fall on the very transmit- 

 ting channels that combine to produce them. These products are harmless 

 since they do not fall on receiving channels and are generally of much lower 

 level than the carrier on the channels in which they do fall. If such products 

 are not counted, there remain 



I (n - l)(n - 2) 



products which fall within the operating band. The formulas presented 

 here and in Table I are empirical and were derived for values of n up to 

 10. However, it is believed that they are reasonably accurate for much 



larger values of n. 



