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THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1953 



ing switches in stage (b) are busy; (2) five links from the switch in 

 stage (c) are busy to five additional switches in stage (b); and (3) a 

 connection is desired between the given switches. Thus eleven switches 

 are required in stage (b). The remaining requirements, namely, eleven 

 verticals per switch in stages (a) and (c) and six by six switches in stage 

 (b) are then easily derived. 



The number of crosspoints required for three stages, where n = A^^^^, 

 is summarized by the following formula : 



1/2 



(7(3) = {2N"' - 1) (3N) 



(2) 

 (2a) 



In Table I it may be noted that the number of crosspoints is less than 

 iV2 for all cases of iV > 36. 



PRINCIPLE INVOLVED 



The principle involved for determining the number of switches re- 

 quired in the intermediary stage is illustrated in Fig. 3. The figure is 

 for a specific case from which one can generalize for n inputs on a given 

 input switch and m outputs on a given output switch. In the figure it 

 is desired to establish a connection from input B to output H. A suf- 

 ficient number of intermediary switches are required to permit the 

 (n — 1) inputs other than B on the particular input switch and the 

 (m — 1) outputs other than H on the particular output switch to have 

 connections to separate intermediary switches plus one more switch 

 for the desired connection between B and H. Thus n + m — 1 inter- 

 mediary switches are required. 



Table I — Crosspoints for Several Values of N 



