THE L3 SYSTEM QUALITY CONTROL REQUIREMENTS 945 



since there is a large area of give and take between the circuit and the 

 component element designers. 



Let us assume that the process of arriving at a satisfactory component 

 element design has been completed and that the spread of the manu- 

 facturing limits has been set at d= ?/ per cent. How will the gain deviations 

 due to this element grow, as more and more repeaters, each containing 

 one unit of this element, are placed in tandem? It is evident that the 

 cumulative magnitude of gain deviations will depend on the distribution 

 pattern describing the departure of individual units of this element from 

 the prescribed value. 



If all units of this element have a systematic deviation (equal in 

 magnitude and sign) from the prescribed value, the cumulative gain 

 deviation will be 



nai db 



where n = number of repeaters in tandem, and 



ai = gain deviation in one repeater due to yi per cent deviation of 



the element. 



If the units of this element have a Normal distribution whose average 



coincides with the prescribed value, and whose extreme limits (say 



3-sigma limits) are zb 2/2 per cent, then the averages of random groups of 



elements in n repeaters will be described by another Normal distribution, 



the corresponding limits of which will be =b 2/2/ V^ per cent. Thus the 



over-all limits of gain deviation for n repeaters will be 



na2 ,, /- 



=h —7=^ db = V ^0:2 db 



If, however, the average of the distribution of individual units does 

 not coincide with the prescribed value but is displaced by yi per cent, 

 then the over-all gain deviation limits for n repeaters in tandem will be 



(nai ± \/na2) db. 



Thus, it is of first importance that the average of the individual units 

 be controlled as closely as possible to the prescribed aimed-at value. 



Of course, distributions other than Normal are possible. However, it 

 is sufficient for most practical purposes to consider only the Normal 

 distribution since a combination of a large number of distributions, 

 which individually are not Normal, will tend to approximate a Normal 

 distribution. This assumption is a reasonable one to make because of the 

 large* number of different elements which are used to make up an L3 



* There are over 100 component elements in the L3 amplifier of which about 12 

 have large element sensitivities and are therefore critical in evaluating perform- 

 ance. There are over 30 additional elements the sensitivities of which are also 

 sufficiently large to require application of distribution requirements. 



