IMPEDANCE CORRECTION OF WAVE FILTERS 



793 



exact values ascribed to them by the design formula. The Hmitations 

 of manufacture, however, demand that elements be permitted to 

 deviate from their mean values by as much as 1 per cent or 2 per cent. 

 These element deviations in general degrade the performance of filters 

 by increasing their reflection coefiicients. The increase in reflection 

 coefficient is largely independent of the initial reflection coefficient, that 

 is, it is about the same for a filter whose normal reflection coefficient is 

 very small as for one of inferior theoretical design having a large normal 

 reflection coefficient. Curve I of Fig. 23 shows the reflection coefficient 

 of a particular filter when all of the elements have their design values; 

 Curve III, the envelop of maximum reflection coefficients for this filter 



100 



80 



to 



z 

 o 



Seo 



—I 



UJ 



a. 



S 40 



o 

 a. 

 a. 



20 



2 4 6 8 10 12 14 



REFLECTION COEFFICIENT REQUIREMENT IN PER CENT 



16 



Fig. 24 — Distribution of the reflection coefficients of a given filter at one frequency in 

 terms of the percentage rejected in meeting any requirement. 



when the coils are permitted to vary ±1.5 per cent and the condensers 

 ± 0.8 per cent from their design values; Curve II the maximum reflec- 

 tion coefficient for the best 99 per cent of the filters manufactured to 

 these limits. The last curve is based on a priori probability computa- 

 tion which assumes that the distribution curves of the element devia- 

 tions follow the normal law. A distribution curve of reflection coeffi- 

 cients for another filter at a particular frequency plotted in terms of the 

 per cent of filters that would be rejected in meeting any requirements is 

 given in Fig. 24. Studies of this sort are too extensive to be included 

 in this paper but they have shown that the advances in the technique 

 of impedance correction here recorded are well ahead of the practical 

 limitations of the problem. 



