452 BELL SYSTEM TECHNICAL JOURNAL 



To sum up; the following relations are applicable when interelectrode 

 capacities or other coupling impedances are to be included : 



_s^^ (45) 



2gi = ^—r- (46) 



2223+^^(22+23) 

 22(^ + 1)+^/- 



Zg2 = —Ti — I -, ^ I .. — (,■*«; 



z-i{\xzz — rp) 



(jU+l)22 + M23 



(48) 



qn=^[ "^^^zX (49) 



2j , M 2„ 



\ vrp-\rZn I 



With the aid of (45), (46), (47), (48), (49), equation (42) may be 

 modified to include all cases where the plate current resulting from 

 detection or modulation in the grid circuit is desired, provided an 

 accuracy greater than about 10% is not required. Where greater 

 accuracy is essential, curves must be made to give the effect of the 

 small terms in the numerator of the expression for &2m in equation (36). 

 Before leaving the subject of grid-leak detectors, w'e will discuss 

 briefly one of the physical aspects of grid-leak detection that the 

 example just given, and the equations on which it is based, have 

 emphasized. This is the fact that the fiction of the time-constant 

 of the grid-leak and condenser combination is not a necessary physical 

 interpretation of the phenomena which occur in the grid circuit. 

 Indeed, in many cases, the time constant method of calculating the 

 leak and condenser gives quite erroneous and misleading results. 

 These cases occur when the impedance looking into the vacuum tube 

 is of such value, as it often is, that the magnitudes and forms of qi„ 

 and 52m are materially changed from those which they would have if 

 Zg were neglected, and when Tg is not large compared with q„ and g,„. 

 Ecjuation (38) shows that, for greatest plate current resulting from 

 grid detection, gi, and Qk should be as small as possible, while g{h-k) 

 should be as large as possible. It is, then, a filter problem, and if 

 treated as such, will give reliable results both as to physical interpre- 

 tation and numerical values. 



