182 BELL SYSTEM TECHNICAL JOURNAL 



results can only be considered a first approximation, but agree with actual 

 conditions sufficiently to be of considerable interest. 



12.24 Crystal Grid to Plate 



The equation (12.20) is general and for the condition of crystal connected 

 between grid and plate of the tube (See Figure 12.12B) Zz represents the 

 crystal impedance which will be called Zc = Re -\- jXc , also : Zi = jXi , 

 Zi = JX2 and Xs = Xi + X2 + Xc . 



Note that Rg and C3 are disregarded in this case because their eflfects are 

 similar to those determined for the foregoing case of crystal connected grid 

 to cathode. 



After substitution of these values in (12.20) the real part is found to be 



R, = (m+ 1)^1^2 + XiZe ^j2.35) 



and the imaginary part is 



X. = -^' (12.36) 



which shows the effect of the various variables on the frequency. The right 

 hand side of equation (12.36) is comparatively small and the frequency is 

 therefore close to a value /o which makes X, = 0. In this case the frequency 

 is above the limiting frequency /o because the right hand side is positive 

 since Xi is negative, whereas it was found that the frequency was below /o 

 for the crystal connected between grid and cathode. As Re and Xi are 

 increased the frequency will increase and as Rp increases the frequency 

 decreases. These interpretations are verified by the G-P curves of Figures 

 12.6, 12.9 and 12.10. 



The effects of the various circuit and crystal constants are determined 

 by Koga^^ by writing the general n^ equation as 



^' + ^' + rfhz, = " ('2-3^) 



After substitution for*the Z's, the real and imaginary parts are respectively, 



\coCo/ 



Ri _^ _M^ 



iCg 



, r 1 1 T CO 



i?? + coLi - — - — 

 |_ coLi coCoJ 



_ . (12.38) 



Rv[ ^ — WC2 ^ 



= 



Ha,i:,~'^^V 



1 + i?' 



