PERFORM A. \CE IXDEX OF QUARTZ PLATES 



225 



where 



Ct = C,-{- 



CaCk 



Cs + c. 



enabling Qi to be expressed as 



Qi = 



eo Ci Ck 



ei (Ct — Cx)^ 

 Expressing Cq in terms of ep , we have 



\fieg\ = \ip\ Vr p + X 



tn = 



Xc 



(15.11) 



(15.12) 



(15.13) 

 (15.14) 



hence 



and 



'^-V'+C^'I ('^-'^ 



eo 



(15.16) 



With the above equations substituted in (15.12), we may express Qi as 



Qi = - oi -^ A — — 



1 + 



X, 



Now 



Therefore 



PI = ^ = QiX, 



PI = ^ A '' 



ei Gm (Ct — CxY 



4/^ + [tI 



If 



PT = ^ 4 iJL 



Ci ^ G„, {Ct - CxY 



(15.17) 



(15.18) 



(15.19) 



(15.20) 



(15.21) 



The simpHtied PI expression (15.21) assumes that the reactance of Cp 

 is small compared to the plate resistance and plate load resistance of V-1. 

 The evaluation of PI from this expression has three obvious difficulties: 



