PIEZOELECTRIC CRYSTALS IN OSCILLATOR CIRCUITS 169 



1 



R\ R2 



L\ Li2 Kp C 6 



1 R1R2 



Pi = + -^— + " 



jLjCo Li\ E^, E 



(12.8) 



\Ch Rp \Li Li) Cb 



LiLiCa LiEoCb Rp\LiCaCb LiLiCb LiCmCm/ 



P = ^ - ^ 4- — ( ^ - ^ !) 



Li L2 Ca Cb Ll L2 Cm Rp \Ll L2 Ca Cb L\ L2 Cm. Cm) _ 



With the substitution of uncoupled frequencies, damping factors and 

 coupling coefficient as described in the previous section, they become 



Pi = 2(«a + a6) + 



RpCb 



1 



P2 = iSa + 4Q!a Oib + ^'b + '^ (tta + Oib) '^> 



R. 



Cb 



If" N 1 1 1 



P3 = 2(a6/3; + oia^b) + "^ (/3a + ^aaab) p/ — ^———r, 



J\p |_ Cb EiCmCm^ 



p, = ^:^i\ 1 - / + 



fl - r^ + — (^f - ^t r^\\ 



|_ Rp \Cb Cm /J 



(12.9) 



Where 



)u = amplification factor of tube 



de 

 Rp = —^ (Cg constant) 



Otv 



Cx Co C2 C3 



C2 + C3 



These equations of conditions for oscillation in this case satisfy (12.4) 

 and (12.5) only when the minus sign is used. That is 



Ps ^ P2 - Vpi - 4P4 



Pi 2 



/3- = 



P2 - VpI - 4P4 



(12.10) 

 (12.11) 



