168 



BELL SYSTEM TECHNICAL JOURNAL 



Note that Ca is the total capacitance across Li and Ri , and Cb is the total 

 capacitance across L2 and i^o- 

 The coefficients of (12.4) become 



Pi = 2(aa + aft) + 



1 



RvC 



p^b 



1 



P2 = 0a -\- 4Q!a «& + /Sfc + " («« + ttfe) „/ 



i?. 



c 



P3 = 



P4 = 0. 



1 r o 1 



2(a6/3; + aa/^b) + — (iS; + 4aa«6) ^/ 



1 



J-'l^m^v 



(12.5) 



The coefficients as given by (12.5) satisfy (12.2) and (12.3) only when the 

 plus sign is used. 



The equations are simplified by dividing through by /S^ thus 



(12.6) 



(12.7) 



which gives the ratio of driven frequency of the crystal to its undriven value. 

 The common variable Rp must satisfy both (12.6) and (12.7). The method 

 of computing the frequency would be to solve for Rp in (12.6) and substitute 

 in (12.7). However, the equations are too complicated a function of Rp 

 for this to be practical. Terry solved them graphically by plotting (12.6) 

 and (12.7) as functions of Rp for assigned values of the circuit, and the inter- 

 section of these curves gave the frequency for the different circuit conditions. 

 The results are shown in Fig. 12.6. The G-P curves show the frequency 

 change as a function of plate circuit tuning for the grid to plate connection 

 of the crystal. 



12.12 Crystal Between Grid and Cathode 



With the crystal connected between the grid and cathode of the tube, 

 the circuit is as shown in Fig. 12.5. The coefficients of equation (12.1) 

 are as follows: 



