526 



BELL SYSTEM TECHNICAL JOURNAL 



such a character as to indicate that the analogy between the two 

 systems of coupled circuits and the crystal modes of vibration is 

 sufficiently good to serve as a useful guide. 



If, then, these parallel cut crystal plates are considered as a system 

 of coupled circuits the reason for the variation of the frequency- 

 thickness constant with dimensional ratios and the presence of the 

 frequency doublets is at once apparent. With the coupling at the 

 various harmonics determined, the character of these variations can 



TUNING OF N0.2 CIRCUIT GROUP Xj 



Fig. 9 — Wave-lengths of the system of coupled circuits of Fig. 7 as a function of the 

 tuning of circuit group No. 2, the tuning of circuit No. 1 being fixed. 



be predicted. Given an experimentally determined series of coupling 

 curves similar to Fig. 10, the coupling at the nth harmonic can be 

 determined from the expression 



k = 



- 1 



(5) 



+ 1 



where X' and X" are the wave-lengths of the coupled system at the 

 point where Xi = WX2. 



