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BELL SYSTEM TECHNICAL JOURNAL 



of the airgap. This may be reduced to the circuit of Fig. 8.1 IB where the 

 constants are given by 



Co = 



c; = 



Ca + Co 



Co 



cj 



{Ca + Co)(Ci + Ca + Co) 



Ci 



The circuit of Fig. 8.1 IB is the same form as that of the original cr^'stal and 

 therefore we may assum.e that the effect of the airgap is to produce a similar 



A A 



A/2 



3A/4 



0.3 



0.2 



03 0.4 



AIRGAP IN M.M. 



Fig. 8.12 — Effect on frequency of the air gap thickness on a 550 kc. AT-cut crj'stal. 



crystal of reduced capacity and reduced effective piezoelectric coupling. In 

 the case of oscillatory crystals the effect of the airgap is to reduce the activity 

 and decrease the range of frequency adjustment with parallel capacity. For 

 filter applications the effect of the airgap is to produce narrower transmission 

 bands and higher characteristic impedance. One other effect of the airgap 

 results from the propagation of acoustic waves from the crystal. 



It is known that most any type of crystal in a vibrating condition will 

 produce acoustic waves in air and if an object capable of reflecting these 

 waves is the proper distance away, these acoustie waves may be reflected 

 back to the crystal surface. The reflections from distances corresponding to 

 even quarter wave-lengths will cause considerable dam^ping while the re- 

 flections from distances corresponding to odd quarter wave-lengths will 



