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BELL SYSTEM TECHNICAL JOURNAL 



However, if the effective resistance in one branch is twice as large as that in 

 the other branch a highly distorted characteristic results as shown by the 

 middle curve of Fig. 14.2. 



Both of these illustrations show that filter performance is degraded rapidly 

 if the crystal units of the lattice have characteristics which depart from 

 their nominal values by different extents for the two branches. A similar 

 effect is produced when the temperature coefficient of resonant frequency 

 for the crystal units in one branch differs frcm the temperature coefficient 

 of the units in the other branch. Deviations occurring in a single unit may 

 also aflfect filter performance. Such deviations include the presence of 

 unwanted resonances of even weak amplitude, inadequate insulation re- 

 sistance between the metalUzed coatings or unbalance between the halves 

 of plates on which the coating has been divided. 



r-W^ — TTZTTHh 



5 5 10 



C. P. S. FROM 92 KC. 



Fig. 14.2. — Effect of deviation in the effective resistance of crystal units on the distor- 

 tion characteristic of a crystal filter. 



The importance of controlling the electrical characteristics of the crystal 

 units is indicated from the above considerations. It is pertinent to correlate 

 deviations in the mechanical properties of the crystal unit with the devia- 

 tions in electrical characteristics. This is the subject of the succeeding 

 sections. Consideration is restricted to the plates commonly used in filters, 

 that is, X-cut plates, vibrating in extensional or flexural modes, and GT-cut 

 plates. 



14.2 The Effect of Deviations That Occur in the Manufacture of 



Quartz Plates 



Quartz is an anisotropic material. Accordingly, plates cut from a quartz 

 crystal exhibit elastic and piezo-electric properties which depend on the 

 orientation of the plates with respect to the principal axes of the crystal. 



