198 BELL SYSTEM TECHNICAL JOURNAL 



The fact that the frequency stabiUty of a crystal oscillator is a function 



of — explains why a BT cut crystal is in general more stable than an ^7" 

 Ci 



cut. The two may be made equal, however, by adding capacitance across 



the A T cut crystal. 



Actually we have compared the frequency stability obtained by the use 



of one type of circuit (the equivalent crystal circuit) with one of a different 



configuration obtained by making Ci — cc . In practice this is usually the 



case since Ci must be large to obtain oscillations when using coils and con- 



densers. The limiting factor is therefore the value of — at which oscilla- 



tions stop and this is determined by the Q of the circuit elements as shown 



in the next section which deals with activity. It will be shown that the Q 



n 

 required is proportional to — and therefore the maximum frequency sta- 



bility that can be obtained is directly related to Q. 



12.70 Relation Between Crystal Quality and Amplitude of 



Oscillations 



The activity of a crystal is usually thought of as the relative amount of 

 grid current produced in an oscillator circuit. This method of defining 

 activity affords a means of comparing the quality of one crystal with another 

 for a particular set of conditions. The disadvantages are first; it is only a 

 relative measure, and second; it is not possible to compute the activity as 

 thus defined by any method of oscillator analysis so far presented. Curves 

 have been shown of amplitude of oscillations as a function of certain circuit 

 variables, but these represent only qualitative changes associated with 

 plate resistance variations. The first objection has been somewhat recti- 

 fied by the use of reference oscillators* in which all the circuit elements 

 including the tubes have been carefully matched. There is still the diffi- 

 culty, however, of comparing crystals of different frequencies for it cannot 

 be assumed that the measurements are independent of this variable. It 

 would be more desirable to have some absolute measure of activity and 

 particularly one which would lend itself to convenient computation from 

 readily measurable constants of the crystal. 



12.71 Definition op Crystal Quality for Oscillator Purposes 



In deriving an expression for the quality of a crystal, it is convenient to 

 use the negative resistance concept of the oscillator as described in section 

 12.40. The equations are general and in a form which admit of separating 



* Developed by G. M. Thurston. 



