220 BELL SYSTEM TECHNICAL JOURNAL 



where the symbols R\ and Co are as shown in Figs. 15.1 A and 15.2 and P is 

 expressed as 



M 

 ^ = G (15.6) 



Co 



With the effective capacitance, Ct, of the remainder of the oscillator added 

 to the paralleling capacitance, Co, in Fig. 15.2, the operating frequency will be 

 that frequency at which the combination will exhibit a pure resistance at 

 the terminals AB (excluding the generator "X" which is involved in the 

 measuring technique). This leads to the definition: 



The Performance Index is the anti-resonant resistance of the crystal and 

 holder having in parallel with it the capacitance introduced by the remainder of 

 the oscillator. 



The Performance Index is therefore a term to express performance not in 

 terms of the grid current of some particular oscillator, but in fundamental 

 circuital units — -impedance. The Performance Index is a term that may be 

 used to compare performance of crystals at different frequencies. Its 

 value is independent of plate voltage, grid leak resistance, or of plate 

 impedance. It provides a measuring stick that should replace the "activity" 

 figures of grid current in so far as the crystal is concerned. It paves the way 

 for the oscillator circuit designers to come forth with standards of measure- 

 ment for the oscillator circuit without the crystal in the hope that the 

 two may be quantitatively associated and lend themselves to theoretical 

 calculation of full oscillator performance. 



15.10 Theory of Measurement 



The problems of measurement are most readily explained by reference to 

 Fig. 15.2. The crystal provides elements Li,Ci, Ri and Co . The circuit of 

 the oscillator provides an effective capacitance, Ct, which is composed of grid 

 and lead wire capacitances plus capacitance introduced from the plate cir- 

 cuit. The frequency at which this combination exhibits anti-resonance as 

 measured at A B is the oscillating frequency. The resistance when added to 

 negative resistance, p, will be zero. Oscillations will start with p numeri- 

 cally smaller than the anti-resonant resistance measured at AB, but the 

 amplitude of oscillations will increase causing p to increase until p and Zab 

 are equal numerically. The primary problem is to measure the anti-resonant 

 resistance at AB at the anti-resonant frequency with p disconnected. 



Measurement of anti-resonant resistance directly is very difficult. The 

 current flowing into an anti-resonant circuit is too small to measure with 

 the usual meters. Other devices for measuring the current are likely to 

 introduce paralleling capacitance that will vitiate the readings. The sug- 



