. The Bell System technical journal . of merit is to be maintained. The fre-quency stability obtainable in a particular oscillator is therefore limitedby the Q of the crystal and the frequency stability coefficients should becompared on this basis. Activity of Crystals In deriving a figure of merit for crystals as oscillators, it was found thatthe amplitude of oscillations in a given circuit not only depends upon Mbut also it is a function of frequency relative to the resonant frequency 202 BELL SYSTEM TECHNICAL JOURNAL of the crystal. This may be explained by referring to Fig. whi
. The Bell System technical journal . of merit is to be maintained. The fre-quency stability obtainable in a particular oscillator is therefore limitedby the Q of the crystal and the frequency stability coefficients should becompared on this basis. Activity of Crystals In deriving a figure of merit for crystals as oscillators, it was found thatthe amplitude of oscillations in a given circuit not only depends upon Mbut also it is a function of frequency relative to the resonant frequency 202 BELL SYSTEM TECHNICAL JOURNAL of the crystal. This may be explained by referring to Fig. whichshows curves of the reactance Xc of the crystal plotted as a function of fre-quency. The frequency at which oscillations occur depends principallyupon the value of circuit capacitance Ci. Equation () shows thatthe frequency must adjust itself to a value at which Ct resonates withthe reactance of the crystal. This value of reactance is represented on thecurve as Xco and the corresponding frequency of oscillations as Jo • The. Fig. —Two crystals having the same figure of merit but with different reactance characteristics A^ and A^ will operate with different amplitudes according to the relative values of <pco and tpo respectively circuit capacitance (or Xco) has been so chosen in the illustration that /<,lies equidistant between the resonant frequency /i and the anti-resonantfrequency/2. Then at this value of/«, </?c is a maximum, as shown by the(pc curve, and for a given value of (pg this will result in the greatest let the capacitance Co of the crystal be increased. The frequencies/iand /2 will then become closer and at the same time the height of the ipccurve is reduced. Assume also that the Q is increased in order to maintainthe same value of M and hence the same maximum value for <^c • Thereactance-frequency curve for the modified crystal and the corresponding PIEZOELECTRIC CRYSTALS IN OSCILLATOR CIRCUITS 203 curve for (pc are repr
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