The Measurement of the Performance Index of Quartz Plates

T HE theory of the general behavior of crystals in oscillator circuits has been described by I. E. Fair 1 . In Fair's paper as well as in others2, it has been pointed out that in the neighborhood of the operating frequency a crystal is equivalent to the circuit shown in Fig. 15.1 A. The crystal possesses two resonant frequencies, a series resonant frequency determined by the effective inductance, L, and effective capacitance, C, and an antiresonant frequency determined by these same elements plus the paralleling capacitance, Co. This paralleling capacitance is the static capacitance between electrodes of the crystal and any capacitance connected thereto by the crystal holder and lead wires within the holder. The dotted resistor, RL , shunting the equivalent crystal circuit represents the effective shunt loss of the holder. In the ideal case and in many practical instances this loss is negligible. It is rather difficult to express the circuital merit of a crystal quantitatively in a single term such as has been found useful for inductances and capacitances. It is customary to express the circuital merit of these two elements in the form of the ratio of reactance to resistance. That is, for an inductance (15.1) and for a capacitance e - Jrr (ls 2)