. The Bell System technical journal . spect tor Co we find that PI is a maximum when Co = C<. Since Co is proportionalto the area of the electrodes this establishes the optimum area for a par-ticular value of circuit capacitance. The capacitance of BT-cut plates is mmf. per square centimeter permegacycle.* Substitution of this for Co in () gives ^ j68 X lO^M^ ^^ ( Af -f QV ^ • ^^ * All frequencies are referred to the time interval of one second throughout this paper; megacycles per second is called simply megacycles as is customary in the radio field. 1 PIEZOELECTRIC CRYS
. The Bell System technical journal . spect tor Co we find that PI is a maximum when Co = C<. Since Co is proportionalto the area of the electrodes this establishes the optimum area for a par-ticular value of circuit capacitance. The capacitance of BT-cut plates is mmf. per square centimeter permegacycle.* Substitution of this for Co in () gives ^ j68 X lO^M^ ^^ ( Af -f QV ^ • ^^ * All frequencies are referred to the time interval of one second throughout this paper; megacycles per second is called simply megacycles as is customary in the radio field. 1 PIEZOELECTRIC CRYSTALS IN OSCILLATOR CIRCUITS 213 where A = the area of the crystal in square = the frequency in megacyclesCt = circuit capacitance in = figure of merit of the crystal (assumed constant) Thus for crystals of a given area, the performance index should decrease asthe frequency increases. Figure () shows the theoretical variations ofPI as the function of the diameter of the electrodes of three frequencies and PI. S 12 16 ELECTRODE DIAMETER IN MM Fig, —-Theoretical curves showing the relations of PI, electrode diameter, andcrystal frequency for BT crystals and a circuit capacitance of 50 n/xi for a circuit capacitance of 50 mmf. The activity of a 4-megacycle crystalwith 11-mm. diameter electrodes is about the same as a 10-megacyclecrystal with 18 mm. electrodes. It must be remembered in making thiscomparison that it is assumed that the damping introduced by the mountingis the same in both cases. Actually the damping is much greater for low-frequency crystals of this type than for high-frequency ones and maximumPI occurs at some intermediate frequency as shown by the curves of , These curves show that the damping caused by the particularmounting used was small for frequencies above 6 megacycles but increasesrapidly below this value. 214 BELL SYSTEM TECHNICAL JOURNAL CALCULATED
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