The Effect of Driving Electrode Shape on the Electrical Properties of Piezoelectric Crystals

Piezoelectric crystals are often used as circuit elements in filters and oscillators. Fig. 1 shows a typical admittance curve for such a crystal and Fig. 2 shows the corresponding equivalent circuit. At very low frequencies the crystal behaves like a capacitor, with a capacitance approximately equal to the static capacitance between the driving electrodes. Due to the piezoelectric effect, an applied alternating electric field causes the crystal to vibrate and, at certain natural frequencies of free vibration, it is driven into mechanical resonance by the applied voltage. In the neighborhood of such natural frequencies, the admittance of the crystal is closely approximated by the simple equivalent circuit of Fig. This is the equivalent circuit commonly used in the applications. It is a good approximation over a frequency range proportional to the spacing between the resonant frequency, at which the admittance is infinite (in the absence of dissipation), and the antiresonant frequency, at which the admittance vanishes. For small electromechanical coupling this spacing is proportional to the capacitance ratio Cu/Co · It is desirable to make this ratio as large as possible. Bechmann and Parsons have shown how this may be done in various simple cases. 1259