Methods of Measurement of the Parameters of Piezoelectric Vibrators

The "IRE Standards on Piezoelectric Crystals-The Piezoelectric Vibrator" specifies nomenclature and methods of measurement of the various quantities associated with piezoelectric vibrators. This paper gives in detail the theoretical considerations of these measurements, which are based on the frequency of maximum transmission through a simple pi resistance network which includes the vibrator in the series arm. The motional resonance frequency of the vibrator and the value of the motional resistance by the substitution of a resistor in place of the vibrator may be obtained from the frequency measurement. The theoretical considerations take into account stray capacitances and other impedances, and show how the somewhat involved formulas may be simplified with the average run of presently available vibrators. By the aid of capacitance-bridge measurements and frequency measurements of the vibrator with series impedances, all of the elements of its equivalent electrical circuit may be determined. Charts based on the formulas are included. They relate the measured to the fundamental values of the vibrator elements with any desired degree of precision. It is shown that when using typical quartz vibrators, the measurement of the frequency at maximum transmission will not differ from its value at motional resonance by more than a few parts in a million. Resistance substitution measurements have been found to compare within about two per cent. In addition to the generally available resistance and capacitance bridges, transmission network measurements require a stable RF generator or oscillator, the transmission network, and a sensitive detector.