The Effect of Load Capacitors on the Frequency of Quartz Crystals

摘要

The equivalent circuit of a piezoelectric vibrator has associated with it a number of critical frequencies in the vicinity of the resonance region. Addition of a capacitor in series or in parallel with the resonator element results in a shifting of these frequencies. The standard practice for measuring the frequency of antiresonance quartz crystal units is to place the load capacitor in series with the crystal unit. The resonance frequency measured with the series capacitor is assumed to be equivalent to the antiresonance frequency obtained with the same capacitor placed in parallel with the crystal unit. The analysis given shows this to be the case only in the limit of lossless crystals, whereas a frequency difference of several parts per million may be encountered with practical units. A simple, approximate formula is derived for the frequency error, and examples are given. (Author)