Detection Principles of Temperature Compensated Oscillators with Reactance Influence on Piezoelectric Resonator

Abstract

This review presents various ways of detection of different physical quantities based on the frequency change of oscillators using piezoelectric crystals. These are influenced by the reactance changes modifying their electrical characteristics. Reactance in series, in parallel, or a combination of reactances can impact the electrical crystal substitute model by influencing its resonant oscillation frequency. In this way, various physical quantities near resonance can be detected with great sensitivity through a small change of capacitance or inductance. A piezoelectric crystal impedance circle and the mode of frequency changing around the resonant frequency change are shown. This review also presents the influence of reactance on the piezoelectric crystal, the way in which the capacitance lost among the crystal's electrodes is compensated, and how the mode of oscillators' output frequency is converted to lower frequency range (1-100 kHz). Finally, the review also explains the temperature-frequency compensation of the crystals' characteristics in oscillators that use temperature-frequency pair of crystals and the procedure of the compensation of crystals own temperature characteristics based on the method switching between the active and reference reactance. For the latter, the experimental results of the oscillator's output frequency stability (f out = ±0.002 ppm) at dynamical change of environment temperature (0-50 • C) are shown.

Sensitivity and Accuracy of Dielectric Measurements of Liquids Significantly Improved by Coupled Capacitive-Dependent Quartz Crystals

“…The experimental setup (see Figure 1) for the measurement of complex permittivity consists of a glass test tube with capacitance, C 01 , and quartz crystal oscillator. The capacitor (metal plates with dimensions 5 × 0.5 cm) is fixed on the external part of the glass test tube (Figure 1a) with a height of 12 cm, diameter 1.2 cm and the glass thickness of 1 mm [32]. The rest of the glass test tube is covered by a metal layer which acts as a shield to reduce the fringing field effect [1][2][3]30].…”

“…In this way, the precision of the measurement is increased by several orders of magnitude. In the case of an AT-cut crystal with a frequency change of ±1 ppm in the temperature range T = 0-40 • C, the two oscillators have approximately the same frequency ( ∼ =4 MHz) [32,36,37]. The quartz crystal data are L 1 = 158.314 mH, C 1 = 10 fF, R 1 = 10 Ω, C 0 = 2 pF, and quality Q = 153 k (measured by a HP4194A impedance analyzer (Hewlett Packard/Agilent)).…”

“…The complex impedance, Z, for the crystal equivalent circuit can be expressed in terms of the normalized frequency Ω = ω/ω 0 , where ω 0 = 2π f s is the resonant angular frequency (for details of derivation see [32,38,41]), as:…”

“…A change of capacitance C d triggers a change of the oscillator's frequency f osc1 in the range between 1 and 20 kHz. Modulation of two frequencies ( f osc1 and f re f ) leads to the formation of a triangular signal on a low-pass filter, with resistance R and capacitance C, which is then changed by the Shmitt circuit (to reduce interference when the frequency, f out , is measured) into a square signal [32,[36][37][38]42], with frequency f out :…”

“…The temperature changes in the frequencies of the detection and reference oscillator (d f osc1 (T) and d f re f (T)) are not fully compensated because the temperature-frequency characteristics of the two oscillators are not exactly equal. The HM 8123 counter frequency measurement error (d f c_err ) represents the frequency instability of the counter, which equals ±1.0 × 10 −8 in the temperature range 0-50 • C [32,36,38,42].…”