Measurements of Small Frequency Differences by Dual Mode 4 MHz Quartz Sensors.

We proposed a method for measuring frequency differences of the order of a few Hz with an experimental error lower than 0.0001% by using two 4 MHz quartz oscillators, the frequencies of which are very close (a few 10 Hz difference) due to the dual mode operation (differential mode with two temperature-compensated signal frequencies or a mode with one signal and one reference frequency). We compared the existing methods for measuring frequency differences with the new method which is based on counting the number of transitions through zero within one beat period of the signal. The measuring procedure requires equal experimental conditions (temperature, pressure, humidity, parasitic impedances etc.) for both quartz oscillators. To ensure equal resonant conditions for oscillation two quartz crystals are needed, which form a temperature pair. The frequencies and resonant conditions of both oscillators must be almost equal, which is achieved by an external inductance or capacitance. In such a way, we minimized all the external effects and ensured highly stable oscillations and high sensitivity of the differential sensors. The counter detects one beat period by an external gate signal former. By using the method of counting transitions through zero within one beat period, we reduced the measuring error by three orders of magnitude, compared to the existing methods.