Method for measuring selected frequencies of a coupled-dual resonator

Abstract

The present invention discloses a method for obtaining frequency parameters to determine the resonator frequencies, the synchronous peak separation frequency, and the normal center frequency of a coupled-dual resonator crystal. Under this method, a plurality of frequencies are applied to a first electrode. This application is performed once while the second electrode and the common electrode are connected by a short circuit, and then again when the second electrode and the common electrode are capacitively connected or open circuited. During each application of the plurality of frequencies to the crystal, the phase response for the output of the resonator circuit is monitored. Then the time response of the crystal is determined. Next, the time delay relative maxima for the time response is determined. Finally, the frequencies at which the time delay relative maxima occur are determined. These frequencies correspond to the inflection points where the change in phase goes from monotonically increasing to monotonically decreasing. These frequencies are used to calculate the resonator frequencies, the synchronous peak separation frequency, and the normal center frequency of the crystal. Alternatively, all of the critical frequencies can be determined with the second electrode and the common electrode connected by a short circuit. In this case, however, the critical frequencies correspond to the time delay maxima and minima for the time response. This method is applicable regardless of the frequencies of the resonators or the amount of frequency separation between the resonators.