Comparison of energy trapping resonators and filters using the AT cut of quartz, berlinite and gallium phosphate

The properties of the AT cuts of quartz, berlinite, and gallium phosphate are compared (velocity of the shear waves, coupling coefficient, and thermal behavior). A more precise evaluation of the properties of AT cut resonators using the quartz analogs is made in considering the computed properties of energy trapped resonators. The computed properties of resonators are obtained using a three dimensional model based upon the theory of the essentially thickness modes. Using computed equivalent schemes, the bandwidths achievable at 20 MHz are calculated for 4 poles Jaumann filters having a Chebishev response with 14 dB ripple and a maximal termination impedance of 2 kohm. The obtained results indicate that berlinite and gallium phosphate produce a filter with much larger bandwidth than quartz. They suggest that the use of new designs (resonators with elliptical electrodes and/or grooved electrodes, integrated filters etc.) will further lower the equivalent inductance and/or the influence of the stray capacitances. Such designs would lead with the high coupling quartz analogs to much better characteristics than the usual designs using round electrodes. Experimental results (equivalent scheme of resonators, observed mode shape etc.) are successfully compared with computed ones to validate the model use for the computations.