Backed and Matched Resonator

The backed and matched thickness extensional resonator has the following geometries;

The arrows represent the sample poling directions. The backing is usually much thicker than the specimen while the top layer, typically used to match the transducer to its projection medium, is thin compared to the piezoelectric. The limits in dimension should ensure that the resonance will be free of coupling with other resonance modes. Note that this can also be used to model the effect of thick electrodes on a thickness extensional resonator.

The resonance observed in the sample impedance is described by the following equation;

where:

By fitting this equation to the observed resonance, the following material properties can be determined;

c^D₃₃, h₃₃, e^S₃₃, c^D_t, c^D_s, k_t, v_p, v_s, v_t

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