Sphere/Hemisphere Resonator

The sphere or hemisphere resonator occurs in a specimen with the following geometry;

The arrow represents the sample poling direction. The limits in dimension should ensure that the resonance will be free of coupling with other resonance modes. This resonance is actually a shell breathing mode resonance.

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

where

and

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

k₁₃, e^T₃₃, s^E₁₁+s^E₁₂

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