Coupled Resonances on the QCM and The Lumped Equivalent Model

QCM interactions with a discretely resonant load much greater in frequency than the quartz resonator’s shows negative frequency changes with increasing mass loading. However, a positive frequency increase of the coupled system occurs when the load resonant frequency is less than the quartz resonator’s. A brief review of the method by which a resonant load can be coupled into the electromechanical equations for the quartz resonator is given. Though this yields exact results, the purpose of this communication is to show the derivation of an equivalent circuit for the resonance following the acoustic impedance approach. This equivalent circuit replicates the characteristics of the exact solutions.