Compound Resonators and Microweighing Sensors

Simplified derivations of the Quimby compound resonator (QCR) equations are provided, with their reduction to the quartz crystal microbalance (QCM) forms, for both the originally assumed condition of negligible transducer piezocoupling, as well as for the much more interesting case where both the transducer and unknown possess arbitrary piezoelectric coupling factors. For the QCM configuration, the accuracy of the mass determination depends somewhat upon where the frequency measurements are made on the impedance circle. For the QCR situation where both transducer and measurand are piezoelectric, the piezocoupling may be determined along with the elastic coefficients, by alterations in the electrical boundary conditions