Comparison of lumped-element and transmission-line models for thickness-shear-mode quartz resonator sensors

Both a transmission-line model and its simpler variant, a lumped-element model, can be used to predict the responses of a thickness-shear-mode quartz resonator sensor. Relative deviations in the parameters computed by the two models (shifts in resonant frequency and motional resistance) do not exceed 3% for most practical sensor configurations operating at the fundamental resonance. If the ratio of the load surface mechanical impedance to the quartz shear characteristic impedance does not exceed 0.1, the lumped-element model always predicts responses within 1% of those for the transmission-line model