Dual-mode quartz resonators suitable for TCXO and OCXO

One of the reasons of TCXO and OCXO thermal frequency instability is existence of thermal gradient between resonator and temperature sensor. Piezoelectric crystal plate and thermo sensor companioning is very difficult technical problem because sensor must be placed in resonator area where amplitude of oscillation is maximal. Only in this case we will have properly information about "own mode" temperature. Unfortunately placing of any external sensor at this surface area will lead to dramatically Q factor worsening and practically unexercised. Some years ago the "self temperature sensing" technology based on dual mode excitation using were proposed. This technology have in mind using of simultaneous excitation of "B" and "C" modes or 1 st and 3 rd mechanical harmonic in SC cut resonators. The second method have low temperature sensitivity and the first method have great one, but disadvantage because in majority of realization it may be obtained as called "activity dips" oscillation decay at specific temperatures. It is shown that the reason of B mode activity dip is acoustic interaction of B mode with C mode inharmonic. The algebraic expression describes this phenomenon are shown. The numerically analytical method of dual mode resonator modeling is described. This method allows obtain modes parameters (motional resistance, modes frequencies, thermal time constants) as a function of plate sizes, electrode sizes and plate curvature.