In this paper, a detailed study of the nonlinearities in a high-Q SOI Lamé-mode bulk resonator is reported. The bulk resonator is designed to operate at 6.35 MHz with a quality factor of 1.7 million at air pressure below 100 Pa. As the vibration amplitude increases, the transmission curve of the resonator progressively bends to lower frequencies due to spring softening effects. The model parameters of the resonator are quantified based on some preliminary experimental results and verified by numerical calculation. Compared with a flexural-mode beam resonator, the Lamé-mode bulk resonator is much less susceptible to nonlinear effects and thus can store three orders of magnitude more vibration energy before frequency hysteresis occurs. Closed-loop measurement further demonstrates that the ultra-high quality factor and superior power handling capability enable the Lamé-mode based oscillator to achieve 42 dB lower phase noise than the flexural-mode one at 10 Hz offset from the carrier frequency.

In this paper, a 10MHz micromechanical reference oscillator is presented by combining lamé-mode bulk resonator with Q above 200,000 and low noise offchip interface circuitry. Benefiting from high quality factor as well as large energy storage capability of the bulk resonator, low phase noise performance has been achieved even when the resonator is operating in nonlinear region with a 4Vp-p oscillation output. A clear sine wave output signal is observed and the oscillator shows -138dBc/Hz noise floor and -132dBc/Hz 1kHz away from the carrier, which meets the cellular phase noise requirement of -130dBc/Hz at 1kHz offset for 13MHz GSM reference oscillators. Such oscillator does not require any gain limiting circuitry and hence makes the implementation much simpler and less noisy.

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