Nonlinear behavior of Lamé-mode SOI bulk resonator

Abstract

In this paper, we report for the first time the detailed analysis of the nonlinear behavior of a Lamé-mode SOI bulk resonator. The measured resonant frequency of the resonator was 6.35MHz with a quality factor of 1.7 million in the ambient pressure of 0.02Pa. We used the two-step semi-analytic approach to characterize the model parameters of the resonator and the nonlinear model of the resonator was verified by the experimental results. Our study shows that the Lamé-mode bulk resonator has three orders of magnitude larger maximum energy storage capability than the flexural beam resonator, leading to improved overall phase noise performance of the resonator-based oscillator.

A low phase noise 10MHz micromechanical lamé-mode bulk oscillator operating in nonlinear region

“…After V P is fixed at 75V, oscillation is settled at 3.94V p-p , as shown in Figure 6. The amount of oscillation amplitudes indicates that the resonator is operating in nonlinear region [8]. Nonetheless, this oscillator still provides undistorted and clean sine wave, implying a less sensitivity to nonlinear effects.…”

Low motional impedance distributed Lamé mode resonators for high frequency timing applications

“…The various parameters measured for different types of resonators are highlighted in Table 1. Figure 2 shows the comparison of high f.Q product in-plane Lamé mode silicon resonators in literature 3,4,6,[16][17][18][19][20][21][22][23][24][25] with the resonators fabricated in this work. With the distributed design, the three DLRs with narrow beam width successfully demonstrated high frequencies beyond the reach of any other in-plane Lamé mode designs, while maintaining a high f.Q product close to the estimated range of Akhiezer limit for shear modes in silicon 18,26 .…”

High-Qbulk-mode SOI square resonators with straight-beam anchors

“…Recent research has focused on micromechanical resonators with a high quality factor (Q) suitable for frequency reference and signal processing applications such as oscillators, mixers and filters [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. For resonators targeted towards VHF and UHF frequency ranges, bulk-mode and contour-mode micromechanical resonators have been shown to provide higher Q values along with better power handling capabilities compared to the flexural-type beam resonators [4][5][6]. Tradeoffs between Q and power handling are critical in setting the close-to-carrier and far-from-carrier phase noise for oscillator applications [4].…”

“…The importance of power handling capabilities for an oscillator can be demonstrated by examining Leeson's equation of phase-noise density to carrier power ratio. According to Leeson's equation, the overall phase noise can be reduced with an increase in oscillation output signal power (P out ) [4], or with an increase in vibration energy stored in the resonator (E stored ) [5]. The expression for P out is given by…”