Micromechanical Resonant Displacement Gain Stages
Bongsang Kim1 and Clark Nguyen
Defense Advanced Research Projects Agency
There have been many breakthrough efforts in RF MEMS over the past decade. In particular, bulk mode resonators, such as disk resonators and square resonators, have substantially raised the resonant frequencies and high quality factors achievable by vibrating micromechanical resonators. In this work, new design techniques are introduced to effect displacement amplification in such bulk mode resonators at resonance. The availability of high-frequency displacement gain strategies enables efficient all-MEMS transmit power amplifiers (e.g., for wireless communications), especially when employing resonant switch (i.e., “resoswitch”) operation principles. Displacement amplified resonators also offer better control over energy loss and energy storage in resonator networks, enabling more efficient engineering towards a higher quality factor.
Micromechanical resonant displacement gain stages have been demonstrated that employ directionally engineered stiffnesses in resonant structures to yield displacement amplifications from a driven input axis to an output axis. Specifically, the introduction of slots along the output axis of a 53-MHz wine-glass mode disk resonator structure (shown in Figures 1 and 2) effects a single gain stage with input-to-output displacement amplification of 3.08x. Multiple such mechanical displacement gain stages can then be cascaded in a series via half-wavelength mechanical couplers as shown in Figure 3 to achieve multiplicative gain factors; e.g., two cascaded gain stages achieves a total measured gain of 7.94x. This effective displacement amplification was verified not only analytically via ANSYS finite element simulation (Figure 4), both also experimentally using polysilicon capacitively transduced MEMS resonators (Figure 5). Also, preliminary “resoswitch” operation of a single gain stage (i.e., slotted disk) has been demonstrated, as shown in Figure 6.
Figure 1: SEMs of a micromechanical resonant single gain stage. Here, slots (5 μm x 16 μm) etched into a polycrystalline silicon wine-glass mode disk resonator constitute the key.
Figure 2: a) ANSYS FEA results of the resonant gain stage in Figure 1. In the wine-glass mode, the displacement along the slotted axis is larger by 2.94x than the orthogonal axis. b) Displacement comparison between a conventional disk resonator and the resonant gain stage. Here, displacements are normalized to the maximum displacement of the conventional disk resonator.
Figure 3: SEM image of mechanically cascaded resonant gain stages. Two gain stages (disk resonators with slots) are coupled via a half-wavelength extensional-mode beam for further displacement amplification. The coupling beam connects a point along the slotted axis of the first resonator to a point along the un-slotted axis of the second to effect multiplication of gains.
Figure 4: ANSYS FEA simulation predicts multiplication of displacement gains when gain stages are series-cascaded. a) A two gain stage cascade yields 8.10x total displacement amplification. b) A four gain stage cascade yields 74x total gain.
Figure 5: Comparison of measured power at each electrode of each resonator design. The displacement along each axis was extracted from the measured current out of each electrode. a) A conventional wine-glass mode disk resonator, b) Single resonant gain stage (slotted disk), c) Cascade of two slotted disk gain stages. The conventional disk resonator had virtually no displacement gain within the measurement error range, while the single-gain stage and two cascaded-gain stages had 3.07x and 7.94x displacement amplification, respectively.