A. Abrol, Z. Zhu, Y. Han, J. Clark
Keywords: zero damping, force feedback
Summary:We experimentally validate near-zero apparent damping of MEMS resonators in air at standard temperature and pressure. The amount of damping is controlled by feeding back an electrostatic force onto the proof mass that is proportional to, and in the direction of, the velocity of the proof mass. The feedback circuit has two main parts: a velocity sensor (BJT-based Current Conveyor) and a damping force actuator (BJT-based square root circuit) that feeds back a force that is proportional to velocity. Previously, we derived the concept of using electrostatic feedback to control the amount of effective damping . This technique may improve certain applications where high-Q or high signal to noise ratio (SNR) is needed, such as navigation-grade gyros, clocks, or high frequency selectivity in wireless communication. A few methods by others to increase Q involved increasing stiffness or mass , optimizing structural designs to reduce damping , or improving high vacuum packaging . What is different about our method is that the damping is dynamically controllable and the method is lower in cost. For this paper, the MEMS device design consists of sense and actuation comb drives attached to a proof mass that is supported by folded flexures. The amount of energy fed back into the system is equivalent to the energy lost per cycle from natural damping. Through this study we experimentally validate our concept for apparent reduction in damping in MEMS by using off-the-self analog electronic components for feedback performance control and the possibility of a high-Q low-cost MEMS resonator. In the full paper, proof of concept will be demonstrated by comparing families of frequency responses where effective damping is reduced by electrostatic force feedback while the MEMS device is exposed to the atmosphere. Values for damping and Q will be measured by electro micro metrology (EMM). EMM is a metrology method where mechanical quantities can be measured by electronic probing.  J. V. Clark, O. Misiats, S. Sayed, “Electrical control of effective mass, damping, and stiffness of MEMS devices”. IEEE Sensors Journal, 2017, 17(5): 1363-1372.  C. Li, M. Miller “Investigation of air damping and Q in a MEMS resonant mass sensor” Proceedings of the ASPE Annual Meeting, 2008  F. R. Blom, S. Bouwstra, M. Elwenspoek, and J. H. J. Fluitman, “Dependence of the quality factor of micromachined silicon beam resonators on pressure and geometry” Journal of Vacuum Science & Technology B: Microelectronics and Nanometer Structures Processing, Measurement, and Phenomena, 1992, pp.19-26  K. Wang, A.-C. Wong, and C. T. Nguyen, "VHF free-free beam high-Q micromechanical resonators," in Journal of Microelectromechanical Systems, vol. 9, no. 3, pp. 347-360, Sept. 2000.