Congzhong Guo

Large-displacement parametric resonance using a shaped comb drive

This paper is the first demonstration of large-stroke parametric resonance excited by an in-plane “shaped-finger” electrostatic comb drive. A custom-shaped comb finger profile is used to produce a quadratic capacitance-engagement response. The ability in selecting electrostatic stiffness coefficients by engineering the comb finger profile allows the excitation of the nonlinear parametric resonance for various applications such as the mode-matched gyroscopes and gravimetric sensors. The shaped-finger comb enables the study of the parametric resonance in systems with high energy storage. The shaped-finger comb parametric resonator is fabricated by a 15 μm-thick SOI-MEMS process.

Behavioral Modeling of a CMOS–MEMS Nonlinear Parametric Resonator

Predictive design of nonlinear microelectromechanical systems featuring parametric resonance provides motivation to refine mixed MEMS/analog behavioral composable modeling and simulation methodologies. Toward this end, a schematic of a canonical parametric resonator testbed is built with primitive beam, plate, and gap models from a MEMS Verilog-AMS library along with a macro model of a non-interdigitated comb with electrostatic spring coefficients extracted from finite element analysis. A CMOS-MEMS parametric resonator for validation experiments exploits the well known non-interdigitated finger design to create a voltage-controlled spring constant as the parametric stimulus. Behavioral modeling and the analytic perturbation solutions are validated by optical vibration measurements matching to 0.2% and 2.1%, respectively.

Electrically driven CMOS-MEMS nonlinear parametric resonator design using a hierarchical MEMS circuit library

We are investigating a class of nonlinear resonators which feature parametric excitation when driven by an electrostatic force whose linear and cubic stiffness can be parametrically controlled by a pump drive oscillating voltage applied across the non-interdigitated comb fingers. The perturbation theory is employed in solving the Mathieu equation to quantitatively explain the nonlinear resonance phenomenon and to provide a closed-form solution which captures the dynamic behavior and its dependence on system parameters. We have implemented an electrically driven CMOS-MEMS nonlinear parametric resonator to validate system-level composable modeling of this complex behavior.

Behavioral modeling and testing of a CMOS-MEMS parametric resonator governed by the nonlinear Mathieu equation

Modeling and simulation of complex phenomena in environments that emulate end applications demonstrate the effectiveness of MEMS composable design methodologies. A CMOS-MEMS nonlinear resonator featuring parametric excitation driven by an oscillating voltage applied across the non-interdigitated comb fingers has been targeted as a demonstration vehicle. This paper reports the schematic-based parameterized behavioral modeling and vibration testbed of parametric resonators governed by the nonlinear Mathieu equation. The linear and cubic stiffness of the electrostatic force and the folded flexure are modeled by Verilog-A MEMS behavioral models. The transition frequencies and the jump amplitudes are characterized optically by sweeping the frequency bi-directionally. The observed parametric resonance, occurring near excitation frequency of twice the resonant frequency, is verified by perturbation solution of Mathieu equation, and validated by circuit-level behavioral model simulation matching to 0.6%. The dynamic behavior and its dependence on system parameters are also analyzed.

Bi-state control of parametric resonance

We report a bi-state controller capable of serving along the microelectromechanical parametric resonant bifurcation point at large displacement amplitudes. The feedback states are two levels of the electrostatic-drive polarization voltage that shift the nonlinear resonance characteristics. The system is driven at a fixed frequency. The feedback states correspond to two steady-state conditions: the “on” state experiencing parametric resonance and the “off” state at zero amplitude. The states are cycled by 200 kHz pulse-width-modulation that circumvents hysteretic latch-on that occurs in an equivalent continuous-time analog feedback. The exemplary system demonstrated has 1.9 μm servo amplitude with 2 A minimum Allan deviation.

Bi-State Bifurcation Control of a Shaped-Comb Parametric Resonator

This work employs behavioral modeling to develop a bi-state control technique capable of servoing at the onset of the microelectromechanical parametric resonant bifurcation setpoint. The parametric resonance features a sharp “turn-on” in oscillation amplitude at the bifurcation, enhancing sensitivity to resonance frequency change. A bi-state controller is constructed to servo at this sharp jump point. It has two states of operation: one state is within the instability tongue where the oscillation amplitude builds up exponentially; another state resides outside of the tongue where the oscillation turns off. The rapid turn on and off of the parametric resonance keeps the resonant amplitude small and circumvents the slow build-up time. Both the simulated and experimental loop transient responses are presented.Copyright

2-DoF twisting electrothermal actuator for Scanning Laser Rangefinder application

This paper reports the design, modeling and characterization of a 2-DoF twisting electrothermal (ET) actuator for reducing parasitic motion in the application of an SOI-CMOS-MEMS-based Scanning Laser Rangefinder (SLR). A schematic-based model was built using a hierarchical MEMS behavioral model library (NODAS) to develop the concept of independently actuating two parallel metal-polysilicon-oxide CMOS-MEMS vertical electrothermal actuators for scanning control. The small in-plane parasitic motion, which is essential for laser alignment, is less than 2 µm. The optical scanning range of 31° about the y-axis and 20° about the x-axis were obtained at 8.6 mW and 14.7 mW, respectively, with a small device footprint of 191 µm – 156 µm.