Parametric amplification of a resonant MEMS mirror with all-piezoelectric excitation

Abstract

We report a resonant torsional micro-mirror with all-piezoelectric driving and tunable spring stiffness. Stiffness modulation finds two practical applications. First is tuning of the resonance frequency, achieved by applying DC bias voltage to the stiffness modulating structures. A tuning rate was found to be 0.95 Hz V−1 with up to 20 Hz of usable frequency range. Second, when direct excitation of the torsional mode is combined with the harmonic modulation of the spring stiffness, an optical scan angle is shown to be increased by more than 4° through 2:1 degenerate parametric amplification. By varying the phase of the parametric pump with respect to the direct excitation, the Q-factor is tuned between 617 and 898, corresponding to the minimum and maximum parametric gain factors of 0.84× and 1.21×, respectively, achieved at a nominal unpumped optical scan angle of 16.3°. Increasing the pump amplitude shows a moderate increase in the amplifier's gain with clear saturation at 1.43× in the superthreshold pumping regime, indicating a presence of the third order stiffness nonlinearity. The results show potential to apply parametric amplification to future piezo-micro-electro-mechanical-system actuators for large frequency and large-stroke mechanical response achieved at ambient pressure.

Parametric Amplification of Acoustically Actuated Micro Beams Using Fringing Electrostatic Fields

“…The modal acoustic force coefficient η was chosen such that for the adopted actuation parameters V spkr = 10 V, ϕ = 0, Q = 100 (and consistently with the experiments), the resulting resonant amplitude deflection would be 0.9 µm. Comparison between the vibrational amplitudes obtained using the approximate asymptotic model, Equation (9), with the results of the direct numerical integration of Equation (2) show good agreement between the two. In our numerical solution, the equation of motion Equation (2) completed by zero initial conditions was solved numerically for several values of the driving ω and pumping ω p frequencies.…”

“…Parametric amplification plays an important role in resonant micro and nanoelectromechanical (MEMS/NEMS) sensors due to its ability to bust vibrational amplitudes, improve frequency stability, and squeeze noise, therefore improving sensitivity [1][2][3][4][5][6][7][8][9][10]. Parametric amplification (also often referred to as parametric pumping [2,8,10,11]) of an external harmonic signal is achieved by time modulating the system's intrinsic, usually stiffness, parameters.…”

“…In microdevices, modulation of the (effective) spring constant is relatively straightforward due to the intrinsic nonlinearity of the actuation forces. The parametric pumping was realized using mainly electrostatic [1,[4][5][6]10,15,16] but also piezoelectric [1,9] or magnetic [7] actuation. Interestingly, the realization of a linear direct forcing in MEMS/NEMS structures could be more challenging than the parametric amplification itself.…”

A C-shaped hinge for displacement magnification in MEMS rotational structures

“…However, these changes are often small and require amplification mechanisms to improve the sensitivity of the device 2 , 3 . Amplifying displacement is a critical aspect of MEMS technology, especially in applications where a large movement or change in capacitance is needed 4 . Different mechanisms have been proposed 1 , 3 , 5 to amplify the displacements in the actuators, sensors, and stress diagnosis structures.…”

Smart Materials and Metamaterials for Mems: A Growing Trend in Microsystems Technology

“…As meaningful and recent examples of the use of smart materials in microsystems we can cite here piezoelectric actuated micro-mirrors [5,6], micro-speakers [7,8], and micro-ultrasonic transducers (PMUT) [9 -12].…”