AVS 62nd International Symposium & Exhibition
    Nanometer-scale Science and Technology Thursday Sessions
       Session NS+MN-ThM

Invited Paper NS+MN-ThM10
Frequency Division Using a Micromechanical Resonance Cascade

Thursday, October 22, 2015, 11:00 am, Room 212B

Session: Nanopatterning and Nanolithography/Nanoscale Mechanics
Presenter: Kimberly Turner, University of California, Santa Barbara
Authors: K. Qalandar, University of California, Santa Barbara
M. Sharma, University of California, Santa Barbara
B. Gibson, University of California, Santa Barbara
K.L. Turner, University of California, Santa Barbara
Correspondent: Click to Email
A coupled micromechanical resonator array demonstrates the first successful realization of multi-stage frequency division. Frequency converters, dividers and multipliers, are necessary over a wide range of frequencies for a variety of applications, including vibration energy harvesters, RF transceivers, phase-locked loops, and quantum cascade lasers. In the VHF and UHF frequency range, solid-state and electromagnetic devices have traditionally dominated on-chip signal processing activities due to their wide bandwidth operation, programmability, and ease of implementation. However, design becomes more complicated and noise increases when cascading electronic dividers, due to buffers, amplifiers, and complex impedance matching circuits. Increasing constraints in size, power, and phase noise have led microelectromechanical systems (MEMS) to be considered in place of many traditional electronic elements. In particular, MEMS resonators are of interest since these high Q narrow bandwidth devices can provide better phase noise characteristics than similar devices that utilize amplifier technology. Coupled vibratory modes in micro-resonators have been shown to provide phase noise improvements in frequency sources, and have been considered in other contexts. This frequency divider combines the benefits of cascading, internal resonance, and mechanical coupling in a single micro-device. The operation is based on nonlinear dynamics and exploits the robustness of parametric resonance. This narrow-band approach uses a subharmonic resonance cascade in a chain of internally resonant subsystems with specific coupling that allows energy exchange between successive divide-by-two stages. The mechanical structure consists of a set of N sequentially perpendicular microbeams that are connected by relatively weak elastic elements such that the system vibration modes are localized to individual microbeams and have natural frequencies with ratios close to 1 : 2 : _ _ _ : 2N. Conservative (passive) nonlinear inter-modal coupling provides the required energy transfer between modes and is achieved by finite deformation kinematics. When the highest frequency beam is excited, this arrangement promotes a cascade of subharmonic resonances that achieve frequency division of 2j at microbeam j for j = 1; : : : ;N. Results are shown for a capacitively driven three-stage divider in which an input signal of 824 kHz is passively divided through three modal stages, producing signals at 412 kHz, 206 kHz and 103 kHz. The system modes are characterized and used to delineate the range of AC input voltages and frequencies over which the cascade occurs. This narrow band frequency divider has simple design rules that are scalable to higher frequencies, and can be extended to a larger number of modal stages.