Frequency division using a micromechanical resonance cascade

Abstract

Frequency conversion mechanisms are essential elements in frequency synthesizers, which are used in many applications ranging from microwave and RF transceivers to wireless applications to vibration energy harvesters. In particular, the frequency divider, which is an integral part of the phase-locked loop circuit, is essential in modern day instrumentation and wireless communications. In most systems requiring frequency conversion, electronic frequency converters are used; these components require significant power input and introduce noise into the system. In this dissertation, we introduce a mechanism for eliminating these noisy electronic components by using coupled mechanical elements. This novel mechanism for frequency division using parametric resonance in MEMS relies on finite deformation kinematics and nonlinear coupling between isolated modes in a structure to divide an input signal through multiple stages using purely mechanical coupling. We present the theoretical framework for a generic subharmonic resonance cascade. Design considerations for one specific implementation are discussed, and x a proof-of-concept for low-noise low-power applications is demonstrated. A single input signal is divided through three modal stages, generating output signals at 1 2 , 1 4 , and 1 8 of the input signal. Coupling and boundary conditions are explored, as well as the noise characteristics of this mechanical frequency divider. We show that this type of cascading frequency conversion improves phase noise performance of each individual mode.

Structural optimization for nonlinear dynamic response

“…Also, as observed in the equation for q 1 in the reduced-order model, β is essentially the amplitude of the parametric excitation provided to mode 1 from mode 2, given by 2β 1 q 2 q 1 , and is therefore related to the stability region of the linear parametric resonance of q 1 . The q 2 1 term in the equation for q 2 captures the back-coupling of the driven mode onto the driving mode, as required for passive coupling, which is beneficial in frequency dividers [32]. The combined effect of this coupling is the possibility of energy transfer between the modes when there is a two-to-one internal resonance.…”

“…The response of the structure is governed by a model in which these two modes are coupled through resonant terms. In application, n such elements are linked to achieve division by 2 n ; division by eight has been experimentally achieved [32]. The reduced-order dynamic model with its conservative dynamics projected onto two nonlinear normal modes in curved, normal coordinates is written as…”

Strong internal resonance in a nonlinear, asymmetric microbeam resonator

“…These features include hysteresis phenomena, multivalued responses, amplitude bifurcations, amplitude-frequency dependencies, and various types of nonlinear resonances [4][5][6][7] . Along with the evolution in micro/nanotechnology, researchers have devoted vigorous efforts to exploring these nonlinear characteristics in various applications, such as mass sensing 8,9 , bio/chemical detection 10,11 , inertial sensors [12][13][14][15] , radio frequency communication circuits [16][17][18] , logic gates [19][20][21][22] , and optical resonators [23][24][25][26] .…”

Frequency doubling in elastic mechanisms using buckling of microflexures

“…Mechanical frequency and speed multiplier transmission mechanisms are necessary for a variety of applications, including tailoring microactuators, [1][2][3][4] quantum cascade lasers, 5 mass sensing, 6 vibration energy harvesting, 7 biosensing, 8 and motion sensors and accelerometers. 9 Furthermore, integration of frequency multiplier transmission mechanisms on a local mechanical resonator can approach the limits on position and displacement measurements, which are ultimately limited by quantum mechanics.…”