Exploiting nonlinearities in MEMS : applications to energy harvesting and RF communication

Abstract

Traditionally, in engineering, nonlinear behaviour is avoided, however engineering applications that are intended to create a nonlinear relationship between inputs and outputs also exist. In this thesis, it is shown that exploiting nonlinear phenomena in MEMS design is instrumental in providing counter intuitive solutions to an application involving a vibrational energy harvester and another two designs with applications to communication signal processing. Vibrational energy harvesters at MEMS scale are generally a challenge since at these scales resonant frequencies are in the kHz range and this makes them insensitive to the lower frequencies that are more abundant in the environment. One solution is to include a nonlinear spring such that the harvester becomes sensitive to broadband base excitations. In this work, one such broadband harvester is designed by making use of a ‘quintic’ stiffness, buckling (bistable) spring. The novel aspect in this work can be attributed to the topological arrangement of the two buckling beams and the mass. The arrangement allows only the required beam modes to dominate and together with the designed beam boundary conditions, it is possible to replace the non-linear partial differential equation model (resulting from continuum mechanics) with a simpler nonlinear differential equation. It is demonstrated that this simpler model can still capture the salient characteristics of the complex buckling behaviour; replacing complex finite element analysis simulations with simple numerical solutions of differential equations and hastening the design process. Although the design was constrained geometrically to satisfy this simpler mathematical model, it is demonstrated that these constraints do not impinge negatively on the harvesting capabilities. The harvester has a power destiny of 0.13 mW cm-3 at 3.5g ms-2 at 560 Hz of vibrational excitation. The second design involves a torsionally vibrating plate which is capable of binary phase shift keying demodulation. This plate is driven by electrostatic forces and electrostatics provide signal mixing. The target application is demodulation of signals encoded according to the 802.15.4 standard which describes a low data rate BPSK signalling with a carrier frequency of 868 MHz and a chip rate of 300 kchips/s. It is shown that the torsional plate has a damped resonant frequency of 1.54 MHz and this being greater than the 3rd harmonic of the data rate recovers the baseband signal successfully with 20 V peak of actuation voltages. At normal temperature and pressure, the resulting Q-factor was found to be 60 which narrows the frequency response and as a result the baseband signal recovered is slightly oscillatory. This same torsional plate is investigated under higher actuation voltages and it is shown that when actuation voltages exceed 75 V, nonlinear spring behaviour dominates the response and chaotic trajectories in phase-space appear. At these higher voltages, this device can be used for different purposes, for example, as a hardware random number generation and a chaotic carrier generator. One drawback of using electrostatics for mixing purposes is that apart from the required pure mixing components, spurious products also appear. This is due to the quadratic relationship in the electrostatic interaction and these would need to be filtered out mechanically. However, it is shown that with a differential electrostatic drive using the same torsional plate, these spurious products are attenuated and the resulting plate displacement becomes practically proportional to pure signal mixing. This relaxes the bandwidth-selectivity trade-off in the mechanical filtering and consequently relieves some of the dimensional constraints of the torsional plate. With this possibility, an in-phase/quadrature mixer is designed that is able to demodulate different quadrature amplitude modulated signals with drive voltage levels at 17 Vrms, a footprint of around 40,000 µm2 and giving output voltage levels of 0.18 Vrms for the in-phase and quadrature signals.Two features are considered novel in this design; the width of application and the ability to approximate pure mixing. These features are a result of the adopted torsional topology. In the final design, also related to communication signal processing, a MEMS device is presented that is able to convert a BPSK signal to a simpler amplitude shift keying modulation scheme. Although the structure involves also rotational motion, the topology is very different and much more complex than the designs mentioned previously. A mathematical model was developed and validated against finite element analysis simulation results and this was used to obtain optimised dimensions using a hybrid particle swarm optimisation algorithm. The design, with a footprint of 2.9 mm2, was fabricated and experimentally validated. It was tested with carrier frequencies ranging from 174 kHz to 1 MHz at a binary phase shift keying (BPSK) data rate of 6.6 kbps and with carrier amplitudes of 9.7 V, resulting in an amplitude shift keying (ASK) modulation index of 0.79 at the output sensors and a power consumption of 2.9 𝜇W. The novelty of this device is that it provides a MEMS solution for BPSK to ASK conversion, a function that has always been realised in CMOS as the first stage to BPSK demodulation. The device is capable of meeting current specification requirements (data rates, power consumption and footprint) for implantable medical devices. It is demonstrated that the power consumption is low enough such that it provides an attractive alternative to CMOS realisations. Moreover, being a MEMS, has potential for integration with MEMS sensors and harvesters in wireless sensor network nodes.