Reduced-order modelling, circuit-level design and SOI fabrication of microelectromechanical resonators

This thesis deals with two important research aspects concerning radio frequency (RF) microresonators and switches. First, a new approach for compact modeling and simulation of these devices is presented. Then, a combined process flow for their simultaneous fabrication on a SOI substrate is proposed. Compact models for microresonators and switches are extracted by applying mathematical model order reduction (MOR) to the devices finite element (FE) description in ANSYS c° . The behaviour of these devices includes forms of nonlinearities. However, an approximation in the creation of the FE model is introduced, which enables the use of linear model order reduction. Microresonators are modeled with the introduction of transducer elements, which allow for direct coupling of the electrical and mechanical domain. The coupled system element matrices are linearized around an operating point and reduced. The resulting macromodel is valid for small signal analysis around the bias point, such as harmonic pre-stressed analysis. This is extremely useful for characterizing the frequency response of resonators. Compact modelling of switches preserves the nonlinearity of the device behaviour. Nonlinear reduced order models are obtained by reducing the number of nonlinearities in the system and handling them as input to the system. In this way, the system can be reduced using linear MOR techniques and nonlinearities are introduced directly in the reduced order model. The reduction of the number of system nonlinearities implies the approximation of all distributed forces in the model with lumped forces. Both for microresonators and switches, a procedure for matrices extraction has been developed so that reduced order models include the effects of electrical and mechanical pre-stress. The extraction process is fast and can be done automatically from ANSYS binary files. The method has been applied for the simulation of several devices both at devices and circuit level. Simulation results have been compared with full model simulations, and, when available, experimental data. Reduced order models have proven to conserve the accuracy of finite element method and to give a good description of the overall device behaviour, despite the introduced approximations. In addition, simulation is very fast, both at device and circuit level. A combined process-flow for the integrated fabrication of microresonators and switches has been defined. For this purpose, two processes that are optimized for the independent fabrication of these devices are merged. The major advantage of this process is the possibility to create on-chip circuit blocks that include both microresonators and switches. An application is, for example, aswitched filter bank for wireless transceiver. The process for microresonators fabrication is characterized by the use of silicon on insulator (SOI) wafers and on a deep reactive ion etching (DRIE) step for the creation of the vibrating structures in single-crystal silicon and the use of a sacrificial oxide layer for the definition of resonator to electrode distance. The fabrication of switches is characterized by the use of two different conductive layers for the definition of the actuation electrodes and by the use of a photoresist as a sacrificial layer for the creation of the suspended structure. Both processes have a gold electroplating step, for the creation of the resonators electrodes, transmission lines and suspended structures. The combined process flow is designed such that it conserves the basic properties of the original processes. Neither the performance of the resonators nor the performance of the switches results affected by the simultaneous fabrication. Moreover, common fabrication steps are shared, which allows for cheaper and faster fabrication.

Tools and methods for the quality assurance of force platforms in human movement analysis

The human movement analysis (HMA) aims to measure the abilities of a subject to stand or to walk. In the field of HMA, tests are daily performed in research laboratories, hospitals and clinics, aiming to diagnose a disease, distinguish between disease entities, monitor the progress of a treatment and predict the outcome of an intervention [Brand and Crowninshield, 1981; Brand, 1987; Baker, 2006]. To achieve these purposes, clinicians and researchers use measurement devices, like force platforms, stereophotogrammetric systems, accelerometers, baropodometric insoles, etc. This thesis focus on the force platform (FP) and in particular on the quality assessment of the FP data. The principal objective of our work was the design and the experimental validation of a portable system for the in situ calibration of FPs. The thesis is structured as follows: Chapter 1. Description of the physical principles used for the functioning of a FP: how these principles are used to create force transducers, such as strain gauges and piezoelectrics transducers. Then, description of the two category of FPs, three- and six-component, the signals acquisition (hardware structure), and the signals calibration. Finally, a brief description of the use of FPs in HMA, for balance or gait analysis. Chapter 2. Description of the inverse dynamics, the most common method used in the field of HMA. This method uses the signals measured by a FP to estimate kinetic quantities, such as joint forces and moments. The measures of these variables can not be taken directly, unless very invasive techniques; consequently these variables can only be estimated using indirect techniques, as the inverse dynamics. Finally, a brief description of the sources of error, present in the gait analysis. Chapter 3. State of the art in the FP calibration. The selected literature is divided in sections, each section describes: systems for the periodic control of the FP accuracy; systems for the error reduction in the FP signals; systems and procedures for the construction of a FP. In particular is detailed described a calibration system designed by our group, based on the theoretical method proposed by ?. This system was the “starting point” for the new system presented in this thesis. Chapter 4. Description of the new system, divided in its parts: 1) the algorithm; 2) the device; and 3) the calibration procedure, for the correct performing of the calibration process. The algorithm characteristics were optimized by a simulation approach, the results are here presented. In addiction, the different versions of the device are described. Chapter 5. Experimental validation of the new system, achieved by testing it on 4 commercial FPs. The effectiveness of the calibration was verified by measuring, before and after calibration, the accuracy of the FPs in measuring the center of pressure of an applied force. The new system can estimate local and global calibration matrices; by local and global calibration matrices, the non–linearity of the FPs was quantified and locally compensated. Further, a non–linear calibration is proposed. This calibration compensates the non– linear effect in the FP functioning, due to the bending of its upper plate. The experimental results are presented. Chapter 6. Influence of the FP calibration on the estimation of kinetic quantities, with the inverse dynamics approach. Chapter 7. The conclusions of this thesis are presented: need of a calibration of FPs and consequential enhancement in the kinetic data quality. Appendix: Calibration of the LC used in the presented system. Different calibration set–up of a 3D force transducer are presented, and is proposed the optimal set–up, with particular attention to the compensation of non–linearities. The optimal set–up is verified by experimental results.

Models and methods for power monolithic microwave integrated circuits

Computer aided design of Monolithic Microwave Integrated Circuits (MMICs) depends critically on active device models that are accurate, computationally efficient, and easily extracted from measurements or device simulators. Empirical models of active electron devices, which are based on actual device measurements, do not provide a detailed description of the electron device physics. However they are numerically efficient and quite accurate. These characteristics make them very suitable for MMIC design in the framework of commercially available CAD tools. In the empirical model formulation it is very important to separate linear memory effects (parasitic effects) from the nonlinear effects (intrinsic effects). Thus an empirical active device model is generally described by an extrinsic linear part which accounts for the parasitic passive structures connecting the nonlinear intrinsic electron device to the external world. An important task circuit designers deal with is evaluating the ultimate potential of a device for specific applications. In fact once the technology has been selected, the designer would choose the best device for the particular application and the best device for the different blocks composing the overall MMIC. Thus in order to accurately reproducing the behaviour of different-in-size devices, good scalability properties of the model are necessarily required. Another important aspect of empirical modelling of electron devices is the mathematical (or equivalent circuit) description of the nonlinearities inherently associated with the intrinsic device. Once the model has been defined, the proper measurements for the characterization of the device are performed in order to identify the model. Hence, the correct measurement of the device nonlinear characteristics (in the device characterization phase) and their reconstruction (in the identification or even simulation phase) are two of the more important aspects of empirical modelling. This thesis presents an original contribution to nonlinear electron device empirical modelling treating the issues of model scalability and reconstruction of the device nonlinear characteristics. The scalability of an empirical model strictly depends on the scalability of the linear extrinsic parasitic network, which should possibly maintain the link between technological process parameters and the corresponding device electrical response. Since lumped parasitic networks, together with simple linear scaling rules, cannot provide accurate scalable models, either complicate technology-dependent scaling rules or computationally inefficient distributed models are available in literature. This thesis shows how the above mentioned problems can be avoided through the use of commercially available electromagnetic (EM) simulators. They enable the actual device geometry and material stratification, as well as losses in the dielectrics and electrodes, to be taken into account for any given device structure and size, providing an accurate description of the parasitic effects which occur in the device passive structure. It is shown how the electron device behaviour can be described as an equivalent two-port intrinsic nonlinear block connected to a linear distributed four-port passive parasitic network, which is identified by means of the EM simulation of the device layout, allowing for better frequency extrapolation and scalability properties than conventional empirical models. Concerning the issue of the reconstruction of the nonlinear electron device characteristics, a data approximation algorithm has been developed for the exploitation in the framework of empirical table look-up nonlinear models. Such an approach is based on the strong analogy between timedomain signal reconstruction from a set of samples and the continuous approximation of device nonlinear characteristics on the basis of a finite grid of measurements. According to this criterion, nonlinear empirical device modelling can be carried out by using, in the sampled voltage domain, typical methods of the time-domain sampling theory.

A Design Method for Flexure-Based Compliant Mechanisms on the Basis of Stiffness and Stress Characteristics

Geometric nonlinearities of flexure hinges introduced by large deflections often complicate the analysis of compliant mechanisms containing such members, and therefore, Pseudo-Rigid-Body Models (PRBMs) have been well proposed and developed by Howell [1994] to analyze the characteristics of slender beams under large deflection. These models, however, fail to approximate the characteristics for the deep beams (short beams) or the other flexure hinges. Lobontiu's work [2001] contributed to the diverse flexure hinge analysis building on the assumptions of small deflection, which also limits the application range of these flexure hinges and cannot analyze the stiffness and stress characteristics of these flexure hinges for large deflection. Therefore, the objective of this thesis is to analyze flexure hinges considering both the effects of large-deflection and shear force, which guides the design of flexure-based compliant mechanisms. The main work conducted in the thesis is outlined as follows. 1. Three popular types of flexure hinges: (circular flexure hinges, elliptical flexure hinges and corner-filleted flexure hinges) are chosen for analysis at first. 2. Commercial software (Comsol) based Finite Element Analysis (FEA) method is then used for correcting the errors produced by the equations proposed by Lobontiu when the chosen flexure hinges suffer from large deformation. 3. Three sets of generic design equations for the three types of flexure hinges are further proposed on the basis of stiffness and stress characteristics from the FEA results. 4. A flexure-based four-bar compliant mechanism is finally studied and modeled using the proposed generic design equations. The load-displacement relationships are verified by a numerical example. The results show that a maximum error about the relationship between moment and rotation deformation is less than 3.4% for a flexure hinge, and it is lower than 5% for the four-bar compliant mechanism compared with the FEA results.

Nonlinear Observers for Sensorless Control of Permanent Magnet Synchronous Motors

In this thesis, the industrial application of control a Permanent Magnet Synchronous Motor in a sensorless configuration has been faced, and in particular the task of estimating the unknown “parameters” necessary for the application of standard motor control algorithms. In literature several techniques have been proposed to cope with this task, among them the technique based on model-based nonlinear observer has been followed. The hypothesis of neglecting the mechanical dynamics from the motor model has been applied due to practical and physical considerations, therefore only the electromagnetic dynamics has been used for the observers design. First observer proposed is based on stator currents and Stator Flux dynamics described in a generic rotating reference frame. Stator flux dynamics are known apart their initial conditions which are estimated, with speed that is also unknown, through the use of the Adaptive Theory. The second observer proposed is based on stator currents and Rotor Flux dynamics described in a self-aligning reference frame. Rotor flux dynamics are described in the stationary reference frame exploiting polar coordinates instead of classical Cartesian coordinates, by means the estimation of amplitude and speed of the rotor flux. The stability proof is derived in a Singular Perturbation Framework, which allows for the use the current estimation errors as a measure of rotor flux estimation errors. The stability properties has been derived using a specific theory for systems with time scale separation, which guarantees a semi-global practical stability. For the two observer ideal simulations and real simulations have been performed to prove the effectiveness of the observers proposed, real simulations on which the effects of the Inverter nonlinearities have been introduced, showing the already known problems of the model-based observers for low speed applications.