A delay line phase shifter for the 30-70 GHz range is presented that uses an aluminum micro-ribbon array fabricated in the ground plane of a microstrip transmission line. Phase shift is achieved by changing the propagation velocity of an RF signal in the transmission line by controlling the effective permittivity of the substrate. This is done by actuating the micro-ribbons away from the substrate. This phase shifter has the benefits of analog phase shifts and high Figure of Merit. Simulations were done to model the micro-ribbon deflections, transmission line performance and phase shift. Arrays of 5, 10, and 20 μm wide micro-ribbons were fabricated and tested. At 40.80 GHz, the 20 μm wide micro-ribbons had a measured phase shift of 33º with an actuation voltage of 120 V. The corresponding Figure of Merit was a negative value indicating that there was no line loss due to ribbon deflection.

A frequency selective surface (FSS) based on switchable slots in the ground plane is presented. The switching is done using an actuating MEMS bridge over the slot. The intent is to demonstrate the control of the resonance frequency of the FSS by deflecting the bridge. It is shown that by applying a voltage between the bridge and the ground plane, the bridge displaces and changes the system capacitance which in turn changes the resonance frequency. Two analyses are presented; (1) Electromechanical analysis to show how the bridge deflects by the voltage, (2) Electromagnetic analysis to show how the resonance frequency changes by the bridge deflection. The device was fabricated and tested. The measurement results are presented for two up and down positions of the MEMS bridge to verify the correctness of the theory and design.

Zugl.: Freiburg (Breisgau), Univ., Diss., 2007

Zugl.: Saarbrücken, Univ., Diss., 2008

abstract: This dissertation proposes a miniature FIR filter that works at microwave frequencies, whose filter response can ideally be digitally programmed. Such a frequency agile device can find applications in cellular communications and wireless networking. The basic concept of the FIR filter utilizes a low loss acoustic waveguide of appropriate geometry that acts as a traveling wave tapped-delay line. The input RF signal is applied by an array of capacitive transducers at various locations on the acoustic waveguide at one end that excites waves of a propagating acoustic mode with varying spatial delays and amplitudes which interfere as they propagate. The output RF signal is picked up at the other end of the waveguide by another array of capacitive transducers. Tuning of the FIR filter coefficients is realized by controlling the DC voltage profile applied to the individual transducers which essentially shapes the overall filter response. Equivalent circuit modeling of the capacitive transducer, acoustic waveguide and transducer-line coupling is presented in this dissertation. A theoretical model for the filter is developed from a general theory of an array of transducers exciting a waveguide and is used to obtain a set of filter design equations. A MATLAB based circuit simulator is developed to simulate the filter responses. Design parameters and simulation results obtained for an example waveguide structure are presented and compared to the values estimated by the theoretical model. A waveguide structure utilizing the Rayleigh-like mode of a ridge is then introduced. A semi-analytical method to obtain propagating elastic modes of such a ridge waveguide etched in an anisotropic crystal is presented. Microfabrication of a filter based on ridges etched in single crystal Silicon is discussed along with details of the challenges faced. Finally, future work and a few alternative designs are presented that can have a better chance of success. Analysis and modeling work to this point has given a good understanding of the working principles, performance tradeoffs and fabrication pitfalls of the proposed device. With the appropriate acoustic waveguide structure, the proposed device could make it possible to realize miniature programmable FIR filters in the GHz range. / Dissertation/Thesis / Ph.D. Electrical Engineering 2013

MEMS based mechanical switches are seen to be the likely replacements for CMOS based switches due to the several advantages that these mechanical switches have over CMOS switches. Mechanical switches can be used in systems under extreme conditions and also provide more reliability and cause less power loss. A major problem with mechanical switches is bouncing. Bouncing is an undesirable characteristic which increases the switching time and causes damage to the switch structure affecting the overall switch life. This thesis proposes a new switch design that may be used to mitigate bouncing by using two voltage sources using a double electrode configuration. The effect of many switch’s tunable parameters is also discussed and an effective tuning technique is also provided. The results are compared to the current control schemes in literature and show that the double electrode scheme is a viable control option.

In this study, we present analytical and experimental investigation of electrically actuated micro cantilever based resonators. These devices are fabricated using polyimide and coated with chrome and gold layers from both sides. The cantilevers are highly curled up due to stress gradient, which is a common imperfection in surface micro machining. Using a laser Doppler vibrometer, we applied a noise signal to experimentally find the first four resonance frequencies. Then, using a data acquisition card, we swept the excitation frequency around the first four natural modes of vibrations. Theoretically, we derived a reduced order model using the Galerkin method to simulate the dynamics of the system. Extensive numerical analysis and computations were performed. The numerical analysis was able to provide good matching with experimental values of the resonance frequencies. Also, we proved the ability to excite higher order modes using partial electrodes with shapes that resemble the shape of the mode of interest. Such micro-resonators are shown to be promising for applications in mass and gas sensing.

This work explores the physics of micro and nano-scale systems immersed in a fluid. Previous literature has established an understanding of the fluid-solid interaction for systems including cantilevers and doubly clamped beams. Building on these advances, this work extends the theory of doubly clamped beams with an arbitrary amount of tension. Both the driven and stochastic dynamics of a doubly clamped beam are explored. The driven dynamics are investigated for a spatially applied harmonic driving force, and demonstrates quantitative agreement with an experimental beam that is driven electrothermally, in both air and in water. For the stochastic dynamics, the noise spectrum describes the thermal fluctuations at a given frequency. The theoretical model provides an analytical expression for the noise spectrum from an arbitrary number of modes. The noise spectrum of the first eleven modes are computed, and show excellent agreement with the noise spectrum from finite element simulations, which is computed from the deterministic ring down. This agreement is shown across different fluids (air and water), and for multiple measuring points including at the beam midpoint and the quarter point. In addition to exploring the linear dynamics of these systems, the case of large perturbations, resulting in nonlinear dynamics, is explored. This regime is motivated by exploring the theoretical dynamics of a uniformly shrinking doubly clamped beam. The challenges of modeling such a beam using finite element simulations are discussed. As a simpler and more direct alternative to access the nonlinear regime, a virtual beam is defined. The virtual beam controls the nonlinearity of the restoring force by modifying the Young's modulus. This work defines the Young's modulus such that the restoring force is like a Duffing oscillator. Then, the dynamics of this virtual beam are explored in air and water, and it is demonstrated that the Duffing oscillator serves as an appropriate reduced order model for this virtual beam. To understand the stochastic dynamics of the virtual beam, the stochastic Duffing oscillator is solved numerically. The ensemble autocorrelation of the beam dynamics are investigated for nonlinearities varying from linear to strongly nonlinear. The numeric autocorrelation is used to quantify the range of nonlinear strength where a deterministic approach, the ring down, can yield a good approximation. In the strongly nonlinear regime, the stochastic numerical approach is used to determine the autocorrelation. This research was supported by the National Science Foundation, grant number CMMI-2001559, and portions of the computations were conducted using the resources of Virginia Tech's Advanced Research Computing center. / Doctor of Philosophy / This work explores the physics of small systems immersed in a fluid, such as air or water. Previous literature has established an understanding of the force from a fluid acting on solids such as cantilevers and doubly clamped beams. Building on these advances, this work extends theory to doubly clamped beams with any amount of tension. Both the driven and stochastic, or randomly driven, dynamics of a doubly clamped beam are explored. The driven dynamics are developed for a driving force applied over part of the beam, and demonstrates quantitative agreement with an experimental beam, in both air and in water. For the stochastic dynamics, the noise spectrum describes the random thermal fluctuations of the beam at a given frequency. These thermal fluctuations are small, but measureable deviations of the system from equilibrium and are significant for these small scale systems. The noise spectrum can be estimated by computing the statistics from many randomly forced simulations. However, previous literature provides a direct computation of the noise spectrum with a single deterministic ring down. This work provides an analytical expression for the noise spectrum of a doubly clamped beam in tension in fluid for multiple modes. The theoretical noise spectrum shows excellent quantitative agreement with the ring down from finite element simulations. The agreement between theory and simulation is demonstrated in air and water, for a measurement of the noise spectrum at the beam midpoint and at the beam quarter point. In addition to exploring the linear dynamics of these systems, the case of large perturbations, resulting in nonlinear dynamics, is explored. This regime is motivated by exploring the theoretical dynamics of a uniformly shrinking doubly clamped beam. The challenges of modeling such a beam using finite element simulations are discussed. As a simpler and more direct alternative to access the nonlinear regime, a virtual beam is defined. The virtual beam controls the nonlinearity of the restoring force such that the system becomes increasingly stiff as the displacements become larger. This definition results in the restoring force following a Duffing oscillator. Then, the dynamics of this virtual beam are explored in air and water, and it is demonstrated that the Duffing oscillator serves as an appropriate reduced order model for this virtual beam. For varying nonlinear strengths, the stochastic numerical approach is used to quantify the dynamics, and the range of usefulness for the deterministic ring down is investigated. This research was supported by the National Science Foundation, grant number CMMI-2001559, and portions of the computations were conducted using the resources of Virginia Tech's Advanced Research Computing center.

Es wird die Umsetzbarkeit eines planar abstandsvariablen Mikrofon-Arrays mithilfe von MEMS-Mikrofonen untersucht. Neben elektrotechnischen Simulationen zur Sicherstellung der EMV für die MEMS-Mikrofone wurden zudem akustische Simulationen bezüglich Beamforming durchgeführt, um geeignete geometrische Parameter des Mikrofon-Arrays zu ermitteln. Mithilfe einer Software in MATLAB können Mikrofon-Daten gespeichert und später als Grundlage für eine adaptive akustische Kamera verwendet werden.:1 Einleitung 2 Stand der Technik 3 Theoretische Grundlagen 3.1 MEMS-Mikrofone 3.2 Pulse Density Modulation 3.3 Elektromagnetische Verträglichkeit 3.4 Beamforming 4 Hardwaretechnische Umsetzung 4.1 Audio Interface 4.2 MEMS-Mikrofone 4.3 Leitungstreiber 5 Platinendesign 6 Simulation — Elektromagnetische Verträglichkeit 6.1 Mikrofon-Platine 6.2 Interface-Platine 7 Simulation — Größe des Arrays 7.1 Vorgehensweise 7.2 Simulationsergebnisse 7.3 Fazit 8 Versuchsaufbau 8.1 Prüfung der Mikrofone 8.2 Mikrofonbefestigung 8.3 Inbetriebnahme der Platinen 8.4 Gesamtaufbau 8.5 Versuchsaufbau zur Validierung 9 Zusammenfassung und Ausblick 10 Anhang 10.1 Konstruktionszeichnung Mikrofonhalterung 10.2 Schaltplan Mikrofonansteuerung

Deformable mirrors (DMs) are needed in optical systems for compensation of aberrations using a control technique known as adaptive optics (AO). DMs are generally comprised of a mirror face sheet supported by an array of underlying actuators that can shape the face sheet with nanometer-scale precision. A challenge in fabrication of such devices is that the adhesive assembly process that is generally used to attach surface-normal actuators to the face sheet results in undesirable stress and strain, leading to uncorrectable deformation of the face sheet. The work described in this dissertation presents an innovative mechanical design that effectively solves that problem. The dissertation details design, fabrication, assembly, and control of an electromagnetically actuated DM comprised of a bulk-micromachined single crystal silicon face sheet, an array of single crystal silicon posts that are integrally attached to the face sheet, and an electromagnetic actuation system. Actuation is achieved using an array of fixed permanent magnets adhesively attached to the distal ends of the posts, which are attracted to or repelled by an array of fixed electromagnetic coils, each of which can be independently controlled. An analysis of the stress-reducing mechanical design for DM assembly is described, along with simulations and experimental results. The approach entails a direct application of St. Venant’s Principle to transform the complex and elevated stress state at the adhesion interface between magnet and post to a smaller and simpler and stress state at the face sheet, resulting in more than an order of magnitude reduction in stress-induced deformation. Two electro-magnetic actuation approaches were explored. The first uses a surface micromachined and then electroplated planar copper coil array, while the second uses an array of three-dimensional coils made from precision wound copper wire, assembled in an aluminum housing. Multiple DMs based on these designs were produced in a design and assembly process that precisely attached magnets to posts, aligned that subassembly with the actuator array, and controlled the gap between the magnets and the actuation coils. An electronic driver circuit was developed to control the actuator array using a commercial DM driver and a custom designed voltage-to-current amplifier array. Measurements of static and dynamic performance of the DM in response to actuation were made using a partitioned aperture wavefront (PAW) surface mapping microscope and a high bandwidth single point fiber-optical displacement probe. The prototype DMs had 19 actuators spaced 1.5 mm apart, supporting a 12 mm diameter, 10 µm thick face sheet. Actuation of up to +/-10 µm was achieved and dynamic performance was evaluated. This new DM design and shows promise in applications of optical aberration correction and high-power laser beamforming. / 2025-05-23T00:00:00Z