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The authors report the fabrication of polymer MEMS transducers, without using any sacrificial layers, on flexible substrates. The elimination of sacrificial layers and the process overhead associated with them is achieved through maskless grayscale UV lithography of SU-8 photoresist, and results in a simplification of the overall fabrication process. Six batches, with a total of 60 cantilevers and 60 double- clamped beams, and three batches, with a total of 1500 circular membranes, have been fabricated on commercially available, 45 um Kapton® polyimide sheets coated with a 35um copper layer. The validation of the fabrication process has been done through functional characterization of the bi-directional electro-mechanical interface and robustness to mechanical bending. The test and measurement results of the fabricated microstructures validate a good design predictability (geometry error

Mobile devices and sensor networks advances have sharply increased the demand for inertial MEMS sensors with a direct digital output. This paper reports on the first implementation of a MEMS-based gyroscope system with all-digital control and readout, using sliding mode and bitstream processing for both the driving and sensing modes. The in-plane vibrating MEMS gyroscope, sensitive to out-of-plane external angular rates, was designed in a custom 50um SOI technology. A band-pass sliding mode control (SMC), equivalent to a digital PLL control, was used for electrically driving one of the resonant modes at its resonant frequency, and track its drift (due to environment variations). Simulations indicate a fast capture time in response to step variations (high tracking speed of 11,486 rad/s2) and small continuous tracking errors, below 0.0083 %. A regular (low-pass) sliding mode control was used for the sensing mode, in order to cancel its vibration and thus improve its linearity. The feedback loop action was proven to attenuate the displacement in the sensing mode by more than 100 times. The resulting bitstream output (that generates in the SMC loop the high-frequency cancelling electrostatic forces) contains the relevant information about the Coriolis force, and a bitstream synchronous demodulation technique is used to reconstruct the input angular rate to be measured, with a reconstruction error of ±0.2 rad/s. The overall system enables an easy future implementation on a MEMS+FPGA of a high-performance angular rate sensing microsystem with digital output.

Heart rate (HR), the number of heart beats every minute, is the most relied upon vital sign for detecting health deterioration. It is no surprise, then, that the recording of HR is required in sleep studies as well. However, the standard monitoring method, the electrocardiogram (ECG), can be uncomfortable and intrusive, especially during sleep. Here, we present an HR monitoring system that uses the angular rate data from a single axis of a MEMS gyroscope to detect heartbeats. With a mean absolute error (MAE) and standard deviation of the absolute error (SDAE) values of -0.3505bpm and $+2.7167\mathrm{bpm}$ , in average, when our tests are compared with a reference ECG signal, we show that our system is accurate enough to track HR changes. Furthermore, the simplicity of our proposed approach makes it an ideal candidate for its implementation as a real-time, portable embedded system.

Low energy consumption and wide operating temperature range of capacitors made them common in sensor designs, e.g., MEMS accelerometers, and hence increased the popularity of capacitive readout circuits. Their main challenges, in either discrete or integrated implementations, are sensitivity, noise, energy consumption, and parasitic components at the analog front end. Compared to conventional “frequency-shift monitoring” which is one of the most accurate and common methods for capacitance measurements, weakly-coupled resonators (well-known in mechanical systems) can offer up to three orders of magnitude increase in sensitivity. Therefore, this concept has been recently applied to the design of micromechanical sensors, e.g., for sensitive mass sensing. This paper applies, for the first time in the electrical domain, the concept of monitoring the eigenstates variations in weakly-coupled resonators as a generic readout circuit technique for measuring very small capacitance changes. The outstanding sensitivity of this method is verified analytically and demonstrated using both extensive circuit simulations and experimental measurements.

This article describes a new low-cost rapid microfabrication technology for high-density interconnects and passive devices on flexible substrates for sensing applications. Silver nanoparticles with an average size of 80 nm were used to create a conductive SU-8 mixture with a concentration of wt 25%. The patterned structures after hard baking have a sheet resistance of 11.17 Ω /□. This conductive SU-8 was used to pattern planar inductors, capacitors and interconnection lines on flexible Kapton film. The conductive SU-8 structures were used as a seed layer for a subsequent electroplating process to increase the conductivity of the devices. Examples of inductors, resistor-capacitor (RC) and inductor-capacitor (LC) circuits, interconnection lines and a near-field communication (NFC) antenna are presented as a demonstration. As an example of high-resolution miniaturization, we fabricated microinductors having line widths of 5 μ m. Mechanical bending tests were successful down to a 5 mm radius. To the best of the authors’ knowledge, this is the first report of conductive SU-8 used to fabricate such planar devices and the first on flexible substrates. This is a proof of concept that this fabrication approach can be used as an alternative for microfabrication of planar passive devices on flexible substrates.

In this paper, we present a disposable inkjet dispenser platform technology and demonstrate the Lab-on-a-Printer concept, an extension of the ubiquitous Lab-on-a-Chip concept, whereby microfluidic modules are directly integrated into the printhead. The concept is demonstrated here through the integration of an inkjet dispenser and a microfluidic mixer enabling control over droplet composition from a single nozzle in real-time during printing. The inkjet dispenser is based on a modular design platform that enables the low-cost microfluidic component and the more expensive actuation unit to be easily separated, allowing for the optional disposal of the former and reuse of the latter. To limit satellite droplet formation, a hydrophobic-coated and tapered micronozzle was microfabricated and integrated with the fluidics to realize the dispenser. The microfabricated devices generated droplets with diameters ranging from 150-220 μm, depending mainly on the orifice diameter, with printing rates up to 8000 droplets per second. The inkjet dispenser is capable of dispensing materials with a viscosity up to ∼19 mPa s. As a demonstration of the inkjet dispenser function and application, we have printed type I collagen seeded with human liver carcinoma cells (cell line HepG2), to form patterned biological structures.

We demonstrate large-area silicon-on-insulator ring resonators with Q values of about 2×10sup6/supat critical coupling and 3.6×10sup6/supfor heavily undercoupled conditions. A model has been developed to understand the impact of waveguide backscattering and subcomponent imperfections on the spectral response of our devices. The model predicts the appearance of signals at ports that would not have them under backscattering-free, ideal-power-splitting conditions. The predictions of our model are shown to match the phenomena observed in our measurements.

This paper describes the application of a novel band-pass sliding mode control (SMC) to the driving mode of MEMS-based resonators and resonant sensors (e.g. vibrating gyroscopes). The proposed technique relies on binary electrostatic actuation of the movable mass, dependent on the dynamics of the sliding/switching surface, in such a way that the generated actuation tracks possible changes in the mechanical resonant frequency induced by external factors (humidity, temperature, pressure, etc.). The core of the proposed adaptive method is the implementation in hardware of an adaptive behavioral reference model used by the controller, able to track the sensed changes in dynamics. The architecture has a low hardware complexity and is suitable for VLSI implementation, in addition to a robust tracking behavior for large variations in the parameters of the resonator (e.g. temperature-induced changes in the stiffness coefficient). Simulation results demonstrate the effectiveness of the proposed technique by maintaining the actuation of the system at its resonance frequency even in the presence of variations of the stiffness coefficient (step, linear)or of applied external forces (external acceleration and noise). Simulations results suggest that the novel SMC-based oscillator offers an advantageous alternative to more complex phase-locked loop (PLL) architectures, traditionally used for the driving of MEMS resonator structures.

We propose a novel adaptive technique based on pseudo-random (PN) sequences for self-calibration and self-testing of MEMS-based inertial sensors (accelerometers and gyroscopes). The method relies on using a parameterized behavioral model implemented on FPGA, whose parameters values are adaptively tuned, based on the response to test pseudo-random actuation of the physical structure. Dedicated comb drives actuate the movable mass with binary maximum length pseudo-random sequences of small amplitude, to keep the device within the linear operating regime. The frequency of the stimulus is chosen within the mechanical spectral operating range of the micro-device, such that the induced response leads to the identification of the mechanical transfer function, and to the tuning of the associated digital behavioral model. In case of a micro-gyroscope, experimental results demonstrate the adaptive tracking of the damping coefficient from 5.57 × 10−5 Kg/s to 7.12 × 10−5 Kg/s and of the stiffness coefficient from 132 N/m to 137.7 N/m. In the case of a MEMS accelerometer, the damping and stiffness coefficients are correctly tracked from 3.4 × 10−3 Kg/s and 49.56 N/m to 4.57 × 10−3 Kg/s and 51.48 N/m, respectively—the former values are designer-specified target values, while the latter are experimentally measured parameters for fabricated devices operating in a real environment. Hardware resources estimation confirms the small area the proposed algorithm occupies on the targeted FPGA device.

Semiconductor ring resonators as the core components of instruments and devices have found applications in the areas of telecommunications and sensors. In this study, the feasibility of using ring resonators as solid-state angular rate sensors (gyroscopes) based on the Sagnac effect is assessed, and an extensive analysis of the optimal values of resonator length, coupling, and detuning is carried out, for the drop port of a double-bus ring, and for an all-pass, single-bus ring, for different values of propagation losses, consistent with different available technologies. We show that for both the all-pass and the drop-port configurations, optimally undercoupled rings show larger extinction ratios and, thus, better resolutions than critically coupled rings of the same length, contrary to our initial intuitive assumption that critically coupled rings should offer the best resolutions. Our analysis also shows that the ring resonator gyroscopes require a technology-constrained optimization, with the propagation loss as the main factor that hinders the resolution, and that determines the optimum values of all other parameters, namely length, coupling, and resonance detuning. According to our model, standard-chip-sized racetrack gyroscopes are suitable for rate- and tactical-grade applications for selected, currently feasible low propagation loss waveguides.

The attainable resolution of inertial sensors is ultimately limited by the cumulated noise level generated in both the mechanical domain (mechano-thermal noise) and the frontend of the electrical readout circuit, provided that deterministic errors, such as quadrature errors in the case of gyroscopes, are kept under control. Improving the resolution performance of MEMS structures mounts to being able to either increase the minimum detectable signal through an increased sensitivity, or to improve the signal-to-noise ratio (SNR). This paper reports on parametric amplification and damping employed in a MEMS gyroscope. Experiments confirm that parametric modulation through electro-mechanical coupling leads to both an increase in spectral selectivity and a reduction of the equivalent input noise angular rate (from 0.0046 ∘ / ( s Hz ) to 0.0026 ∘ / ( s Hz ) for a parametric gain of 5). In a more general analysis of a MEMS resonant structure, electro-mechanical parametric amplification decreases the mechano-thermal noise associated with the resonant mode motion – the equivalent input noise acceleration was diminished from 0.033 m s−2 to 0.022 m s−2 for a parametric gain of 5. Either signal amplification or an attenuation of undesired signal components can be achieved by tuning the phase difference between the driving force and the parametric coupling. Therefore, the technique can be applied as well to reduce the quadrature error signal, which strongly constrains the maximum gain of the sensing circuit. Our experiments show a 2.2 improvement factor in SNR using a parametric amplification with a gain of 25.

This paper reports on the simulation and characterization of a microelectromechanical system (MEMS) micromirror fabricated with PolyMUMPs. The overall diameter of the hexagonal micrimirror, including mirror plate and 3 supporting cantilevers fixed around, is 450um. A 3D model is built in finite element method (FEM) with COMSOL. Simulations of the elevated height of mirror plate, pull-in voltage and eigenfrequency of the micromirror are carried out. The static and dynamic performances of the fabricated micromirror are characterized by Veeco Optical Profiler and Polytek MEMS System Analyzer. The comparison between measurement and simulation exhibits good concordance. Surface topography measurement shows the elevated height and stress-induced concave deformation of mirror plate almost the same scale as demonstrated in FEM simulation. The Pull-In voltages are measured to be around 32V in current-voltage curve which is almost the same as in FEM simulation with one electrode biased. The fundamental resonant frequency is measured to be 4.3k Hz in torsional motion and 4.9k Hz in piston motion.

The present paper analyzes numerically and experimentally the dependence of the dynamic pull-in voltage amplitude on the values of externally-induced accelerations (e.g. Coriolis accelerations in the case of vibratory gyroscopes). We have investigated the nonlinear dynamic behavior on two different device types, a micro-gyroscope (A) and a micro-accelerometer (B), both fabricated in the SOI-MUMPs process (25 μm thick structural layer). Experimental measurements on the MEMS structures have been performed using Polytec MSA-500 equipment for analyzing the mechanical motion. They indicate that the dynamic pull-in voltages reduce from 100 V to 56 V for device A and from 21.77 V to 17.3 V for device B, for an equivalent acceleration of 0.319 ms-2, when the structures are actuated at their resonance frequency. If the induced acceleration is translated into an equivalent angular rate, _ equivalent, modulating the Coriolisinduced motion, the dynamic pull-in voltages vary from 57.612 V to 56.5 V for device A type and from 20.9 V to 10.75 V for device B type, for a change of 1 rad/s to 5 rad/s in _equivalent.

This paper describes the application of a novel band-pass sliding mode control (SMC) to MEMS-based resonators and resonant sensors (e.g. vibrating gyroscopes). The proposed technique relies on a binary electrostatic actuation of the movable mass, dependent on the dynamics of the sliding surface, in such a way that the generated oscillations track changes in the mechanical resonant frequency. The architecture has a low hardware complexity and is suitable for VLSI implementation, in addition to a robust tracking behavior for large variations in the parameters of the resonator (e.g. temperature-induced changes in the stiffness coefficient). The results suggests that the novel SMC- based oscillator offers an advantageous alternative to more costly phased-locked loop (PLL) architectures traditionally used for the driving of MEMS resonator structures.

This work reports the design, modelling, fabrication and preliminary functionality testing of a dual-mass MEMS vibratory gyroscope for application in medical instrumentation, among others. The two-framed gyro has drive and sense mode resonance frequencies of 2500Hz and 2830Hz, with its bandwidth tunable between 40-330Hz. Adopted design and technological features such as the use of double-folded springs, quadrature-error-compensation electrodes and 50μm thick-SOI mechanical layer enable high resolution sensing. The designed sensor characteristics have been validated using FEM simulation and equivalent circuit modelling.

In this paper, we describe the system architecture and prototype measurements of a MEMS gyroscope system with a resolution of 0.025 degrees/s/root Hz. The architecture makes extensive use of control loops, which are mostly in the digital domain. For the primary mode both the amplitude and the resonance frequency are tracked and controlled. The secondary mode readout is based on unconstrained Sigma Delta force-feedback, which does not require a compensation filter in the loop and thus allows more beneficial quantization noise shaping than prior designs of the same order. Due to the force-feedback, the gyroscope has ample dynamic range to correct the quadrature error in the digital domain. The largely digital setup also gives a lot of flexibility in characterization and testing, where system identification techniques have been used to characterize the sensors. This way, a parasitic direct electrical coupling between actuation and readout of the mass-spring systems was estimated and corrected in the digital domain. Special care is also given to the capacitive readout circuit, which operates in continuous time.

The paper presents a combined noise and damping analysis for MEMS structures, based on frequency-dependent behavioral models extracted from finite element simulations. The design of high sensitivity MEMS-based microsystems needs to consider the frequency noise shaping induced by damping phenomena on micro scale motion, for its contribution can be significant in the system level noise analysis. Frequency-dependent behavioral models for squeeze-film damping are generated from finite element analysis simulations. Unlike existing noise analysis reported in literature, based on frequency-independent damping assumption, the paper integrates the damping and noise aspects using the same frequency-dependent models. The results can be used for a noise-based optimization procedure applied to the design of resonating microsensors, as illustrated for the case of a MEMS-based gyroscope.

The nonlinear dynamics of the parallel-plate electrostatically driven microstructure have been investigated with the objective of finding a dynamic voltage drive suitable for full-gap operation. Nonlinear dynamic modeling with phase-portrait presentation of both position and velocity of a realistic microstructure demonstrate that instability is avoided by a timely and sufficient reduction of the drive voltage. The simulation results are confirmed by experiments on devices fabricated in an epi-poly process. A 5.5-V peak harmonic drive voltage with frequency higher than 300 Hz allows repetitive microstructure motion up to 70% of gap without position feedback. The results of the analysis have been applied to the design of a new concept for positioning beyond the static pull-in limitation that does include position feedback. The measured instantaneous actuator displacement is compared with the desired displacement setting and, unlike traditional feedback, the voltage applied to the actuator is changed according to the comparison result between two values. The "low" level is below the static pull-in voltage and opposes the motion, thus bringing the structure back into a stable regime, while the "high" level is larger than the static pull-in voltage and will push the structure beyond the static pull-in displacement. Operation is limited only by the position jitter due to the time delay introduced by the readout circuits. Measurements confirm flexible operation up to a mechanical stopper positioned at 2 /spl mu/m of the 2.25 /spl mu/m wide gap with a 30 nm ripple.

Harmonic displacement of a parallel-plate electrostatic actuator up to 50% of the static pull-in displacement has been achieved despite the non-linear voltage-to-displacement function using a driving voltage with a pre-distorted waveform. The microstructure is fabricated in an epi-poly process and the circuit is implemented in a CMOS process and designed for operation of the MEMS in a frequency range up to 1 kHz. The pre-distorted waveform is synthesized using 16 samples per period with 16 non-uniformly spaced quantization levels, using a ladder with accurately scaled resistors. Harmonic actuation has been demonstrated with 34 dB reduction of second-order distortion compared to systems with sinusoidal actuation. The residual second harmonic content in the harmonic displacement is typically −42 dB.

The pull-in voltage of one- and two-degrees-of-freedom (DOF) structures has been symbolically and numerically analyzed with respect to drive mode dependence and hysteresis. Moreover, the time and temperature stability has been investigated and tested. Modeling results have been applied in the design of both folded-spring-suspended 1-DOF structures and single-side-clamped 2-DOF beams with a nominal pull-in voltage in the 5-10 V range and fabricated in an epi-poly process. Asymmetrically driven structures reveal pull-in close to the value predicted by the model (V/sub pi/ 1-DOF is 4.65 V analytically simulated and 4.56 V measured; V/sub pi/ 2-DOF is 9.24 V analytically simulated, 9.30 V in FEM and 9.34 V measured). Also the hysteresis is in close agreement (release voltage, V/sub r/, 1-DOF is 1.41 V analytically simulated and 1.45 V measured; V/sub r/ 2-DOF is 9.17 V analytically simulated, 9.15 V in FEM and 9.27 V measured). In symmetrically operated devices the differences between the computed and measured V/sub pi/ and V/sub r/ are much larger and are due to process dependencies, which make these devices very suitable for process monitoring. The 2-DOF asymmetrically operated device is the most suitable for MEMS-based voltage reference. The stability in time is limited by charge build-up and calls for a 100-hour initial burn-in. Temperature dependence is -100 /spl mu/V/K at V/sub pi//spl ap/5 V, however, is calculable and thus can be corrected or compensated.

Large-area silicon-on-insulator (SOI) ring resonators, to be used as optical gyroscopes, have been designed and fabricated using an e-beam process. To characterize the devices, an automated turntable stage with an embedded high resolution gyroscope has been built. Its large payload capacity allows for safe rotation of a temperature-controlled opto-mechanical setup. A field programmable gate array interface has been implemented for mechanical actuation and signal acquisition. Various rotation schemes have been implemented to characterize the apparatus and devices. The turntable exhibits a bandwidth of 0.54 Hz, and minimum and maximum repeatable angular rates of 27 and 74.3 degrees per second (dps), with a maximum associated angular rate noise level of 2 dps.

The pull-in voltage of a single-side anchored freestanding beam, under lateral deflection, has been investigated for application as a DC voltage reference. Two sets of electrodes, along side the tip, are used for parallel-plate type of electrostatic actuation of the 200 /spl mu/m long beam in the plane of the wafer. Another set of buried electrodes is aligned with the plate electrode at the free-standing tip and is used as a differential capacitor for the simultaneous detection of the displacement, with the purpose to determine the stability border and thus the pull-in voltage. The single-end clamping ensures that the pull-in voltage is insensitive to technology-induced stresses. A 2D energy-based analytical model for the static pull-in is compared with measurements. Bifurcation diagrams are computed numerically, based on a local continuation method. Devices have been designed and fabricated in an epi-poly process. Measurements are in agreement with modeling and confirm a pull-in voltage in the 9.1-9.5 V range. Reproducibility is limited by hysteresis and charging of the dielectric layer in between the electrodes. The device can be operated in feedback or as a seesaw, by using the two sets of electrodes.

In this paper slope-shaped comb are designed, modeled and experimentally verified for electrostatic parametric amplification of micro-displacements. Parametric resonance techniques applied to inertial sensors requires a periodic stiffness modulation, as expressed by the Mathieu equation, and is generally implemented using gap-varying and non-overlapping combs. MEMS vibratory gyroscopes provide the opportunity for applying parametric amplification for both the sensing and driving modes. While gap-varying combs are efficiently used for small displacements (e.g. the sensing mode), larger displacements require a different approach, where slope-shaped combs are a good alternative. Analytical model of slope shaped combs is carried out and compared with experimental characterization of fabricated devices. The analytical model predicts a spring modulation of 0.1%-0.65% spring modulation for 10 V to 40V applied common mode DC bias, and it can be increased for steeper slopes. The parametric amplification operation was experimentally tested using linear differential voltage actuation on the area-varying combs and a phase-synchronised common mode voltage (using a PXIe 1062Q DAQ controller) applied to the left and right shaped combs.

We report novel low-cost and rapid fabrication technologies for the fabrication of movable polymer-based MEMS structures, electrically actuated. Using SU-8 photoresist as structural material, both ordinary and functionalized by conductive fillers (nano-Ag particles and carbon nanotubes), the novel fabrication methods provide simple processes, without the use of any sacrificial layer, for achieving suspended structures (beams and membranes) through either binary or gray-scale photolithography. Experimental validation has demonstrated high yields (over 99% for one of the process flows) in achieving electrostatically actuated microstructures with resonant frequencies in the 0.5–0.8 MHz range, with a stable dynamic behavior tested for a period longer than three months. The technology also confirms that 'doping' SU-8 with conductive fillers can preserve its photo-patterning capabilities, while modifying other physical properties (electrical conductivity). As the patterning of SU-8 films can take place on either rigid or flexible substrates, this low-cost technology promises a wide range of applications.

We propose a novel adaptive technique based on pseudo-random (PN) sequences for self-calibration and self-testing of capacitive-based sensing and resonator microstructures, using an FPGA-implemented algorithm. The movable mass is actuated electrically with maximum length pseudo-random sequences (PN) of small amplitude, to keep the device in the linear operating regime. The frequency of the stimulus is chosen within the spectral operating range of the microdevice, such that the induced mechanical response is used for the identification of the mechanical transfer function. The proposed technique uses the steady-state and dynamic responses and it is applied to a MEMS gyroscope, for closed-loop characterization and real-time calibration. The core of the adaptive method is the implementation in FPGA of a reference model of the device under test (DUT). Experimental results demonstrate the real-time model-based identification of the damping and stiffness coefficients for the sensing mode of the fabricated vibratory microgyroscope, using modest hardware resources.

The attainable resolution of inertial sensors is ultimately limited by the cumulated noise level generated in both the mechanical domain (mechano-thermal noise) and the frontend of the electrical readout circuit, provided that deterministic errors, such as quadrature errors in the case of gyroscopes, are kept under control. Improving the resolution performance of MEMS structures mounts to being able to either increase the minimum detectable signal through an increased sensitivity, or to improve the signal-to-noise ratio (SNR). This paper reports on parametric amplification and damping employed in a MEMS gyroscope. Experiments confirm that parametric modulation through electro-mechanical coupling leads to both an increase spectral selectivity and a reduction of the equivalent input noise angular rate (from 0.046deg/ (sec equations ) to 0.0026deg (sec · equations) for a parametric gain of 5). In a more general analysis of a MEMS resonant structure, electro-mechanical parametric amplification decreases the mechano-thermal noise associated with the mode motion - the equivalent input noise acceleration was diminished from 0.033m · s−2 to 0.022m · sࢤ2 for a parametric gain of 5. Both signal amplification and an attenuation of undesired signal components can be achieved by tuning the phase difference between the driving force and the parametric coupling. Therefore, the technique can be applied to reduce the quadrature error signal, which strongly constrains the maximum gain of the sensing circuit.

This paper presents a detailed noise analysis and noise-based optimization procedure for resonant MEMS structures. A design for high sensitivity of MEMS structures needs to take into account the noise shaping induced by damping phenomena at micro scale. The extraction of a behavioral model of the solid gas interaction is obtained by matching the FEA simulations with a parametric expression for the squeeze-film damping, suggested by the analytical modeling.

Electrostatic parallel-plate actuators are classically limited to displacements up to 1/3 of the gap due to the pull-in effect [1],[2|. A closed-loop feedback based method presented in [3] is recently introduced to overcome this limitation. Optimized structures are designed to minimize residual position ripple while maintaining bandwidth, effectively reducing the required device size of positioning electrostatic actuators by a factor three.

A complete topological equivalence between network representations of mechanical and electrical systems is hindered by the inertial mass element, represented as an equivalent capacitor with a pin always connected to ground (inertial reference system). This limits the class of synthesizable mechanical filters from equivalent electrical prototypes by excluding the schematics that have floating capacitors. This restriction motivates the introduction of a differential mass component. It is shown that this new component would make it possible to implement a simple third order Chebyshev bandpass filter which can not be implemented using standard masses, springs and dampers.

An important feature of MEMS, still underutilized, is the tight coupling between the electrical and mechanical quantities in the micro domain. This paper demonstrates the benefits of such a functional coupling for a specific device: a real-time mechanical spectrum analyzer. A surface micromachined accelerometer was designed, with a voltage-controlled gain. By applying an harmonic common-mode voltage on the actuation capacitors, the intrinsic nonlinear coupling performs a correlation between the input acceleration and an electrically-controlled signal. To reduce the distortion, a differential, twin-accelerometer scheme is used. Time-multiplexed signal processing gives both the real and the imaginary components of the selected spectral line. A mechanical spectrum analyzer for low-frequency domains is obtained when the driving electrical frequency is swept over the range of interest. The operating principle has been confirmed by measurements, and is expected to yield new opportunities in the field of low-power, low-cost condition monitoring equipment.

The pull-in voltage of a parallel plate electrostatic transducer is used to determine the amount of over-etching in fabricated devices. A detailed analysis of the capacitor behaviour over the full displacement range yields a model, which is used to describe the relation between over-etching and measured pull-in voltage. SEM photos confirm the over-etching measurement based on pull-in voltage. This information is used to linearize a charge amplifying read-out circuit with an intrinsic nonlinear transfer function. The remaining nonlinearity error of the read-out is less than 1%.

In this paper we describe the system architecture and prototype measurements of a MEMS gyroscope with a resolution of 0.055°/s/√Hz. Two innovations are presented. The first is the complete migration of control and demodulation tasks to the digital domain. For this purpose, interfacing circuits based on ΣΔ techniques are introduced for both primary and secondary mode. The advantage is that complex analog electronics for tracking the resonant frequency, stabilizing the amplitude of the primary mode oscillation and phase-sensitive demodulation can be replaced by their digital counterpart. A second innovation relates to the ΣΔ force-feedback loop. In previously reported structures a compensation filter is introduced for stabilizing the loop [ 1– 3]. Unfortunately, the compensation filter introduces extra poles and influences the noise-shaping characteristic, which makes the loop difficult to design and optimize. We demonstrate the possibility of obtaining a stable ΣΔ force-feedback loop without an explicit compensation filter.