<p dir="ltr">Gyroscopes have become an integral part of many application spaces ranging from consumer electronics to navigation. As navigation and movement tracking becomes necessary through inertial measurement units (that comprises gyroscopes and accelerometers) in myriad of scenarios especially when global navigation and satellite system (GNSS) is not available, stability of gyroscopes plays a detrimental role in the accuracy of navigation. Recent developments in micro-electromechanical systems (MEMS) based gyroscopes enabled them to penetrate into navigation grade application spaces. MEMS based miniaturization approach also revived the interest in nuclear magnetic resonance gyroscopes (NMRGs). In parallel, emerging atomic gyroscope technologies are getting attention such as using quantum defects in single crystal diamond. </p><p><br></p><p dir="ltr">Considering innovative ways MEMS can improve gyroscopes, we investigate solid state gyroscope technologies in piezoelectric MEMS and nuclear spin based platforms for next generation rotation sensing that is shock and vibration insensitive. For the first part of this study, we explore a piezoelectric resonator that can excite wine-glass mode (WGM) and tangential mode. WGM is used for rotation sensing applications in various excitation mechanisms in literature. However, we demonstrate the capability of exciting WGM without the need for segmented electrodes in piezoelectric domain that allows self-alignment of the excitation electrodes using a unique property of Lead Magnesium Niobate-Lead Titanate (PMN-PT). In the second part of the study, we explore Nitrogen-Vacancy (NV) centers in diamond to be used as gyroscopes exploiting the rotation sensitivity of nuclear spins. NV center-based gyroscopes provide solid-state solution with comparable or superior performance without any moving parts. We propose mechanical coupling to NV centers in diamond using piezoelectrically excited bulk acoustic waves (BAW) to extend the coherence time of nuclear spins by dynamical decoupling. We explore piezoelectric coupling design space of AlN thin film BAW resonators (FBARs) to enable efficient mechanical drive to improve Rabi oscillations in diamond to overcome one of the most important bottlenecks of realizing a gyroscope, which is the mitigation and control of nuclear spin and electron spin interaction in diamond NV center system.</p>

This thesis, for the first time in the literature, presents the effect of quadrature error compensation on the performance of a fully decoupled MEMS gyroscope and provides experimental data on the sources of quadrature error. Dedicated quadrature error cancellation electrodes operating with only differential DC potentials are designed. Gyroscopes with intentionally placed imperfections are fabricated with SOG based SOI process which provides higher yield and uniformity compared to SOG process. Tests show that the fully closed loop system with quadrature cancellation operates as expected. Gyroscope performance is improved up to 7.8 times for bias instability, 10 times for angle random walk (ARW) and 800 times for output offset with quadrature cancellation. The actual improvement is higher since some sensors cannot be operated without quadrature cancellation and they are not included in improvement calculations. The best obtained performance is bias instability of 0.39

This thesis, for the first time in the literature, presents an automatic mode-matching system that uses the phase relationships between the residual quadrature and drive signals in a gyroscope to achieve and maintain the frequency matching condition, and also the system allows controlling the system bandwidth by adjusting the closed loop parameters of the sense mode controller, independently from the mechanical sensor bandwidth. There are two mode-matching methods, using the proposed mode-matching system, presented in this thesis. In the first method, the frequency matching between the resonance modes of the gyroscope is automatically accomplished by changing the proof mass potential. The main motivation behind the first method is to tune the sense mode resonance frequency with respect to the drive mode resonance frequency using the electrostatic tuning capability of the sense mode. In the second method, the mode-matched gyroscope operation is accomplished by using dedicated frequency tuning electrodes that only provides a capability of tuning the sense mode resonance frequency generating an electrostatic spring effect on the sense frame, independently from the proof mass potential. This study mainly focuses on the second method because the proof mass potential variation is not desired during the gyroscope operation since the proof mass potential directly affects the drive and sense mode dynamics of the gyroscope. Therefore, a single-mass fully-decoupled gyroscope including the dedicated frequency tuning electrodes are designed. To identify mode shapes and mode frequencies of the designed gyroscope, FEM simulations are performed. The designed gyroscopes are fabricated using SOI-based SOG process. The fabrication imperfections are clarified during the formation of the structural layer of the gyroscope. Next, the closed loop controllers are designed for the drive amplitude control, sense force-feedback, quadrature cancellation, and mode-matching regarding the phase relationship between the quadrature and drive signals. Mode-matching is achieved by using a closed loop controller that provides a DC tuning potential. The mode-matching system consisting of vacuum packaged sensor, drive amplitude control, sense force-feedback, quadrature cancellation, and mode-matching modules is implemented on a printed circuit board (PCB), and then the system level tests are performed. Tests illustrate that the mode-matching system operates in a desired manner. Test results demonstrate that the performances of the studied MEMS gyroscopes are improved up to 2.6 times in bias instability and 2 times in ARW under the mode-matched condition compared to the mismatched (~200 Hz) condition, reaching down to 0.73 &deg / /hr and 0.024 &deg / /&radic / hr, respectively. At the mode-matched gyroscope operation, the better performance is obtained to be bias instability of 0.87

This thesis reports development of three different high performance, low g-sensitive micromachined gyroscopes having single, double, and quadruple masses. The single mass gyroscope (SMG) is developed for comparison of its performance with the double mass gyroscope (DMG) and quadruple mass gyroscope (QMG). DMG is a tuning fork gyroscope, diminishing the effects of unpredictable g-loadings during regular operation, while QMG is a twin tuning fork gyroscope, developed for a uniform and minimized g-sensitivity. DMG and QMG use novel ring spring connections for merging the masses in drive modes, providing uniform and anti-phase drive mode vibrations that minimize the cross-coupling and the effects of intrinsic and extrinsic accelerations on the scale factor and bias levels of the gyroscopes. The sense mode of each mass of the multi-mass gyroscopes is designed to have higher resonance frequencies than that of the drive mode for possible matching requirements, and these sense modes have dedicated frequency tuning electrodes for frequency matching or tuning. Detailed performance simulations are performed with a very sophisticated computer model using the ARCHITECT software. These gyroscopes are fabricated using a standard SOIMUMPs process of MEMSCAP Inc., which provides capacitive gaps of 2 &micro / m and structural layer thickness of 25 &micro / m. Die sizes of the fabricated gyroscope chips are 4.1 mm x 4.1 mm for the single mass, 4.1 mm x 8.9 mm for the double mass, and 8.9 mm x 8.9 mm for the quadruple mass gyroscope. Fabricated gyroscopes are tested with dedicated differential readout electronics constructed with discrete components. Drive mode resonance frequencies of these gyroscopes are in a range of 3.4 kHz to 5.1 kHz. Depending on the drive mode mechanics, the drive mode quality (Q) factors of the fabricated gyroscopes are about 300 at atmospheric pressure and reaches to a value of 2500 at a vacuum ambient of 50 mTorr. Resolvable rates of the fabricated gyroscopes at atmospheric pressure are measured to be 0.109 deg/sec, 0.055 deg/sec, and 1.80 deg/sec for SMG, DMG, and QMG, respectively. At vacuum, the respective resolutions of these gyroscopes improve significantly, reaching to 106 deg/hr with the SMG and 780 deg/hr with the QMG, even though discrete readout electronics are used. Acceleration sensitivity measurements at atmosphere reveal that QMG has the lowest bias g-sensitivity and the scale factor g sensitivity of 1.02deg/sec/g and 1.59(mV/(deg/sec))/g, respectively. The performance levels of these multi-mass gyroscopes can be even further improved with high performance integrated capacitive readout electronics and precise sense mode phase matching.

The main aim of this thesis is to design and build automatic calibration system for inertial measurement sensors. The calibration system is intended to support the development of devices with inertial measurement sensors. The great emphasis is placed on the configurability of system and for this reason all calculations are realized by Matlab system, which is well known by engineers. There is also presented design of inertial measurement unit, which is used as a~model sensor unit for calibration system development.

This thesis reports the development of advanced readout and control electronics for MEMS gyroscopes developed at METU. These gyroscope electronics are separated into three main groups: high sensitive interface circuits, drive mode amplitude controlled self oscillation loops, and sense mode phase sensitive amplitude demodulators. The proposed circuits are first implemented with discrete components, and then integrated on CMOS chips. A self oscillation loop enabling constant amplitude drive mode vibrations independent of sensor parameters and ambient conditions is developed. A fully functional angular rate system, which is constructed by employing this advanced control electronics together with the transresistance amplifier type interfaces and sense mode electronics, is implemented on a dedicated PCB having 5.4x2.4 cm2 area. This system demonstrates an impressive performance far better than the best performance achieved by any angular rate system developed at METU. Bias instability and angle random walk values are measured as 14.3 &ordm / /hr and 0.126 &ordm / /&amp / #8730 / hr, respectively. The scale factor of the system is found as 22.2 mV/(&ordm / /sec) with a nonlinearity of 0.01%, and a zero rate output of 0.1 &ordm / /sec, in &plusmn / 50 &ordm / /sec measurement range. CMOS unity gain buffer (UGB) and transimpedance amplifier (TIA) type resistive and capacitive interfaces are characterized through AC, transient, and noise tests. It is observed that on chip biasing mechanisms properly DC-bias the high impedance nodes to 0 V potential. UGB type capacitive interfaces demonstrate superior performance than TIA counterparts due to stability problems associated with TIA interfaces. CMOS differential drive mode control and sense mode demodulation electronics give promising results for the future performance tests.

This thesis reports the development of various high performance readout and control electronics for implementing angular rate sensing systems using MEMS gyroscopes developed at METU. First, three systems with open loop sensing mechanisms are implemented, where each system has a different drive-mode automatic gain controlled (AGC) self-oscillation loop approach, including (i) square wave driving signal with DC off-set named as OLS_SquD, (ii) sinusoidal driving signal with DC off-set named as OLS_SineD, and iii) off-resonance driving signal named as OLS_OffD. A forth system is also constructed with a closed loop sensing mechanism where the drive mode automatic gain controlled (AGC) self-oscillation loop approach with square wave driving signal with DC off-set named as CLS_SquD. Sense and drive mode electronics employ transimpedance and transresistance amplifiers as readout electronics, respectively. Each of the systems is implemented with commercial discrete components on a dedicated PCB. Then, the angular rate sensing systems are tested with SOG (Silicon-on-Glass) gyroscopes that are adjusted to have two different mechanical bandwidths, more specially 100 Hz and 30 Hz. Test results of all of these cases verify the high performance of the systems. For the 100 Hz bandwidth, the OLS_SquD system shows a bias instability of 4.67 &amp / #730 / /hr, an angle random walk (ARW) 0.080 &amp / #730 / /&amp / #8730 / hr, and a scale factor of 22.6 mV/(&amp / #730 / /sec). For the 30 Hz bandwidth, the OLS_SquD system shows a bias instability of 5.12 &amp / #730 / /hr, an ARW better than 0.017 &amp / #730 / /&amp / #8730 / hr, and a scale factor of 49.8 mV/(&amp / #730 / /sec). For the 100 Hz bandwidth, the OLS_SineD system shows a bias instability of 6.92 &amp / #730 / /hr, an ARW of 0.049 &amp / #730 / /&amp / #8730 / hr, and a scale factor of 17.97 mV/(&amp / #730 / /sec). For the 30 Hz bandwidth, the OLS_SineD system shows a bias instability of 4.51 &amp / #730 / /hr, an ARW of 0.030 &amp / #730 / /&amp / #8730 / hr, and a scale factor of 43.24 mV/(&amp / #730 / /sec). For the 100 Hz bandwidth, the OLS_OffD system shows a bias instability of 8.43 &amp / #730 / /hr, an ARW of 0.086 &amp / #730 / /&amp / #8730 / hr, and a scale factor of 20.97 mV/(&amp / #730 / /sec). For the 30 Hz bandwidth, the OLS_OffD system shows a bias instability of 5.72 &amp / #730 / /hr, an ARW of 0.046 &amp / #730 / /&amp / #8730 / hr, and a scale factor of 47.26 mV/(&amp / #730 / /sec). For the 100 Hz bandwidth, the CLS_SquD system shows a bias instability of 6.32 &amp / #730 / /hr, an ARW of 0.055 &amp / #730 / /&amp / #8730 / hr, and a scale factor of 1.79 mV/(&amp / #730 / /sec). For the 30 Hz bandwidth, the CLS_SquD system shows a bias instability of 5.42 &amp / #730 / /hr, an ARW of 0.057 &amp / #730 / /&amp / #8730 / hr, and a scale factor of 1.98 mV/(&amp / #730 / /sec). For the 100 Hz bandwidth, the R2 nonlinearities of the measured scale factors of all systems are between 0.0001% and 0.0003% in the &plusmn / 100 &amp / #730 / /sec measurement range, while for the 30 Hz bandwidth the R2 nonlinearities are between 0.0002% and 0.0062% in the &plusmn / 80&amp / #730 / /sec measurement range. These performance results are the best results obtained at METU, satisfying the tactical-grade performances, and the measured bias instabilities and ARWs are comparable to the best results in the literature for a silicon micromachined vibratory gyroscope.

Today's state-of-the-art rate vibratory gyroscopes use a large proof mass that vibrates at a low resonance frequency (3-30 kHz), a condition that creates a performance tradeoff in which the gyroscope can either offer large bandwidth or high resolution, but not both. This tradeoff led to the development of the capacitive bulk acoustic wave (BAW) silicon disk gyroscope, a new class of micromachined rate vibratory gyroscopes operating in the frequency range of 1-10MHz with high device bandwidth and shock/vibration tolerance. By scaling the frequency, BAW gyroscopes can provide low mechanical noise without sacrificing the high bandwidth performance needed for most commercial applications. The drive loop of the BAW gyroscope can also be exploited as a timing device that can be integrated in existing commercial systems to provide competitive clock performance to the state-of-the-art using less area and power. This dissertation discusses the design and implementation of a CMOS ASIC architecture that interfaces with a high-Q, wide-bandwidth BAW gyroscope and the challenges associated with optimizing the noise performance to achieve navigation-grade levels of sensitivity as the frequency is scaled into the MHz regime. Mathematical models are derived to describe the operation of the sensor and are used to generate equivalent electrical circuit models of the gyroscope. A design strategy is then outlined for the ASIC to optimize the drive loop and sense channel for power and noise, and steps toward reducing this noise as the system is pushed to navigation-grade performance are presented that maintain optimum system power consumption. After analyzing the BAW gyroscope and identifying a strategy for developing the drive and sense interface circuitry, a complete fully-differential ASIC is designed in 0.18μm CMOS to interface with a bulk acoustic wave (BAW) disk gyroscope. As an oscillator, the gyroscope provides an uncompensated clock signal at ~9.64 MHz with a temperature sensitivity of -27 ppm/°C and phase noise of -104 dBc at 1 kHz from carrier. When the complete ASIC is interfaced with the gyroscope, the sensor shows a measured rate sensitivity of 1.15 mV/o/s with an open-loop bandwidth of 280 Hz and a bias instability of 0.095 o/s, suitable for the rate-grade performance commonly required for commercial and consumer electronics applications. The system is recorded to have a total power of 1.6 mW and a total area of 0.64 mm2. Following the design of the interface ASIC, this dissertation investigates in further detail the requirements for designing and optimizing charge pumps for capacitive MEMS devices. Basic charge pump design is outlined, followed by an overview of techniques that can be used to generate larger polarization voltages from the ASIC. Lastly, an alternate measurement technique for measuring the rotation rate of the gyroscope is discussed. This technique is based on the phase-shift modulation of the gyroscope output signal when the device is driven with two orthogonal signal inputs and can be easily modified to provide either linear scale factor measurement or a linear calibration curve that can be used to track and adjust the variation of the sensor scale factor over time.

Design and analysis of polysilicon and single crystal silicon gyroscopes have been carried out. Variations in suspension design have been explored. Designs that utilize in-plane and out-of-plane sensing are studied. Damping plays an important role in determining the sense response. Reduction in damping directly affects sensor performance. The various damping mechanisms that are prevalent in gyroscopes are studied. Perforations on the proof mass are observed to significantly reduce the damping in the device when operated in air. The effects of perforation geometry and density have been analyzed. The analysis results show that there is a two orders of magnitude reduction in damping of thick gyroscope structures with optimized perforation design. Equivalent circuit lumped parameter models have been developed to analyze gyroscope performance. The simulation results of these models have been compared with results obtained from SABER, a MEMS specific system level design tool from Coventor-ware. The lumped parameter models are observed to produce faster simulation results with an accuracy comparable to that of Coventorware Three gyroscopes specific to the PolyMUMPS fabrication process have been designed and their performance analyzed. Two of the designs sense motion out-of-plane and the other senses motion in-plane. Results of the simulation show that for a given damping, the gyro design with in-plane modes gives a resolution of 4◦/s. The out-of-plane gyroscopes have two variations in suspension. The hammock suspension resolves a rate of 25◦/s in a 200 Hz bandwidth while the design with folded beam suspension resolves a rate of 2◦/s in a 12 Hz bandwidth. A single crystal silicon in-plane gyroscope has been designed with vertical electrodes to sense Coriolis motion. This design gives an order of magnitude higher capacitance change for a given rotation in comparison to conventional comb-finger design. The effects of process induced residual stress on the characteristic frequencies of the polysilicon gyroscopes are also studied. The in-plane gyroscope is found to be robust to stress variations. Analysis results indicate that the tuning fork gyroscope with the hammock suspension is the most susceptible to compressive residual stress, with a significant drop in sensitivity at high stress values.

A new type of cantilever beam gyroscope is introduced, modeled, and analyzed. The main structure includes a cantilever beam and a rigid body attached to the free end of the beam. The model accounts for the eccentricity, that is the offset of the center of mass of the rigid body relative to the beam's free end. The first and second moments of mass and the rotary inertia appear in the equations of motion and boundary conditions. The common mechanism of electrostatic actuation of microgyroscopes is used with the difference of computing the force at the center of mass resulting in the electrostatic force and moment in the boundary conditions. By using the extended Hamilton's principle, the method of assumed modes, and Lagrange's differential equations, the equations of motion, boundary conditions, and the discretized model are developed. The generalized model simplifies to other beam gyroscope models by setting the required parameters to zero. Considering the DC and AC components of the actuating and sensing methods, the response is resolved into the static and dynamic components. The static configuration is studied for an increasing DC voltage. For the uncoupled system of equations, the explicit equation relating the DC load and the static configuration is computed and solved for the static configuration of the beam-rigid body in each direction. Including the rotation rate, the stationary analysis is performed, the stationary pull-in voltage is identified, and it is shown that the angular rotation rate does not affect the static configuration. The modal frequencies of the beam-rigid body gyroscope are studied and the instability region due to the rotation rate is computed. It is shown that the gyroscope can operate in the frequency modulation mode and the amplitude modulation mode. To operate the beam-rigid body gyroscope in the frequency modulation mode, the closed-form relation of the observed modal frequency split and the input rotation rate is computed. The calibration curves are generated for a variety of DC loads. It is shown that the scale factor improves by matching the zero rotation rate natural frequencies. The method of multiple scales is used to study the reduced-order nonlinear dynamics of the oscillations around the static equilibrium. The modulation equations, the ``slow'' system, are derived and solved for the steady-state solutions. The computational shooting method is employed to evaluate the results of the perturbation method. The frequency response and force response plots are generated. For combinations of parameters resulting in a single-valued response, the two methods are in excellent agreement. The synchronization of the response occurs in the sense direction for initially mismatched natural frequencies. The global stability of the system is studied by drawing phase-plane diagrams and long-time integration of response trajectories. The separatrices are computed, the jump phenomena is numerically shown, and the dynamic pull-in of the response is demonstrated. The fold bifurcation points are identified and it is shown that the response jumps to the higher/lower branch beyond the bifurcation points in forward/backward sweep of the amplitude and the excitation frequency of AC voltage. The mechanical-thermal (thermomechanical) noise effect on the sense response is characterized by using a linear approximation of the system and the nonlinear "slow" system obtained by using the method of multiple scales. To perform linear analysis, the negligible effect of Coriolis force on the drive amplitude is discarded. The second-order drive resonator is solved for the drive amplitude and phase. Finding the sense response due to the thermal noise force and the Coriolis force and equating them computes the mechanical-thermal noise equivalent rotation rate in terms of system parameters and mode shapes. The noise force is included in the third-order equation of the perturbation and equation to account for that in the reduced-order nonlinear response. The numerical results of linear and reduced-order nonlinear thermal noise analyses agree. It is shown that higher quality factor, higher AC voltage, and operating at lower DC points result in better resolution of the microsensor.