Design and Modelling of MEMS Vibrating Internal Ring Gyroscopes for Harsh Environments.

This paper presents a design, model, and comparative analysis of two internal MEMS vibrating ring gyroscopes for harsh environmental conditions. The proposed design investigates the symmetric structure of the vibrating ring gyroscopes that operate at the identical shape of wine glass mode resonance frequencies for both driving and sensing purposes. This approach improves the gyroscope's sensitivity and precision in rotational motion. The analysis starts with an investigation of the dynamic behaviour of the vibrating ring gyroscope with the detailed derivation of motion equations. The design geometry, meshing technology, and simulation results were comprehensively evaluated on two internal vibrating ring gyroscopes. The two designs are distinguished by their support spring configurations and internal ring structures. Design I consists of eight semicircular support springs and Design II consists of sixteen semicircular support springs. These designs were modelled and analyzed using finite element analysis (FEA) in Ansys 2023 R1 software. This paper further evaluates static and dynamic performance, emphasizing mode matching and temperature stability. The results reveal that Design II, with additional support springs, offers better mode matching, higher resonance frequencies, and better thermal stability compared to Design I. Additionally, electrostatic, modal, and harmonic analyses highlight the gyroscope's behaviour under varying DC voltages and environmental conditions. Furthermore, this study investigates the impact of temperature fluctuations on performance, demonstrating the robustness of the designs within a temperature range from -100 °C to 100 °C. These research findings suggest that the internal vibrating ring gyroscopes are highly suitable for harsh conditions such as high temperature and space applications.

Analysis of Intentional Electromagnetic Interference on GENEC Model Using Cylindrical Mode Matching.

In recent times, due to the high operating frequency and low operating voltage of modern electronic devices, intended electromagnetic interference (IEMI) has been the cause of increasing damage. In particular, targets with precision electronics such as aircrafts or missiles have shown that a high-power microwave (HPM) may cause malfunction or partial destruction of the GPS or the avionic control system. Analysis of the effects of IEMI requires electromagnetic numerical analyses. However, there are limitations to conventional numerical techniques, such as the finite element method, method of moment, or finite difference time domain method, due to the complexity and large electrical length of a real target system. In this paper, we proposed a new cylindrical mode matching (CMM) technique to analyze IEMI of the generic missile (GENEC) model, which is a hollow metal cylinder with multiple apertures. Using the CMM, we can quickly analyze the effect of the IEMI inside the GENEC model from 1.7 to 2.5 GHz. The results were compared with those of the measurements and, for verification, with the FEKO, a commercial software program developed by Altair Engineering, and showed good agreement. In this paper, the electro-optic (EO) probe was used to measure the electric field inside the GENEC model.

Design and Demonstration of a Microelectromechanical System Single-Ring Resonator with Inner Ring-Shaped Spring Supports for Inertial Sensors.

This paper presents a novel single-ring resonator design and experimentally demonstrates its dynamic behavior. The proposed ring resonator design is simple and has a solid anchor at its center connected to an outside ring via inner ring-shaped springs. The mode shapes and frequency of the ring resonator were determined numerically and compared with analytical approaches, and the minimum split frequency was observed for the n = 3 mode of vibration. Numerical and analytical methods were used to determine the resonance frequencies, pull-in voltage, resonance frequency shift and harmonic response of the ring resonator for different silicon orientations. The split frequency in the n = 3 mode of vibration increases by the applied DC bias voltage almost by the same amount for all types of silicon. When an AC voltage with a 180-degree phase is applied to two opposite electrodes, the ring has two resonance frequencies in mode n = 2, and when the AC voltage applied to two opposite electrodes is in the same phase, the ring has one resonance frequency regardless of the crystal orientation of silicon. Prototypes were fabricated using a double silicon-on-insulator-based wafer fabrication technique and were tested to verify the resonator performance.

Glide-Symmetric Holey Structures Applied to Waveguide Technology: Design Considerations.

Recently, there has been an increased interest in exploring periodic structures with higher symmetry due to various possibilities of utilizing them in novel electromagnetic applications. The aim of this paper is to discuss design issues related to the implementation of holey glide-symmetric periodic structures in waveguide-based components. In particular, one can implement periodic structures with glide symmetry in one or two directions, which we differentiate as 1D and 2D glide symmetry, respectively. The key differences in the dispersion and bandgap properties of these two realizations are presented and design guidelines are indicated, with special care devoted to practical issues. Focusing on the design of gap waveguide-based components, we demonstrate using simulated and measured results that in practice it is often sufficient to use 1D glide symmetry, which is also simpler to mechanically realize, and if larger attenuation of lateral waves is needed, a diagonally directed 2D glide symmetric structure should be implemented. Finally, an analysis of realistic holes with conical endings is performed using a developed effective hole depth method, which combined with the presented analysis and results can serve as a valuable tool in the process of designing novel electrically-large waveguide-based components.

A Novel, Portable and Fast Moisture Content Measuring Method for Grains Based on an Ultra-Wideband (UWB) Radar Module and the Mode Matching Method.

To perform fast and portable grain moisture measurements under field conditions, a novel moisture sensor was designed, which consisted of a coaxial waveguide, a circular waveguide, and an isolation layer. The electromagnetic characteristics of the sensor were simulated and measured. The analytical model, which represented the relationship between the reflection coefficient of the sensor and the complex permittivity of grain, was established by using the mode matching method. The reflection coefficient of the sensor was measured by using an ultra-wideband (UWB) radar module, and the moisture content of grains was calculated from the complex permittivity by using density-independent model. To verify the performance of the proposed method, wheat, rough rice, and barley were taken as examples. The measured results in the range from 1.0% to 26.0%, wet basis, agreed well with the reference values (R2 was more than 0.99), and the maximum absolute errors for wheat, rough rice, and barley were 1.1%, 1.0%, and 1.4%, respectively. In addition, the effect of isolation layer was discussed. Both the simulation results and the experimental results showed that the isolation layer improved the stability of sensor.

MEMS Gyroscope Automatic Real-Time Mode-Matching Method Based on Phase-Shifted 45° Additional Force Demodulation.

In order to solve the problem where existing mode-matching methods in microelectromechanical systems (MEMS) vibrating gyroscopes fail to meet real-time and reliability requirements, this paper presents a novel method to accomplish automatic and real-time mode-matching based on phase-shifted 45° additional force demodulation (45° AFD-RM). The phase-shifted 45° additional force signal has the same frequency as the quadrature force signal, but it is phase-shifted by 45° and applied to the sense mode. In addition, two-way phase-shifted 45° demodulations are used at the sense-mode detection output to obtain a phase metric that is independent of the Coriolis force and can reflect the mode-matching state. Then, this phase metric is used as a control variable to adaptively control the tuning voltage, so as to change the sense-mode frequency through the negative stiffness effect and ultimately achieve real-time mode-matching. Simulation and experimental results show that the proposed 45° AFD-RM method can achieve real-time matching. The mode frequency split is controlled within 0.1 Hz, and the gyroscope scale factor, zero-bias instability, and angle random walk are effectively improved.

Mechanical and Electrical Noise in Sense Channel of MEMS Vibratory Gyroscopes.

This paper presents a theoretical analysis of mechanical and electrical noise in the sense channel of micro-electromechanical systems (MEMS) vibratory gyroscopes. Closed-form expressions for the power spectral density (PSD) of the noise equivalent rate (NER) of gyroscopes in the open-loop and the force-rebalance operations are derived by using an averaged PSD model and an equivalent transfer function. The obtained expressions are verified through numerical simulations, demonstrating close agreements between the analytic and the numerical models. Based on the derived expressions for the PSD of the NER, the impacts of the modal frequency split, quality factor, and the gain of the feedback forcer, as well as the gain of the signal conditioning circuit, on the gyroscope noise characteristics are theoretically analyzed. In addition, the angle random walk (ARW) and the standard deviation of the NER are also discussed through the PSD models. Finally, the effects of the loop closing, the mode matching, and the gain of the feedback forcer on the PSD of the NER were verified via a MEMS vibratory gyroscope with a tunable modal frequency split.

Design and Analysis of a Novel Fully Decoupled Tri-axis Linear Vibratory Gyroscope with Matched Modes.

We present in this paper a novel fully decoupled silicon micromachined tri-axis linear vibratory gyroscope. The proposed gyroscope structure is highly symmetrical and can be limited to an area of about 8.5 mm × 8.5 mm. It can differentially detect three axes' angular velocities at the same time. By elaborately arranging different beams, anchors and sensing frames, the drive and sense modes are fully decoupled from each other. Moreover, the quadrature error correction and frequency tuning functions are taken into consideration in the structure design for all the sense modes. Since there exists an unwanted in-plane rotational mode, theoretical analysis is implemented to eliminate it. To accelerate the mode matching process, the particle swam optimization (PSO) algorithm is adopted and a frequency split of 149 Hz is first achieved by this method. Then, after two steps of manual adjustment of the springs' dimensions, the frequency gap is further decreased to 3 Hz. With the help of the finite element method (FEM) software ANSYS, the natural frequencies of drive, yaw, and pitch/roll modes are found to be 14,017 Hz, 14,018 Hz and 14,020 Hz, respectively. The cross-axis effect and scale factor of each mode are also simulated. All the simulation results are in good accordance with the theoretical analysis, which means the design is effective and worthy of further investigation on the integration of tri-axis accelerometers on the same single chip to form an inertial measurement unit.

A Mode Matched Triaxial Vibratory Wheel Gyroscope with Fully Decoupled Structure.

To avoid the oscillation of four unequal masses seen in previous triaxial linear gyroscopes, a modified silicon triaxial gyroscope with a rotary wheel is presented in this paper. To maintain a large sensitivity and suppress the coupling of different modes, this novel gyroscope structure is designed be perfectly symmetrical with a relatively large size of about 9.8 mm × 9.8 mm. It is available for differentially detecting three-axis angular rates simultaneously. To overcome the coupling between drive and sense modes, numerous necessary frames, beams, and anchors are delicately figured out and properly arranged. Besides, some frequency tuning and feedback mechanisms are addressed in the case of post processing after fabrication. To facilitate mode matched function, a new artificial fish swarm algorithm (AFSA) performed faster than particle swarm optimization (PSO) with a frequency split of 108 Hz. Then, by entrusting the post adjustment of the springs dimensions to the finite element method (FEM) software ANSYS, the final frequency splits can be below 3 Hz. The simulation results demonstrate that the modal frequencies in drive and different sense modes are respectively 8001.1, 8002.6, 8002.8 and 8003.3 Hz. Subsequently, different axis cross coupling effects and scale factors are also analyzed. The simulation results effectively validate the feasibility of the design and relevant theoretical calculation.

Virtual Coriolis-Force-Based Mode-Matching Micromachine-Optimized Tuning Fork Gyroscope without a Quadrature-Nulling Loop.

A VCF-based mode-matching micromachine-optimized tuning fork gyroscope is proposed to not only maximize the scale factor of the device, but also avoid use of an additional quadrature-nulling loop to prevent structure complexity, pick-up electrode occupation, and coupling with a mode-matching loop. In detail, a mode-matching, closed-loop system without a quadrature-nulling loop is established, and the corresponding convergence and matching error are quantitatively analyzed. The optimal straight beam of the gyro structure is then modeled to significantly reduce the quadrature coupling. The test results show that the frequency split is narrowed from 20 Hz to 0.014 Hz. The scale factor is improved 20.6 times and the bias instability (BI) is suppressed 3.28 times. The observed matching accuracy demonstrates that a mode matching system without a quadrature suppression loop is feasible and that the proposed device represents a competitive design for a mode-matching gyroscope.

Stability Boundary and Enhanced Solution of Dual-Mode Based Micro Gyroscope Mode Matching Technology.

During in-run mode matching under a dual-mode gyro scheme, the stability of the closed-loop control system has a boundary. This phenomenon will lead to the failure of the in-run frequency split calibration scheme when the initial mode mismatch is too severe to exceed the stability boundary. This paper gives a detailed analysis of this stability boundary through simulations and experiments. Results show that the length of the stable region will be affected by the resonant frequency and the Q value. High resonant frequency and low Q value will widen the stable region, but also reduce the sensitivity and rapidity of the calibration. In order to remove the limitation of the stability boundary while applying the in-run frequency split calibration under dual-mode architecture, this paper proposes an enhanced solution that combines both the dual-mode scheme and technology of mode switching. The application of mode switching achieves a pre-calibration of frequency split before the normal gyro operation. This solution is implemented in engineering on a hybrid gyro interface circuit prototype with single-mode and dual-mode. Validation experiments confirmed the effectiveness of this solution.

Electromagnetic characteristics of in vivo nerve fibers at the terahertz-far-infrared band.

How terahertz signals perform in the neural system has attracted widespread interest in the life sciences community. Relevant experimental reveals that in animal nerve cells, the myelin sheath of the nerve axon has a higher refractive index than the intracellular and extracellular fluids in the Terahertz-far-infrared (THz-FIR) frequency band. This makes THz-FIR wave transmission possible in nerve fibers. Based on this premise, this article carries out the following work from the theoretical level to investigate the electromagnetic (EM) characteristics of in vivo nerve fibers at the THz-FIR band. First, the EM transmission model of the nerve fibers is established and studied theoretically. The dispersion curves of THz-FIR wave modals transmission in nerve fibers are calculated, which predict that nerve fibers can act as dielectric waveguides for transmitting THz-FIR waves and the THz-FIR waves can transmit at speeds up to 108 m/s. Second, a mode matching algorithm is proposed, which is named RNMMA, to calculate the transmission characteristics of THz-FIR waves at the nodes of Ranvier. The scattering matrix obtained from the proposed algorithm is in good agreement with the results from EM simulation software, which reveals how THz-FIR signals are transmitted forward through the nodes of Ranvier with low loss.

Using Waveguides to Model the Dynamic Stiffness of Pre-Compressed Natural Rubber Vibration Isolators.

A waveguide model for a pre-compressed cylindrical natural rubber vibration isolator is developed within a wide frequency range-20 to 2000 Hz-and for a wide pre-compression domain-from vanishing to the maximum in service, that is 20%. The problems of simultaneously modeling the pre-compression and frequency dependence are solved by applying a transformation of the pre-compressed isolator into a globally equivalent linearized, homogeneous, and isotropic form, thereby reducing the original, mathematically arduous, and complex problem into a vastly simpler assignment while using a straightforward waveguide approach to satisfy the boundary conditions by mode-matching. A fractional standard linear solid is applied as the visco-elastic natural rubber model while using a Mittag-Leffler function as the stress relaxation function. The dynamic stiffness is found to depend strongly on the frequency and pre-compression. The former is resulting in resonance phenomena such as peaks and troughs, while the latter exhibits a low-frequency magnitude stiffness increase in addition to peak and trough shifts with increased pre-compressions. Good agreement with nonlinear finite element results is obtained for the considered frequency and pre-compression range in contrast to the results of standard waveguide approaches.

Automatic Mode-Matching Method for MEMS Disk Resonator Gyroscopes Based on Virtual Coriolis Force.

An automatic mode-matching method for MEMS (Micro-electromechanical Systems) disk resonator gyroscopes (DRGs) based on virtual Coriolis force is presented in this paper. For this mode-matching method, the additional tuning electrodes are not required to be designed, which simplifies the structure design. By using the quadratic relationship between the driving voltage and the electrostatic force, the virtual Coriolis force is obtained by applying an AC voltage whose frequency is half of the driving mode resonant frequency to the sense electrode. The phase difference between the virtual Coriolis force and the sense output signal is used for mode-matching. The structural characteristics and electrode distribution of the DRG are briefly introduced. Moreover, the mode-matching theories of the DRG are studied in detail. The scheme of the mode-matching control system is proposed. Simultaneously, the feasibility and effectiveness of the mode-matching method are verified by system simulation. The experimental results show that under the control of mode-matching at room temperature, the bias instability is reduced from 30.7575 ° /h to 2.8331 ° /h, and the Angle Random Walk (ARW) decreases from 1.0208 ° / h to 0.0524 ° / h . Compared with the mode mismatch condition, the ARW is improved by 19.48 times.

A Digital Calibration Technique of MEMS Gyroscope for Closed-Loop Mode-Matching Control.

A digital excitation-calibration technique of dual-mass MEMS gyroscope for closed-loop mode-matching control is presented in this paper. The technique, which takes advantage of the symmetrical amplitude response of MEMS gyroscope, exploits a two-side excitation signal to actuate the sense mode to obtain the corresponding DC tuning voltage. The structural characteristics of dual-mass decoupled MEMS gyroscope and the tuning principle of excitation-calibration technique are introduced firstly. Then, the scheme of digital excitation-calibration system for the real-time mode-matching control is presented. Simultaneously, open-loop analysis and closed-loop analysis are deduced, respectively, to analyze the sources of tuning error and system stability. To verify the validity of the scheme and theoretical analysis, the system model was established by SIMULINK. The simulation results are proved to be consistent with the theoretical analysis, verifying the feasibility of the digital excitation-calibration technique. The control algorithms of the system were implemented with a FPGA device. Experimental results demonstrate that digital excitation-calibration technique can realize mode-matching within 1 s. The prototype with real-time mode-matching control has a bias instability of 0.813 ∘ /h and an ARW (Angular Random Walk) of 0.0117 ∘ / h . Compared to the mode-mismatching condition, the bias instability and ARW are improved by 3.25 and 4.49 times respectively.

A Low Power Energy-Efficient Precision CMOS Temperature Sensor †.

This paper presents a low power, energy-efficient precision CMOS temperature sensor. The front-end circuit is based on bipolar junction transistors, and employs a pre-bias circuit and bipolar core. To reduce measurement errors arising from current ratio mismatch, a new dynamic element-matching mode is proposed, which dynamically matches all current sources in the front-end circuit. The first-order fitting and third-order fitting are used to calibrate the output results. On the basis of simulation results, the sensor achieves 3σ-inaccuracies of +0.18/-0.13 °C from -55 °C to +125 °C. Measurement results demonstrate sensor 3σ-inaccuracies of ±0.2 °C from 0 °C to +100 °C. The circuit is implemented in 0.18 µm CMOS, and consumes 6.1 µA with a 1.8 V supply voltage.