Magnetostatic potential analysis outside mems plate by boundary element method

MEMS ve NEMS cihazlarının, gittikçe küçülen yapılarıyla beraber kararlı ve verimli çalışabilmesi için tasarımları önem kazanmaktadır. Sınır elemanları yöntemi bu tür cihazların tasarımı için son zamanlarda yaygın olarak kullanılan bir yöntemdir. Bu çalışmada, klasik yöntemler olarak ifade edilen sonlu farklar yöntemi ve sonlu elemanlar yöntemine göre daha yeni bir metot olan sınır elemanları metodu araştırılmıştır. Sınır elemanları yönteminin MEMS tasarımındaki performansını incelemek için MEMS plakası dışında oluşan skaler manyetik potansiyel analiz edilmiştir. İlk olarak problem bölgesi sınırları, sabit sınır elemanı ile bölümlenmiş ve Dirichlet sınır şartları tanımlanarak problem modellenmiştir. Problemi çözmek için Matlab ortamında yeni bir program geliştirilmiştir. Tasarlanan program, limitleri ve eleman sayıları belirlenen iki boyutlu problem bölgesinde, otomatik olarak sonlu elemanlar yöntemi ve sınır elamanları yöntemi için çözüm yapmaktadır. Sonuçların doğruluk derecesini kontrol etmek için problem analitik olarak çözülerek tüm sonuçlar karşılaştırılmıştır. Uygulamada elde edilen sonuçlara göre sınır elemanları yönteminin sonlu elemanlar yöntemine göre problem çözmek için gerekli veriler, uygulama kolaylığı ve sonuçların doğruluğu açısından birçok pozitif yöne sahip olduğu ifade edilebilir. Bu çalışmada elde edilen sonuçlara göre MEMS ve NEMS cihazların elektrostatik ve manyetostatik algılama mesafeleri tespitinde sınır elamanları metodunun kullanılması önerilebilir. Geliştirilen yeni program, bu tür cihazların daha iyi bir tasarıma sahip olmalarına katkı sunabilirDesigns of MEMS and NEMS devices are gaining importance for their stable and efficient operation with their shrinking structures. Boundary element method is a widely used method for design of such devices, recently. In this study, finite difference method, which is expressed as classical methods, and boundary element method, which is a newer method compared to finite element method, was investigated. To examine the performance of boundary element method in MEMS design, the scalar magnetic potential formed outside the MEMS plate was analyzed. Firstly, the boundaries of problem region are divided with a fixed boundary element and the problem is modeled by defining Dirichlet boundary conditions. A new program has been developed in Matlab environment to solve the problem. The designed program automatically solves the finite element method and the boundary element method in two-dimensional problem region whose limits and number of elements are determined. To check the accuracy of the results, the problem was solved analytically and all results were compared. According to the results obtained in the application, it can be stated that boundary element method has many positive aspects in terms of the data required for problem solving, the ease of application and the accuracy of the results according to the finite element method. According to the results obtained in this study, it may be suggested to use the boundary element method in detection of electrostatic and magnetostatic sensing distances of MEMS and NEMS devices. The developed program can contribute to better design of such devices

A dual-mass resonant mems gyroscope design with electrostatic tuning for frequency mismatch compensation

The micro-electro-mechanical systems (MEMS)-based sensor technologies are considered to be the enabling factor for the future development of smart sensing applications, mainly due to their small size, low power consumption and relatively low cost. This paper presents a new structurally and thermally stable design of a resonant mode-matched electrostatic z-axis MEMS gyroscope considering the foundry constraints of relatively low cost and commercially available silicon-on-insulator multi-user MEMS processes (SOIMUMPs) microfabrication process. The novelty of the proposed MEMS gyroscope design lies in the implementation of two separate masses for the drive and sense axis using a unique mechanical spring configuration that allows minimizing the cross-axis coupling between the drive and sense modes. For frequency mismatch compensation between the drive and sense modes due to foundry process uncertainties and gyroscope operating temperature variations, a comb-drive-based electrostatic tuning is implemented in the proposed design. The performance of the MEMS gyroscope design is verified through a detailed coupled-field electric-structural-thermal finite element method (FEM)-based analysis

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