Jinghui Xu

Hybrid macromodels for modeling and simulation of a z-axis micro accelerometer

A design method based on hybrid macromodels for system-level modeling and simulation of MEMS devices was presented, by which the MEMS device was firstly divided into several substructures, then macromodels for the substructures with regular geometry were generated by analytical method and the ones with odd geometry by numerical method. After that, the created macromodels were interconnected according to the original topology of the MEMS device for system-level simulation. The method combines the advantages of both the analytical and numerical methods. Therefore, not only the parameterized design for some key components can be performed, but also the innovative design for some odd substructures can be realized. In the paper, we took the design of a z-axis micro accelerometer as an example to demonstrate the feasibility and efficiency of the proposed method.

A Hybrid System-Level Modeling and Simulation Methodology for Structurally Complex Microelectromechanical Systems

We present a hybrid system-level modeling and simulation methodology by combining numerical macromodels with parameterized lumped-element behavioral models for structurally complex microelectromechanical systems (MEMS). We decompose the MEMS into several functional components. For those components with complex geometry and boundary conditions, we model them using numerical macromodels, whereas for those with simple geometry, we model them using parameterized lumped-element behavioral models. Both models are represented by the same syntax and similar equation forms to ensure the compatibility. Afterward, the hybrid numerical macromodels and parameterized behavioral models are inserted into the same simulator and then interconnected to each other according to the original topography of the MEMS for system-level simulation. As one of the key technologies of the proposed methodology, macromodeling has been improved in two aspects. First, macromodeling for the component with dynamic boundary condition is achieved by combining modal analysis with a novel iterated improved reduced system method. Second, angular parameterization for the components with the same geometry but different initial orientation is achieved by the matrix coordinate transformation. A z-axis micromachined gyroscope is used to demonstrate the proposed methodology. Simulation results show that the method can efficiently support the design for structurally complex MEMS.

Angularly parameterized macromodel extraction for unconstrained microstructures

In this paper, we present an angularly parameterized model order reduction (APMOR) technique for macromodel extraction of unconstrained microstructures by combining a new, iterated IRS (improved reduced system) method with coordinate transformation theory. The extracted macromodels are encapsulated in the MAST hardware description language and can be exported automatically as components which can be inserted directly into an analog circuit simulator for dynamics simulation. An in-plane micro accelerometer including four variable cross-section folded beams is used to demonstrate the proposed macromodeling method. The folded beams are treated as unconstrained microstructures, and numerical simulation results in a SABER simulator show that the macromodels can dramatically reduce the computation cost while capturing the device behavior faithfully. Compared with FEM results, the relative error is less than 1.4%, while the computational efficiency improves about 22 times. Once the macromodel of one of the folded beams is obtained, the macromodels of all other folded beams can be obtained easily by setting the corresponding angle parameters. With the help of an APMOR technique and the existing model library which is developed in our previous work, the hybrid system-level model of the in-plane micro accelerometer can be constructed rapidly, and the scale factor of the accelerometer is simulated. Compared with experimental results, the relative error is about 8.16%.

Design of a new MEMS-based tunable grating with electrostatic comb drive

A new MEMS-based tunable grating with programmable grating period, driven by electrostatic comb, was designed. Finite element model was developed and finite element simulation was performed with ANSYS. Modal analysis and static analysis were carried out. To improve the calculation efficiency, electrostatic driving force at each movable comb was directly computed by analytical method instead of time-consuming coupled-field analysis. The results show that this MEMS-based tunable grating functions quite well when a driving voltage is provided. To operate at its working resonating mode much easier, thicker grating structure is needed, revealing the necessity in using the bulk micromachining such as SOI technology to fabricate the grating. Also, larger the length of connecting beam and spring beam, and smaller the width of spring beam, larger the deflection we can get for a specific driving voltage. The designed MEMS-based tunable grating can be applied in many fields.

System-level modeling and verification of a micro pitch-tunable grating

Micro Pitch-tunable Grating based on microeletromechanical systems(MEMS) technology can modulate the grating period dynamically by controlling the drive voltage. The device is so complex that it is impossible to model and sumulation by FEA method or only analysis macromodel. In this paper, a new hybrid system-level modeling method was presented. Firstly the grating was decomposed into function components such as grating beam, supporting beam, electrostatic comb-driver. Block Arnoldi algorithm was used to obtain the numerical macromodel of the grating beams and supporting beams, the analytical macromodels called multi-port-elements(MPEs) of the comb-driver and other parts were also established, and the elements were connected together to form hybrid network for representing the systemlevel models of the grating in MEME Garden, which is a MEMS CAD tool developed by Micro and Nano Electromechanical Systems Laboratory, Northwestern Polytechnical University. Both frequency and time domain simulation were implemented. The grating was fabricated using silicon-on-glass(SOG) process. The measured working displacement is 16.5μm at a driving voltage of 40V. The simulation result is 17.6μm which shows an acceptable agreement with the measurement result within the error tolerance of 6.7%. The method proposed in this paper can solve the voltage-displacement simulation problem of this kind of complex grating. It can also be adapted to similar MEMS/MOEMS devices simulations.

Angularly parameterized macromodel extraction for microstructures with a large number of terminals

In this paper, we report a novel method for extracting the angular parameterized macromodels of the microstructures with a large number of input terminals. First, the macromodels are extracted by combining the block Arnoldi approach with the superposition theory of linear systems. Then, the angular parameterization for the macromodels is achieved by applying the equivalent matrix coordinate transformation. A pitch-tunable micro programmable grating is used to demonstrate the proposed macromodeling method. Numerical simulation results show that the macromodels can dramatically reduce the computation cost while capturing the device behavior faithfully. Compared with the FEM results, the relative error is less than 1.1%, and the efficiency for transient analysis improves about 45 times.