%0 Journal Article %1 9431345 %A Wagner, Andreas %A Putnik, Martin %A Ramici, Kreshnik %A Degenfeld-Schonburg, Peter %A Zimmermann, André %D 2021 %J Journal of Microelectromechanical Systems %K degenfeld-schonburg from:samethalvaci ifm_article wagner_a zimmermann %N 4 %P 530-538 %R 10.1109/JMEMS.2021.3078320 %T Determining the Nonlinear Motion of MEMS Gyroscopes Using the Harmonic Balancing Method %U https://ieeexplore.ieee.org/document/9431345 %V 30 %X In this paper, the usability of the classical Harmonic Balancing method (cHB) to calculate the weakly nonlinear motion of phase- and amplitude controlled MEMS resonators is demonstrated. A polynomial mechanical stiffness description and linearized electrostatic effects are considered, which allow determining the Jacobian analytically. The effects of amplitude and phase control are taken into account by applying boundary conditions in the iteration process. With a customized cHB, it is possible to efficiently simulate the behavior of a MEMS gyroscope undergoing nonlinear resonance with higher parasitic modes. The presented results of a virtual model compare very well with solutions obtained with the Shooting method. Furthermore, we compare the measurement of a drive frequency discontinuity, taken from a different prototype, with the prediction from our linear extrapolated model and from a model with artificially fitted parameters. The cHB approach yields an order of magnitude speed-up in comparison to the transient simulation method. Besides some restrictions, customized cHB methods are interesting candidates for fast system-type simulation considering the MEMS-ASIC interface. 2021-0028

@article{9431345, abstract = {In this paper, the usability of the classical Harmonic Balancing method (cHB) to calculate the weakly nonlinear motion of phase- and amplitude controlled MEMS resonators is demonstrated. A polynomial mechanical stiffness description and linearized electrostatic effects are considered, which allow determining the Jacobian analytically. The effects of amplitude and phase control are taken into account by applying boundary conditions in the iteration process. With a customized cHB, it is possible to efficiently simulate the behavior of a MEMS gyroscope undergoing nonlinear resonance with higher parasitic modes. The presented results of a virtual model compare very well with solutions obtained with the Shooting method. Furthermore, we compare the measurement of a drive frequency discontinuity, taken from a different prototype, with the prediction from our linear extrapolated model and from a model with artificially fitted parameters. The cHB approach yields an order of magnitude speed-up in comparison to the transient simulation method. Besides some restrictions, customized cHB methods are interesting candidates for fast system-type simulation considering the MEMS-ASIC interface. [2021-0028]}, added-at = {2023-06-16T10:20:21.000+0200}, author = {Wagner, Andreas and Putnik, Martin and Ramici, Kreshnik and Degenfeld-Schonburg, Peter and Zimmermann, André}, biburl = {https://puma.ub.uni-stuttgart.de/bibtex/2e5614914b91e61fc3389f70024da7f61/ifm}, doi = {10.1109/JMEMS.2021.3078320}, interhash = {efbdf6f03619a7f6e2a96364f92d6283}, intrahash = {e5614914b91e61fc3389f70024da7f61}, journal = {Journal of Microelectromechanical Systems}, keywords = {degenfeld-schonburg from:samethalvaci ifm_article wagner_a zimmermann}, number = 4, pages = {530-538}, timestamp = {2023-06-26T13:48:29.000+0200}, title = {Determining the Nonlinear Motion of MEMS Gyroscopes Using the Harmonic Balancing Method}, url = {https://ieeexplore.ieee.org/document/9431345}, volume = 30, year = 2021 }