Transactions of the Korean Society of Mechanical Engineers A (대한기계학회논문집A)

The Korean Society of Mechanical Engineers (대한기계학회)
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Frequency Response Analysis of Array-Type MEMS Resonators by Model Order Reduction Using Krylov Subspace Method

크리로프 부공간법에 근거한 모델차수축소기법을 통한 배열형 MEMS 공진기의 주파수응답해석

  • 한정삼 (안동대학교 기계공학부) ;
  • 고진환 (서울대학교 기계항공공학부)
  • Published : 2009.09.01
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Abstract

One of important factors in designing MEMS resonators for RF filters is obtaining a desired frequency response function (FRF) within a specific frequency range of interest. Because various array-type MEMS resonators have been recently introduced to improve the filter characteristics such as bandwidth, pass-band, and shape factor, the degrees of freedom (DOF) of finite elements for their FRF calculation dramatically increases and therefore raises computational difficulties. In this paper the Krylov subspace-based model order reduction using moment-matching with non-zero expansion points is represented as a numerical solution to perform the frequency response analyses of those array-type MEMS resonators in an efficient way. By matching moments at a frequency around the specific operation range of the array-type resonators, the required FRF can be efficiently calculated regardless of their operating frequency from significantly reduced systems. In addition, because of the characteristics of the moment-matching method, a minimal order of reduced system with a prearranged accuracy can be determined through an error indicator using successive reduced models, which is very useful to automate the order reduction process and FRF calculation for structural optimization iterations. We also found out that the presented method could obtain the FRF of a $6\times6$ array-type resonator within a seventieth of the computational time necessary for the direct method and in addition FRF calculation by the mode superposition method could not even be completed because of a data overflow with a half after calculation of 9,722 eigenmodes.

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