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TECHNICAL PAPERS

Tunable Microelectromechanical Filters that Exploit Parametric Resonance

[+] Author and Article Information
Jeffrey F. Rhoads

Department of Mechanical Engineering, Michigan State University, 2555 Engineering Building, East Lansing, MI 48824

Steven W. Shaw1

Department of Mechanical Engineering, Michigan State University, 2555 Engineering Building, East Lansing, MI 48824rhoadsje@egr.msu.edu

Kimberly L. Turner

Department of Mechanical and Environmental Engineering, University of California, Santa Barbara, 1171 Engineering Building II, Santa Barbara, CA 93106

Rajashree Baskaran2

Department of Mechanical and Environmental Engineering, University of California, Santa Barbara, 1171 Engineering Building II, Santa Barbara, CA 93106turner@engineering.ucsb.edu

1

Visiting Professor, Department of Mechanical and Environmental Engineering, University of California, Santa Barbara

2

Currently employed at Intel Corp., Phoenix, AZ

J. Vib. Acoust 127(5), 423-430 (Jan 10, 2005) (8 pages) doi:10.1115/1.2013301 History: Received July 16, 2004; Revised January 10, 2005

Background: This paper describes an analytical study of a bandpass filter that is based on the dynamic response of electrostatically-driven MEMS oscillators. Method of Approach: Unlike most mechanical and electrical filters that rely on direct linear resonance for filtering, the MEM filter presented in this work employs parametric resonance. Results: While the use of parametric resonance improves some filtering characteristics, the introduction of parametric instabilities into the system does present some complications with regard to filtering. Conclusions: The aforementioned complications can be largely overcome by implementing a pair of MEM oscillators with tuning schemes and some processing logic to produce a highly effective bandpass filter.

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Copyright © 2005 by American Society of Mechanical Engineers
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Figures

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Figure 1

Transmission characteristics of a bandpass filter (adapted from (8))

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Figure 2

(a) Parametrically excited MEM oscillator. The backbone “B” is the main oscillator mass, the springs “S” provide attachment to ground as well as the mechanical restoring force, and the noninterdigitated combs “N” are used for parametric excitation. “AC” and “DC” indicate voltage sources; (b) enlarged view of the noninterdigitated combs.

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Figure 3

CAD design of a representative MEM oscillator

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Figure 4

The regions of parametric instability in the VA−Ω parameter space. (a) the case of pure ac voltage excitation; (b) a nominal case produced through linear tuning, as described in Sec. 5, which results in a symmetric wedge of instability.

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Figure 5

Regions of parametric instability in the VA−Ω parameter space; for (a) ρ=0 and ρ=1∕2 (for r1A>0) and (b) ρ=0 and ρ=−1∕2 (for r1A>0)

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Figure 6

Sample response curves–amplitude vs frequency: (a) ρ=1∕2 and (b) ρ=−1∕2

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Figure 7

Hardware implementation scheme (from (4))

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Figure 8

Simulation results from the filter system of Fig. 7. Data points are frequency thresholds for the passband boundaries at various ac amplitude levels. The insets show the system outputs at the points indicated.

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