Seminar Series - 2001-2002

Langrangean Formulation for the Frequency-Temperature Behavior of Piezoelectric Quartz Devices

Yook-Kong Yong
yong@jove.rutgers.edu
Dept. of Civil and Environmental Engineering, Rutgers University
623 Bowser Road, Piscataway, NJ   08854-8014
Sponsored by the Department of Engineering Mechanics

Date: Tuesday, March 26, 2002
Time: 2:30 p.m.
Place: W183 Nebraska Hall


The frequency-temperature behavior of piezoelectric resonators and filters is an important device specification. The design of frequency stable resonators or filters such as the choice of materials, mounting supports, device geometry and electrodes is greatly influenced by considerations of its frequency-temperature behavior. A first step in modeling the frequency-temperature behavior of these devices is the characterization of the temperature coefficients of the elastic constants, piezoelectric stress constants and dielectric permittivities. Traditionally this characterization is done in an ad hoc formulation, and almost all the temperature coefficients reported and published in references are based on this ad hoc formulation which we shall call the “classical” formulation. The need for accurate characterization of new materials and for accurate modeling of new high frequency miniaturized devices such as micro electromechanical resonators or filters provides us with an opportunity to revisit the classical formulation and promote the more accurate Lagrangean formulation. A major drawback of the classical formulation is its lack of frame invariance.

In this seminar, we discuss both the classical formulation and Lagrangean formulation. The Lagrangean temperature coefficients of elastic constants, piezoelectric stress constants and dielectric permittivities of quartz are calculated from an existing set of experimental data and with the published classical temperature coefficients. We show that in certain crystallographic axes, the classical temperature coefficients could be related to the Lagrangean temperature coefficients. These relationships could be employed to convert to Lagrangean temperature coefficients the existing data on classical temperature coefficients of materials.


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