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Trapped‐Energy Modes in Quartz Filter Crystals

 

作者: W. Shockley,   D. R. Curran,   D. J. Koneval,  

 

期刊: The Journal of the Acoustical Society of America  (AIP Available online 1967)
卷期: Volume 41, issue 4B  

页码: 981-993

 

ISSN:0001-4966

 

年代: 1967

 

DOI:10.1121/1.1910453

 

出版商: Acoustical Society of America

 

数据来源: AIP

 

摘要:

The behavior of thickness/shear‐mode quartz resonators is explained both mathematically and experimentally in terms of lateral standing‐wave trapped‐energy modes. A cutoff phenomenon, similar to that occurring in optical total internal reflection, results in energy trapping or the restriction of vibratory energy almost exclusively to the electroded region of a resonator, with an energy distribution decreasing exponentially with distance from the electrode edge. Consideration of boundary conditions at the electrode edges of an idealized two‐dimensional model yields an expression for the eigenfrequencies of symmetric inharmonic overtone modes (lateral standing waves) that can exist in the electroded region of fundamental‐ and harmonic‐mode resonators. Design formulas for the suppression of these unwanted modes are included. They show that electrode thickness and lateral dimensions can be traded off against one another to obtain a wide range of motional parameters. Previously, unwanted responses were eliminated by restricting the electrode diameter to empirically established values. The present understanding has led to a reduction in resonant resistance and an increase in motional capacitance by at least a factor of four with hf and vhf fundamental‐ and harmonic‐mode filter crystals. Experimental data that verify results predicted by energy‐trapping theory are given, and application to design of single‐ and multi‐electrode resonators is considered. Specific examples in the 10‐ to 180‐MHz frequency range are given.

 

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