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Harmonic admittance and dispersion equations--the theorem
Viktor P Plessky1, Sergey V Biryukov, Julius Koskela
1Thales Microsonics, SAW Design Bureau, Neuchâtel, Switzerland. vplessky-tmx@bluewin.ch
Summary
Harmonic admittance analysis of surface acoustic waves (SAWs) in periodic electrodes reveals a direct relationship between system eigen-modes and admittance. This method simplifies calculating SAW propagation and excitation without solving complex equations.
Area of Science:
- Physics
- Materials Science
- Electrical Engineering
Background:
- Harmonic admittance is crucial for analyzing surface acoustic waves (SAWs) in periodic electrode arrays.
- Dispersion relationships for open- and short-circuited systems are linked to the zeros and poles of harmonic admittance, respectively.
Purpose of the Study:
- To demonstrate a strict reverse relationship between harmonic admittance and system eigen-modes.
- To present a method for calculating harmonic admittance as a ratio of determinants derived from open- and short-circuited system eigen-modes.
Main Methods:
- Expressing harmonic admittance as a ratio of two determinants.
- Constructing determinants based on the eigen-modes of open- and short-circuited systems.
- Reproducing and detailing Biryukov's theorem on the admittance-eigenmode connection.
Main Results:
- Harmonic admittance can be directly calculated from determinants representing system eigen-modes, bypassing the need to solve complex equations.
- The study provides examples of calculations using this theorem.
- Calculated results are compared with experimentally measured admittance curves.
Conclusions:
- A rigorous mathematical framework connects harmonic admittance to the eigen-modes of periodic electrode systems.
- This approach offers a simplified and direct method for analyzing SAW excitation and propagation.
- The findings validate the theoretical model through experimental comparison.