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Plessky VP, Biryukov SV, Koskela J. Harmonic admittance and dispersion equations--the theorem. IEEE Trans Ultrason Ferroelectr Freq Control. 2002;49(4):528-34doi: 10.1109/58.996573.
Plessky, V. P., Biryukov, S. V., & Koskela, J. (2002). Harmonic admittance and dispersion equations--the theorem. IEEE transactions on ultrasonics, ferroelectrics, and frequency control, 49(4), 528-34. https://doi.org/10.1109/58.996573
Plessky, Viktor P, et al. "Harmonic admittance and dispersion equations--the theorem." IEEE transactions on ultrasonics, ferroelectrics, and frequency control vol. 49,4 (2002): 528-34. doi: https://doi.org/10.1109/58.996573
Plessky VP, Biryukov SV, Koskela J. Harmonic admittance and dispersion equations--the theorem. IEEE Trans Ultrason Ferroelectr Freq Control. 2002 Apr;49(4):528-34. doi: 10.1109/58.996573. PMID: 11989710.
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IEEE Trans Ultrason Ferroelectr Freq Control. 2002 Apr;49(4):528-34. doi: 10.1109/58.996573.

Harmonic admittance and dispersion equations--the theorem.

IEEE transactions on ultrasonics, ferroelectrics, and frequency control

Viktor P Plessky, Sergey V Biryukov, Julius Koskela

Affiliations

  1. Thales Microsonics, SAW Design Bureau, Neuchâtel, Switzerland. [email protected]

PMID: 11989710 DOI: 10.1109/58.996573

Abstract

The harmonic admittance is known as a powerful tool for analyzing the excitation and propagation of surface acoustic waves (SAWs) in periodic electrode arrays. In particular, the dispersion relationships for open- and short-circuited systems are indicated, respectively, by the zeros and poles of the harmonic admittance. Here, we show that a strict reverse relationship also exists: the harmonic admittance of a periodic system of electrodes may always be expressed as the ratio of two determinants, which have been specifically constructed to describe the eigen-modes of the open- and short-circuited systems. There is no need to solve these equations to find the admittance. The existence of a connection between the excitation and propagation problems was recognized within the coupling-of-modes theory by Chen and Haus and was recently used to model surface transverse waves by Koskela et al., but a rigorous mathematical proof was only found later by Biryukov. Here, we reproduce this theorem in detail, give some examples of calculations based on this theorem, and compare the results with measured admittance curves.

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