Subject: Eigenvalue Problems in SAW-Filter Simulations
Author: Sabine Zaglmayr
Supervisor:Prof. Dr. Ulrich Langer

This diploma thesis is concerned to the development of numerical methods in calculating so-called "dispersion diagrams" of periodic surface acoustic wave (SAW) filter structures. These piezoelectric devices are used in telecommunications for frequency filtering.

dispersion diagram

The mathematical problem is governed by two main points, the underlying periodic structure and the indefinite coupled field problem due to the properties of the used piezoelectric materials. Floquet-Bloch theory allows to restrict the infinite periodic computation domain to one reference cell by introducing quasi-periodic boundary conditions. Due to the Bloch-ansatz the dispersion context between "excitation frequency" and the "propagation constants" of the surface acoustic wave is described by parameter depending eigenvalue problems.

Three different solution approaches are developed for gaining these non-hermitian eigenvalue problems of generalized linear or quadratic form. Expanding the solution methods of periodic structures to the piezoelectric coupled field equations has the consequence that the eigenvalue problems get indefinite and worse-conditioned, i.e. special sealing methods, which ensure accurate numerical results, are required. A comprehensive collection of abstract theory and numerical solution methods for the occuring algebraic eigenvalue problems is provided.

filter

Three different solvers for the numerical simulation of the dispersion context are developed and implemented. The used eigenvalue solver is concerned with the direct QZ-method or the interative Implicitly Restarted Anoldi-method, respectively.

The influence of peridoc perturbations in the computation geometry is shown in numerical experiment for a pure mechanical model problem. Simulation results for the dispersion context of simplified periodic structures related to real-life TV- and GSM-filters are presented.

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