A software package that provides an interactive and graphical environment for surface acoustic wave (SAW) and plate-mode propagation studies in arbitrarily oriented anisotropic and piezoelectric multilayers is described. The software, which runs on an IBM PC with math coprocessor, is based on a transfer-matrix formulation for calculating the characteristics of SAW propagation in multilayers that was originally written for a mainframe computer. The menu-driven software will calculate wave velocities and field variable variations with depth for any desired propagation direction: the graphics capability provides a simultaneous display of slowness or velocity and of SAW Deltav/v coupling constant curves, and their corresponding field profiles in either polar or Cartesian coordinates, for propagation in a selected plane or as a function of one of the Euler angles. The program generates a numerical data file containing the calculated velocities and field profile data. Examples illustrating the usefulness of the software in the study of various SAW and plate structures are presented.

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A systematic procedure for modeling, simulating, and designing SAW (surface acoustic wave) grating filters, taking losses into account, is described. Grating structures and IDTs (interdigital transducers) coupling to SAWs are defined by cascadable transmission-matrix building blocks. Driving point and transfer characteristics (immittances) of complex architectures consisting of gratings, transducers, and coupling networks are obtained by chain-multiplying building-block matrices. This modular approach to resonator filter analysis and design combines the elements of lossy filter synthesis with the transmission-matrix description of SAW components. A multipole filter design procedure based on a lumped-element-model approximation of one-pole two-port resonator building blocks is given and the range of validity of this model examined. The software for simulating the performance of SAW grating devices based on this matrix approach is described, and its performance, when linked to the design procedure to form a CAD/CAA (computer-aided design and analysis) multiple-filter design package, is illustrated with a resonator filter design example.

The various relations for bulk acoustic wave (BAW) propagation in materials of arbitrary anisotropy and piezoelectricity have been expressed in forms suitable for an interactive graphics presentation of the wave properties. The resulting menu-type program a1 lows the simultaneous display of curves in polar or Cartesian coordinates of slowness or velocity, power-flow angle, and electromechanical coupling constant for propagation in an arbitrary plane. Numerical data for propagation in a particular direction in such a plane is displayed when a line cursor is moved to the desired direction. The computational part of the program generates a numerical data file containing all the calculated BAW properties for an arbitrarily selected crystal plane. The interactive part of the program allows the user a variety of choices for displaying simultaneously up to four seperate panels for data and curves pertaining to the selected plane. I . INTRODUCTIONIn the analysis, design and application of bulk acoustic waves (BAW) transducers and delay lines 11-31. surface skimning bulk waves [41, surface acoustic waves [SI, reflective BAW devices using interdigital transducers [61, in acoustooptics research [71, and in the study of reflection and refraction phenomena in anisotropic media [31, one often needs rather detailed information on BAW properties for various directions of propagation in media of arbitrary anisotropy and piezoelectricity. Since BAW properties are not normally catalogued, it is extremely useful to be able to display on a video terminal (VDT) graphs showing how these bulk wave properties vary with the BAW propagation direction.In this paper, section I1 briefly sumnarizes the theortical approach of the BAW calculation, section I11 illustrates the computer program structure and the diversities of the various menus, and explains the reasons for choosing an IBM personal computer and some of the peripheral hardware and software. Some examples are givev in section I V to demonstrate the usefulness of this interactive menu-type computer program. Section V constitutes a summary of the main results and identifies some potentially useful applications not specifically addressed in the paper. CALCULATION OF BAW PROPERTIESChoosing an orthogonal coordinate system X I , X2, X3 with X1 as the propagation direction, the material stiffness [ C], piezoelectric [el, and permittivity [ E I constants with respect to this coordinate system are obtained from those with respect to the crystalline X, Y, Z axes [el,, and I E loby the simple matrix operations:a ][e lo[M1, t L E I = [a ][E Io[a 1 , and where the transformation matrices [a 1 and [M 1 are given in [3, ch.3D 1, and the superscript t means transpose. Efficient and simple computer programs for carrying out these transformations I 8 1 are usually expressed in terms of the Euler angles S I e, Y .In this rotated X1, X2, X3 coordinate the Christoffel equation for propagation X 1 direction is written as I3, Eq. 8.1471 vector-matrix equation -ClJ = P V 2 L , system in the he 3x3 (2) where...

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