Network modelling of a class of Surface Acoustic Wave filters

We focus on the modelling aspects of a wide class of Surface Acoustic Wave (SAW) filters built by cascading two electro-acoustic transducer three-ports that convert electrical signals into acoustic waves on a piezoelectric substrate, and vice versa. It is this conversion of voltages or currents into acoustic waves that requires the use of mixed coordinates for the natural parameterization of SAW transducers. This modelling problem in mixed coordinates offers a variety of basic and interesting aspects that might be useful in other fields. On the level of a general black-box description, we develop a systematic theory of ‘mixed’ matrix representations including cascade decomposition, lossless or Darlington embedding, state-space realization, and additional constraints imposed by losslessness and reciprocity. Hereby, we identify Redheffer's star product and the pertaining linear fractional transformation as the main structural elements of the underlying matrix algebra. At the detailed level, we are not interested in the analysis and modelling of the various physical effects. Instead, we look for a linear network model that produces rational transfer functions and parameterizes them by physically measurable quantities (reflection and excitation coefficients), that is, we present a mathematically tractable network model for SAW filters that is simple enough to serve as the basis for the future solution of the synthesis problem of such structures under idealized assumptions.