Analysis of general planar waveguides with N segments

For the simulation of SAW-filters it can be useful to model the filters as planar waveguides, consisting of several segments with assigned material parameters (phase velocities, stiffness constants). For symmetric waveguides with three segments the corresponding theory has been provided in [1]. In the case of more complex structures (such as transversely coupled resonator filters, TCRF-filters) a transverse velocity profile consisting of more than three (N) segments can be determined. For such structures the present work provides the complete analysis based on a scalar potential as the wave-describing quantity. We obtain a complete set of orthonormal modes into which a transverse excitation can be expanded in order to study its propagation. The general mode spectrum consists of a discrete spectrum of bound modes, a continuous spectrum of semi-bound modes and finally a continuous spectrum of radiation modes. All types of modes are calculated using the stack matrix approach. As to radiation modes, two solutions per eigenvalue exist. Therefore, they must be orthogonalized to enable expansion with a scalar product.