Approximate expressions for generalized Green's functions

The traditional Green's function has been widely used to analyze the behavior of surface acoustic wave (SAW) devices for many years because of its clear physical meaning and its ability to model all propagation modes. Simplifications introduced in its derivation, however, cause it to ignore some important effects such as mass loading due to surface electrodes. The generalized Green's function method is able to characterize these effects, but its computation is numerically intensive and complex. In this paper, we present a method of deriving approximate expressions similar in concept to Ingebrigtsen's approximation that can be applied to all sixteen elements of the generalized Green's functions. Results are shown for two representative substrates.