Universal functions for 3D analysis of the massloading effect in SAW- and BAW devices

This paper is devoted to the 3D analysis of the massloading effect in surface- and bulk acoustic wave devices. The presented theory is a refinement of our earlier contributions and allows the application of high performance computing techniques such as the Fast-MoM. We provide two equivalent representations for the involved dyadic dynamic (frequency dependent) Green´s Functions (GFs), and briefly comment on the calculation of the universal functions (UFs) associated with the massloading problem in acoustic devices. The UFs are defined in a sophisticated way as moments of the GFs or their spatial derivatives. Thereby, by way of construction the singularities of the GFs are regularized. The UFs are astonishingly smooth and, therefore, can easily be stored and processed digitally. The edge- and corner effects associated with 3D electrode models can reliably be described in terms of our precalculated UFs. The UFs are independent of the electrode material, electrode geometry and the operating frequency. Based on this work it is fairly straightforward to calculate higher order moments of the GFs (or of their derivatives) and therefore, calculate higher order UFs. The resulting UFs allow the calculation of 3D electrode models with an arbitrary complex geometry.