A generalised P-matrix model for SAW filters

The P-matrix model, which can be seen as a discrete version of the continuous COM model, is a well established tool to analyse the electro-acoustic properties of IDTs and reflector gratings. It relates both outgoing acoustic surface waves and the electric current to both incoming acoustic surface waves and the electric voltage. If an acoustic track consists of several IDTs and reflectors, it can be described by cascading the P-matrices of its building blocks. However, this approach has its clear limitations. Let us consider, e.g., a DMS track: if a voltage is applied to one IDT it will generate electric charges not only on the fingers of this IDT but also on its neighbouring fingers. These charges cause capacitive coupling between neighbouring elements and change the electro-acoustic excitation and detection of forward and backward propagating surface waves. Both effects are ignored in the building block model. The resulting inaccuracies are most pronounced, if short elements, such as in DMS tracks, are used. In this paper, I will present a generalisation of the classical P-matrix model, which relates the outgoing acoustic surface waves and all electric currents to the incoming acoustic surface waves and all electric voltages in a general acoustic track. This track might consist of an arbitrary number of IDTs, reflectors, and delay lines. To demonstrate the advantage of this model it will be compared to the simpler building block model and to measurements for two typical filters.