A generalised P-matrix model for SAW filters

Abstract

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.

FEM Modeling of the Temperature Influence on the Performance of SAW Sensors Operating at GigaHertz Frequency Range and at High Temperature Up to 500 °C

“…To predict the behavior of a SAW devices in harsh conditions and to design high-performance devices, modeling techniques such as the δ function model [22], the coupling of mode (COM) model [23], the P-matrix model [24,25], and the equivalent circuit model [26,27] have become essential in their design. The Finite Element Method, which can be implemented using commercial software such as COMSOL Multiphysics, has an excellent ability to model and analyze SAW devices and has a simplicity advantage compared to other methods when it comes to multilayer structures, which are the focus of the present study (Pt/AlN/Sapphire).…”

Optimization of focusing SAW propagation in piezoelectric medium for microfluidic applications

“…Several methods have been used to solve the coupled wave equations and model the SAW devices. These includes Green's function model [9] that applies the field theory, coupling-of-modes (COM) [10] and P matrix models that uses the network theory [11] and impulse response method [12] which utilizes the signal theory model. All these models are suited for simpler device geometry like the conventional ones and often neglecting the second-order effects such as wave diffraction, electrode reflections, refraction and beam steering which are significant in annular shaped interdigital fingers.…”

P2M-6 Between FEM/BEM and COM - Generalized Reflecting Array Model

“…Matrices in (4) and (5) being written in a total matrix form are quasi-diagonal, as well as some additional matrices intended to spread the potentials of incoming waves over discrete points on an electrode. By introducing incoming waves into the total structure the generalized P-matrix [7] can be calculated. Note that this method can be applied also to structures with arbitrary electrode polarities as in DART and containing floating electrodes, if additional electro-neutrality relations are used.…”