A general P-matrix model to calculate second-order nonlinearity in TC-SAW devices

With increasing number of simultaneously active frequency bands in RF front ends due to carrier aggregation and continuing device miniaturization, nonlinear effects may lead to spurious signals at receiving ports or unwanted interaction of bands. It is crucial to model nonlinear effects in order to identify critical devices and take countermeasures. Effects of third and second order dominate here. Within this work we developed a P-matrix based model, computing nonlinearities of second order in TC-SAW devices. This includes the generation of signals at twice the input frequency, as well as intermodulation of two input tones, namely the second harmonic H2 and the intermodulation product IMD2, respectively. The model includes effects of nonlinear dielectricity, stiffness, piezoelectricity as well as electrostriction. Both electric and acoustic nonlinear sources are considered. Model parameters were determined by fit of the model to second harmonic measurements of resonators. Electric and acoustic nonlinear sources are distinguished by considering two cases: Excitation frequencies around and at half of the resonance frequency, i.e. self generated harmonics and subharmonics, respectively, are measured. The resulting nonlinear dataset allows for a good prediction of H2 and IMD2 in complete TC-SAW filters.