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Nonlinearity can give rise to intermodulation distortions in surface acoustic wave (SAW) devices operating at high input power levels. To understand such undesired effects, a finite element method (FEM) simulation model in combination with a perturbation theory is applied to find out the role of different materials and higher order nonlinear tensor data for the nonlinearities in such acoustic devices. At high power, the SAW devices containing metal, piezoelectric substrate, and temperature compensating (TC) layers are subject to complicated geometrical, material, and other nonlinearities. In this paper, third-order nonlinearities in TC-SAW devices are investigated. The materials used are LiNbO 3 -rot128YX as the substrate and copper electrodes covered with a SiO 2 film as the TC layer. An effective nonlinearity constant for a given system is determined by comparison of nonlinear P-matrix simulations to third-order intermodulation measurements of test filters in a first step. By employing these constants from different systems, i.e., different metallization ratios, in nonlinear periodic P-matrix simulations, a direct comparison to nonlinear periodic FEM-simulations yields scaling factors for the materials used. Thus, the contribution of the different materials to the nonlinear behavior of TC-SAW devices is obtained and the role of metal electrodes, substrate, and TC film are discussed in detail.

Increasing power density causes increased self-generation of harmonics and intermodulation. As this leads to violations of the strict linearity requirements, especially for carrier aggregation (CA), the nonlinearity must be considered in the design process of RF devices. This raises the demand of accurate simulation models. Linear and nonlinear P-Matrix/COM models are used during the design due to their fast simulation times and accurate results. However, the finite element method (FEM) is useful to get a deeper insight in the device's nonlinearities, as the total field distributions can be visualized. The FE method requires complete sets of material tensors, which are unknown for most relevant materials in nonlinear micro-acoustics. In this work, we perform nonlinear FEM simulations, which allow the calculation of nonlinear field distributions of a lithium tantalate based layered SAW system up to third order. We aim at achieving good correspondence to measured data and determine the contributions of each material layer to the nonlinear signals. Therefore, we use approximations circumventing the issue of limited higher order tensor data. Experimental data for the third order nonlinearity is shown to validate the presented approach.

A Nonlinear FEM Model to Calculate Third-Order Harmonic and Intermodulation in TC-SAW Devices
(2018)

Nonlinearities in Temperature Compensated SAW (TC-SAW) devices in the 2 GHz range are investigated using a nonlinear finite element model by simultaneously considering both third-order intermodulation distortion (IMD3)and third harmonic (H3). In the employed perturbation approach, different contributions to the total H3, the direct and indirect contribution, are discussed. H3 and IMD3 measurements were fitted simultaneously using scaling factors for SiO 2 film and Cu electrode nonlinear material tensors in TC-SAW devices. We employ a P-Matrix simulation as intermediate step: Firstly, measurement and nonlinear P-Matrix calculations for finite devices are compared and coefficients of the P-Matrix simulation are determined. The nonlinear tensor data of the different materials involved in periodic nonlinear finite element method (FEM) computations are optimized to fit periodic P-Matrix calculations by introducing scaling factors. Thus, the contribution of different materials to the nonlinear behavior of TC-SAW devices is obtained and the role of materials is discussed.

In einer SAW-Vorrichtung, welche einen SAW-Chip umfasst, der einen SAW-Wandler aufweist, welcher innerhalb einer ersten Signalleitung angeordnet ist, werden Parasitärsignale infolge höherer Harmonischer der Betriebsfrequenz der SAW-Vorrichtungen durch Kompensationsmittel elektrisch beseitigt, welche zumindest eine zweite Signalleitung mit Mitteln zum Erzeugen eines Aufhebungssignals, das im Vorzeichen oder in der Phase vom Parasitärsignal verschieden ist, oder eine Nebenschlussleitung zum elektrischen Verbinden des SAW-Wandlers mit einer rückseitigen Metallisierung des SAW-Chips umfassen.

In a recent paper it has been shown that the effective nonlinear constant which is used in a P-Matrix approach to describe third-order intermodulation (IMD3) in surface acoustic wave (SAW) devices can be obtained from finite element (FEM) calculations of a periodic cell using nonlinear tensor data [1]. In this paper we extend this FEM calculation and show that the IMD3 of an infinite periodic array of electrodes on a piezoelectric substrate can be directly simulated in the sagittal plane. This direct approach opens the way for a FEM based simulation of nonlinearities for finite and generalized structures avoiding the simplifications of phenomenological approaches.

In a SAW device comprises a SAW chip bearing a SAW transducer arranged within a first signal line parasitic signals due to higher harmonics of the operating frequency of the SAW devices are electrically eliminated by compensating means comprising at least one second signal line having means for producing a cancelling signal different in sign or phase to the parasitic signal, or a shunt line to electrically connect the SAW transducer to a back side metallization of the SAW chip.

In this work a set of nonlinear coupled COM equations at interacting frequencies is derived on the basis of nonlinear electro-elasticity. The formalism is presented with the aim of describing intermodulation distortion of third-order (IMD3) and triple beat. The resulting COM equations are translated to the P-matrix formalism, where care is taken to obtain the correct frequency dependence. The scheme depends on two frequency-independent constants for an effective third-order nonlinearity. One of these two constants is negligibly small in the systems considered here. The P-matrix approach is applied to single filters and duplexers on LiTaO 3 (YXl)/42° operating in different frequency ranges. Both IMD3 and triple beat show good agreement with measurement.

This work focuses on the dependencies between typical design parameters of surface acoustic wave (SAW) resonators and the nonlinear emitted signals of second and third order. The parameters metalization ratio and pitch are used as examples, but the approach can be extended to other design parameters as well. It is shown, that the interaction between the nonlinear current generation and the linear admittance is defining the measured nonlinear power signals. It is also discussed, that changes in linear properties get more pronounced in nonlinear responses. Therefore, slight effects on linear parameters will have significant influence on the observed nonlinearity.