Open Access

The advantages of the coupling-of-modes (COM) formalism and the transmission-matrix approach are combined to create exact and computationally efficient analysis and synthesis CAD tools for the design of SAW-resonator filters. The models for the filter components, especially gratings, interdigital transducers (IDTs). and multistrip couplers (MSCs), are based on the COM approach, which delivers closed-form expressions. In order to determine the relevant COM parameters, the integrated COM differential equations are compared with analytically derived expressions from the transmission-matrix approach. The most important second-order effects such as energy storage, propagation loss and mechanical and electrical loading are fully taken into account. As an example, the authors investigate a two-pole, acoustically coupled resonator filter at 914.5 MHz on AT quartz. Excellent agreement between theory and measurement is found.

Rotation of an elastic medium gives rise to a shift of frequency of its acoustic modes, i.e., the time-period vibrations that exist in it. This frequency shift is investigated by applying perturbation theory in the regime of small ratios of the rotation velocity and the frequency of the acoustic mode. In an expansion of the relative frequency shift in powers of this ratio, upper bounds are derived for the first-order and the second-order terms. The derivation of the theoretical upper bounds of the first-order term is presented for linear vibration modes as well as for stable nonlinear vibrations with periodic time dependence that can be represented by a Fourier series.

Recently a P-matrix and COM formalism was presented, which predicts third order intermodulation (IMD3) and triple beat with good accuracy and needs only a single nonlinearity constant. This formalism describes frequency dependence correctly. In this work the dependence of this nonlinearity constant on metalization ratio is investigated for aluminum metalization on LiTaO 3 (YXl)/42°. By comparison to test devices the nonlinearity constant is shown to be largely independent of metalization ratio. The nonlinear effect, however, strongly depends on metalization ratio, which is well described by the model. The linearity of a duplexer is optimized by reduction of metalization ratio and redesign of Tx branch topology.

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.