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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.
The advantages of the coupled-mode (COM) formalism and the transmission-matrix approach are combined in order to create exact and computationally efficient analysis and synthesis tools for the design of coupled surface acoustic wave resonator filters. The models for the filter components, in particular gratings, interdigital transducers (IDTs) and multistrip couplers (MSCs), are based on the COM approach that delivers closed-form expressions. To determine the pertinent COM parameters, the COM differential equations are solved and the solution is compared with analytically derived expressions from the transmission-matrix approach and the Green's function method. 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, a two-pole, acoustically coupled resonator filter at 914.5 MHz on AT quartz is investigated. Excellent agreement between theory and measurement is found.
A simple model is introduced that describes the interaction of surface acoustic waves (SAWs) with a 2D periodic array of objects on the surface that give rise to internal resonances. Such objects may be high-aspect ratio structures like micro-pillars fabricated of a material different from that of the substrate. The model allows for an approximate determination of the band structure for the acoustic modes in such systems. Results are presented for the dependence on structural parameters of a total bandgap in the non-radiative regime of a semi-infinite substrate, and it is shown how the frequency and radiation damping of vibrational modes can be determined that are associated with defects in the periodic 2D array.
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.
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.
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.