The coupling-of-modes approach for modeling and analyzing surface-acoustic wave devices is reviewed. We discuss the established formalism and survey the modifications introduced to account for phenomena such as resistivity, dispersion and in particular, the effects related to surface transverse wave and leaky surface-acoustic wave devices. The extraction of the COM parameters from experiments and theoretical simulations are considered. The design of various SAW devices such as resonators and resonator filters as well as practical aspects are discussed. Finally, the unresolved modeling problems are addressed.

Coupling-of-modes analysis of saw devices

The most frequently used models for surface acoustic wave (SAW) devices are the impulse model, the equivalent circuit models, the Coupling-of-Modes model, and the matrix models. While the impulse-model is only a first order model the other models include second order effects, e.g. reflections, dispersion, and charge distribution effects. The influence of diffraction and refraction on the transfer function of a SAW filter can be described by the angular spectrum of straight-crested waves model. A survey of these different models will be given. The simulation of low-loss filters requires flexible analysis tools, which can cope with different geometries and substrates. Operating with a parameter set, which depends only on the substrate crystal and not on the specific geometry of the SAW filter, is advantageous. Due to the high insertion attenuation of conventional transversal filters the requirements on the accuracy of the analysis are focused on S21, whereas for low-loss filters all elements of the S-matrix are important. The comparison of simulations with a P-matrix model, which fulfills the above mentioned prerequisites, and measurements of different types of low-loss filters, e.g. SPUDT, DMS, and transverse-mode coupled resonator filters are presented

Review of models for low-loss filter design and applications

A novel surface acoustic wave (SAW)-based gyroscope with an 80 MHz central frequency was developed on a 128° YX LiNbO 3 piezoelectric substrate. The developed sensor was composed of a SAW resonator, metallic dots, and two SAW delay lines. A SAW resonator was employed to generate a stable standing wave with a large amplitude, metallic dots were used to induce a Coriolis force and to form a secondary SAW, and two delay lines were formed to extract the Coriolis effect by comparing the resonance frequencies between these two delay lines. Coupling of modes (COM) modeling was conducted to determine the optimal device parameters prior to fabrication. According to the simulation results, the device was fabricated and then measured on a rate table. When the device was subjected to an angular rotation, resonant frequency differences between the two oscillators were observed because of the secondary wave, generated by the Coriolis force, perturbed the propagation of the SAW in the sense element. Depending on the angular velocity, the difference of the resonance frequency was linearly modulated. The obtained sensitivity was approximately 172 Hz deg −1  s −1 at an angular rate range of 0–500 deg/s. Device performances depending on different mass weights and temperatures were also characterized. Good thermal and shock stabilities were observed during the evaluation process.

Development of SAW based gyroscope with high shock and thermal stability

We develop an efficient analysis and synthesis tool for the design of transverse-mode coupled resonator filters. We describe the energy storage effect and the electrical and mechanical loading effect with a one-dimensional model. The two-dimensional nature of the problem is taken into account by shape functions, representing the nonuniform velocity, excitation, and reflection profile across the waveguide structure. We model the wave propagation, excitation, and reflection separately and use the P-matrix algorithm to piece all effects together. This approach enables us to calculate the filter transfer function with standard material data in a general way. Thus we are not restricted to a specific filter design. Our approach can be applied to all two-port devices

P-matrix modeling of transverse-mode coupled resonator filters

In the past few years a new class of SAW devices has been under development based on the use of one port SAW resonators as lumped elements with their impedance strongly changing in a frequency range of effective SAW excitation These 'SAW impedance elements' can be connected in ladder type, balanced bridge type, or others types of networks to provide desired filter characteristics In this paper the admittance characteristics of a single element are analyzed using coupling of mode (COM) model simulations It is found that resonant type characteristics of a long transducer can be described by very simple formulas The frequency gap between resonance and anti-resonance, important for filter design, is determined practically by the /spl Delta/V/V parameter of the piezoelectric substrate used, while the minimum magnitude of the impedance at the resonant frequency is determined by the SAW attenuation The internal reflections only shift the resonance to the left edge of the stopband not changing other characteristics A case of a synchronous resonator comprising a relatively short transducer and two reflectors placed on both sides of it is also analyzed This type of impedance element has smaller frequency shift between resonance and anti-resonance points >

SAW impedance elements

A modeling method is described for using coupling-of-modes to model each transverse mode of a surface acoustic wave (SAW) transversely coupled resonator filter (TCF). Closed-form expressions are obtained which accurately describe the characteristics of this device class. The derivation of the model is described, a comparison between theory and experimental device performance is given, and the use of the model to synthesize optimized SAW TCFs is illustrated. The model is compared to experimental results in which excellent agreement is obtained over a 60- to 80-dB range, depending upon the device design. The accuracy of the model combined with closed-form expressions for filter performance allows for the use of nonlinear least-squares fitting techniques for experimentally determining coupling-of-modes (COM) model parameter values. >

C.S. Hartmann

Papers

Modelling of SAW transversely coupled resonator filters using coupling-of-modes modeling technique