MODELLING OF SURFACE ACOUSTIC WAVE SIGNAL PROCESSING DEVICES

Abstract

Surface Acoustic Wave ( SAW ) devices are finding applications in many diverse electronic equipment. Analysis and synthesis of any operational device ( like a SAW device ) associated with a complicated physics can be performed by some equivalent model. Many models have been developed for the analysis of SAW devices. There are two approaches for such modelling namely; field theory approach and circuit theory approach. The existing models are such as the Delta function model, the Impulse model, the Equivalent Circuit model, the Green's function model, the Coupling Of Modes model,..etc. The main goal of this study is to try to find out a proper model that can describe different types of SAW signal processing devices, specially low loss transducers and filters. It also aims to simulate different types of filters and study the techniques for improving the performances of these filters. The model which is aimed to be developed is supposed to be an aidfull tool to the designers of signal processing equipments using SAW devices. The crossed field equivalent circuit model has been studied in three approaches for modelling SAW transducers and filters. Using the scattering matrix theory and the simplified equivalent circuit model of Smith; the possibility of calculating the scattering matrix of a finger pair directly from the simplified equivalent circuit and building up the full transducer has been studied, and the relevant computations have been done. The scattering matrix for Group-type Uni-Directional Transducer ( GUDT ) as an example for Uni-Direct ional Transducer has been derived under tuned and matched conditions. The different losses and the frequency responses of matched and tuned Bl-directional Inter Digital Transducers ( BIDTs ) with different number of finger pairs have been computed. It has been found that the scattering matrix method can directly give many informations that can not be calculated directly using other methods, such as the Electric Mismatch losses, Triple Transit Echo, Acousto Electric Transmission loss,etc. In the second approach, a single SAW IDT finger has been modeled by a 3 X 3 transfer matrix. A pair of fingers has been represented by cascading a positive and a negative voltage derived fingers. It has been found that the model can be used to analyze successfully different types of BIDTs, split-finger BIDTs, CHIRP and COMB filters. The frequency responses of filters of BIDTs with single and split fingers have been computed for different number of finger pairs. A chain matrix was used to model BIDT, GUDT and Three Phase Uni- Directional Transducer ( TPUDT ) with 4x4, 6x6 and 8x8 matrices, respectively. Forward and backward frequency responses, directiveties and input and output admittances, phases, conductances and susceptances of filters with various possible combinations and types of unidirectional transducers have been computed. Normal/Modified/New-type GUDTs and TPUDTs with different number of active finger pairs, groups and periodic sections in various possible combinations were used at the transmitting as well as the receiving ends with both transducers properly tuned and matched. The results obtained using the three approaches are quite good and give good agreement with experimental results available in literature. Moreover, using different types of transducers at both ends gave interesting results in terms of 3dB bandwidth and stopband rejection Apodization is another way to get filters with lower insertion losses, good bandwidths and larger side-lobe suppressions. The usual practice is to have a low insertion loss, wide band, uniform transducer at one end and a narrower bandwidth. low insertion loss, higher side-lobe suppression, apodized transducer at the other end. Forward, backward frequency responses and relative directivities of different filters having one uniform and one apodized transducer at the two ends with different combinations of Normal/Modified/New- type GUDTs and TPUDTs have been computed. The apodized transducer's effective apertures were apodized using SINC function weighting. The results obtained were interesting in terms of bandwidth and side-lobe suppression. The SINC function is an Infinite Impulse Response ( IIR ) function (of infinite time duration) and since an IDT has finite number of fingers in it (similar to FIR filters); it is always the practice that the SINC function is truncated, hence some Gibbs may appear in the frequency response of the filter. If a COSINE window function is additionally included to modify the IDT apodization these Gibbs can be eliminated or the frequency response can be improved to some extent. In this case, a longer part of the SINC function can be used. The responses of the filters mentioned above were computed using a COSINE window along with different lengths of the SINC function. Good results have been obtained. This windowing technique can also be used to improve the stopband rejection. A Modified Bessel Function (MBF) window family was considered. Filters of different combinations of UDTs, having different number of periodic sections, active fingers and groups have been computed using different types of windows. It has been fount that proper selection of number of periodic sections or groups is very essential in getting good responses. The software modelling package that has been developed seem to be promising and expandable to include the modelling of more SAW signal processing devices and it is expected to be useful and helpful to the designers of SAW devices for signal processing applications.