Admittance Calculation for Periodic SAW Transducers
Abstract
This lecture focuses on the calculation of periodic SAW transducer admittance. The SAW transducer admittance accurately accounts for both acoustic radiation conductance and susceptance in the quasi-static approximation (i.e. neglecting interelectrode SAW reflections). For calculation, the author introduces the concept of a nodal admittance matrix of a SAW transducer. First, self- and mutual elemental nodal admittances of a periodic SAW transducer with uniform aperture are deduced in the closed-form. Physical meaning of the elemental admittances is explained.
Closed-Form Admittance Calculation
Next, given the closed-form nodal admittance matrix and transducer electrode voltages, an analytic expression for the admittance of a SAW transducer with uniform aperture and arbitrary polarity sequence of electrodes is derived. Admittance of the aperture-weighted (apodized) SAW transducer is found by applying this equation to an arbitrary intersection of an apodized transducer and then closed-form integration over the entire transducer aperture.
Nodal Interelectrode Admittances and Effective Apertures
In particular, within model constraints applied, acoustic admittance of the aperture-weighted SAW transducer is a weighted sum of the nodal interelectrode admittances, with weights given by the effective apertures. Effective apertures are defined as the total overlaps for all the nearest electrodes, next nearest ones, and so on, respectively. They are frequency-independent and depend only on the SAW transducer topology (apodization).
Computational Time Reduction
Furthermore, the author applies a special summation technique for the apodized periodic SAW transducers with a fixed pitch and metallization ratio. The summation takes into account periodic properties of the nodal admittance matrix allowing to convert two-dimensional summation into one-dimensional one. As a result, computation time is drastically reduced if compared to the wide-spread aperture channelizing technique.
FFT Implementation
Moreover, the full periodic SAW transducer admittance (comprising both conductance and susceptance) is given by the Fourier transform of a set of effective apertures. Assumed for the set of the effective apertures to be determined a priori, acoustic admittance calculation takes no more time than frequency response calculation of a SAW transducer, in the quasi-static approximation.
Furthermore, the Fast Fourier Transform (FFT) can be effectively applied to calculate the admittance characteristic in the wide frequency range for the narrowband SAW transducers with the large number of electrodes.
The method is quite general and can be generalized to capacitively-weighted, polarity-weighted, multi-phase, and other periodic SAW transducers having the central frequency away from the synchronous frequency.
Simulation and Measurent Results
Finally, the results of admittance calculation for apodized SAW transducers with split (double) fingers are presented which agree well with the measured admittance characteristics.
Contents
1. Introduction
2. Nodal admittance matrix of a SAW transducer
2.1 Modeling assumptions of the quasi-static approximation
2.2 Nodal admittance matrix and its properties
2.3 Calculation of self- and mutual nodal admittances
3. Admittance of an unapodized SAW transducer
3.1 Definition of the transducer admittance matrix
3.2 Admittance calculation in terms of finger potentials
3.3 Admittance calculation in terms of gap voltages
3.4 Contribution of guard electrodes into admittance
3.5 Examples of the SAW transducer admittance calculation
3.6 Comparison with the known results
4. Admittance of an apodized SAW transducer
4.1 Calculation in terms of finger taps
4.2 Calculation in terms of gap taps (finger overlaps)
4.3 Physical meaning of the weighted elemental admittances
4.4 Double summation reduction
5. MATLAB Implementation of the SAW transducer admittance computation algorithm
6. Simulation examples and experimental results of periodic SAW transducers
7. Conclusions