Acoustoelectric Conversion Function: Properties and Calculation
Abstract
In this lecture, properties and calculation of the acoustoelectric (or electroacoustic) conversion function for periodic unapodized and apodized interdigital transducers (IDT) are discussed. For simplicity, the quasi-static approximation is applied, where interelectrode reflections are supposed to be negligible. In particular, this approximation is valid for split-finger IDTs mostly used in IF SAW filter designs.
Acoustoelectric Conversion Function of Unapodized IDTs
First, unapodized IDTs with constant period (pitch) and constant electrode width (duty factor) are considered. The IDT frequency response is represented as the product of the array factor and the element factor. The array factor shapes the bandpass response, whereas the element factor is a wideband frequency-dependent function that distorts an ideal array factor response. Inherently, the element factor accounts for the dependence on the metallization ratio and describes IDT harmonic behavior.
Analysis of Apodized IDTs
The basic closed-form equations for the acoustoelectric conversion function of an unapodized SAW transducer are deduced both in terms of finger potentials and gap voltages. The results are generalized to the case of apodized IDTs, with the finger taps and gap overlaps properly defined in terms of IDT topology. Merits of using the gap overlaps instead of finger taps are discussed in detail.
Furthermore, SAW transducers can be classified according to symmetry type, sampling rate in time and frequency domains, and the even or odd number of electrodes. Their magnitude and phase symmetry properties are also analyzed.
Guard Electrodes and End Effects
Finite-length IDTs are subject to electrostatic end effects. To suppress these effects, guard equipotential electrodes are added at both IDT ends. The analysis shows that, contrary to widespread opinion, these guard electrodes may provide a non-negligible contribution to the overall acoustoelectric conversion function if calculated in terms of finger taps.
The known equations are correct in the particular case of grounded guard fingers with zero potential at both transducer ends. However, these equations fail to predict correct results for antisymmetric or non-symmetric IDT structures. The correction terms are deduced by the author, for this case.
Gap Taps versus Finger Taps
It is shown that using gap taps instead of finger taps automatically ensures zero contribution of the guard electrodes regardless of the IDT apodization pattern. This provides an important advantage of gap taps over finger taps. The lecture illustrates the comparison of both tap types using examples of misuse and correct use of finger taps in practical SAW filter design.
Another advantage of gap taps is a much flatter element factor response over a wide frequency range. As a result, its contribution becomes negligible in most practical cases.
Finally, the lecture material is illustrated with SAW filter design and modeling examples.
Contents
1. Introduction
2. Acoustoelectric Conversion Function Definition and Properties
2.1 Generalized Wave Amplitude and Surface-Wave Potential
2.2 Acoustoelectric Conversion in the Quasi-Static Approximation
3. Quasi-Static Analysis of Periodic Unapodized SAW Transducers
3.1 Active and Guard Electrodes
3.2 Array and Element Factors in the Acoustoelectric Conversion Function
3.3 Contribution of Guard Electrodes
3.4 Finger (Potential) and Gap (Voltage) Taps of the Apodized SAW Transducer
3.5 Element Factor Contribution to the Acoustoelectric Conversion Function
3.6 Array Factor and Ideal IDT Response
3.7 Examples of Misusing Finger Taps in SAW Filter Design
4. Acoustoelectric Conversion Function of Apodized Periodic SAW Transducers
4.1 Basic Assumptions
4.2 Generalization of Finger and Gap Taps
5. Design and Modeling Examples
6. Conclusions