Charge Distribution and Capacitance Calculation for Periodic SAW Transducers

Abstract

This lecture focuses on the closed-form calculation of the surface charge density distribution, electrode charges, and capacitance of generalized periodic SAW transducers with uniform finger spacing (pitch, or period) and constant metallization ratio. An electrostatic problem for a finite-length transducer is approximated by an auxiliary one with periodic boundary conditions on the surface.

Periodic SAW Transducer Replication

A SAW transducer containing N electrodes with arbitrary voltages Vi is treated as one generalized period of the infinite periodic array derived by subsequential periodic replications of the initial transducer. The closed-form electrostatic solution for one generalized transducer period is deduced using Floquet's theorem, superposition principle, and the known analytic solution for the charge density in a periodic phased array of strips — a system with the same strip voltages and voltage phase progressing uniformly along the infinite array.

Periodic SAW Transducer Capacitance and Potential Coefficients

Within one generalized period of N electrodes, electrode charges and voltages are interrelated via the closed-form capacitance matrix or the (pseudo-)inverse potential matrix. As a result, the general expression for the transducer static capacitance is derived in terms of weighted interelectrode capacitors between nearest-neighbor electrodes, next-nearest ones, and so on. The derived equation for the static capacitance is applicable both to uniform and apodized (aperture-weighted) SAW transducers.

Mixed Electrostatic Problem for Periodic SAW Transducers

The lecture also considers the general solution of the mixed electrostatic problem, where each electrode is characterized either by its potential or by its charge. First, the mixed set of unknown variables (whether charges or potentials) is determined in terms of the prescribed subset of known voltages and charges using capacitance or potential matrices.

As a special case, the solution for SAW transducers with floating electrodes follows from the general solution by imposing the charge-neutrality condition on single floating electrodes or floating sections (several interconnected floating electrodes).

Finally, examples of charge distributions and capacitance calculations for practical periodic SAW transducers are presented.

Contents

1. Introduction

2. Electrostatic problem for periodic SAW transducers

3. Properties of periodic phased-arrays and SAW transducers

4. Calculation of the surface charge density distribution in periodic SAW transducers

5. Capacitance calculation for periodic SAW transducers

5.1 Interrelation of electrode charges and voltages

5.2 Capacitance and potential matrices. Interelectrode capacitors

6. Mixed electrostatic problem for periodic SAW transducers

7. Analysis of periodic SAW transducers with floating electrodes

8. Simulation examples of periodic SAW transducers

9. Conclusions