Showing papers in "IEEE Transactions on Sonics and Ultrasonics in 1977"

Analysis of Generation and Detection of Surface and Bulk Acoustic Waves by Interdigital Transducers

Abstract: Ahrroct-A method of analysis which uses a combination of analytical and numerical techniques has been developed to obtain an accurate solution to the coupled electromagnetic and acoustic fields set up by an interdigital transducer on the surface of a piezoelectric substrate. Full account is taken of the coupling to bulk modes as well as surface modes, and the solution for the charge on the electrodes includes both electrostatic charge and piezoelectrically regenerated charge. Programs have been written for interdigital arrays with uniform aperture but varying electrode width and pitch and arbitrary electrical connections. The theory is also valid for arbitrary crystal orientations. Generation and detection may be analyzed separately with information being provided on the partition of power into the various acoustic modes and the external load impedance, and the bulk wave radiation patterns are also computed. The program may also be used to find the insertion loss of a pair of transducers. Results are presented for the BleusteinGulyaev orientation of PZT-4 ceramic and the YZ and 41” rotated YX orientations of lithium niobate.

Multifrequency Acoustooptic Diffraction

Abstract: Absrract-A coupled mode formulation is developed for the analysis of acoustooptic diffraction with multiple acoustic waves at different carrier frequencies For the Raman-Nath (thin ultrasonic grating) regime, analytic solutions are obtained for N s i g n a l s In the Bragg (thick ultrasonic grating) limit, analytic solutions are obtained for two independent signals. Truncated series approximations for N small signals are given for both regimes. The theory is applied to the quantitative evaluation of linear and nonlinear effects occurring in acoustooptic spectrum analysis, optical information processing, multichannel recording, and multiple beam deflection and modulation. These include diffraction efficiency, compression, cross modulation, and spurious intermodulation intensities. The results show that all nonlinear effects considered are substantially reduced in the Brag limit. This is supported by experimental measurements of the various effects, in good agreement with the Bragg limit theory.

Reconstruction of Ultrasound Propagation Speed Distributions in Soft Tissue: Time-Of-Flight Tomography

Abstract: A soft tissue imaging/characterization technique is described which is based on computerized reconstruction of twodimensional velocity distributions from one-dimensional time-of-flight (TOF) projections. The projection data are obtained by measuring short-pulse propagation delay from transmitter to receiver along many paths through the specimen. The velocity reconstruction provides a true measure of bulk tissue properties and is presented in both digital and video display formats. The concept is demonstrated with results on phantoms and beef liver as well as live human breasts.

Theory of Nonspecular Reflection. Effects for an Ultrasonic Beam Incident on a Solid Plate in a Liquid

Abstract: Poles and zeroes of the infinite plane wave amplitude reflection coefficient are used to derive a theoretical prediction of the nonspecular reflection effects which have been observed for an ultrasonic beam incident on an isotropic solid plate in a liquid. It is shown that there are two types of nonspecular reflections, and they can be characterized in terms of a single parameter which requires a knowledge of the imaginary part of a pole of the infinite plane wave reflection coefficient. Theoretical predictions of nonspecular reflection intensities are presented. Finally, it is shown that the reflection characteristics for high-frequency beams incident on thick plates are the same as those expected for the reflection from a single liquidisolid interface, i.e., two infinite half-spaces. T INTRODUCTION HEORETICAL and experimental aspects of beam displacement phenomena have been actively studied since 1947 when Coos and Hanchen [ l ] demonstrated that a beam of light is displaced from the expected geometrically reflected beam upon reflection from the interface between two transparent media. In 1950 Schoch predicted [2] and later experimentally verified [3 J the beam displacement effect for an acoustic beam incident on a liquid/solid (L/S) interface. Schoch’s theory predicted that an incident bounded acoustic beam would be nonspecularly reflected in that the reflected beam would be displaced laterally along the interface while the reflected beam profile retained the same general shape as the incident beam profile. analysis of nonspecular reflection phenomena has been used Although the basic framework of Schoch’s theoretical Manuscript received May 17, 1976. This work was supported by the L. E. Pitts was with the Department of Physics, Georgetown UniverOffice of Naval Research, U.S. Navy. sity, Washington, DC 20057. He is now with the Department of Physics, Mary Washington College, Fredericksburg, VA 22401. sity, Washington, DC 20057. He is now with the Schlumberger-Doll Research Center, Ridgefield, CT 06877. sity, Washington, DC 20057. T. J. Plona was with the Department of Physics, Georgetown UniverW. G. Mayer is with the Department of Physics, Georgetown Univerby later authors [4] , [ 5 ] , his theory did not account for two experimentally observed phenomena: 1) the reflected sound field for certain bounded acoustic beams has a point of null sound intensity which is not present in the incident sound beam and 2) the main portion of the reflected sound field is accompanied by a sound field which becomes weaker as it extends for a considerable distance along the interface, away from the incident beam. This field is called the “trailing sound field.” Assuming an incident beam which is approximately Gaussian, a schematic example of these two phenomena is shown in Fig. 1. have since been reconciled by Bertoni and Tamir [5]. A principle difference between Schoch’s analysis and that of Bertoni and Tamir is that the latter has emphasized the use of complex poles of the plane wave amplitude reflection coeffiThese discrepancies between Schoch’s theory and experiment

Use of Interface Waves for Nondestructive Inspection

Abstract: Fabry-Perot cavity analysis and circuit theorems me used to obtain the approximate terminal characteristics of a general two-port surface acoustic wave (SAW) resonator. The results are cast such that the performance of a two-port device with two transducers between the reflectors can be predicted simply from the insertion loss of the transducer pair without the cavity and the externally measured cavity parameters unloaded by the internal transducers. The analysis gives relative power levels within the device allowing a greater physical understanding of the individual effects of the various loss and reflection elements. Also, the analysis provides a very simple technique for deriving element values in proposed two-port equivalent circuits.

Ultrasonic Measurement of Some Mineral Filled Plastics

Abstract: Absrroct-Several composite systems such as vinyl-tungsten, polymethylmethacrylatecrystabolite, and epoxycrystabolite have been examined for the variation of the longitudinal velocity as a function of volume fraction of the hard constituent. When the Voigt and Reuss velocity bounds rather than elastic bounds are plotted for these composite systems, the bounds are widely divergent and the V-bound is concave downward, while the R-bound is concave upward and has a well-defined minimum velocity. The experimental data for all the systems conform to the R-bounds indicating that the composite systems are families of true Reuss solids. The velocity minimum occurs because the density increases more rapidly than the elastic modulus. C OMPOSITE materials, where the matrix is soft and the filler is hard, are encountered in many situations. Our experience includes backing materials for ultrasonic transducers, dental restorative materials, and hard biological tissues like bone and teeth. Composites are materials made of two or more constituents in intimate contact. The composite is homogeneous and isotropic when the filler is a powder uniformly distributed throughout the matrix. When the filler is fibrous, the composite can exhibit anisotropic behavior and hard tissues are fibrous and anisotropic. In this paper only homogeneous isotropic composites will be discussed and only with respect to the performance of the longitudinal sonic velocity as it is affected by the amount of the hard filler included in the solid. The ultrasonic transducers employed in the measurements emitted well-damped pulses. For the vinyl-tungsten composite system listed in Table 11, the pulse duration was about one microsecond, but for the other materials it was 100 nanoseconds. Hence in all instances, the use of ultrasonics ensured that the measurements were made at high strain rates with very little displacement, so that only the elastic properties affected the measurements and plastic deformation was negligible. The samples could be retested since there was no deformation or destruction. Moreover, the ultrasonic tests could be repeated with little variation on the same sample and the results were repeatable for similar samples. What is desired is a technique for predicting the velocity characteristics of the composite system as a function of the volume fraction of the hard filler constituent. In a 1973 paper [l] it was shown that the longitudinal sonic velocity of the tungsten-vinyl composite decreased markedly to a

Acoustic Clad Fiber Delay Lines

Abstract: V. CONCLUSIONS Although the various intensities of a diffracted light wave are described in a totally different way in the Raman-Nath and in the Bragg region, the final results for the molecular parameters G and T are identical. Furthermore, we found in both the cases the same correction term containing p . This term is not negligible for the first diffraction order in the Bragg region and for higher diffraction orders in the Raman-Nath region.

Influence of Elastic Properties on Rayleigh Wave Scattering by Normal Discontinuities

Abstract: A numerical study of Rayleigh wave scattering at various discontinuities, like edges and steps, is presented. The influence of elastic properties of the substrate on scattering parameters is emphasized. Reflection measurements have been done for a 90\" comer, and they agree with numerically computed values. INTRODUCTION T HE SCATTERING of acoustic surface waves at various types of discontinuities is important to the development of surface wave devices. In particular, some workers [ l ] -[4] have been interested for several years in realizing devices whose fundamental mechanism is the scattering of surface waves at grooves with the aim of developing reflectors and filters with isotropic and piezoelectric substrates. The study presented here is an attempt to illuminate some of the phenomena in such devices. rise to parasitic scattering phenomena closely related to the finite dimensions of substrates. Some discontinuities may be artificially created on a substrate with a view to guiding [ S ] , [6] or filtering [ l ] , [2] waves. Whatever the case, the problem of a surface wave reaching a discontinuity is central to the study of such devices, and several earlier contributions have been made in this area [7] -[l21 . The purpose of this paper is to present a method for the study of scattering phenomenon on homogeneous isotropic media. Analytical investigations have already been performed [ 5 ] -[ 121 but with important errors due to the approximations used. We present here a method of numerical simulation based upon finite differences with iteration over time and applied to certain types of discontinuities. Such methods have been used before [ 131 -[l S ] , but applied to the very special case of propagating and diffracting particularly shaped pulses. In ou r work, we have chosen to study the scattering of a Rayleigh-type sinusoidal monochromatic wave, starting suddenly, that is equivalent to the propagation of a semiinfinite wave train. The two examples chosen for a basic statement of the problem are 90\" and 270\" corners normal to the direction of propagation cut into isotropic substrates. The results obtained are then extended to a study of more complicated discontinuities of large size such as steps, ridges, or slots. An acoustic surface wave propagating upon a substrate gives I. STUDY OF ELEMENTARY DISCONTINUITIES A . &sic Structures Two elementary discontinuities are shown Fig. 1 ((a) : 90\" corner, (bj: 270\" corner). The substrate is isotropic, and the perpendicular planar sides limiting corner B are semiinfinite. Manuscript received June 1, 1976; revised December 10, 1976. The authors are with the Laboratoire d'Electronique, Facult6 des Sciences et des Techniques, 06034 Nice Cedex, France. I I l : m : I I l I I l

Transmission Response of Cascaded Gratings

Abstract: Poles and zeroes of the infinite plane wave amplitude reflection coefficient are used to derive a theoretical prediction of the nonspecular reflection effects which have been observed for an ultrasonic beam incident on an isotropic solid plate in a liquid. It is shown that there are two types of nonspecular reflections, and they can be characterized in terms of a single parameter which requires a knowledge of the imaginary part of a pole of the infinite plane wave reflection coefficient. Theoretical predictions of nonspecular reflection intensities are presented. Finally, it is shown that the reflection characteristics for high-frequency beams incident on thick plates are the same as those expected for the reflection from a single liquidisolid interface, i.e., two infinite half-spaces.

A Detailed Theory of the Acoustic Wave Semiconductor Convolver

Abstract: [6 ] M. Hirsch, W. J . Sanders, R. L. Popp, and P. C. Harrison, “Computer Processing of Ultrasonic Data from the Cardiovascular System,“ Compt. and Biomed. Res. , 6:336-346, 1973. [ l ] S. E. Wixson. L. R. Smith, and J . A. Mantle. “Computer Acquisition and Processing of Left Ventricular Echocardiograms,” in Ultrasound in Medicine, Academic Press, 1:363-371, 1975. (81 H . F. Greenleaf, F. A. Duck, W. F. Samayoe, and S. A. Johnson, “Ultrasonic Data Acquisition and Processing System for Atherosclerotic Tissue Characterization,” I974 Ultrasonics Symposium Proceedings, IEEE cat. #74 CH0 896-1SU:738-743, November 1974. [9] J . M. Griffith and W. L. Henry, “Video Scanner-Analog Computer

High Piezoelectric Coupling Temperature-Compensated Cuts of Berlinite (AlPO 4 ) for SAW Applications

Abstract: Calculations of the surface acoustic wave (SAW) properties of berlinite (AIPO4) show that it is temperature compensated with more than four times the piezoelectric coupling of STcut quartz. High coupling, temperature compensated orientations have been found for doubly rotated cuts as well as for singly rotated cuts. The best singly rotated orientation is the X axis boule 80.4' cut which, because of the structural similiarity between berlinite and quartz, is a direct analog of the ST cut of quartz. This cut has, like ST quartz, a zero electromc- chanical power flow angle, but the distinct advantage of morc than four times the piezoelectric coupling. Even more promising are the results obtained for two doubly rotated cuts which combine all the advantages of the 80.4' singly rotated cut with the added feature of better diffrac- tion properties than ST cut quartz. As good quality berlinite becomes available, it will be attractive for use in broadband, low insertion loss surface acoustic wave devices.

Theory for SAW Grooved Reflector Arrays

Abstract: The reflection and bulk-wave loss characteristics of a SAW grooved reflector array are treated using an approach which integrates field theory with the theory of two-mode coupling well-known in the area of optical gratings. The present treatment offers the following distinct advantages over the previously reported equivalent network approach: i) it derives the array characteristics directly in terms of the material constants of the substrate; ii) it provides quantitative information on the power loss resulting from bulk-wave radiation; and iii) it can readily and accurately accommodate changes in groove profile or height among the individual array elements, making this approach amenable for use in the design of tapered arrays. Computed SAW scattering characteristics of a uniform reflector array comprised of a varying number of trapezoidal (but almost rectangular) grooves are presented. I

A Detailed Theory of the Monolithic Zinc Oxide on Silicon Convolver

Abstract: A detailed theory of the monolithic zinc oxide on silicon convolver is described. T h e variation of the convolver efficiency and the propagation loss with bias is discussed, and the various parameters affecting the convolver performance are identified. The presence of surface states at the silicon-silicon dioxide interface and bulk traps in the zinc oxide are shown to be a reasonable hypothesis which explains the differences between the theory and the experimental results obtained. It is shown that efficient monolithic zinc oxide convolvers can be designed and experimentally realized. I . INTRODUCTION W E SHALL describe how the zinc oxide on silicon structure can be used to obtain the convolution of two electrical signals. We will use the so-called “depletion layer approximation” to derive a simple theory of operation of the monolithic convolver. Then we shall derive a more complete theory and discuss experimental results which are in reasonable agreement with this theory. So far, most surface wave convolvers have been constructed using the separated medium structure. This structure consists of a piezoelectric delay line over which a slice of silicon is placed, uniformly spaced from it by an airgap. The advantage of such a structure is that a piezeoelectric material such as LiNb03 has a very large coupling constant, and the semiconductor material can be changed at wdl. However, the structure suffers from the disadvantage of having to maintain a uniform air gap spacing of the order of 1000 ji and the need for very large bias potentials of the order of several hundred volts, if it is required to modulate the surface potential of the silicon. We have constructed the ZnO on Si monolithic structure of Fig. 1 to solve the problems of the separated medium structure, a configuration which gives only a small loss in efficiency over that of the separated medium device. The parameters of the devices used in our work are summarized in Table I . Silicon dioxide is thermally grown on the silicon to reduce the surface state density at the surface of the silicon. The top plate shown in Fig. 1 is used to detect the output. Notice that the acoustic coupling coefficient of the region under the top plate is different from the one under the transducers, because the ground plane is at the top surface, rather than at the lower surface, and the ZnO is deposited on SiOz, rather than gold P I 7 P I . Manuscript received March 22, 1976;revised May 27, 1976. This work was supported in part by the Advanced Research Projects Agency of the Department of Defense, monitored by ONR under Contract N00014-67-A-0084, and in part by the United States Air Force under Contract F30602-74-C-0038. Stanford, CA 94305. The authors are with the Microwave Laboratory, Stanford University, I D T R A N S D U C E R /nu TRANSPARENT I , CONTACT A u PADS, Z n O

Bulk Scattering Loss Of SAW Grating Cascades

Abstract: I:: Synthetic Aperture Images of Other Sitnple Objects Other examples of synthetic aperture images are given in Fig. 9 t o show the characteristics of the fine azimuthal resolution of the system. In these cases the objects were plates o f aluminum of 2 m m thickness, and here the surfaces of the plates were notched by a punch t o permit the ultrasonic waves t o be well scattered. I t is seen, for example, from the results of (B) and (C) that even the edges of the aluminum plates are sharply imaged.

Equivalent Circuit Parameters of Interdigital Transducers Derived from Dispersion Relations for Surface Acoustic Waves in Periodic Metal Gratings

Abstract: Abstrucr-Relations between "exact" field solutions for acoustic surface waves in structures of metal gratings on piezoelectric surfaces and an equivalent circuit model of interdigital transducers are estab- lished. One of the previously proposed equivalent circuit models is applied, and by matching the dispersion relation for the surface wave derived from this model with that obtained from the field analysis, analytic expressions for the equivalent circuit parameters are deter- mined. The approach used in this paper is to match the dispersion relations near resonance obtained from the field analysis with those obtained from the circuit model, and to use the field solutions far off resonance to determine the transducer capaci- tance. Principally, we are using the field solution for an infinite periodic array to develop a circuit model for the unit cell of the array. The model therefore fails to describe transducer end effects and neighbor coupling effects in a transducer with arbitrarily changing polarity on neighboring fingers ( IO) . The field solution for surface waves in split-strip periodic arrays is applied to analyze thinned transducers with several half wavelengths between neighboring finger pairs. Neighbor coupling can be estimated from the dependence of the circuit parameters on the distance between pairs. Another special case considered is the regular split-strip transducer with neigh- boring strips connected to one electrode in pairs of opposite polarity.

Scattering Parameters of Interdigital Surface Acoustic Wave Transducers

Abstract: Abslracf-A simple physical model is proposed to obtain the scattering parameters of an interdigital surface acoustic wave transducer. The model is useful in predicting the transient response of the scattering parameters. Experimental measurements of the transient response are found to be in good agreement with theory. Scattering parameters of apodized transducers and of transducers in which surface waves are incident on both the acoustic ports are calculated. The model does not take into account impedance discontinuities produced by the transducer electrodes, but apart from this limitation is sufficiently general and should be applicable to a wide range of electroacoustic transducers. HEN A surface acoustic wave is incident on an electrically loaded interdigital transducer (IDT), a part of the wave energy is absorbed, a part is transmitted forward, and a part is reflected. The IDT can thus be considered as a scatterer of surface waves. A knowledge of the scattering parameters is obviously important in the design of surface wave devices. The scattering parameters of the IDT have been calculated as a function of the electrical load by Smith et al. [l] using an equivalent circuit model. Their method however needs laborious calculations and does not give any physical insight into the problem. The purpose of this paper is to present a simple physical model which can be readily used to obtain the scattering parameters. The basis of the model is the realization of the fact that the voltage developed across the receiving transducer by the incident wave is responsible for the regeneration of acoustic waves by the receiving transducer. The net acoustic field in the medium is then the sum of the incident and the regenerated fields. This approach readily leads to simple formulae for the scattering coefficients. The scattering coefficients obtained by this approach are found to be in agreement with those obtained by Smith ef al. The utility of the model however extends much beyond the mere calculation of scattering parameters at the resonant frequency. The transient response of the scattering parameters can be calculated from the model. The predictions of the model have been experimentally verified by studying the transient response of the reflection and transmission coefficients of the IDT. Knowledge about the transient response enables one to calculate the maximum fractional bandwidth of a surface wave reflector and of a unidirectional transducer using such a reflector. Other applications of the model include the calculation of scattering parameters when i) acoustic waves are incident simultaneously on both ports of the IDT, and ii) the width of the incident acoustic beam is different than the aperture of the transducer. The latter situation is important in the study of apodized transducers. The model proposed here is sufficiently general and should be applicable to any electroacoustic transducer of either bulk or surface acoustic waves.

Doppler Ultrasound: A Technique for Obtaining Arterial Wall Motion Parameters

Abstract: tricle, and the third echo is from the left internal carotid artery. The major arterial echo activity occurs about 135 ms after the R-wave for the right internal carotid artery and about 125 ms for the left internal carotid artery. This results in a difference of 10 ms between the right and left sides with the left internal carotid artery being active earlier after the R-wave of the ECG. The pulse repetition rate was 5 ms, memory size was 1, and delay time multiplier was 4 for a time between subtractions of 20 ms.

A Simple Method of Approximating Surface Acoustic Wave Power Densities

Abstract: An approximate expression for the power density in a surface acoustic wave is derived which avoids the necessity of an exact numerical solution of the wave equation and associated boundary conditions. Comparisons between available exact solutions and the approximate result for several materials and crystalline orientations show agreement within a factor of two in nll cases and much closer in most cases. L 1 1 N MANY surface wave studies including harmonic generation ,mixing [ 21 , and convolution [ 31 , it is convenient to express the power carried by the surface wave beam in terms Manuscript received February 7, 1977. This work was supported in part by the National Science Foundation under Grant ENG 75-18077. The author is with the Department of Electrical Engineering, University of Minnesota, Minneapolis, MN 55455. 339

Fields of Flat Conductor Electromagnetic Surface Acoustic Wave Transducers

Abstract: Magnetic field distributions from flat conductor electromagnetic surface acoustic wave transducers have been investigated for meander and grating line geometries. Expressions are derived for magnetic fields and inductance of electromagnetic transducers, and for space harmonic amplitudes of surface currents induced in a metal ground plane. Lift off, that is, separation gap between conductors and ground plane, and transducer geometry are accounted for in the theory. Experimental measurements of inductance are presented and compared with predicted inductance values, and good agreement is found. INTRODUCTION E LECTROMAGNETIC surface acoustic wave (SAW) transducers [ l ] -[7] consisting of an array of parallel conductors have been used to generate surface acoustic waves up to low megahertz frequencies. The transduction mechanism which can be noncontact for generation on metals, involves periodic stresses caused by Lorentz forces acting on eddy currents below the array in the presence of a static magnetic field. In the case of insulators, the transduction is achieved by the Lorentz stresses applied directly on a conducting array that is bonded to the insulator. By reciprocity, the transducers also function as receivers. The relatively simple geometries of SAW electromagnetic transducers (EMT’s) and their noncontact generation/reception capability for metals are reasons why they are being used in an increasing number of applications, including the measurement of physical phenomena [g] -[lo] , nondestructive testing of metal parts [3] , [S], [ lo] , and new uses such as rotation rate sensing [ 101 . Models for predicting EMT efficiency have appeared recently: one for noncontact wire wound meander geometries by Thompson [4] and another for a flat conductor meander thin film pattern deposited on an insulator by Lawrence [6]. Frost, Szabo, and Sethares [ l l ] reported on a new model for the contact (and noncontact) flat conductor transducer that is in good agreement with experiment. This model is based on an examination of the dynamic magnetic fields surrounding a flat conductor EMT array. In this case, the dynamic fields of an EMT play a role similar to the electric fields of the well-known interdigital SAW transducer on peizoelectric materials. Like the technique used by Engan [l21 in his analysis of the fields and capacitance of an interdigital transducer, in this paper we derive expressions for Manuscript received January 29, 1976; revised March 18, 1976. J. C. Sethares and T. L. Szabo are with the RADCjDeputy for Elee tronic Technology, Hanscom Air Force Base, MA 01731. H. M . Frost was with the Air Force Cambridge Research Laboratories, Hanscom Air Force Base, MA. He is now with the Bureau of Radiological Health, Food and Drug Administration, Rockville, MD 20852. the inductance and magnetic fields of the SAW EMT. These expressions serve as a starting point for a comprehensive theoretical understanding of the electrical, as well as the acoustic, properties of these transducers. This approach introduces in a natural manner the conductor width/spacing ratio, multiple conductor and ground plane proximity effects, and an exponential coupling term that describes the effect of liftoff of the transducer from the ground plane. In this paper we lay the groundwork for designing both meander and grating transducer geometries for more efficient fundamental operation, and harmonic enhancement or suppression, and for predicting the behavior of transducer inductance as a function of liftoff from the ground plane. Experimental measurements of inductance compare well with this theory. MAGNETIC FIELDS The geometry is defined in Fig. 1. The EMT consists of a planar array of parallel flat conducting strips connected electrically either in series as a meander line pattern or in parallel as a grating. From a practical viewpoint, the ground plane forms an integral part of the EMT in that it strongly influences the magnitude and orientation of the dynamic magnetic fields set up by current in the transducer. As discussed later in more detail, these dynamic fields generate currents in the ground plane on which Lorentz forces act in the elastic medium in the presence of a static magnetic field. For the purposes of the analysis, an infinite array of conductors of width S are spaced periodically in the X direction. They have center/center spacing b and are infinite in length in the 2 direction. In this configuration, the dynamic magnetic field set up by a current I has X and Y components only. In the lower part of the figure are additional geometrical factors. Parameter q distinguishes between parallel (q = +l ) and antiparallel (q = 1) currents in adjacent strips. The sought-after expressions for the magnetic fields are solutions to Laplace’s equation and consist of an infinite number of spatial harmonics. The total solution satisfies both magnetic field intensity and magnetic flux density boundary conditions. All restrictions and assumptions made in obtaining the solution are listed below. 1) End effects caused by arrays of finite extent are neglected; an infinite array of current carrying strip conductors is assumed. 2) In this weak coupling approximation the reaction of acoustic waves on the field distribution is negligible. 3) The thickness 1 of the strip conductors is assumed to be infinitely thin. SETHARES et al. : ELECTROMAGNETIC TRANSDUCERS 89 T I 6: 1 Roglon II (y>o) a . . b . . Roalon I (-G*y'o) 9 =-I, rnoondmr lino (shown oboval (b) 7 = t I ,grotlng (conducton connactod in parol ld ) Fig. 1 . Geometry of meander line surface acoustic wave electromagnetic transducer. (a) Flat ribbon conducting strips connected in series (51 = -1). (b) The xz plane at y = 0 contains a periodic array of strips separating Regions I and 11. 4) For the magnetostatic approximation V X 2 = 0 in free space regions. 5) All conductors are isotropic and homogeneous and have infinite conductivity (i.e., good conductors are assumed) 1131. The required boundary conditions are specified with reference to Fig. l(b) where the X2 plane at Y = 0 defines an infinitely thin boundary layer separating regions 1 and 11. Within the two regions, excluding boundaries, V2 9 = 0 and 2 = V 9 . 9 is a magnetic potential and h' is the magnetic field intensity. Across the infinitely thin boundary layer il X (h'' 2\") = 2 and 2' 9 (2' 2\") = 0. is the surface current within the boundary layer, magnetic flux density B' = poh', and surface current K = I /S or r] I / S at the strips and zero elsewhere. I is the total current in one strip and r] = f 1 . At the ground plane 3' = 0 , that is, normal component of magnetic flux density vanishes. The conditions set forth above uniquely determine the magnetic fields created by a current I. Although the form taken by total field solutions is not unique, the magnitude and spatial distribution of total field solutions is unique. Final total solutions are arbitrarily close to actual ones. The difference between the two can be made infinitesimally small by taking more terms in the series solution. Many practical cases (such as when S/b = i) will require only a few terms in the series for accuracies of a few percent. intensity $ is to first find suitable solutions for magnetic potential q in both regions. 9 is then subjected to boundary conditions on its first partial space derivatives W / a X (= h,) and N / a Y (= h,). A solution of 9 satisfying V 2 9 = 0 is The approach taken to derive expressions for magnetic field = (AA sin k , X +BA cos k , X ) (C: d k n y +D: e-kny). Any linear combination of *A, in particular,

Microwave Network Analyses of Surface Acoustic Waveguides - I. Flat Overlay Guides

Abstract: A new approach is described for the systematic analysis of a variety of waveguides for surface acoustic waves on isotropic solids, and explicit results are presented which in most cases are either the only analytical solutions available or ones which furnish superior accuracy. This new approach adapts the techniques of microwave network theory to guided acoustic wave problems, so that many of the powerful methods developed in the context of electromagnetic microwaves can be applied to advantage. These methods utilize transmission lines and equivalent networks which look electrical but are actually purely acous- tic. They furnish physical insight and are particularly helpful to those trained in transmission line theory. The basic elements of this new ap- proach are explained in the paper. Waveguides for acoustic surface waves fall into two classes: overlay guides and topographic guides; the most important ones in each class are treated here. In Paper I, the strip and slot guides are discussed, and in Paper 11, the topographic and overlay rectangular ridge guides are analyzed. For each of the waveguides treated, analytical (not simply numerical) results for the dispersion relations are presented, curves for the dispersion behavior are included, and comparisons with other theories and with measurements (where available) are indicated. I. INTRODUCTION N A PAIR of papers by the present authors (l), (2), the foundation was laid for the systematic application of well- established and proven microwave network techniques to problems involving acoustic waves in isotropic media. This foundation involved the formulation of a rigorous transmission- line formalism for guided acoustic waves. The formalism makes possible, in principle, the derivation of equivalent network rep- resentations for acoustic wave junctions and discontinuities. As an illustration of this new approach, transmission-line representations were derived for the bulk plane-wave modes in isotropic media, and equivalent networks were obtained for a large variety of planar interfaces. With these results, the solution for the modal propagation characteristics of two- dimensional, plane-stratified structures becomes systematic and straightforward, as seen, for example, in (3), (4). Al- though such a method of solution does have the very definite virtues of minimizing the algebra required in the analysis and furnishing physical insight, its full utility and value are not clearly manifested in the context of such two-dimensional problems because the latter can always be solved analytically by classical techniques.

Acoustic Surface Waves in Split Strip Periodic Metal Gratings on a Piezoelectric Surface

Abstract: Ahrruct-The propagation of acoustic surface waves in configurations of split periodic metal gratings on the surfaces of piezoelectric materials is analyzed. The analysis is based on analytic solutions for the electric field distribution. Particular attention is paid to the details of the dis- persion relations near the resonances, where the stopband frequencies for various combinations of externally interconnected or disconnected strips are calculated as functions of strip geometry for stopbands of various order. several wavelengths is frequently used either to create multiple passbands or to minimize phase errors and bulk wave conver- sion which may be a problem, especially at high frequencies. So far the models used to analyze these transducers have been equivalent circuits with adjustable empirical parameters for the effective coupling coefficient, as well as for the electrostatic coupling between distantly spaced neighboring taps. The subject of the present paper is a field analysis of split strip periodic gratings with two metal strips per period. The analysis leads to analytic expressions for the dispersion rela- tions. Particular emphasis is paid to the behavior around the stopbands where the period of the structure is close to an in- tegral number of half wavelengths. From the dispersion rela- tion one can easily derive the decay of waves in the stopbands, a figure which is of central importance in the design of surface wave resonators. Numerical results are given for the promi- nent cases with one half wavelength between neighboring strips to show the effect of thinning as well as for a regular array with four strips per wavelength corresponding to the split finger transducer. models can be derived from the dispersion relations and the field solutions without the necessity of empirically adjustable parameters. In an accompanying paper, it is shown that equivalent circuit

Microwave Network Analyses of Surface Acoustic Waveguides - II. Rectangular Ridge Guides

Abstract: Ahfruct-The microwave network approach to the solution of guided acoustic wave problems was applied in Paper I to two examples of the class of flat overlay guides: the strip and the slot guides. In this paper, the methods are applied to two different rectangular ridge StNChIeS, the well-known topographic ridge guide and the newer overlay ridge guide. In contrast to the flat overlay guides, for which good analytical results were previously available, no other analytical results have been published for the ridge guides which furnish good accuracy (although excellent numerical methods have been described). In addition, little information is available elsewhere on the pseudo-Rayleigh mode of the ridge guides, which is treated here in detail, and the overlay ridge structure itself is a new one whose properties are not yet appreciated. N THE COMPANION paper [l81 , a microwave network approach was presented for the analysis of waveguides for acoustic surface waves. The philosophy underlying this new approach was discussed, the basic features of the method were presented, and the method was applied to two examples of flat overlay waveguides, the strip and the slot guides. In the present paper, this method is applied to a different class of waveguides: rectangular ridge guides. The rectangular ridge waveguides themselves are of two types: the topographic ridge guide, for which the ridge and the substrate are composed of the same material, and the overlay ridge guide, in which the ridge is comprised of a material different from that of the substrate. The two structures are shown in Figs. l(a) and l(b). Both of these ridge guides are fundamentally different from the strip and slot guides, which appear respectively in Figs. l(a) and l(b) of Paper I. In the latter two guides, thin platings are employed to perturb the Rayleigh mode of the substrate, with the result that almost all of the energy in the waveguide mode resides in the sub

Sequential Synthetic Aperture Sonar System-A Prototype of a Synthetic Aperture Sonar System

Abstract: A prototype of a synthetic aperture sonar system is presented which displays computationally reconstructed images on a CRT. The image information is obtained sequentially by the scanning in twodimensions of a transmitter-receiver unit which produces and detects pulsed ultrasonic waves. The system consists of the scanning transmitter-receiver unit, computing parts designed especially for image reconstruction, IC memory devices and a display unit including a CRT. The signal processing and the control of each part of the system are carried out computationally. The system repeats at each sampling point the processes of registration of the received signal, image reconstruction from the dataand display of the sequentially synthesized image. Typically, ultrasonic waves of 1 MHz are used in water, and the images for the case of scanning along a circle of 40 mm diameter are obtained in less than a minute. With the system described in this paper, various fundamental characteristics of synthetic aperture sonar are verified experimentally. In addition, a practical imaging effect similar to zooming in a TV camera is shown as an example of the versatility of the system.

Characteristics of Surface Acoustic Wave Resonators Obtained from Cavity Analysis

Abstract: Fabry-Perot cavity analysis and circuit theorems me used to obtain the approximate terminal characteristics of a general two-port surface acoustic wave (SAW) resonator. The results are cast such that the performance of a two-port device with two transducers between the reflectors can be predicted simply from the insertion loss of the transducer pair without the cavity and the externally measured cavity parameters unloaded by the internal transducers. The analysis gives relative power levels within the device allowing a greater physical understanding of the individual effects of the various loss and reflection elements. Also, the analysis provides a very simple technique for deriving element values in proposed two-port equivalent circuits.

Ultrasonic Imaging with an Acoustic Lens

Abstract: Absrracr-An acoustic system is discussed, which is composed of a planar array of ultrasonic transducers placed before a convergent acoustic lens. For pulseecho imaging, the array elements are used one at a time, for both the transmission of pulses and the ensuing reception of their echoes. It is shown that such a system constitutes a sector scanner with the sector apex at the focal point of the lens. An acoustic lens is described which, with a linear array at 2.25 MHz, will produce a sector scan having a 60” field of view and approximately 4-mm lateral resolution, over a depth o f focus in excess of 15 cm. Sensitivity is optimum on axis and varies no more than 8 dB over the entire sector. This design is equally applicable to imaging with a two-dimensional array, in which case the region covered by high resolution electronic scanning is a pyramidal volume whose apex is at the focal point of the lens.

Numerical Analysis on Isotropic Elastic Waveguides by Mode-Matching Method - I. Analytical Foundations and General Algorithms

Abstract: A new method for computer-aided calculation, the mode- motching merhod, based on the Rayleigh expansion theorem, is pro- posed in order to analyze the boundary condition problem of elastic fields, and its analytical foundations and general algorithms are dis- cussed. The alastic fields are represented by scalar potential functions which are solutions of Helmholtz equations and expanded by the well- known separated solutions. Introducing the formal Green functions, the integral representations of the potentials are derived. The Rayleigh expansion theorem assures the existence of the infinite sequence of the truncated modal expansions which uniformly converges to the true field in arbitrarily shaped cross section. Through this theorem and the integral representations, the procedure of the mode-matching method is described simply so that the truncated modal expansions are made to fit for the boundary conditions in the least squares sense. Conse- quently this new method may ensure more precise analyses not only on the dispersion characteristics, but also on the field distributions of the particle velocity or the stress by small amount of computational efforts, than the other numerical methods reported so far. The general algo- rithm for the mode-matching method is described in the cases of forced and free vibrations of the homogeneous isotropic elastic waveguide with arbitrarily shaped cross section.