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EEE 558 Lecture Notes

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Chapter 1 Introduction Electroacoustic transduction is the interface between the electronics and acoustic wave propagation. EEE 558 Electroacoustic Transduction - Lecture Notes (Lecture Notes) discusses transduction entirely on circuit theory basis. In this text, no prior background in acoustics is assumed, but it is expected that the reader is familiar with circuit theory. There are occasional material like Chapter 3 in the Lecture Notes, which are specific to this text and included in order to justify the presented the results like radiation impedance. The reader is not expected to follow the details of the theory presented there. The results, however, are used in the circuit theory based treatment of transduction. On the other hand, it is hoped that the readers who are well informed in acoustics will appreciate the occasional acoustics content in the Notes. Similarly, the prominence of such material will be clearer as the acoustics expertise of the reader improves. The argument that any text on electroacoustic transduction must rely on a foundation in acoustic wave and propagation theory is well justified. The combination of acousticstransduction-electronics is analogous to the one in electromagnetics-antennas-electronics interrelation, except a different discipline, applied mechanics, is employed for electromechanical transduction. Any mastery in the field requires a comprehensive command of related fields, no doubt. The modern teaching practice, however, must provide the materials on this diverse field in isolated single courses, which adequately furnishes the student with reasonable expertise in the respective sub-field. In this approach, it must be expected that a comprehensive understanding can emerge from the combination of several such isolated courses. Electroacoustic Transduction is not an exception to this paradigm. There are subtle issues in electroacoustic transduction, which are often lost in the crowd in piezoelectricity based texts. The magic material piezo has a formidable theory and a wealth of experience, which must be adequately covered prior to using it for transduction. The capacitive transduction, however, has simple and naïve theory, which lead to incredibly accurate equivalent circuit models. This makes it possible to discuss these subtle issues in transduction at an early stage and in depth, if the introductory transduction mechanism is capacitive. Piezoelectricity is the most prominent transduction technology in waterborne applications like medical ultrasound at present, despite the fact that capacitive technology has a larger market share due to its position in mobile communications. The piezoelectricity and the piezoelectric transducers are covered in the latter half of this text, as can be seen in the Contents. 1.1. Transduction Acoustics: electronics, vibration, propagation Electroacoustic transduction theory and engineering is an exciting combination of classical physics, applied mechanics, material science and electronics. All these fields are interlaced in acoustic transduction and their effects must be considered all together. For example, a novice to the field may have the observation that the electroacoustic energy conversion is confined to that marvelous material called PZT. This view misses the point that the performance of this conversion, however, is fully dependent on how the emerging acoustic energy propagates into

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the medium. Further, designing a transducer for optimized performance requires intricate use of applied mechanics on the design of piezo material. Lecture Notes attempts to lead the reader through basic science and engineering principles and the practice to the design of optimized electroacoustic transducers. 1.2. Electromechanical energy conversion Electromechanical energy conversion can be implemented either using inductive transduction as in the case of electric motors or solenoids, moving coil transducers (e.g. loudspeaker), magnetostrictive transducers, etc. or capacitive transduction, which also includes electrostrictive (e.g. piezoelectric) transducers. We confine our interest to electromechanical conversion for acoustic transducers in Lecture Notes and in particular to transduction employing electric field. The dependence of mechanical variables to electrical variables in electromechanical energy conversion is inherently nonlinear. Force is proportional to the square of the voltage. The linear transduction between electrical and acoustic (or mechanical) variables is therefore only possible by using a large dc electric field bias such that the transduction can be linearized around the bias level. Then the transduction variable magnitudes in a particular application are small compared to bias and hence a linear transduction is ensured. Use of same transduction mechanisms without bias for certain purposes is also common. Transduction is maintained in a polarized medium. This medium is the electrostrictive material employed in the transducer structure or the gap, where a d.c. electric field is maintained, in capacitive transducers. 1.3. Units in acoustics and transduction The field variables in acoustics are pressure and particle velocity whereas acoustics-related transducer variables are force and velocity. 1.3.1. Pressure and force Pressure is a scalar variable, which means that pressure at any point in space has the same effect in all directions around that point. Pressure is measured in Pascal, Pa. 1 Pa is 1 Nt/m2, which is 1 kg-m/sec2/m2. For example, ambient static pressure of 1 standard atmospheric pressure (atm) is 101,325 Pa. Any environment in which acoustic energy can exist must have matter. Acoustics cannot exist in vacuum, 0 Pa. Consequently, any acoustical application has a static (or d.c.) pressure component. Airborne applications, e.g. human voice, always consist of time varying pressure signal super imposed on 1 atm static pressure. In underwater acoustics Static component depends on the depth and can be very large. We shall use capital letter P for static pressure and small case letter p(t) for time varying pressure signals in this set of notes. Pressure measurements are always referred to a standard reference pressure unit. This unit is 20 Pa for airborne applications and 1 Pa for waterborne applications. The pressure levels are often expressed as Sound Pressure Level (SPL). Pressure magnitude of Pa at any point in space is described as

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/20E-6) dB//20Pa

for airborne applications and SPL= 20log(

/1E-6) dB//1Pa

for waterborne applications. There is a wealth of units and definitions for pressure measurements in acoustics. Only Pa is used as pressure unit in this text and some other measurement definitions are introduced in the text as necessary. This text, however, is not an acoustics text. This text is on transduction. The relevant variable at the acoustic port of a transducer is not pressure. The variables at the transducer port are force (Nt) and velocity (m/sec). We distinguish between acoustical/mechanical variables in transducers and the acoustic field with which the transducers interact in the medium. We shall study this interface in detail in this course. 1.3.2. Particle velocity and velocity Acoustic fields move the matter in the medium as it propagates. In order to define this motion to the highest possible resolution, volume that the motion refers to must be as small as possible. The smallest discrete volume in any medium is the molecule. But molecules also move in response to the thermal energy in the medium, the Brownian motion, as well as due to acoustic energy. This motion must be clearly separated from the acoustic velocity variable and separately evaluated, since Brownian motion of the molecules represents the thermal noise in the transduction. Particle velocity is a special definition referring to the velocity of a small volume of medium, the particle. The size of this volume must be sufficiently larger than the molecular dimensions so that all random motion of the molecules in the particle volume averages out statistically[1]. But Particle volume must also be very small compared to the minimum wavelength of interest at the same time. The acoustic velocity or displacement component is defined as the motion of such small volume, the particle velocity or particle displacement. Units are m/sec and m, respectively. Unlike pressure particle velocity and particle displacement are vector quantities. Again, on the transducer’s radiating surface, the variable is obviously the velocity of the surface. However, the transducer surface is a boundary to the medium and motion in the medium exists in the vicinity of this boundary, whether in transmission or in reception. Therefore the correspondence between the surface velocity at the transducer and the particle velocity it interacts in medium must be clearly defined so that the energy is conserved and the mistakes are avoided. 1.4. Transducer structure: a system All acoustic transducers are designed to meet various requirements for the specific application they are meant to be used. These can include requirements like resonance or center frequency, frequency bandwidth, output power, transmit sensitivity, receiver sensitivity, low noise Hayrettin Köymen

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performance, where some of which may be competing and requires trade off. Transducers may be designed for resonant operation or off resonant operation. Transducers can be designed for operation as a single element or in an array. Transducers contain various sub elements such as a polarized element where the transduction takes place, Passive mechanical sub elements to shape the performance and electrical components to complement the electrical termination. The medium of propagation is also considered as an essential component in the design, since it modifies the performance. 1.4.1. Active (Polarized) component Active components are the components made of piezoelectric materials or its composites in piezo-based transducers. These components are electrically pre polarized and perform the electro-mechanical conversion. Common piezoelectric materials include ceramics like various grades of PZT (lead zirconate titanate), PMN-PT, Zinc oxide and polymers like PVDF. The gap in the capacitive transducers are polarized by applying electric field. The gap is the active component in such transducers. Capacitive Micromachined Ultrasonic Transducers (CMUT) and most precision microphones with very high dynamic range fall into this class. In electret microphones, the polarization to the gap is provided by a layer of electrets material, which is pre-polarized such that sufficient electric field is subtended in the gap upon proper electrical termination. 1.4.2. Load or medium for propagation The effect of the medium on the transducer performance is most important. Medium is the most critical component in transducer design. This effect appears as impedance, the radiation impedance, with resistive and reactive (positive) parts which are functions of frequency and shape and size of the transducer. In other words, effect of the medium on the transducer is considered as a physical part of the transducer during the design process. In arrays, the interaction between elements through the medium, referred to as mutual impedance, modifies the radiation impedance radically. The mutual radiation impedance has to be taken into account during the design as the most critical component. The baffle, its material, geometry, size, etc., in which the transducer/array resides is also critical and must be considered as part of the transduction. 1.4.3. Passive components Required acoustic performance such as resonance frequency, frequency bandwidth, efficiency sensitivity, self noise, etc., of a transducer is achieved by using various materials as passive components in the design. These may vary from radiation plates or matching layers on the radiating face to tail masses and backing materials at the back face. 1.4.4. Electrical termination Electrical components that will be used at the transducer terminals in order to facilitate the connection to electronic circuits must also be considered as part of the design process at the

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very beginning. These may be as simple as a transformer or may have tobe a section of a filter which complements the transducers electromechanical parts designed as an implicit filter. 1.5. Modeling transduction and transducers Modern transducer design relies on very accurate mathematical modeling of transducers. Finite Element Analysis (FEA) is a very powerful numerical modeling technique, where the basic mathematical model of vibration in the structure is numerically solved. Few very comprehensive FEA tools, like ANSYS, COMSOL, ATILA are commercially available. In FEA tools:  Almost all physical phenomena can be numerically modeled using FEA;  A particular design can be thoroughly simulated by FEA and tested before production;  Accuracy depends on the detail of the model, which results in very long simulation times;  This problem is aggravated particularly in arrays. The periodic boundary conditions used to make shorter simulations often result in erroneous predictions;  Modeling the medium is a challenge. Boundary Element Method (BEM) is an efficient alternative, where the Rayleigh integral is directly evaluated at the radiating face(s) instead of modeling the medium.  Requires mastering the technique, e.g. to avoid artifacts caused by sharp edges/corners Other powerful but difficult to get models are equivalent circuit models representing the accurate mathematical model of the transducer. These models can be lumped element or distributed circuit models and lend themselves to be used with very powerful circuit analysis techniques for analysis and design. Furthermore these models are used in circuit simulators, like ADS, Microwave Studio, Cadence, etc., where very large arrays can be modeled and simulated together with the terminating electronics very quickly. All these methods are employed in expert approaches to transducer design. The purpose of EEE Lecture Notes is to present how a designer can benefit from all these techniques.

1.6. References [1] C.H.Sherman and J.L.Butler, Transducers and Arrays for Underwater Sound, Springer, 2007. [2] D.T. Blackstock, Fundamentals of Physical Acoustics, Wiley, p.26, 2000. [3] Ansys, Inc., Pittsburgh, Pennsylvania. [4] COMSOL Group, Stockholm Sweden. [5] ATILA [6] ADS- Advanced Design Systems, Keysight Technologies, http://www.keysight.com/en/pc1297113/advanced-design-system-ads?cc=TR&lc=eng [7] Microwave Studio, CST-Computer Simulation Technology, https://www.cst.com/Company/News/Details?newsId=54

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[8] Spectre Circuit Simulator, http://www.cadence.com/products/cic/spectre_circuit/pages/default.aspx

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