DOCSLIB.ORG

Modeling of the Electroacoustic Coupling of Electrostatic Microphones Including the Preamplifier Circuit

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Modeling of the Electroacoustic Coupling of Electrostatic Microphones Including the Preamplifier Circuit Electroacoustics and Audio Engineering: Paper ICA2016-193 Modeling of the electroacoustic coupling of electrostatic microphones including the preamplifier circuit Bernardo Henrique Pereira Murta(a), Eric Brandão(b), Julio Cordioli(c), William D’A. Fonseca(d), Paulo H. Mareze(e) (a, b, d, e)Federal University of Santa Maria, Acoustical Engineering, Santa Maria, RS, Brazil, [email protected], [email protected] (c)Universidade Federal de Santa Catarina, Florianópolis, Brazil, [email protected] Abstract: This research aims to study tools to model and design electrostatic microphones coupled with its preamplifier circuits. The outcome is the access to their combined sensitivities curves, which allows the design of microphones with a wider and flat bandwidth. Analytical and numerical mod- eling techniques are explored and compared. On one hand, the lumped parameters approach is the basis of the analytical modeling of acoustic transducers. That is, this technique allows the engineer to design the transducer and its preamplifier circuit by predicting its sensitivity changes due to variations of model properties with low computational cost. On the other hand, numerical analysis is carried out using the Finite Element Method with a multiphysics approach, which is able to solve both the transducer model and the coupled electrical circuit. Two microphones with different complexities and constructive characteristics are studied. For validation of the proposed techniques, the behavior of a commercial measurement microphone model that has been well studied in the literature is considered. Once the validation of the modeling approach is satisfac- tory, one can use the same methodology to study a piezoelectric microphone for hearing aid applications, for instance. Its frequency response requires a designed preamplifier which should be able to make its sensitivity flatter over the audio bandwidth and to improve its output voltage level. The research also objectifies to analyze the whole chain of energy transducing and signal conditioning in order to prepare the fully coupled model for optimization procedures. The goal is to conceive efficient high-performance systems with low cost hardware. Keywords: electroacoustics, microphone modelling, finite element method Modeling of the electroacoustic coupling of electrostatic microphones including the preamplifier circuit 1 Introduction Computational modeling of microphones has been extensively used during design stages of transducers, mainly, in order to reduce unnecessarily prototyping costs. Thus, it is possible to select arbitrary geometries and material compositions to achieve microphones with specific characteristics as wide and flat bandwidth or particular sensitivities. Optimization methods, as the genetic algorithm, can be implemented to solve transducer models aiming to select the best fit for shapes and materials, searching for desired responses [1,2]. Robust numeric methods as the Finite Element Method (FEM) and the Boundary Element Method (BEM) are implemented in several commercial software, allowing the multiphysics modeling of complex geometry transducers with different materials [3]. However, as an outcome, a high computational cost is a common obstacle in the application of optimization techniques to such models. An alternative is the development of analytical methods to solve simplified situations. Generally, it is possible to achieve smaller solution time with a satisfactory representation of the designed transducer. A common approach to solve such devices is the equivalent circuit method, which was extensively used during the 60’s and 70’s, especially due to the advent of computers [4]. This approach consists of replacing the differential equations that represent each relevant characteristic of the transducer by analog electrical circuit elements, such as capacitors, inductors and resistors. For each of the physics that comprehend the transducer (acoustical, mechanical and electrical) a sub-circuit is derived and coupled by means of transformers to the adjacent physics. Therefore, a single circuit representing the whole acoustic-mechanic-electrical transducing chain of a microphone can be constructed and solved via the Kirchhoff Laws [5]. Many limitations and simplifications are required to apply correctly the analog circuit technique. On one hand, analyzed wavelengths must be larger than the transducer’s dimensions. Thus, the energy will be evenly (or with low variations) spatially distributed [6, 7], meaning that the microphone’s diaphragm moves as a rigid body. On the other hand, the complexity of the transducer’s elements as multi-material diaphragms or non-basic and asymmetric geometries cannot be well represented. To circumvent those limitations, new researches aim to develop higher complexity methods considering boundary conditions, geometries and materials [6, 8, 9]. Based on different models, it is possible to forge small details of microphones, for example, the influence of a perforated backplate facing the transducer’s diaphragm [10] in its frequency response [11]. All that brings an important role in computational models in the industry [12] may be a relevant tool to decrease design costs. There are still several limitations when considering the development of modern transducers such as microelectromechanical systems (MEMS). They may present multi-material non-usual geometries [7, 9] when compared to regular microphones as well when modeling anisotropic piezoelectric materials [13]. Thus, the development of new studies to include such conditions in equivalent circuit approach is desired Another step in the modeling process is considering integrated designed preamplifiers capable 2 of providing adequate signal conditioning for the studied transducer. Such circuits are required, for example, to couple the high output impedance of capacitive and piezoelectric microphones with the small input impedance of the following stages such as analog-to-digital converter (ADC) and digital signal processing devices. Furthermore, analog filters and gain stages to adjust the frequency response of the modeled transducer may be necessary when low-cost devices are the target of a study. 2 Equivalent circuit method The equivalent circuit of a transducer depends on its geometrical properties, composition of materials and the boundary conditions of its mounting. The analysis is subdivided into three domains, each one containing its own circuit and coupled by means of ideal transformers. There is the acoustic circuit, in which the incident sound pressure and the volume velocity of air around the diaphragm are modeled. Then, the mechanical domain models the diaphragm as a one degree of freedom system, computing its velocity and the associated forces. Finally, the electrical domain solves the electromechanical coupling and the voltage across the microphone’s terminal. 2.1 Acoustical domain (A.D.) The acoustical equivalent circuit is dependent of the transducer’s geometry, as shown in Figure1. Thus, to each element interacting with the sound pressure waves an impedance is attributed. The acoustical impedances are defined as the ratio between the incident pressure Pe and the produced volume velocity Qe˙, thus Zea = Pe=Qe˙ [kg=sm4]. Here the tilde notation represents the complex harmonic amplitude and the dot is the time derivative. Passive circuit elements are used to model those impedances. Thus, resistors are used to represent the damping elements while the reactive parts of the impedances are modeled by ca- pacitors (associated to acoustical compliance) and inductors (corresponding to acoustical mass). Specific properties and analytical equations describing some commonly found impedances in equivalent acoustical circuits of microphones are presented in the following. The incident pressure over the transducer’s diaphragm is modeled by an ideal AC voltage source, which magnitude is defined as the sound pressure in Pascal (Pa). Cavities delimiting air volumes V are represented by an acoustical compliance, as the capaci- 3 tance Ca m =Pa [6], given as: V Ca = 2 ; (1) r0c0 where r0 is the air density and c0 the speed of sound in the medium for the ambient conditions. Tube elements with radius at smaller than at < 0;4 mm are considered small ducts [14]. This impedance is commonly present in measurement microphones as the pressure equalization vent. Their acoustical impedance Zat is given by: 8h0l 4r0l Zat = 4 + jw 4 ; (2) pat 3pat 3 Rabp Mabp P Raslit Maslit ˙ e Zeraddia P2 Qe 1:Sd Xe˙ P1 Mateq Rateq Ca2 Ca1 ... M.D.,E.D. Zeradteq P0 A.D. Figure 1: Equivalent circuit of the capacitive B&K 4134 microphone (right) and its schematic (left). where w = 2p f is the angular frequency, h the air’s viscosity and l tube’s length. The small duct acoustical resistance Rat kg=m4s is obtained by 8h0l Rat = 4 ; (3) pat where h0 is air viscosity and l tube length. The reactive part, with inductive behavior, is modelled by the acoustical mass Mat kg=m4 calculated by 4r0l . Mat = 4 (4) 3pat The slits can be found between the microphone’s backplate andp its carcass, for example. A narrow slit is defined when its thickness tslit is smaller than 0,003/ f or tslit <0,6 mm. According to Beranek and Mellow [4], its acoustical resistance Rslit can be estimated by 12h0l Rslit = 3 ; (5) tslitwslit where wslit is the slit’s width and lslit its length. The acoustical mass Mslit is given by 6r0lslit Mslit = . (6) 5tslitwslit A rigid disk is considered micro-perforated when the diameter (2aholes) of its holes is sub-
Load more

Recommended publications
  • Analysis and Measurement of Anti-Reciprocal Systems By
    ANALYSIS AND MEASUREMENT OF ANTI-RECIPROCAL SYSTEMS BY NOORI KIM DISSERTATION Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Electrical and Computer Engineering in the Graduate College of the University of Illinois at Urbana-Champaign, 2014 Urbana, Illinois Doctoral Committee: Associate Professor Jont B. Allen, Chair Professor Stephen Boppart Professor Steven Franke Associate Professor Michael Oelze ABSTRACT Loudspeakers, mastoid bone-drivers, hearing-aid receivers, hybrid cars, and more – these “anti-reciprocal” systems are commonly found in our daily lives. However, the depth of understanding about the systems has not been well addressed since McMillan in 1946. The goal of this study is to provide an intuitive and clear understanding of the systems, beginning from modeling one of the most popular hearing-aid receivers, a balanced armature receiver (BAR). Models for acoustic transducers are critical in many acoustic applications. This study analyzes a widely used commercial hearing-aid receiver, manufactured by Knowles Electron- ics, Inc (ED27045). Electromagnetic transducer modeling must consider two key elements: a semi-inductor and a gyrator. The semi-inductor accounts for electromagnetic eddy cur- rents, the “skin effect” of a conductor, while the gyrator accounts for the anti-reciprocity characteristic of Lenz’s law. Aside from the work of Hunt, to our knowledge no publications have included the gyrator element in their electromagnetic transducer models. The most prevalent method of transducer modeling evokes the mobility method, an ideal transformer alternative to a gyrator followed by the dual of the mechanical circuit. The mobility ap- proach greatly complicates the analysis. The present study proposes a novel, simplified, and rigorous receiver model.
    [Show full text]
  • ELEC-E5650 Electroacoustics
    ELEC-E5650ELECElectroacoustics-E5650 ElectroacousticsLecture 1: Overview, Electroacoustics introduction & Circuit Elements pt1 Lecture 2: SteadyRaimundo -GonzalezState Analysis / Dynamic Analogies Department of Signal Processing and Acoustics Aalto University School of Electrical Engineering Raimundo2 2GonzalezFebruary 2018 Department of Signal Processing and Acoustics Aalto University School of Electrical Engineering March 7, 2019 ELEC-E5650 Electroacoustics, Lecture 1 Raimundo Gonzalez 1 Aalto, Signal Processing & Acoustics ELEC-E5650 ElectroacousticsLecture 1: Overview, Electroacoustics introduction & Circuit Elements pt1 LectureRaimundo Gonzalez 2: Department of Signal Processing and Acoustics Aalto University School of Electrical Engineering 22 February 2018 I. Steady State Analysis ELEC-E5650 Electroacoustics, Lecture 1 Raimundo Gonzalez 2 Aalto, Signal Processing & Acoustics Steady state sinusoidal response When designing Electroacoustics systems we are usually more interestedELEC in the-E5650 steady state behavior of the system. This will ElectroacousticsLecture 1: Overview, Electroacoustics introduction & Circuit Elements pt1 lead into Raimundomostly Gonzalez working in the frequency domain. Department of Signal Processing and Acoustics Aalto University School of Electrical Engineering 22 February 2018 ELEC-E5650 Electroacoustics, Lecture 1 Raimundo Gonzalez Aalto, Signal Processing & Acoustics 3 Phasors to represent sinusoidal signals ELEC-E5650 ElectroacousticsLecture 1: Overview, Electroacoustics introduction & Circuit Elements
    [Show full text]
  • Application Notes
    Application Note Accurate Determination of Loudspeaker Parameters using Audio Analyzer Type 2012 and Laser Velocity Transducer Type 3544 by Søren Jønsson, Brüel & Kjær, Denmark A method to determine the parame- ters characterising low frequency, mid- range and high frequency loudspeaker units is presented. A laser velocity transducer is used to detect the veloc- ity of the diaphragm. All measure- ments are made with the loudspeaker in free air. The method uses an im- proved model of the loudspeaker and takes into account the frequency de- pendent behaviour of some of the ele- ments. It produces accurate results and is easy to implement compared with conventional methods. The proce- dure is fully automated using an au- tosequence program for the analyzer. The process of automation is discussed and results of a typical driver are in- cluded. 1. Introduction Over the last two decades, it has be- The method presented here is a ance. From these functions the loud- come almost an industrial standard compilation of the traditional method speaker parameters can be calculated. to measure the parameters of a loud- and the method introduced by Applying the post-processing capa- speaker by the method introduced by J. N. Moreno [6]. It uses an improved bilities of the analyzer to the meas- A.N. Thiele and Dr. Richard Small [1 model of the loudspeaker and takes ured data, it is shown how to correct & 2]. various non-linearities in frequency the loudspeaker parameters and ex- Since the method was introduced, into account. The method produces tract information about the frequency more research in loudspeaker model- accurate results regardless of the dependent behaviour of some of the ling has been made, (e.g., [3, 4 & 5], components in the equivalent circuit type of driver used.
    [Show full text]
  • Analysis and Design of Piezoelectric Sonar Transducers. Rodrigo, Gerard Christopher
    Analysis and design of Piezoelectric sonar transducers. Rodrigo, Gerard Christopher The copyright of this thesis rests with the author and no quotation from it or information derived from it may be published without the prior written consent of the author For additional information about this publication click this link. http://qmro.qmul.ac.uk/jspui/handle/123456789/1712 Information about this research object was correct at the time of download; we occasionally make corrections to records, please therefore check the published record when citing. For more information contact [email protected] -1- ANALYSIS AND DESIGN OF PIEZOELECTRIC SONAR TRANSDUCERS Gerard Christopher Rodrigo Department of Electrical and Electronic Engineering, Queen Mary College, London E.l. Thesis presented for the Degree of Doctor of Philosophy of the University of London August 1970 -2- ABSTRACT In this study techniques are developed for the analysis and design of piezoelectric sonar transducers based on equivalent circuit representations. For the purposes of analysis, equivalent circuits capable of accurately representing every element of a transducer in the full operating frequency range, are developed. The most convenient fashion in which these equivalents could be derived is also discussed. For the purposes of design the accurate equivalents are approximated by L-C-R circuits. The limits of both representations are discussed in detail. The technique of analysis developed is capable of determining the frequency characteristics as well as the transient response to any electrical or acoustic input which can be specified analytically or numerically in the time domain. The design technique is based on the formulation of a ladder-type generalized circuit incorporating the essential components of any transducer.
    [Show full text]
  • Analysis and Measurement of Anti-Reciprocal Systems
    University of Illinois, Urbana-Champaign Electrical and Computer Engineering Department The Doctoral Preliminary Examination Document Analysis and measurement of anti-reciprocal systems Committee: Associate Professor Jont B. Allen Author: (Advisor, Chair) Noori Kim Professor Stephen Boppart (UIN:677205530) Professor Steven Franke Associate Professor Michael Oelze October 12, 2014 1 Abstract 2 Loudspeakers, mastoid bone-drivers, hearing-aid receivers, hybrid cars, and more - these 3 “anti-reciprocal” systems are commonly found in our daily lives. However, the depth of un- 4 derstanding about the systems has not been well addressed since McMillan in 1946. The goal 5 of this study is to guide an intuitive and clear understanding of the systems, beginning from 6 modeling one of the most popular hearing-aid receivers, a balanced armature receiver (BAR). 7 Models for acoustic transducers are critical in many acoustic applications. This study ana- 8 lyzes a widely used commercial hearing-aid receiver ED series, manufactured by Knowles Elec- 9 tronics, Inc. Electromagnetic transducer modeling must consider two key elements: a semi- 10 inductor and a gyrator. The semi-inductor accounts for electromagnetic eddy-currents, the 11 “skin effect” of a conductor (Vanderkooy, 1989), while the gyrator (McMillan, 1946; Tellegen, 12 1948) accounts for the anti-reciprocity characteristic [Lenz’s law(Hunt, 1954, p. 113)]. Aside 13 from Hunt (1954), to our knowledge, no publications have included the gyrator element in their 14 electromagnetic transducer models. The most prevalent method of transducer modeling evokes 15 the mobility method, an ideal transformer alternative to a gyrator followed by the dual of the 16 mechanical circuit (Beranek, 1954).
    [Show full text]
  • Electrical Schematic of the Earth and Solar System
    Fundamental Journal of Modern Physics ISSN: 2249-9768 Volume 13, Issue 2, 2020, Pages 121-139 This paper is available online at http://www.frdint.com/ Published online June 22, 2020 ELECTRICAL SCHEMATIC OF THE EARTH AND SOLAR SYSTEM GREG POOLE Industrial Tests, Inc. Rocklin, CA USA e-mail: [email protected] Abstract By visualizing the Sun and Earth coupled together by a mechanical spring, I have shown how gravity is like spring tension. This rotating spring coupler example is then exchanged for an analogous rotating electrical capacitor which leads to an improved electrical circuit diagram of the solar system. The series capacitive coupled circuit is the electrical transmission system for the solar system. Low frequency electrical energy is transferred from the Sun to the planets via flux transfer events. A capacitive coupled system inherently develops torque which provides rotation and centripetal/centrifugal force or what we call gravity. The paralleling of electricity generating Suns indicates that the power of the universe is virtually unlimited as James Clerk Maxwell inferred. Harnessing the power of the universe is one step closer to reality by virtue of the electrical schematic of the solar system. Keywords and phras :es flux transfer events, gravity, Newton’s cradle, spring coupler, series capacitive coupling, wireless transmission system. Received May 28, 2020; Accepted June 2, 2020 © 2020 Fundamental Research and Development International 122 GREG POOLE 1. Introduction In 1686, a controversy arose when the first book of Newton’s Principia was presented to the Royal Society. Robert Hooke accused Newton of plagiarism by claiming that he had taken from his paper “System of the World” [1].
    [Show full text]
  • Modeling of MEMS Piezoelectric Energy Harvesters Using Electromagnetic and Power System Theories
    Modeling of MEMS piezoelectric energy harvesters using electromagnetic and power system theories Mahmoud Al Ahmad1, Amro M. Elshurafa2, Khaled N. Salama2 and H. N. Alshareef1,* 1 Material Sciences and Engineering, Physical Sciences and Engineering Division, King Abdullah University of Science & Technology (KAUST), Thuwal, Saudi Arabia, 23955-6900. 2 Electrical Engineering, Physical Sciences and Engineering Division, King Abdullah University of Science & Technology (KAUST), Thuwal, Saudi Arabia, 23955-6900. *Corresponding author: [email protected] Abstract This work proposes a novel methodology for estimating the power output of piezoelectric generators. An analytical model that estimates, for the first time, the loss ratio and output power of piezoelectric generators, based on the direct mechanical-to-electrical analogy, electromagnetic theory, and power system theory, is developed and takes into account the dimensions and material properties of the generator. The mechanical-to-electrical analogy and power system theory allow deriving an equivalent input impedance expression for the network. Further, electromagnetic theory allows deducing the equivalent electromechanical loss of the piezoelectric generator. By knowing the mechanical input power and the loss of the network, calculating the output power of the piezoelectric device becomes a straightforward procedure. Experimental results based on published data are also presented to validate the analytical solution. Moreover, and to fully benefit from the well established electromagnetic and electric circuit theories, further analysis efforts on the resonant frequency, bandwidth, and sensitivity are presented. Compared to conventional modeling methods currently being adopted in the literature, the proposed method provides, relatively easily, significant additional information that is crucial for enhanced device operation. Finally, and with the study provided in this paper, optimizing piezoelectric harvesters is simplified.
    [Show full text]
  • Section 2.2 : Electro-Mechanical Analogies
    Section 2.2 : Electro- mechanical analogies PHILIPE HERZOG AND GUILLAUME PENELET Paternité - Pas d'Utilisation Commerciale - Partage des Conditions Initiales à l'Identique : http://creativecommons.org/licenses/by-nc-sa/2.0/fr/ Table des matières I - Introduction 5 A. Objective.....................................................................................................5 B. Test your knowledge.....................................................................................5 C. Context........................................................................................................7 II - Elementary phenomena 9 A. Mechanical elements.....................................................................................9 1. Mechanical elements..........................................................................................................9 2. Inertia of an object............................................................................................................9 3. Deformation of an object..................................................................................................10 4. Damping........................................................................................................................10 5. Mechanical lever.............................................................................................................10 III - Electro-mechanical analogies 13 A. Electro-mechanical analogies........................................................................13 B. Direct analogy............................................................................................13
    [Show full text]
  • Experience Teaching Electrical Energy Systems to Non-Electrical Engineering Students
    EXPERIENCE TEACHING ELECTRICAL ENERGY SYSTEMS TO NON-ELECTRICAL ENGINEERING STUDENTS Federico Milano University College Dublin (IRELAND) Abstract This paper describes the author's experience in teaching modules on electrical energy systems to Civil and Mechanical Engineering students at University of Castilla-La Mancha, Spain, and University College Dublin, Ireland, respectively. Teaching electrical energy systems to non-electrical engineering students presents several didactic and methodological challenges. These are originated mainly due to the lack of knowledge of circuit theory and electrical machines as well as to the little motivation of the students to learn and understand concepts apparently not related to their programmes. The paper describes the teaching approach adopted by the author through several practical examples. Keywords: Electrical energy systems; mechanical engineering; civil engineering; impedance analogy. 1 INTRODUCTION Teaching electrical energy systems to non-electrical engineering students presents several didactic and methodological challenges. First, when they attend such modules, the students have only a very basic knowledge of circuit theory and lack fundamental concepts of electrical machine modelling and control theory. Then, since the students are not going to specialize in electrical energy systems, they often have little motivation to learn and understand concepts related to power systems. It is thus crucial that the matter of the module is delivered in an appealing way. Including examples where the students can see the similarities and differences with respect to other disciplines that are better known or more interesting to them appears a sensible way to deliver the module. This paper describes the author's experience in teaching modules on electrical energy systems to two different groups of non-electrical engineering students, as follows.
    [Show full text]
  • Transformer Couplings for Equivalent Network Synthesis
    Web: http://www.pearl-hifi.com 86008, 2106 33 Ave. SW, Calgary, AB; CAN T2T 1Z6 E-mail: [email protected] Ph: +.1.403.244.4434 Fx: +.1.403.245.4456 Inc. Perkins Electro-Acoustic Research Lab, Inc. ❦ Engineering and Intuition Serving the Soul of Music Please note that the links in the PEARL logotype above are “live” and can be used to direct your web browser to our site or to open an e-mail message window addressed to ourselves. To view our item listings on eBay, click here. To see the feedback we have left for our customers, click here. This document has been prepared as a public service . Any and all trademarks and logotypes used herein are the property of their owners. It is our intent to provide this document in accordance with the stipulations with respect to “fair use” as delineated in Copyrights - Chapter 1: Subject Matter and Scope of Copyright; Sec. 107. Limitations on exclusive rights: Fair Use. Public access to copy of this document is provided on the website of Cornell Law School at http://www4.law.cornell.edu/uscode/17/107.html and is here reproduced below: Sec. 107. - Limitations on exclusive rights: Fair Use Notwithstanding the provisions of sections 106 and 106A, the fair use of a copyrighted work, includ- ing such use by reproduction in copies or phono records or by any other means specified by that section, for purposes such as criticism, comment, news reporting, teaching (including multiple copies for class- room use), scholarship, or research, is not an infringement of copyright.
    [Show full text]
  • Understanding Interdependencies Between Mechanical Velocity and Electrical Voltage in Electromagnetic Micromixers
    micromachines Article Understanding Interdependencies between Mechanical Velocity and Electrical Voltage in Electromagnetic Micromixers Noori Kim 1,* , Wei Xuan Chan 2, Sum Huan Ng 3, Yong-Jin Yoon 4 and Jont B. Allen 5 1 Department of Electrical and Electronic Engineering, Newcastle University in Singapore, 172A Ang Mo Kio Avenue 8, ]05-01 SIT@NYP Building, Singapore 567739, Singapore 2 Department of Biomedical Engineering, National University of Singapore, 21 Lower Kent Ridge Rd, Singapore 119077, Singapore; [email protected] 3 Singapore Institute of Manufacturing Technology, 2 Fusionopolis Way, Singapore 138634, Singapore; [email protected] 4 Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, Daejeon 34141, Korea; [email protected] 5 Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA; [email protected] * Correspondence: [email protected] Received: 18 May 2020; Accepted: 25 June 2020; Published: 29 June 2020 Abstract: Micromixers are critical components in the lab-on-a-chip or micro total analysis systems technology found in micro-electro-mechanical systems. In general, the mixing performance of the micromixers is determined by characterising the mixing time of a system, for example the time or number of circulations and vibrations guided by tracers (i.e., fluorescent dyes). Our previous study showed that the mixing performance could be detected solely from the electrical measurement. In this paper, we employ electromagnetic micromixers to investigate the correlation between electrical and mechanical behaviours in the mixer system. This work contemplates the “anti-reciprocity” concept by providing a theoretical insight into the measurement of the mixer system; the work explains the data interdependence between the electrical point impedance (voltage per unit current) and the mechanical velocity.
    [Show full text]
  • Calculations for Piezoelectric Ultrasonic Transducers
    DfcfctøooWa g T~m TTrt^ /H\ Risø-R-536 tå • 9 Calculations for Piezoelectric Ultrasonic Transducers Henrik Jensen Risø National Laboratory, DK-4000 Roskilde, Denmark May 1986 RISØ-R-536 CALCULATIONS FOR PIEZOELECTRIC ULTRASONIC TRANSDUCERS Henrik Jensen Abstract. Analysis of piezoelectric ultrasonic transducers im­ plies a solution of a boundary value problem, for a boay which consists of different materials, including a piezoelectric part. The problem is dynamic at frequencies, where a typical wavelength is somewhat less than the size of the body. Radiation losses as well as internal losses may be important. Due to the complexity of the problem, a closed form solution is the exception rather than the rule. For this reason, it is necessary to use approxi­ mate methods for the analysis. (Continued next page) May 1986 Risø National laboratory, DK 4000 Roskilde, Denmark Equivalent circuits, the Rayieigh-Ritz method, Mindlin plate theory and in particular the finite element method are con­ sidered. The finite element method is utilized for analysis of axisymmetric transducers. An explicit, fully piezoelectric, tri­ angular ring element, with linear variations in displacememnt and electric potential is given. The influence of a fluid half-space is also given, in the form of a complex stiffness matrix. A special stacking procedure, for analysis of the backing has been developed. This procedure gives a saving, which is similar to that of the fast fourier transform algorithm, and is also wellsuited for analysis of finite and infinite waveguides. Results optained by the finite element method are shown and com­ pared with measurements and exact solutions. Good agreement is obtained.
    [Show full text]