DOCSLIB.ORG

Two-Port Network Analysis and Modeling of a Balanced Armature Receiver

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Two-Port Network Analysis and Modeling of a Balanced Armature Receiver Hearing Research 301 (2013) 156e167 Contents lists available at SciVerse ScienceDirect Hearing Research journal homepage: www.elsevier.com/locate/heares Research paper Two-port network analysis and modeling of a balanced armature receiver Noori Kim*, Jont B. Allen Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, 1206 W. Green Street, 2137 Beckman Institute, 405 N. Mathews, Urbana, IL 61801, USA article info abstract Article history: Models for acoustic transducers, such as loudspeakers, mastoid bone-drivers, hearing-aid receivers, etc., Received 20 September 2012 are critical elements in many acoustic applications. Acoustic transducers employ two-port models to Received in revised form convert between acoustic and electromagnetic signals. This study analyzes a widely-used commercial 9 January 2013 hearing-aid receiver ED series, manufactured by Knowles Electronics, Inc. Electromagnetic transducer Accepted 7 February 2013 modeling must consider two key elements: a semi-inductor and a gyrator. The semi-inductor accounts for Available online 26 February 2013 electromagnetic eddy-currents, the ‘skin effect’ of a conductor (Vanderkooy, 1989), while the gyrator (McMillan, 1946; Tellegen, 1948) accounts for the anti-reciprocity characteristic [Lenz’slaw(Hunt, 1954, p. 113)]. Aside from Hunt (1954), no publications we know of have included the gyrator element in their electromagnetic transducer models. The most prevalent method of transducer modeling evokes the mobility method, an ideal transformer instead of a gyrator followed by the dual of the mechanical circuit (Beranek, 1954). The mobility approach greatly complicates the analysis. The present study proposes a novel, simplified and rigorous receiver model. Hunt’s two-port parameters, the electrical impedance Ze(s), acoustic impedance Za(s) and electro-acoustic transduction coefficient Ta(s), are calculated using ABCD and impedance matrix methods (Van Valkenburg, 1964). The results from electrical input impedance measurements Zin(s), which vary with given acoustical loads, are used in the calculation (Weece and Allen, 2010). The hearing-aid receiver transducer model is designed based on energy transformation flow [electric/ mechanic/ acoustic]. The model has been verified with electrical input impedance, diaphragm velocity in vacuo, and output pressure measurements. This receiver model is suitable for designing most electromagnetic transducers and it can ultimately improve the design of hearing-aid devices by providing a simplified yet accurate, physically motivated analysis. This article is part of a Special Issue entitled “MEMRO 2012”. Published by Elsevier B.V. 1. Introduction eddy-current diffusion (the ‘skin effect’). In 1989, Vanderkooy demonstrated that, at high frequencies, the behavior of the A transducer converts energy from one modality to another. impedance of a loudspeaker changes from the behavior of a A hearing-aid receiver is an electromagnetic loudspeaker that normal inductor to that of a semi-inductor, because of the eddy converts an electrical signal to acoustical pressure. It is referred to current diffusing into the iron pole structure of the loudspeaker. as an electromagnetic transducer in part, because small magnets Using a Bessel function ratio, Warren and LoPresti (2006) repre- are involved. Since these miniature loudspeakers are widely used in sented Vanderkooy’s semi-inductor model as a ‘diffusion ladder modern hearing-aids, and remain one of the most expensive network,’ a combination of resistors and inductors. In 2010, Weece components of the hearing-aids, a detailed understanding of them and Allen used this representation in a bone driver model.pffiffi After is therefore critical to optimize their design. demagnetizing the bone driver, they established the s behavior There are two poorly understood elements of special interest and determined the ladder network elements from the measured in the electromagnetic transducer: the semi-inductor and the gy- electrical impedance of the transducer. Thorborg et al. (2007) also rator. The semi-inductor component is required to account for introduced a loudspeaker model with lumped circuit elements, including a semi-inductor. * Corresponding author. In 1946, McMillan introduced the anti-reciprocal component as E-mail address: [email protected] (N. Kim). a network element. Two years later, Tellegen (1948) coined the 0378-5955/$ e see front matter Published by Elsevier B.V. http://dx.doi.org/10.1016/j.heares.2013.02.007 N. Kim, J.B. Allen / Hearing Research 301 (2013) 156e167 157 term ‘gyrator,’ and categorized it as a fifth network element, along with the capacitor, resistor, inductor, and ideal transformer. Other than Hunt’s 1954 publication, we remain unaware of any publica- tions which implement anti-reciprocity in their electromagnetic transducer model using a gyrator. Fig. 1. Schematic representation of an electro-magnetic transducer and the equivalent Referring back to the original formulation of Wegel (1921), Hunt factored ABCD matrix representation. The electrical and mechanical sections are (1954) proposed the basic 2-port impedance matrix which converts coupled with a gyrator. Eq. (1) is the equivalent impedance matrix representation electrical signals to mechanical force, (Hunt, 1954). EðuÞ Z ðsÞTðsÞ IðuÞ models allows for an intuitive yet accurate interpretation of physical ¼ e ; (1) FðuÞ TðsÞ zmðsÞ VðuÞ properties. For example, when using a gyrator to represent the me- chanical and electrical transformation, stiffness can be represented where E is the voltage, I is the current, F is the force and V is the as a capacitor and mass as an inductor in the series combination. particle velocity. The direction of I and V is defined as into the Given the mobility (dual) network, it is necessary to swap the E inductor and capacitor, placing them in parallel combination. Thus network. This matrix involves an electrical impedance Ze ¼ j ¼ , I V 0 we feel that this dual network is less intuitive for understanding the F a mechanical impedance z ¼ j , and an electromagnetic system. m V I¼0 F E transduction coefficient T ¼ j ¼ j . We call Z , z , and T 1.1. A balanced armature receiver I V¼0 V I¼0 e m the Hunt parameters,1 which are functions of the Laplace (complex) The Knowles Electronics2 ED series receivers shown in Fig. 2(a), frequency s ¼ sþju. When the two off-diagonal elements of Eq. (1) including the ED7045 and ED1913, are balanced armature receivers are equal, the system is reciprocal; if they are opposite in sign, the (BAR),3 widely used in hearing-aids. The ED receiver is system is anti-reciprocal, which is a necessary condition of the 6.32 Â 4.31 Â 2.97[mm] in size. These receivers consist of a coil, electromagnetic transducer, due to Lenz’s law. Eq. (1) is equivalent armature, two magnets, and a diaphragm. Unlike the alternative to the ‘factored’ ABCD (transmission) matrix of Fig. 1. moving-coil drivers, the coil of the BAR has a fixed position (does The impedance matrix (Eq. (1)) is useful when making mea- not move) (Jensen et al., 2011), thereby reducing the mass and surements. For instance, system’s electrical input impedance and providing more space for a much longer coil. As the result of the output acoustic impedance (or output mechanical impedance) can lower mass, the BAR frequency response is higher, and due to the be represented with the impedance matrix elements, Z and Z (or e a greater coil length, the sensitivity (T) is greater. The armature used z ). The ABCD matrix representation (Fig. 1) is useful for network m for the ED7045 is an E-shaped metal reed (Bauer, 1953), whereas a modeling, but then may be transformed into an impedance matrix U-shaped armature is widely used for the telephone instruments for experimental verification. (Mott and Miner, 1951). Both shapes have advantages and disad- One may convert between an impedance matrix to an ABCD vantages. For example, the U-shape armature has better acoustic matrix using the relationship: performance (i.e., wide band frequency response) while the E- shaped armature lowers the vibration of the body more effectively. AB 1 Ze DZ ¼ ; (2) The armature is placed through the center of the coil and in be- CD Ta 1 Za tween two magnets, without touching them. The movement of the 2 armature is directly connected to the diaphragm through a thin rod where D ¼ ZeZa þ T ,and Ta is the acoustic transduction imped- Z a (Fig. 2 (a)). ance (Van Valkenburg, 1964). Inverting the acoustical and electrical variables in Eq. (2) gives the inverse ABCD system: 1.2. Sensitivity analysis of ED series SPICE model ðuÞ À ð Þ ð Þ ðuÞ P ¼ 1 D s B s E ; ðuÞ D ð Þ ð Þ ðuÞ (3) U ABCD C s A s I Fig. 3 shows the Knowles Electronics commercial SPICE circuit model (Killion, 1992). This SPICE model contains a gyrator and where DABCD ¼ DA þ BC ¼1, due to anti-reciprocity. Eq. (3) allows is meant to be equivalent to the physical system, but does not one to calculate the Thevenin pressure or Norton velocity in terms accordingly represent the system in an one-to-one physical manner. of the electrical input. In order to fully understand each component, we implemented In the electromagnetic transducer models of both Weece and the Knowles PSpice model in Matlab using transmission matrices. Allen (2010) and Thorborg et al. (2007), an ideal transformer was Unlike PSpice, Matlab provides a more flexible platform for a matrix used to convert electrical current into mechanical force (or acoustical model manipulation. Matlab does not critically depend on the pressure) of the transducer. As described in Beranek (1954),the user’s operating system (Knowles’ PSpice model is inflexibly tied to mobility strategy (along with the impedance or admittance analogy) both the Cadence Orcad Schematics and Capture, and Windows is appropriate to represent electrical to mechanical transduction XP). PSpice requires a DC path to ground from all nodes, thus R1, when modeling anti-reciprocal electromagnetic transducers using RK512, RK513, and RK514 components have been added for this an ideal transformer.
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]
  • The Stripline Circulator Theory and Practice
    The Stripline Circulator Theory and Practice By J. HELSZAJN The Stripline Circulator The Stripline Circulator Theory and Practice By J. HELSZAJN Copyright # 2008 by John Wiley & Sons, Inc. All rights reserved Published by John Wiley & Sons, Inc. Published simultaneously in Canada No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 750-4470, or on the web at www.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008, or online at http:// www.wiley.com/go/permission. Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages.
    [Show full text]
  • ETD Template
    DESIGN ISSUES IN ELECTROMECHANICAL FILTERS WITH PIEZOELECTRIC TRANSDUCERS by Michael P. Dmuchoski B.S. in M.E., University of Pittsburgh, 2000 Submitted to the Graduate Faculty of School of Engineering in partial fulfillment of the requirements for the degree of Master of Science University of Pittsburgh 2002 UNIVERSITY OF PITTSBURGH SCHOOL OF ENGINEERING This thesis was presented by Michael P. Dmuchoski It was defended on December 11, 2002 and approved by Dr. Jeffrey S. Vipperman, Professor, Mechanical Engineering Department Dr. Marlin H. Mickle, Professor, Electrical Engineering Department Dr. William W. Clark, Professor, Mechanical Engineering Department Thesis Advisor ii ________ ABSTRACT DESIGN ISSUES IN ELECTROMECHANICAL FILTERS WITH PIEZOELECTRIC TRANSDUCERS Michael P. Dmuchoski, MS University of Pittsburgh, 2002 The concept of filtering analog signals was first introduced almost one hundred years ago, and has seen tremendous development since then. The majority of filters consist of electrical circuits, which is practical since the signals themselves are usually electrical, although there has been a great deal of interest in electromechanical filters. Electromechanical filters consist of transducers that convert the electrical signal to mechanical motion, which is then passed through a vibrating mechanical system, and then transduced back into electrical energy at the output. In either type of filter, electrical or electromechanical, the key component is the resonator. This is a two-degree-of-freedom system whose transient response oscillates at its natural frequency. In electrical filters, resonators are typically inductor-capacitor pairs, while in mechanical filters they are spring-mass systems. By coupling the resonators correctly, the desired filter type (such as bandpass, band-reject, etc.) or specific filter characteristics (e.g.
    [Show full text]
  • Doppler-Based Acoustic Gyrator
    applied sciences Article Doppler-Based Acoustic Gyrator Farzad Zangeneh-Nejad and Romain Fleury * ID Laboratory of Wave Engineering, École Polytechnique Fédérale de Lausanne (EPFL), 1015 Lausanne, Switzerland; farzad.zangenehnejad@epfl.ch * Correspondence: romain.fleury@epfl.ch; Tel.: +41-412-1693-5688 Received: 30 May 2018; Accepted: 2 July 2018; Published: 3 July 2018 Abstract: Non-reciprocal phase shifters have been attracting a great deal of attention due to their important applications in filtering, isolation, modulation, and mode locking. Here, we demonstrate a non-reciprocal acoustic phase shifter using a simple acoustic waveguide. We show, both analytically and numerically, that when the fluid within the waveguide is biased by a time-independent velocity, the sound waves travelling in forward and backward directions experience different amounts of phase shifts. We further show that the differential phase shift between the forward and backward waves can be conveniently adjusted by changing the imparted bias velocity. Setting the corresponding differential phase shift to 180 degrees, we then realize an acoustic gyrator, which is of paramount importance not only for the network realization of two port components, but also as the building block for the construction of different non-reciprocal devices like isolators and circulators. Keywords: non-reciprocal acoustics; gyrators; phase shifters; Doppler effect 1. Introduction Microwave phase shifters are two-port components that provide an arbitrary and variable transmission phase angle with low insertion loss [1–3]. Since their discovery in the 19th century, such phase shifters have found important applications in devices such as phased array antennas and receivers [4,5], beam forming and steering networks [6,7], measurement and testing systems [8,9], filters [10,11], modulators [12,13], frequency up-convertors [14], power flow controllers [15], interferometers [16], and mode lockers [17].
    [Show full text]
  • Modeling & Simulation 2019 Lecture 8. Bond Graphs
    Modeling & Simulation 2019 Lecture 8. Bond graphs Claudio Altafini Automatic Control, ISY Linköping University, Sweden 1 / 45 Summary of lecture 7 • General modeling principles • Physical modeling: dimension, dimensionless quantities, scaling • Models from physical laws across different domains • Analogies among physical domains 2 / 45 Lecture 8. Bond graphs Summary of today • Analogies among physical domains • Bond graphs • Causality In the book: Chapter 5 & 6 3 / 45 Basic physics laws: a survey Electrical circuits Hydraulics Mechanics – translational Thermal systems Mechanics – rotational 4 / 45 Electrical circuits Basic quantities: • Current i(t) (ampere) • Voltage u(t) (volt) • Power P (t) = u(t) · i(t) 5 / 45 Electrical circuits Basic laws relating i(t) and u(t) • inductance d 1 Z t L i(t) = u(t) () i(t) = u(s)ds dt L 0 • capacitance d 1 Z t C u(t) = i(t) () u(t) = i(s)ds dt C 0 • resistance (linear case) u(t) = Ri(t) 6 / 45 Electrical circuits Energy storage laws for i(t) and u(t) • electromagnetic energy 1 T (t) = Li2(t) 2 • electric field energy 1 T (t) = Cu2(t) 2 • energy loss in a resistance Z t Z t Z t 1 Z t T (t) = P (s)ds = u(s)i(s)ds = R i2(s)ds = u2(s)ds 0 0 0 R 0 7 / 45 Electrical circuits Interconnection laws for i(t) and u(t) • Kirchhoff law for voltages On a loop: ( X +1; σk aligned with loop direction σkuk(t) = 0; σk = −1; σ against loop direction k k • Kirchhoff law for currents On a node: ( X +1; σk inward σkik(t) = 0; σk = −1; σ outward k k 8 / 45 Electrical circuits Transformations laws for u(t) and i(t) • transformer u1 = ru2 1 i = i 1 r 2 u1i1 = u2i2 ) no power loss • gyrator u1 = ri2 1 i = u 1 r 2 u1i1 = u2i2 ) no power loss 9 / 45 Electrical circuits Example State space model: d 1 i = (u − Ri − u ) dt L s C d 1 u = i dt C C 10 / 45 Mechanical – translational Basic quantities: • Velocity v(t) (meters per second) • Force F (t) (newton) • Power P (t) = F (t) · v(t) 11 / 45 Mechanical – translational Basic laws relating F (t) and v(t) • Newton second law d 1 Z t m v(t) = F (t) () v(t) = F (s)ds dt m 0 • Hook’s law (elastic bodies, e.g.
    [Show full text]
  • Bond Graph Methodology
    Bond Graph Methodology • An abstract representation of a system where a collection of components interact with each other through energy ports and are placed in a system where energy is exchanged. • A domain-independent graphical description of dynamic behavior o physical systems • System models will be constructed using a uniform notations for al types of physical system based on energy flow • Powerful tool for modeling engineering systems, especially when different physical domains are involved • A form of object-oriented physical system modeling Bond Graphs Use analogous power and energy variables in all domains, but allow the special features of the separate fields to be represented. The only physical variables required to represent all energetic systems are power variables [effort (e) & flow (f)] and energy variables [momentum p (t) and displacement q (t)]. Dynamics of physical systems are derived by the application of instant-by-instant energy conservation. Actual inputs are exposed. Linear and non-linear elements are represented with the same symbols; non-linear kinematics equations can also be shown. Provision for active bonds . Physical information involving information transfer, accompanied by negligible amounts of energy transfer are modeled as active bonds . A Bond Graph’s Reach Mechanical Rotation Mechanical Hydraulic/Pneumatic Translation Thermal Chemical/Process Electrical Engineering Magnetic Figure 2. Multi-Energy Systems Modeling using Bond Graphs • Introductory Examples • Electrical Domain Power Variables : Electrical Voltage (u) & Electrical Current (i) Power in the system: P = u * i Fig 3. A series RLC circuit Constitutive Laws: uR = i * R uC = 1/C * ( ∫i dt) uL = L * (d i/dt); or i = 1/L * ( ∫uL dt) Represent different elements with visible ports (figure 4 ) To these ports, connect power bonds denoting energy exchange The voltage over the elements are different The current through the elements is the same Fig.
    [Show full text]
  • Microwave Engineering Lecture Notes B.Tech (Iv Year – I Sem)
    MICROWAVE ENGINEERING LECTURE NOTES B.TECH (IV YEAR – I SEM) (2018-19) Prepared by: M SREEDHAR REDDY, Asst.Prof. ECE RENJU PANICKER, Asst.Prof. ECE Department of Electronics and Communication Engineering MALLA REDDY COLLEGE OF ENGINEERING & TECHNOLOGY (Autonomous Institution – UGC, Govt. of India) Recognized under 2(f) and 12 (B) of UGC ACT 1956 (Affiliated to JNTUH, Hyderabad, Approved by AICTE - Accredited by NBA & NAAC – ‘A’ Grade - ISO 9001:2015 Certified) Maisammaguda, Dhulapally (Post Via. Kompally), Secunderabad – 500100, Telangana State, India MALLA REDDY COLLEGE OF ENGINEERING & TECHNOLOGY IV Year B. Tech ECE – I Sem L T/P/D C 5 -/-/- 4 (R15A0421) MICROWAVE ENGINEERING OBJECTIVES 1. To analyze micro-wave circuits incorporating hollow, dielectric and planar waveguides, transmission lines, filters and other passive components, active devices. 2. To Use S-parameter terminology to describe circuits. 3. To explain how microwave devices and circuits are characterized in terms of their “S” Parameters. 4. To give students an understanding of microwave transmission lines. 5. To Use microwave components such as isolators, Couplers, Circulators, Tees, Gyrators etc.. 6. To give students an understanding of basic microwave devices (both amplifiers and oscillators). 7. To expose the students to the basic methods of microwave measurements. UNIT I: Waveguides & Resonators: Introduction, Microwave spectrum and bands, applications of Microwaves, Rectangular Waveguides-Solution of Wave Equation in Rectangular Coordinates, TE/TM mode analysis, Expressions
    [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]
  • Gyrator Capacitor Modeling Approach to Study the Impact of Geomagnetically Induced Current on Single-Phase Core Transformer
    University of Tennessee, Knoxville TRACE: Tennessee Research and Creative Exchange Masters Theses Graduate School 5-2017 Gyrator Capacitor Modeling Approach to Study the Impact of Geomagnetically Induced Current on Single-Phase Core Transformer Parul Kaushal University of Tennessee, Knoxville, [email protected] Follow this and additional works at: https://trace.tennessee.edu/utk_gradthes Recommended Citation Kaushal, Parul, "Gyrator Capacitor Modeling Approach to Study the Impact of Geomagnetically Induced Current on Single-Phase Core Transformer. " Master's Thesis, University of Tennessee, 2017. https://trace.tennessee.edu/utk_gradthes/4752 This Thesis is brought to you for free and open access by the Graduate School at TRACE: Tennessee Research and Creative Exchange. It has been accepted for inclusion in Masters Theses by an authorized administrator of TRACE: Tennessee Research and Creative Exchange. For more information, please contact [email protected]. To the Graduate Council: I am submitting herewith a thesis written by Parul Kaushal entitled "Gyrator Capacitor Modeling Approach to Study the Impact of Geomagnetically Induced Current on Single-Phase Core Transformer." I have examined the final electronic copy of this thesis for form and content and recommend that it be accepted in partial fulfillment of the equirr ements for the degree of Master of Science, with a major in Electrical Engineering. Syed Kamrul Islam, Major Professor We have read this thesis and recommend its acceptance: Yilu Liu, Benjamin J. Blalock Accepted for the Council: Dixie L. Thompson Vice Provost and Dean of the Graduate School (Original signatures are on file with official studentecor r ds.) Gyrator-Capacitor Modeling Approach to Study the Impact of Geomagnetically Induced Current on Single-Phase Core Transformer A Thesis Presented for the Master of Science Degree The University of Tennessee, Knoxville Parul Kaushal May 2017 Copyright © 2017 by Parul Kaushal All rights reserved.
    [Show full text]
  • Electrical-Mechanical-Acoustical Analogies
    analogies mechanical systems describing quantities mechanical elements Mechanical sources Mechanical resonance - spring pendulum acoustical systems Acoustics II: describing quantities Acoustical elements analogies electrical-mechanical- potential and flow quantities Impedances Measurement of acoustical impedances acoustical distributed elements coupling interfaces Dual conversion analogies thin absorbers measurement of the impedance at the ear Kurt Heutschi Model of the middle ear Diagnosis 2013-01-18 Experiments back analogies Motivation mechanical systems describing quantities mechanical elements I microphones, loudspeakers consist of mechanical, Mechanical sources Mechanical resonance - spring pendulum acoustical and electrical subsystems acoustical systems I due to their interaction an analysis has to consider describing quantities Acoustical elements all subsystems in integral way analogies potential and flow I the fundamental differential equations have identical quantities Impedances form in all systems Measurement of acoustical impedances distributed elements I introduction of analogies and conversion of coupling mechanical and acoustical systems into electrical interfaces Dual conversion ones thin absorbers I excellent tools available for analysis of electrical measurement of the impedance at networks the ear Model of the middle ear Diagnosis Experiments back analogies mechanical systems describing quantities mechanical elements Mechanical sources Mechanical resonance - spring pendulum acoustical systems describing quantities Acoustical
    [Show full text]
  • Bond Graph Fundamentals
    SECTION 2: BOND GRAPH FUNDAMENTALS MAE 3401 – Modeling and Simulation Bond Graphs ‐ Introduction 2 As engineers, we’re interested in different types of systems: Mechanical translational Mechanical rotational Electrical Hydraulic Many systems consist of subsystems in different domains, e.g. an electrical motor Common aspect to all systems is the flow of energy and power between components Bond graph system models exploit this commonality Based on the flow of energy and power Universal –domain‐independent Technique used for deriving differential equations from a bond graph model is the same for any type of system K. Webb MAE 3401 3 Power and Energy Variables K. Webb MAE 3401 Bonds and Power Variables 4 Systems are made up of components Power can flow between components We represent this pathway for power to flow with bonds A and B represent components, the line connecting them is a bond Quantity on the bond is power Power flow is positive in the direction indicated –arbitrary Each bond has two power variables associated with it Effort and flow The product of the power variables is power K. Webb MAE 3401 Power Variables 5 Power variables, e and f, determine the power flowing on a bond The rate at which energy flows between components Effort Flow Domain Quantity Variable Units Quantity Variable Units Power General Effort –Flow – ∙ Mechanical Force NVelocity m/s ∙ Translational Mechanical Angular Torque N‐m rad/s ∙ Rotational velocity Electrical Voltage VCurrent A ∙ Pa Hydraulic Pressure Flow rate m3/s ∙ (N/m2) K. Webb MAE 3401 Energy Variables 6 Bond graph models are energy‐based models Energy in a system can be: Supplied by external sources Stored by system components Dissipated by system components Transformed or converted by system components In addition to power variables, we need two more variables to describe energy storage: energy variables Momentum Displacement K.
    [Show full text]
  • Lstl Ter Tional
    FINITE ELEMENT MODELING OF FLUID SYSTEMS USING THE MOBILITY ANALOGY APPROACH Ronald J. Gaines* Rajendra Singh Research Assistant Assistant Professor Department of Mechanical Engineeri ng The Ohio State University 206 West 18th Avenue Columbus, Ohio 43210 Proceedings of the lstl ter tional •International Mo alAn...... ysis Modal Analysis Co...... nee 1ft·Exhibit November 8-10, 1982 Holiday Inn, International Driv~ Orlando, Florida FINITE ELEMENT MODELING OF FLUID SYSTEMS USING THE MOBILITY ANALOGY APPROACH Ronald J. Gaines* Rajendra Singh Research Assistant Assistant Professor Department of Mechanical Engineering The Ohio State University 206 West 18th Avenue Columbus, Ohio 43210 *Currently with Toledo Scale Div., Reliance Electric, Worthington, Ohio 43D85 ABSTRACT obtained good agreement between SUPERB and WAVENET (a fluid transients computer program based on the One-dimensional fluid systems can be analyzed for method of characteristics [9] ) . However, in order natural frequencies and modes using an available to establish the mobility analogy solution tech­ structural finite element program, wi th the aid of nique, a sufficient number of example cases must the mobility analogy. In this paper, the be analyzed, and an adequate error analysis should methodology, strength and limitation of the be performed. Thi s i s the focu s of this paper as solution technique are discussed . Th i s method is we will consider several one-dimensional fluid validated by considering several example cases and systems and compare the computed results, using comparing results with theory, experiment or other the mobility analogy-finite element analysis, with numerical techniques. the solutions obtained by theory, experiment, or other numerical techniques. INTRODUCTION SCOPE The physical variables of a dynamic system could be classified either according to the dynamic and We are interested in obtaining an eigenvalue kinematic variables (impedance approach) , or solution (i .e.
    [Show full text]