Contents Chapter 1 Introduction to Electrical Network Analysis 55 Circuit Variables 56 Engineering 1 Ground 57 1.1 Electrical Engineering 2 1.2 Electrical Engineering Chapter 3 Resistive Network as a Foundation for the Design Analysis 71 of Mechatronic Systems 4 1.3 Fundamentals of Engineering Exam 3.1 The Node Voltage Method 72 Review 8 Nodal Analysis with Voltage Source 77 1.4 Brief History of Electrical Engineering 9 3.2 The Mesh Current Method 78 1.5 Systems of Units 10 Mesh Analysis with Current Sources 82 1.6 Special Features of This Book 11 3.3 Nodal and Mesh Analysis with Controlled Sources 84 PART I CIRCUITS 14 Remarks on Node Voltage and Mesh Current Methods 86 Chapter 2 Fundamentals of Electric 3.4 The Principle of Superposition 86 3.5 One-Port Networks and Equivalent Circuits 15 Circuits 89 Thévenin and Norton Equivalent Circuits 90 2.1 Charge, Current, and Kirchhoff’s Determination of Norton or Thévenin Current Law 16 Equivalent Resistance 91 2.2 Voltage and Kirchhoff’s Voltage Law 21 Computing the Thévenin Voltage 95 2.3 Ideal Voltage and Current Sources 23 Computing the Norton Current 99 Ideal Voltage Sources 24 Source Transformations 101 Ideal Current Sources 25 Experimental Determination of Thévenin Dependent (Controlled) Sources 25 and Norton Equivalents 104 2.4 Electric Power and Sign Convention 26 3.6 Maximum Power Transfer 107 2.5 Circuit Elements and Their 3.7 Nonlinear Circuit Elements 110 i-vCharacteristics 29 Description of Nonlinear Elements 110 2.6 Resistance and Ohm’s Law 30 Graphical (Load-Line) Analysis of Nonlinear Open and Short Circuits 38 Circuits 111 Series Resistors and the Voltage Divider Rule 39 Chapter 4 AC Network Parallel Resistors and the Current Divider Rule 42 Analysis 125 2.7 Practical Voltage and Current Sources 49 2.8 Measuring Devices 50 4.1 Energy-Storage (Dynamic) Circuit The Ohmmeter 50 Elements 126 The Ammeter 51 The Ideal Capacitor 126 The Voltmeter 51 Energy Storage in Capacitors 130 2.9 Electrical Networks 52 The Ideal Inductor 133 Branch 52 Energy Storage in Inductors 137 Node 55 4.2 Time-Dependent Signal Sources 141 Loop 55 Why Sinusoids? 141 Mesh 55 Average and RMS Values 142 xii Contents xiii 4.3 Solution of Circuits Containing Dynamic The Laplace Transform 263 Elements 145 Transfer Functions, Poles, and Zeros 267 Forced Response of Circuits Excited Chapter 7 AC Power 281 by Sinusoidal Sources 146 4.4 Phasors and Impedance 148 Euler’s Identity 148 7.1 Power in AC Circuits 282 Phasors 149 Instantaneous and Average Power 282 Superposition of AC Signals 151 AC Power Notation 284 Impedance 153 Power Factor 288 The Resistor 153 7.2 Complex Power 289 The Inductor 154 Power Factor, Revisited 294 The Capacitor 155 7.3 Transformers 308 Admittance 161 The Ideal Transformer 309 4.5 AC Circuit Analysis Methods 162 Impedance Reflection and Power AC Equivalent Circuits 166 Transfer 311 7.4 Three-Phase Power 315 Balanced Wye Loads 318 Chapter 5 Transient Analysis 181 Balanced Delta Loads 319 5.1 Introduction 181 7.5 Residential Wiring; Grounding 5.2 Solution of Circuits Containing Dynamic and Safety 322 Elements 183 7.6 Generation and Distribution of AC Power 325 5.3 Transient Response of First-Order PART II ELECTRONICS 336 Circuits 186 Natural Response of First-Order Circuits 187 Chapter 8 Semiconductors Forced and Complete Response of First-Order Circuits 191 and Diodes 337 Continuity of Capacitor Voltages and Inductor Circuits 192 8.1 Electrical Conduction in Semiconductor Complete Solution of First-Order Circuits 194 Devices 338 5.4 Transient Response of First-Order 8.2 The pnJunction and the Semiconductor Circuits 203 Diode 340 Deriving the Differential Equations 8.3 Circuit Models for the Semiconductor for Second-Order Circuits 204 Diode 343 Natural Response of Second-Order Large-Signal Diode Models 343 Circuits 205 Small-Signal Diode Models 351 Overdamped Solution 208 Piecewise Linear Diode Model 357 Critically Damped Solution 209 8.4 Practical Diode Circuits 360 Underdamped Solution 209 The Full-Wave Rectifier 360 Forced and Complete Response The Bridge Rectifier 362 of Second-Order Circuits 210 DC Power Supplies, Zener Diodes, and Voltage Regulation 364 Chapter 6 Frequency Respose Signal-Processing Applications 370 Photodiodes 377 and System Concepts 231 6.1 Sinusoidal Frequency Response 232 Chapter 9 Transistor 6.2 Filters 238 Fundamentals 391 Low-Pass Filters 239 High-Pass Filters 245 9.1 Transistors as Amplifiers and Switches 392 Band-Pass Filters 248 9.2 The Bipolar Junction Transistor (BJT) 394 Decibel (db) or Bode Plots 257 Determining the Operating Region 6.3 Complex Frequency and the Laplace of a BJT 397 Transform 260 Selecting an Operating Point for a BJT 399 xiv Contents 9.3 BJTLarge-Signal Model 407 Power MOSFETs 505 Large-Signal Model of the npnBJT 407 Insulated-Gate Bipolar Transistors 9.4 Field-Effect Transistors 415 (IGBTs) 508 9.5 Overview of Enhancement-Mode 11.5 Rectifiers and Controlled Rectifiers MOSFETs 415 (AC-DC Converters) 508 Operation of the n-Channel Enhancement- Three-Phase Rectifiers 511 Mode MOSFET 416 Thyristors and Controlled Rectifiers 512 p-Channel MOSFETs and CMOS 11.6 Electric Motor Drives 518 Devices 421 Choppers (DC-DC Converters) 518 9.6 Depletion MOSFETs and JFETs 423 Inverters (DC-AC Converters) 523 Depletion MOSFETs 423 Chapter 12 Operational Junction Field-Effect Transistors 424 Depletion MOSFETand JFET Amplifiers 531 Equations 426 12.1 Amplifiers 532 Ideal Amplifier Characteristics 532 Chapter 10 Transistor Amplifiers 12.2 The Operational Amplifier 533 and Switches 437 The Open-Loop Model 534 The Operational Amplifier 10.1 Small-Signal Models of the BJT 438 in the Closed-Loop Mode 535 Transconductance 441 12.3 Active Filters 553 10.2 BJTSmall-Signal Amplifiers 443 12.4 Integrator and Differentiator Circuits 559 DC Analysis of the Common-Emitter The Ideal Differentiator 562 Amplifier 446 12.5 Analog Computers 562 AC Analysis of the Common-Emitter Scaling in Analog Computers 564 Amplifier 453 12.6 Physical Limitations of Op-Amps 569 Other BJTAmplifier Circuits 457 Voltage Supply Limits 569 10.3 FETSmall-Signal Amplifiers 457 Frequency Response Limits 571 The MOSFETCommon-Source Input Offset Voltage 574 Amplifier 461 Input Bias Currents 575 The MOSFETSource Follower 465 Output Offset Adjustment 576 10.4 Transistor Amplifiers 468 Slew Rate Limit 577 Frequency Response of Small-Signal Short-Circuit Output Current 579 Amplifiers 468 Common-Mode Rejection Ratio 580 Multistage Amplifiers 470 10.5 Transistor Gates and Switches 472 Chapter 13 Digital Logic Analog Gates 473 Circuits 599 Digital Gates 473 13.1 Analog and Digital Signals 600 Chapter 11 Power Electronics 495 13.2 The Binary Number System 602 Addition and Subtraction 602 11.1 Classification of Power Electronic Multiplication and Division 603 Devices 496 Conversion from Decimal to Binary 603 11.2 Classification of Power Electronic Complements and Negative Numbers 604 Circuits 497 The Hexadecimal System 606 11.3 Voltage Regulators 499 Binary Codes 606 11.4 Power Amplifiers and Transistor 13.3 Boolean Algebra 610 Switches 502 AND and OR Gates 610 Power Amplifiers 502 NAND and NOR Gates 617 BJTSwitching Characteristics 504 The XOR (Exlusive OR) Gate 619 Contents xv 13.4 Karnaugh Maps and Logic Design 620 15.2 Wiring, Grounding, and Noise 695 Sum-of-Products Realizations 623 Signal Sources and Measurement System Product-of-Sums Realizations 627 Configurations 695 Don’t Care Conditions 631 Noise Sources and Coupling 13.5 Combinational Logic Modules 634 Mechanisms 697 Multiplexers 634 Noise Reduction 698 Read-Only Memory (ROM) 635 15.3 Signal Conditioning 699 Decoders and Read and Write Memory 638 Instrumentation Amplifiers 699 Active Filters 704 15.4 Analog-to-Digital and Digital-to-Analog Chapter 14 Digital Systems 647 Conversion 713 Digital-to-Analog Converters 714 14.1 Sequential Logic Modules 648 Analog-to-Digital Converters 718 Latches and Flip-Flops 648 Data Acquisition Systems 723 Digital Counters 655 15.5 Comparator and Timing Circuits 727 Registers 662 The Op-Amp Comparator 728 14.2 Sequential Logic Design 664 The Schmitt Trigger 731 14.3 Microcomputers 667 The Op-Amp Astable Multivibrator 735 14.4 Microcomputer Architecture 670 The Op-Amp Monostable Multivibrator 14.5 Microcontrollers 671 (One-Shot) 737 Computer Architecture 672 Timer ICs: The NE555 740 Number Systems and Number Codes 15.6 Other Instrumentation Integrated Circuits in Digital Computers 674 Amplifiers 742 Memory Organization 675 DACs and ADCs 743 Operation of the Central Processing Unit Frequency-to-Voltage, (CPU) 677 Voltage-to-Frequency Converters Interrupts 678 and Phase-Locked Loops 743 Instruction Set for the MC68HC05 Other Sensor and Signal Conditioning Microcontroller 679 Circuits 743 Programming and Application Development 15.7 Data Transmission in Digital in a Microcontrollerr 680 Instruments 748 14.6 ATypical Automotive Engine The IEEE 488 Bus 749 Microcontroller 680 The RS-232 Standard 753 General Description 680 Processor Section 681 Memory 682 PART III ELECTROMECHANICS 766 Inputs 684 Outputs 685 Chapter 16 Principles Chapter 15 Electronic of Electromechanics 767 Instrumentation 16.1 Electricity and Magnetism 768 and Measurements 689 The Magnetic Field and Faraday’s Law 768 15.1 Measurement Systems and Transducers 690 Self- and Mutual Inductance 771 Measurement Systems 690 Ampère’s Law 775 Sensor Classification 690 16.2 Magnetic Circuits 779 Motion and Dimensional 16.3 Magnetic Materials and B-HCircuits 793 Measurements 691 16.4 Transformers 795 Force, Torque, and Pressure 16.5 Electromechanical Energy Conversion 799 Measurements 691 Forces in Magnetic Structures 800 Flow Measurements 693 Moving-Iron Transducers 800 Temperature Measurements 693 Moving-Coil Transducers 809 xvi Contents Chapter 17 Introduction Find Chapter 19 on the Web to Electric Machines 827 http://www.mhhe.com/engcs/electrical/rizzoni Chapter 19 Introduction 17.1 Rotating Electric Machines 828 Basic Classification of Electric Machines 828 to Communication Performance Characteristics of Electric Systems Machines 830 Basic Operation of All Electric 19.1 Introduction to Communication Systems Machines 837 Information, Modulation, and Carriers Magnetic Poles in Electric Machines 837 Communications Channels 17.2 Direct-Current Machines 840 Classification of Communication Systems Physical Structure of DC Machines 840 19.2 Signals and Their Spectra Configuration of DC Machines 842 Signal Spectra DC Machine Models 842 Periodic Signals: Fourier Series 17.3 Direct-Current Generators 845 Non-Periodic Signals: The Fourier Transform 17.4 Direct-Current Motors 849 Bandwidth Speed-Torque and Dynamic Characteristics 19.3 Amplitude Modulation and Demodulation of DC Motors 850 Basic Principle of AM DC Drives and DC Motor Speed AM Demodulaton: Integrated Circuit Receivers Control 860 Comment on AM Applications 17.5 AC Machines 862 19.4 Frequency Modulation and Demodulation Rotating Magnetic Fields 862 Basic Principle of FM 17.6 The Alternator (Synchronous FM Signal Models Generator) 864 FM Demodulation 17.7 The Synchronous Motor 866 19.5 Examples of Communication Systems 17.8 The Induction Motor 870 Global Positioning System Performance of Induction Motors 877 Sonar AC Motor Speed and Torque Control 879 Radar Adjustable-Frequency Drives 880 Cellular Phones Local-Area Computer Networks Chapter 18 Special-Purpose Electric Machines 889 Appendix A Linear Algebra and Complex Numbers 933 18.1 Brushless DC Motors 890 18.2 Stepping Motors 897 Appendix B Fundamentals 18.3 Switched Reluctance Motors 905 Operating Principles of SR Machine 906 of Engineering 18.4 Single-Phase AC Motors 908 (FE) Examination 941 The Universal Motor 909 Single-Phase Induction Motors 912 Appendix C Answers Classification of Single-Phase Induction to Selected Problems 955 Motors 917 Summary of Single-Phase Motor Index 961 Characteristics 922 18.5 Motor Selection and Application 923 Motor Performance Calculations 923 Motor Selection 926 C H A P T E R 1 Introduction to Electrical Engineering heaimofthischapteristointroduceelectricalengineering. Thechapteris organizedtoprovidethenewcomerwithaviewofthedifferentspecialties makingupelectricalengineeringandtoplacetheintentandorganization ofthebookintoperspective. Perhapsthefirstquestionthatsurfacesinthe mindofthestudentapproachingthesubjectis,Whyelectricalengineering? Since this book is directed at a readership having a mix of engineering backgrounds (includingelectricalengineering),thequestioniswelljustifiedanddeservessome discussion. Thechapterbeginsbydefiningthevariousbranchesofelectricalengi- neering,showingsomeoftheinteractionsamongthem,andillustratingbymeans ofapracticalexamplehowelectricalengineeringisintimatelyconnectedtomany other engineering disciplines. In the second section, mechatronic systems engi- neeringisintroduced,withanexplanationofhowthisbookcanlaythefoundation for interdisciplinary mechatronic product design. This design approach is illus- tratedbyanexample. ThenextsectionintroducestheEngineer-in-Training(EIT) nationalexamination. Abriefhistoricalperspectiveisalsoprovided,tooutlinethe growthanddevelopmentofthisrelativelyyoungengineeringspecialty. Next,the fundamentalphysicalquantitiesandthesystemofunitsaredefined,tosetthestage forthechaptersthatfollow. Finally,theorganizationofthebookisdiscussed,to givethestudent,aswellastheteacher,asenseofcontinuityinthedevelopment ofthedifferentsubjectscoveredinChapters2through18. 1 2 Chapter1 IntroductiontoElectricalEngineering 1.1 ELECTRICAL ENGINEERING Thetypicalcurriculumofanundergraduateelectricalengineeringstudentincludes thesubjectslistedinTable1.1. Althoughthedistinctionbetweensomeofthese subjectsisnotalwaysclear-cut,thetableissufficientlyrepresentativetoserveour purposes. Figure1.1illustratesapossibleinterconnectionbetweenthedisciplines ofTable1.1. Theaimofthisbookistointroducethenon-electricalengineering studenttothoseaspectsofelectricalengineeringthatarelikelytobemostrelevant to his or her professional career. Virtually all of the topics of Table 1.1 will be touchedoninthebook,withvaryingdegreesofemphasis. Thefollowingexample illustratesthepervasivepresenceofelectrical, electronic, andelectromechanical devicesandsystemsinaverycommonapplication: theautomobile. Asyouread Table1.1 Electrical throughtheexample,itwillbeinstructivetorefertoFigure1.1andTable1.1. engineeringdisciplines Circuitanalysis Electromagnetics Engineering Solid-stateelectronics applications Electricmachines Electricpowersystems Power systems Digitallogiccircuits Computersystems Communicationsystems Electric machinery Electro-optics Mathematical Physical Instrumentationsystems foundations foundations Controlsystems Network Analog Electro- theory electronics magnetics Logic Digital Solid-state theory electronics physics System Computer Optics theory systems Control systems Communication systems Instrumentation systems Figure 1.1 Electricalengineeringdisciplines EXAMPLE 1.1 ElectricalSystemsinaPassengerAutomobile Afamiliarexampleillustrateshowtheseeminglydisparatespecialtiesofelectrical engineeringactuallyinteracttopermittheoperationofaveryfamiliarengineering system: theautomobile. Figure1.2presentsaviewofelectricalengineeringsystemsina Chapter1 IntroductiontoElectricalEngineering 3 Body Vehicle Power train electronics control Airbags Antilock brake Engine Climate Traction Transmission Security and Suspension Charging keyless entry Power steering Cruise Auto belts 4-wheel steer Cooling fan Memory seat Tire pressure Ignition Memory mirror 4-wheel drive MUX Instrumentation Entertainment Analog dash Cellular phone Digital dash CD/DAT Navigation AM/FM radio Digital radio TV sound Figure 1.2 Electricalengineeringsystemsintheautomobile modernautomobile. Eveninoldervehicles,theelectricalsystem—ineffect,anelectric circuit—playsaveryimportantpartintheoveralloperation. Aninductorcoilgeneratesa sufficientlyhighvoltagetoallowasparktoformacrossthesparkpluggap,andtoignite theairandfuelmixture;thecoilissuppliedbyaDCvoltageprovidedbyalead-acid battery. Inadditiontoprovidingtheenergyfortheignitioncircuits,thebatteryalso suppliespowertomanyotherelectricalcomponents,themostobviousofwhicharethe lights,thewindshieldwipers,andtheradio. Electricpoweriscarriedfromthebatteryto allofthesecomponentsbymeansofawireharness,whichconstitutesaratherelaborate electricalcircuit. Inrecentyears,theconventionalelectricalignitionsystemhasbeen supplantedbyelectronicignition;thatis,solid-stateelectronicdevicescalledtransistors havereplacedthetraditionalbreakerpoints. Theadvantageoftransistorizedignition systemsovertheconventionalmechanicalonesistheirgreaterreliability,easeofcontrol, andlifespan(mechanicalbreakerpointsaresubjecttowear). Otherelectricalengineeringdisciplinesarefairlyobviousintheautomobile. The on-boardradioreceiveselectromagneticwavesbymeansoftheantenna,anddecodesthe communicationsignalstoreproducesoundsandspeechofremoteorigin;othercommon communicationsystemsthatexploitelectromagneticsareCBradiosandtheevermore commoncellularphones. Butthisisnotall! Thebatteryis,ineffect,aself-contained 12-VDCelectricpowersystem,providingtheenergyforalloftheaforementioned functions. Inorderforthebatterytohaveausefullifetime,achargingsystem,composed ofanalternatorandofpowerelectronicdevices,ispresentineveryautomobile. The alternatorisanelectricmachine,asarethemotorsthatdrivethepowermirrors,power windows,powerseats,andotherconveniencefeaturesfoundinluxurycars. Incidentally, theloudspeakersarealsoelectricmachines! 4 Chapter1 IntroductiontoElectricalEngineering Thelistdoesnotendhere,though. Infact,someofthemoreinterestingapplications ofelectricalengineeringtotheautomobilehavenotbeendiscussedyet. Consider computersystems. Youarecertainlyawarethatinthelasttwodecades,environmental concernsrelatedtoexhaustemissionsfromautomobileshaveledtotheintroductionof sophisticatedengineemissioncontrolsystems. Theheartofsuchcontrolsystemsisatype ofcomputercalledamicroprocessor. Themicroprocessorreceivessignalsfromdevices (calledsensors)thatmeasurerelevantvariables—suchastheenginespeed,the concentrationofoxygenintheexhaustgases,thepositionofthethrottlevalve(i.e.,the driver’sdemandforenginepower),andtheamountofairaspiratedbytheengine—and subsequentlycomputestheoptimalamountoffuelandthecorrecttimingofthesparkto resultinthecleanestcombustionpossibleunderthecircumstances. Themeasurementof theaforementionedvariablesfallsundertheheadingofinstrumentation,andthe interconnectionbetweenthesensorsandthemicroprocessorisusuallymadeupofdigital circuits. Finally,asthepresenceofcomputersonboardbecomesmorepervasive—in areassuchasantilockbraking,electronicallycontrolledsuspensions,four-wheelsteering systems,andelectroniccruisecontrol—communicationsamongthevariouson-board computerswillhavetooccuratfasterandfasterrates. Somedayinthenot-so-distant future,thesecommunicationsmayoccuroverafiberopticnetwork,andelectro-optics willreplacetheconventionalwireharness. Itshouldbenotedthatelectro-opticsisalready presentinsomeofthemoreadvanceddisplaysthatarepartofanautomotive instrumentationsystem. 1.2 ELECTRICAL ENGINEERING AS A FOUNDATION FOR THE DESIGN OF MECHATRONIC SYSTEMS Manyoftoday’smachinesandprocesses, rangingfromchemicalplantstoauto- mobiles,requiresomeformofelectronicorcomputercontrolforproperoperation. Computercontrolofmachinesandprocessesiscommontotheautomotive,chem- ical,aerospace,manufacturing,testandinstrumentation,consumer,andindustrial electronics industries. The extensive use of microelectronics in manufacturing systemsandinengineeringproductsandprocesseshasledtoanewapproachto thedesignofsuchengineeringsystems. TouseatermcoinedinJapanandwidely adoptedinEurope, mechatronicdesignhassurfacedasanewphilosophyofde- sign,basedontheintegrationofexistingdisciplines—primarilymechanical,and electrical,electronic,andsoftwareengineering.1 A very important issue, often neglected in a strictly disciplinary approach toengineeringeducation, istheintegratedaspectofengineeringpractice, which isunavoidableinthedesignandanalysisoflargescaleand/orcomplexsystems. One aim of this book is to give engineering students of different backgrounds exposuretotheintegrationofelectrical,electronic,andsoftwareengineeringinto their domain. This is accomplished by making use of modern computer-aided tools and by providing relevant examples and references. Section 1.6 describes howsomeofthesegoalsareaccomplished. 1D.A.Bradley,D.Dawson,N.C.Burd,A.J.Loader,1991,“Mechatronics,ElectronicsinProducts andProcesses,”ChapmanandHall,London.SeealsoASME/IEEETransactionsonMechatronics, Vol.1,No.1,1996. Chapter1 IntroductiontoElectricalEngineering 5 Example1.2illustratessomeofthethinkingbehindthemechatronicsystem designphilosophythroughapracticalexampledrawnfromthedesignexperience ofundergraduatestudentsatanumberofU.S.universities. EXAMPLE 1.2 MechatronicSystems—DesignofaFormula LightningElectricRaceCar TheFormulaLightningelectricracecarcompetitionisaninteruniversity2competition projectthathasbeenactivesince1994. Thisprojectinvolvesthedesign,analysis,and testingofanelectricopen-wheelracecar. Aphotoandthegenericlayoutofthecarare showninFigures1.3and1.4. Thestudent-designedpropulsionandenergystorage systemshavebeentestedininteruniversitycompetitionssince1994. Projectshave includedvehicledynamicsandracetracksimulation,motorandbatterypackselection, batterypackandloadingsystemdesign,andtransmissionanddrivelinedesign. Thisisan ongoingcompetition,andnewprojectsaredefinedinadvanceofeachraceseason. The objectiveofthiscompetitiveseriesistodemonstrateadvancementinelectricdrive technologyforpropulsionapplicationsusingmotorsportsasameansofextendingexisting technologytoitsperformancelimit. Thisexampledescribessomeofthedevelopmentthat hastakenplaceattheOhioStateUniversity. Thedescriptiongivenbelowisrepresentative ofworkdoneatalloftheparticipatinguniversities. Instrumentation panel DC-AC converter (electric drive) AC + – + – motor + – + – + – + – + – + – + – + – + – + – + – + – Battery + – + – 24 V 24 V pack Differential Gearbox Figure 1.3 TheOhioStateUniversitySmokin’ Figure 1.4 Blockdiagramofelectricracecar Buckeye DesignConstraints: TheFormulaLightningseriesisbasedonaspecificationchassis;thus,extensive modificationstotheframe,suspension,brakes,andbodyarenotpermitted. Thefocusof thecompetitionisthereforetooptimizetheperformanceofthespecvehiclebyselectinga 2UniversitiesthathaveparticipatedinthiscompetitionareArizonaStateUniversity,BowlingGreen StateUniversity,CaseWesternReserveUniversity,KetteringUniversity,GeorgiaInstituteof Technology,IndianaUniversity—PurdueUniversityatIndianapolis,NorthernArizonaUniversity, NotreDameUniversity,OhioStateUniversity,OhioUniversity,RennselaerPolytechnicInstitute, UniversityofOklahoma,andWrightStateUniversity.