NI myDAQ AND MULTISIM PROBLEMS FOR CIRCUITS Fawwaz T. Ulaby and Michel M. Maharbiz By Ed Doering
Contents71 Introduction81.1Resources81.2Goals for Student Deliverables111.3StudentDeliverablesChecklist121.4Acknowledgements.132Resistive Circuits132.1Kirchhoff's Laws (2-3)2.216Equivalent Resistance (2-4)2.319Currentand VoltageDividers (2-4)2.421Wye-Delta Transformation (2-5)253Analysis Techniques253.1Node-Voltage Method (3-1)293.2Mesh-Current Method (3-2)323.3Superposition (3-4)353.4 Thevenin Equivalents, Maximum Power Transfer (3-5, 3-6)41OperationalAmplifiers4414.1Ideal Op-Amp Model (4-3)444.2Noninverting Amplifier (4-3)494.3Summing Amplifier (4-5).4.453Signal Processing Circuits (4-8)575 RCand RLFirst-OrderCircuits575.1Capacitors (5-2)5.262Inductors (5-3) .665.3Response of the RC Circuit (5-4)705.4ResponseoftheRLCircuit(5-5)
Contents 1 Introduction 7 1.1 Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.2 Goals for Student Deliverables . . . . . . . . . . . . . . . . . 8 1.3 Student Deliverables Checklist . . . . . . . . . . . . . . . . . 11 1.4 Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . 12 2 Resistive Circuits 13 2.1 Kirchhoff’s Laws (2-3) . . . . . . . . . . . . . . . . . . . . . . 13 2.2 Equivalent Resistance (2-4) . . . . . . . . . . . . . . . . . . . . 16 2.3 Current and Voltage Dividers (2-4) . . . . . . . . . . . . . . . 19 2.4 Wye-Delta Transformation (2-5) . . . . . . . . . . . . . . . . . 21 3 Analysis Techniques 25 3.1 Node-Voltage Method (3-1) . . . . . . . . . . . . . . . . . . . 25 3.2 Mesh-Current Method (3-2) . . . . . . . . . . . . . . . . . . . 29 3.3 Superposition (3-4) . . . . . . . . . . . . . . . . . . . . . . . . 32 3.4 Thevenin Equivalents, Maximum Power Transfer (3-5, 3-6) . 35 ´ 4 Operational Amplifiers 41 4.1 Ideal Op-Amp Model (4-3) . . . . . . . . . . . . . . . . . . . . 41 4.2 Noninverting Amplifier (4-3) . . . . . . . . . . . . . . . . . . 44 4.3 Summing Amplifier (4-5) . . . . . . . . . . . . . . . . . . . . . 49 4.4 Signal Processing Circuits (4-8) . . . . . . . . . . . . . . . . . 53 5 RC and RL First-Order Circuits 57 5.1 Capacitors (5-2) . . . . . . . . . . . . . . . . . . . . . . . . . . 57 5.2 Inductors (5-3) . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 5.3 Response of the RC Circuit (5-4) . . . . . . . . . . . . . . . . . 66 5.4 Response of the RL Circuit (5-5) . . . . . . . . . . . . . . . . . 70
4CONTENTS756RLCCircuits756.1Initial and Final Conditions (6-1)796.2 Natural Response of the Series RLC Circuit (6-3)846.3General Solution for Any Second-Order Circuit (6-6)876.4Two-Capacitor Second-Order Circuit (6-6)91ACAnalysis7917.1 Impedance Transformations (7-5)977.2 Equivalent Circuits (7-6)1007.3 Phase-Shift Circuits (7-8)7.4 Phasor-Domain Analysis Techniques (7-9)1021058ACPower1058.1Periodic Waveforms (8-1)8.2111Average Power (8-2)8.3114Complex Power (8-3)1178.4ThePower Factor (8-4)FrequencyResponse of Circuits and Filters12191219.1Scaling (9-2)1249.2Bode Plots (9-3)9.3127FilterOrder(9-5)1309.4Cascaded Active Filters (9-7)13310 Laplace Transform Analysis Techniques13310.1 s-Domain CircuitAnalvsis (10-7)13710.2 Step Response (10-8)14010.3 TransferFunctionand ImpulseResponse (10-8)14310.4 Convolution Integral (10-9)14711 Fourier Analysis Techniques14711.1 Fourier Series Representation (11-2)15211.2 Circuit Applications (11-3)15411.3FourierTransform (11-5)15711.4 Circuit Analysis with Fourier Transform (11-8)159A Parts List163B LM317 Voltage and Current Sources164B.1 Variable Voltage Source.164B.2Current Source
4 CONTENTS 6 RLC Circuits 75 6.1 Initial and Final Conditions (6-1) . . . . . . . . . . . . . . . . 75 6.2 Natural Response of the Series RLC Circuit (6-3) . . . . . . . 79 6.3 General Solution for Any Second-Order Circuit (6-6) . . . . . 84 6.4 Two-Capacitor Second-Order Circuit (6-6) . . . . . . . . . . . 87 7 AC Analysis 91 7.1 Impedance Transformations (7-5) . . . . . . . . . . . . . . . . 91 7.2 Equivalent Circuits (7-6) . . . . . . . . . . . . . . . . . . . . . 97 7.3 Phase-Shift Circuits (7-8) . . . . . . . . . . . . . . . . . . . . . 100 7.4 Phasor-Domain Analysis Techniques (7-9) . . . . . . . . . . . 102 8 AC Power 105 8.1 Periodic Waveforms (8-1) . . . . . . . . . . . . . . . . . . . . . 105 8.2 Average Power (8-2) . . . . . . . . . . . . . . . . . . . . . . . 111 8.3 Complex Power (8-3) . . . . . . . . . . . . . . . . . . . . . . . 114 8.4 The Power Factor (8-4) . . . . . . . . . . . . . . . . . . . . . . 117 9 Frequency Response of Circuits and Filters 121 9.1 Scaling (9-2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 9.2 Bode Plots (9-3) . . . . . . . . . . . . . . . . . . . . . . . . . . 124 9.3 Filter Order (9-5) . . . . . . . . . . . . . . . . . . . . . . . . . 127 9.4 Cascaded Active Filters (9-7) . . . . . . . . . . . . . . . . . . . 130 10 Laplace Transform Analysis Techniques 133 10.1 s-Domain Circuit Analysis (10-7) . . . . . . . . . . . . . . . . 133 10.2 Step Response (10-8) . . . . . . . . . . . . . . . . . . . . . . . 137 10.3 Transfer Function and Impulse Response (10-8) . . . . . . . . 140 10.4 Convolution Integral (10-9) . . . . . . . . . . . . . . . . . . . 143 11 Fourier Analysis Techniques 147 11.1 Fourier Series Representation (11-2) . . . . . . . . . . . . . . 147 11.2 Circuit Applications (11-3) . . . . . . . . . . . . . . . . . . . . 152 11.3 Fourier Transform (11-5) . . . . . . . . . . . . . . . . . . . . . 154 11.4 Circuit Analysis with Fourier Transform (11-8) . . . . . . . . 157 A Parts List 159 B LM317 Voltage and Current Sources 163 B.1 Variable Voltage Source . . . . . . . . . . . . . . . . . . . . . . 164 B.2 Current Source . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
5CONTENTS169CTL072Operational Amplifier173DDG413QuadAnalogSwitchE177Transient ResponseMeasurementTechniquesE.1TimeConstant..177F179Sinusoid Measurement Techniques179F.1Amplitudeand PhaseMeasurements183G Video Links
CONTENTS 5 C TL072 Operational Amplifier 169 D DG413 Quad Analog Switch 173 E Transient Response Measurement Techniques 177 E.1 Time Constant . . . . . . . . . . . . . . . . . . . . . . . . . . . 177 F Sinusoid Measurement Techniques 179 F.1 Amplitude and Phase Measurements . . . . . . . . . . . . . . 179 G Video Links 183
Chapter 1IntroductionThis supplement toCircuits byUlabyand Maharbiz contains40additionalend-of-chapter problems designed for three-way solution: analytical, sim-ulation,andmeasurement.Aftersolvingtheproblemanalyticallythestu-dent continues by solving the same problem with NI Multisim and thenonce again with NI myDAQ computer-based instrumentation and circuitcomponents. By iterating on each dimension of the problem until all threeagree students "triangulate on the truth" and develop confidence in theiranalyticaland laboratoryskills.Each problem requests at least one common numerical value for com-parison among the three methods.The percent difference between sim-ulated and analytical results as well as measured-to-analytical results in-dicates the degree to which the student has achieved a correct solution.Normally simulation and analytical results agree to within a percentagepoint, and measurements often agree with analytical results to within fivepercent.The problems are organized as four per chapter for Chapters 2 through11 of Circuits.The table of contents indicates the associated section numberof the textbook in parentheses. Each problem contains the problem state-ment and sufficient detail to guide the student through the simulation andphysical measurement steps.Short video tutorials are linked to each prob-lem to provide detailed guidance on Multisim techniques and ELVISmxcomputer-based instruments for the myDAQThis document is fully hyperlinked for section and figure references,and all video links are live hyperlinks. Opening the PDF version of thisdocument is the most efficient way to access all links, and clicking a videohyperlink automatically launches the video in a browser. Within the PDF
Chapter 1 Introduction This supplement to Circuits by Ulaby and Maharbiz contains 40 additional end-of-chapter problems designed for three-way solution: analytical, simulation, and measurement. After solving the problem analytically the student continues by solving the same problem with NI Multisim and then once again with NI myDAQ computer-based instrumentation and circuit components. By iterating on each dimension of the problem until all three agree students “triangulate on the truth” and develop confidence in their analytical and laboratory skills. Each problem requests at least one common numerical value for comparison among the three methods. The percent difference between simulated and analytical results as well as measured-to-analytical results indicates the degree to which the student has achieved a correct solution. Normally simulation and analytical results agree to within a percentage point, and measurements often agree with analytical results to within five percent. The problems are organized as four per chapter for Chapters 2 through 11 of Circuits. The table of contents indicates the associated section number of the textbook in parentheses. Each problem contains the problem statement and sufficient detail to guide the student through the simulation and physical measurement steps. Short video tutorials are linked to each problem to provide detailed guidance on Multisim techniques and ELVISmx computer-based instruments for the myDAQ. This document is fully hyperlinked for section and figure references, and all video links are live hyperlinks. Opening the PDF version of this document is the most efficient way to access all links, and clicking a video hyperlink automatically launches the video in a browser. Within the PDF
8CHAPTER1.INTRODUCTIONuse ALT+leftarrow to navigate back to a startingpoint.1.1Resources.Appendix A details the parts list required to implement all of the cir-cuits and includes links to component distributors.· Appendix B describes how to implement a variable voltage sourceand two styles of current sources with the LM317 adjustable voltageregulator. Many of the circuits require a DC voltage other than thestandard ±15V and 5V power supplies offered by the NI myDAQ.The adjustable voltage source pictured in Figure B.3 on page 165 shouldbe constructed at the beginning of the term and left in place for sub-sequent circuits.Appendix Cdescribes the Texas Instruments TL072 dual operationalamplifier used in many of the circuits. The op amp is frequently usedas a voltage follower to strengthen the 2 mA current drive of the my-DAQ analog outputs. Appendix D describes the Intersil DG413 quadanalogswitchusedinmanyofthetransientresponseproblems.Appendix E details a laboratory technique to measure time constantswhile Appendix F explains how to measure amplitude and phaseshift for sinusoidal signals..Appendix G lists all of the available video links.1.2GoalsforStudentDeliverablesStudents should document their work in sufficient detail so that it couldbe replicated by others. Present your work on the"Analysis" section asyou would on a standard problem set. Be sure to include a"Given"sectionwithyour own drawing ofthecircuitdiagram,a"Find"sectionthatliststhe requested results for the problem, a detailed solution process, and aclearly-identified endresult.Doall of thiswork on engineeringgreen paperor in a lab book or as otherwise required by your instructor.The"Simulation" section presents your work to set up the circuit simu-lation in NI Multisim and the simulation results you used to obtain mean-ingful information. Createawordprocessingdocumentthat containsanorganized set of screenshots with highlights and annotations as well as text
8 CHAPTER 1. INTRODUCTION use ALT+leftarrow to navigate back to a starting point. 1.1 Resources • Appendix A details the parts list required to implement all of the circuits and includes links to component distributors. • Appendix B describes how to implement a variable voltage source and two styles of current sources with the LM317 adjustable voltage regulator. Many of the circuits require a DC voltage other than the standard ±15V and 5V power supplies offered by the NI myDAQ. The adjustable voltage source pictured in Figure B.3 on page 165 should be constructed at the beginning of the term and left in place for subsequent circuits. • Appendix C describes the Texas Instruments TL072 dual operational amplifier used in many of the circuits. The op amp is frequently used as a voltage follower to strengthen the 2 mA current drive of the myDAQ analog outputs. Appendix D describes the Intersil DG413 quad analog switch used in many of the transient response problems. • Appendix E details a laboratory technique to measure time constants while Appendix F explains how to measure amplitude and phase shift for sinusoidal signals. • Appendix G lists all of the available video links. 1.2 Goals for Student Deliverables Students should document their work in sufficient detail so that it could be replicated by others. Present your work on the “Analysis” section as you would on a standard problem set. Be sure to include a “Given” section with your own drawing of the circuit diagram, a “Find” section that lists the requested results for the problem, a detailed solution process, and a clearly-identified end result. Do all of this work on engineering green paper or in a lab book or as otherwise required by your instructor. The “Simulation” section presents your work to set up the circuit simulation in NI Multisim and the simulation results you used to obtain meaningful information. Create a word processing document that contains an organized set of screenshots with highlights and annotations as well as text
1.2.GOALSFORSTUDENTDELIVERABLESto lead the reader through the screenshots.Include the circuit schematicand dialog box setup parameters for information not already visible on theschematic-circleparametersthatyouenteredorchanged awayfromde-fault values.Also include simulation results,again circling control settingsthat you changed and highlighting regions where you obtained informa-tion. Figure 1.1 illustrates a screenshot from NI Multisim properly high-lighted to indicate control settings that were adjusted away from defaultvalues aswell asregionsonthescreen wheremeasurements wereobtainedInterpret the simulation results by writing them in standardform includingunits, and write any additional calculations that were necessary to reach anend resultfor simulation.XOscilloscope-XsC1ChannelT1Reverse200.00005169.593m-173.706mVT20.000VSave-200.000usT2-T1173.706mV-169.593mVExt.triggerChannelAChannelTriggerScale:50us/DivScale:5v/Div100m/DiVEdge:Scale:Expos.(DiV)Ypos.(DiV):0Ypos.(Div)LevelYTTAddB/AABACLOACLODCNFigure 1.1: NI Multisim screenshot showing proper markings to indicatecontrol settings adjusted away from default values as well as regions wheremeasurementwas obtained.NOTE:Screen shots in Microsoft Word 2010 can be easily captured andhighlighted as follows:
1.2. GOALS FOR STUDENT DELIVERABLES 9 to lead the reader through the screenshots. Include the circuit schematic and dialog box setup parameters for information not already visible on the schematic – circle parameters that you entered or changed away from default values. Also include simulation results, again circling control settings that you changed and highlighting regions where you obtained information. Figure 1.1 illustrates a screenshot from NI Multisim properly highlighted to indicate control settings that were adjusted away from default values as well as regions on the screen where measurements were obtained. Interpret the simulation results by writing them in standard form including units, and write any additional calculations that were necessary to reach an end result for simulation. Figure 1.1: NI Multisim screenshot showing proper markings to indicate control settings adjusted away from default values as well as regions where measurement was obtained. NOTE: Screen shots in Microsoft Word 2010 can be easily captured and highlighted as follows:
10CHAPTER1.INTRODUCTION1.Select"Insert"tabandthen"Screenshot,"2. Choose the desired window or select "Screen Clipping" to define anarbitraryregion,3. Select"Shapes,"and4. Place circles or boxes to highlight important values.The"Measurement" section presents your work to set up the physicalcircuit and NI ELVISmx signal generators and measurement instrumentsThis section also includes your measurement results. Follow the generalguidelines for the"Simulation"section.Your instructor may require aphoto of your breadboard circuit and myDAQ connections along with yourstudent IDwhen you work on the problem outside of scheduled class time.Also includea schematicdiagram showing allmyDAQconnections.Finally, the"Summary" section compares the requested numerical re-sults from each of the three methods. Tabulate three results for each re-quested numerical quantity (analytical, simulation,and measurement)andtabulate twopercentagedifferences for each requested numerical quantity. Simulation-to-Analytical: [(Xs -XA)/XA] × 100%· Measurement-to-Analytical: [(XM -XA)/XA] × 100%
10 CHAPTER 1. INTRODUCTION 1. Select “Insert” tab and then “Screenshot,” 2. Choose the desired window or select “Screen Clipping” to define an arbitrary region, 3. Select “Shapes,” and 4. Place circles or boxes to highlight important values. The “Measurement” section presents your work to set up the physical circuit and NI ELVISmx signal generators and measurement instruments. This section also includes your measurement results. Follow the general guidelines for the “Simulation” section. Your instructor may require a photo of your breadboard circuit and myDAQ connections along with your student ID when you work on the problem outside of scheduled class time. Also include a schematic diagram showing all myDAQ connections. Finally, the “Summary” section compares the requested numerical results from each of the three methods. Tabulate three results for each requested numerical quantity (analytical, simulation, and measurement) and tabulate two percentage differences for each requested numerical quantity: • Simulation-to-Analytical: [(XS − XA)/XA] × 100% • Measurement-to-Analytical: [(XM − XA)/XA] × 100%
111.3.STUDENTDELIVERABLESCHECKLIST1.3StudentDeliverablesChecklist1. Engineering paper or lab book -submit directly to instructor:(a) Analysisi."Given / Find" section including original circuiti.Detailed solutionii. End result clearly identified(b)Simulation-interpreted results from simulation screen shots(c) Measurementi.Circuit schematic with myDAQconnectionsii.Interpreted results(d)Results comparison table2. Word processor document-submit electronically to instructor:(a) Simulation screen shotsi.Circuit schematicii. Dialog box parameters with circles around entered or mod-ified control valuesii. Simulation results marked up to highlightkey results(b) Photo of circuit on breadboard and myDAQ connections (if re-quired)(c) Measurement screen shotsi. ELVISmx signal generator instruments with circles aroundentered or modified valuesi.ELVISmx measurement instrumentsmarked up to highlightkey results and circles around entered ormodified controlvalues
1.3. STUDENT DELIVERABLES CHECKLIST 11 1.3 Student Deliverables Checklist 1. Engineering paper or lab book – submit directly to instructor: (a) Analysis i. “Given / Find” section including original circuit ii. Detailed solution iii. End result clearly identified (b) Simulation – interpreted results from simulation screen shots (c) Measurement i. Circuit schematic with myDAQ connections ii. Interpreted results (d) Results comparison table 2. Word processor document – submit electronically to instructor: (a) Simulation screen shots i. Circuit schematic ii. Dialog box parameters with circles around entered or modified control values iii. Simulation results marked up to highlight key results (b) Photo of circuit on breadboard and myDAQ connections (if required) (c) Measurement screen shots i. ELVISmx signal generator instruments with circles around entered or modified values ii. ELVISmx measurement instruments marked up to highlight key results and circles around entered or modified control values
12CHAPTER1.INTRODUCTION1.4AcknowledgementsI gratefully acknowledge contributions from the following individuals:. Tom Robbins (NTS Press) for his editorial support throughout thisproject,·Erik Luther (National Instruments)for his enthusiastic support of theNI myDAQ product for engineering education,.David Salvia (Penn State University) for his helpful suggestions re-garding the design of this project, and. Rose-Hulman students in Electrical Systems ES203 (Spring 2011) whoofferedmuchhelpful feedbackon theirexperiencewith selectedprob-lems.Ed DoeringDepartment of Electrical and Computer EngineeringRose-Hulman Institute of TechnologyTerre Haute, IN 47803doering@rose-hulman.edu
12 CHAPTER 1. INTRODUCTION 1.4 Acknowledgements I gratefully acknowledge contributions from the following individuals: • Tom Robbins (NTS Press) for his editorial support throughout this project, • Erik Luther (National Instruments) for his enthusiastic support of the NI myDAQ product for engineering education, • David Salvia (Penn State University) for his helpful suggestions regarding the design of this project, and • Rose-Hulman students in Electrical Systems ES203 (Spring 2011) who offered much helpful feedback on their experience with selected problems. Ed Doering Department of Electrical and Computer Engineering Rose-Hulman Institute of Technology Terre Haute, IN 47803 doering@rose-hulman.edu