CIRCUITS LABS STUDENT MANUAL
CIRCUITS LABSSTUDENTMANUALLAB EXPERIMENTSUSING NI ELVIS IIAND NI M ULTISIMALEXANDER GANAGOJASON LEE SLEIGHTUniversity of MichiganAnn Arbor
ISBN-10: 1-934891-07-XISBN-13: 978-1-934891-07-0Publisher: Tom RobbinsGeneral Manager: Erik LutherMarketing Manager: Brad Armstrong 2010 National Technology and Science Press.All rights reserved. Neither this book, nor any portion of it, may be copied or reproduced in any form orby any means without written permission of the publisher.NTS Press respects the intellectual property of others, and we ask our readers to do the same. This bookis protected by copyright and other intellectual property laws. Where the software referred to in this bookmay be used to reproduce software or other materials belonging to others, you should use such softwareonly to reproduce materials that you may reproduce in accordance with the terms of any applicablelicense or other legal restriction.LabVIEW, NI Multisim, and NI are trademarks of National Instruments.MATLAB is a registered trademark of The MathWorks, Inc., 8 Apple Hill Drive, Natick, MA 017602098.PPAll other trademarks or product names are the property of their respective owners.Additional Disclaimers:The reader assumes all risk of use of this book and of all information, theories, and programs contained or described in it. This book maycontain technical inaccuracies, typographical errors, other errors and omissions, and out-of-date information. Neither the author nor the publisherassumes any responsibility or liability for any errors or omissions of any kind, to update any information, or for any infringement of any patent orother intellectual property right.Neither the author nor the publisher makes any warranties of any kind, including without limitation any warranty as to the sufficiency of the bookor of any information, theories, or programs contained or described in it, and any warranty that use of any information, theories, or programscontained or described in the book will not infringe any patent or other intellectual property right. THIS BOOK IS PROVIDED "AS IS." ALLWARRANTIES, EITHER EXPRESS OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, ANY AND ALL IMPLIED WARRANTIES OFMERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE, AND NON-INFRINGEMENT OF INTELLECTUAL PROPERTYRIGHTS, ARE DISCLAIMED.No right or license is granted by publisher or author under any patent or other intellectual property right, expressly, or by implication or estoppel.IN NO EVENT SHALL THE PUBLISHER OR THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, SPECIAL, INCIDENTAL,COVER, ECONOMIC, OR CONSEQUENTIAL DAMAGES ARISING OUT OF THIS BOOK OR ANY INFORMATION, THEORIES, ORPROGRAMS CONTAINED OR DESCRIBED IN IT, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGES, AND EVEN IFCAUSED OR CONTRIBUTED TO BY THE NEGLIGENCE OF THE PUBLISHER, THE AUTHOR, OR OTHERS. Applicable law may notallow the exclusion or limitation of incidental or consequential damages, so the above limitation or exclusion may not apply to you.
TABLE OFCONTENTSLAB 1Introduction to Measurements with NI ELVIS II1LAB 2Introduction to Multisim47LAB 3Thevenin Equivalent Circuit; Beyond Parallel and Series65LAB 4Operational Amplifiers (Op Amps)93LAB 5Transient Responses of First-Order RC Circuits139LAB 6Transient Responses of Second-Order RLC Circuits159LAB 7AC Analysis183LAB 8AC Power211LAB 9Filters and Transfer Functions249LAB 10 Laplace Transform Analysis Technique289LAB 11 Fourier Analysis313
Lab 1: Introduction to Measurements with NI ELVIS IILAB EXPERIMENTS USINGNI ELVIS IIAND NI MULTISIMAlexander GanagoJason Lee SleightUniversity of MichiganAnn ArborLab 1Introduction to Measurementswith NI ELVIS II 2010 A. GanagoIntroduction Page 1 of 241
2Lab 1: Introduction to Measurements with NI ELVIS IIGoals for Lab 1 Learn how to build circuits on the prototyping board (PB) and how to connect themto NI ELVIS (Educational Laboratory Virtual Instrumentation Suite) test/measurementinstruments Learn about Ohm’s law for resistors and the offset model for semiconductor diodes Learn about voltage division in DC and AC measurements Build your own circuits on PB and connect them to NI ELVIS test/measurementinstruments Perform DC current–voltage measurements:o First, point-by-pointo Then automatically with NI ELVIS Two-Wire Current–Voltage Analyzer Obtain distinct current–voltage characteristics:o Linear for a component that obeys Ohm’s law, such as a resistoro Nonlinear for a component that does not obey Ohm’s law, such as a LightEmitting Diode (LED) Perform AC voltage measurements with NI ELVIS function generator andoscilloscope Observe voltage division:o In a circuit with 2 resistors, where the output voltage is proportional to the inputo In a circuit with a resistor and an LED, where the output voltage is distinct Observe rectification of the input AC voltage in the resistor-LED circuit and relate thewaveforms obtained with oscilloscope to the current–voltage curves obtained in DCmeasurements Explore [for extra credit] the rectification in various resistor–LED circuits and explainyour observations Explore [for extra credit] whether the offset model explains the output waveforms ofyour resistor–LED circuit Explore [for extra credit] the responses of a circuit with 2 LEDs and a load resistor Explore [for extra credit] the responses of a circuit with a resistor and an LED totriangular input waveform Explore [for extra credit] the range of amplitudes and frequencies, within which theNI ELVIS oscilloscope measures clean signals produced by the NI ELVIS functiongenerator. 2010 A. GanagoIntroduction Page 2 of 24
Lab 1: Introduction to Measurements with NI ELVIS IIIntroductionCongratulations! You are about to begin experiments with electric circuits! Even if youhave worked with circuits before, the lab projects described in this book will be full ofinformation and fun; they will relate to your studies of theory and help you developintuitive understanding of how circuits behave.Each lab project includes introduction, pre-lab, in-lab, and post-lab:o Introduction provides background information that you need for lab work: read itbefore doing the pre-labo Pre-lab includes assignments that help you prepare for lab work; complete thepre-lab before you begin in-lab worko In the lab, you will build circuits, measure voltages and currents, carefully recordthe results and relate your results to sample data and the theoryo In the post-lab, you will explain your results and draw conclusions on theiragreement/disagreement with theory.You will do all lab experiments with NI ELVIS II (Educational Laboratory VirtualInstrumentation Suite)—the educational design and prototyping platform built byNational Instruments (NI) and based on NI LabVIEW, industry standard for automaticdata acquisition and control.NI ELVIS incorporates:o Prototyping board, on which you will build circuitso Several data acquisition (DAQ) electronic boards that serve as test/measurementinstruments such as:o Power supplyo Digital multimeter (DMM)o Function generatoro OscilloscopeEach NI ELVIS unit is connected to a PC with software that:o Controls voltages applied to the prototyping boardo Tailors data collection to your specifications, ando Provides real-time data processing.This combination of NI ELVIS hardware and computer software enables the designer tocreate many Virtual Instruments (VIs) for specialized instruments.For example, in Lab 1 you will use a Two-Wire Current–Voltage Analyzer, which allowsyou to collect a lot of data very quickly, compared to point-by-point measurements doneby hand, it will be really fun. 2010 A. GanagoIntroduction Page 3 of 243
4Lab 1: Introduction to Measurements with NI ELVIS IIBasic Measurements with Electric CircuitsVoltage MeasurementsRecall the basics of voltage and current measurements, which you learned in the prerequisite courses. By definition, voltage is the difference of electric potentials between two nodes in acircuit, which we may denote Node A and Node B. Every voltmeter hastwo terminals for thetwo cables thatensure electricalconnections to thetwo nodes. This sketch showshow to measurevoltage across aresistor. If we swap thewires, as shown onthe sketch below, the voltmeter will still measureV probe – referenceBBBBbut, due to the reverse connections, the reading has the opposite sign. We will read:V BA V B (the probe) – V A (the reference)BBBBBBAvoid the blunder made by students who neglected to build the right connections. Compare the two sketches.Notice the differentconnections and theopposite signs. When you do pre-labcalculations, keep 3 or 4significant digits to matchthe accuracy of labmeasurements. 2010 A. GanagoIntroduction Page 4 of 24
Lab 1: Introduction to Measurements with NI ELVIS II The voltmeter has its own internal(input) resistance, which is usuallyvery high. For an ideal voltmeter theinput resistance is infinitely largeR Ideal voltmeter In real instruments, the voltmeterinput resistance usually exceeds 1MΩ (or 1 10 6 Ω).BBPP When we measure voltage V AB , the voltmeter’s internal resistance (between its twoterminals) is connected in parallel with all circuit components that are also connectedbetween these two terminals. In other words, the internal or input resistance of thevoltmeter R Voltmeter is in parallel with the equivalent resistance R AB . We expect that agood voltmeter, whose input resistance is very high, does not disturb the circuit: allvoltages in the circuit remain unchanged after you connected the voltmeter betweenNode A and Node B.BBBBBB Note that you do not have to change anything in your circuit to measure voltages: justconnect the voltmeter to the nodes of interest. Thus the voltage measurement is simpleand noninvasive. 2010 A. GanagoIntroduction Page 5 of 245
6Lab 1: Introduction to Measurements with NI ELVIS IICurrent Measurements To measure the current that flows through a branch of your circuit we should makethis current flow through the ammeter. An ammeter has two terminals for two wires.Through one terminal labeled Current In on the diagrams below, the current from thecircuit enters the ammeter; through the other terminal the current leaves the ammeterand flows back into the circuit. On the diagrams below this terminal is labeledCurrent Out. Notice that in order to measure the current we have to interrupt the circuit: thediagrams show that instead of one Node A we work with Node A1 and Node A2.These two nodes play distinct roles in our measurements: at Node A1 the currentleaves the circuit for the ammeter, and at Node A2 the current is returned to thecircuit. The current from the circuitenters the ammeter’sCurrent In terminal asshown on this diagram(arrows indicate the currentdirection). This diagram shows how tomeasure the current througha resistor. Notice that thecircuit is broken at the pointwhere we measure thecurrent and the ammeterbridges the gap. Notice that we make thecurrent pass through the ammeter. Thus the ammeter is connected in series with theresistor in the circuit. If we swap the wires as shownon this diagram, the current fromthe circuit will enter the CurrentOut terminal and the sign of thecurrent measured by the ammeterwill be reversed. Take a close look at these twodiagrams and make sure youunderstand the relationshipbetween the connections of wiresand the readings on the ammeter. 2010 A. GanagoIntroduction Page 6 of 24
Lab 1: Introduction to Measurements with NI ELVIS II If we swap the wires, we will measure the current that enters the Current Outterminal of the ammeter and leaves from the Current In terminal: thus it has the samemagnitude but the opposite sign compared with the current measured before the wireswere swapped. Notice that you have to change your circuit in order to measure the current: Before each measurement, you have to create a new node (on the diagramsabove, Node A1 and Node A2 were created from one Node A) After the measurement, you have to restore the original circuit (connectthe new Node A1 and Node A2 into the same Node A and disconnect theammeter).Thus a measurement of current is more complicated and more invasive than a voltagemeasurement.The ammeter being used to measure the current through a circuit component is connectedin series with that component. In other words, the internal or input resistance of theammeter R Ammeter is in series with the resistance of the component through which wemeasure the current.BB We expect that agood ammeter, whichdoes not disturb thecircuit, should have avery low internal (orshunt) resistance.Usually,R Ammiter 1Ω or lessAn ideal ammeter is expected to have zero internal resistanceR Ideal ammiter 0BBBB 2010 A. GanagoIntroduction Page 7 of 247
8Lab 1: Introduction to Measurements with NI ELVIS IIHow to Build Circuits on the PBIn the lab, you will connect resistors, LEDs, and othercomponents to each other on a PB, which allows you tobuild the circuit without soldering.The PB used in the lab consists of several plastic blocks ofvarious sizes, all about 0.4 inch (10 mm) thick. Each plasticblock has many holes, into which you insert wires and plugin resistors and other circuit components.Inside the plastic block, metal clips snugly hold your wires,etc., and ensure electric connections between circuitcomponents.Some of the holes on PB are connected to each other behind the plastic: they form nodes,to which you can connect several things such as a resistor and a wire that goes to thepower supply.The picture above shows a bare PB; the picture below also includes solid lines drawnacross each group of connected holes.The long rows of connected holes are typically used as bus lines such as 5 V or theground; in many experiments, they are connected to the power supply.Note that the bus lines at the top and the bottom of the board are separated in the middle.If you wish to have a continuous bus line throughout the length of the board, add jumperwires.Also, note that colored stripes along the bus lines serve for color-coding: for example, ifyou choose blue for ground, you will easily see all ground bus lines are on your board. 2010 A. GanagoIntroduction Page 8 of 24
Lab 1: Introduction to Measurements with NI ELVIS IIShort rows of 5 holes each are used to build nodes in your circuit. For example, you canplug a resistor and a wire that goes to the power supply, as shown on the picture below.Zoomed-in view of the same picture clearly shows that the wires are inserted in the samerows of holes as the ends of the resistor. 2010 A. GanagoIntroduction Page 9 of 249
10Lab 1: Introduction to Measurements with NI ELVIS IIHow to Sketch Connections BeforeBuilding Your Circuit on a PBThe grid shown here can be used to sketch connectionsin your circuit: it is a clever way to plan the physicallayout before building the real circuit on a PB.The connections (nodes) between the holes are shown onthe sketch below.Note that the grid shows a small fraction of a PB used inthe lab (see 3-D pictures on previous pages), but it isenough for simple circuits you will build in Lab 1.The sketch at the bottom of this page shows connectionsfor measurements of the current through and the voltageacross a resistor.Make sure you understand all connections on the sketchbelow (if needed, reread the previous sections).In the pre-lab, you will have to draw similar connectionsthat will prepare you for effective circuit building on theNI ELVIS PB in the lab. 2010 A. GanagoIntroduction Page 10 of 24
Lab 1: Introduction to Measurements with NI ELVIS IIOhm’s Law for ResistorsOhm’s law, formulated by Georg Ohm in 1820, claims that voltage Vthrough a circuit element and current I across the circuit element areproportional to each other: V IR, where the coefficient R is calledresistance and is expected to be constant (independent of voltage orcurrent). The circuit symbol for a resistor looks like azigzag line.When current is plotted as a function of voltage,according to Ohm’s law, a straight line is obtained, withthe slope determined by the resistance, as sketched here.NI ELVIS II’s Two-Wire Current–Voltage Analyzermeasures such plots automatically. The screenshotbelow shows a current–voltage plot obtained with NIELVIS for a 200-Ω resistor. Note that the axes areclearly labeled, which allows the user to calculate theresistance from lab data. The control panel to the right ofthe plot allows you to set the initial and final voltage, the size of voltage increment, thecurrent limits and other parameters of the experiment.Ohm’s law is valid for metals and some other materials, of which we build resistors,although their resistance depends on many parameters such as temperature. We use theterm ohmic for circuit elements that obey Ohm’s law. Nonohmic components havenonlinear current–voltage relationships. 2010 A. GanagoIntroduction Page 11 of 2411
12Lab 1: Introduction to Measurements with NI ELVIS IIThe Offset Model for Semiconductor DiodesThere are many important exceptions to Ohm’s law, such as semiconductordiodes; we call them nonohmic. The circuit symbol for a diode looks likean arrow, emphasizing that currents flow through diodes only in onedirection, along with the arrow, when the voltage across the diode ispositive. This case is called forward-biased. (Under negative voltage, muchsmaller currents can leak in the opposite direction, but we often neglectthem. This case is called reverse-biased.)Even for a forward-biased diode, the current is not directly proportional to voltage. Forexample, the screenshot below shows a plot obtained with NI ELVIS for a 1NG14 diode:Note that, at low voltages (here, below 0.5 V), the current is negligibly small; at highervoltages (here, above 0.7 V), it grows very rapidly. In other words, the current–voltagedependence is strongly nonlinear.In order to simplify algebraic equations for solving circuitproblems, this nonlinear dependence is replaced with two straightlines in the so-called offset model sketched here. According to theoffset model, the current through a diode remains dead zero untilthe voltage across it exceeds V D0 0.7 V (the exact value of thisoffset voltage depends on the semiconductor material; for the LEDin the lab, V D0 1.7 V). When the bias voltage reaches V D0 , thediode conducts any positive current. In this model, the voltage across the diode neverexceeds V D0 .BBBBBBB 2010 A. GanagoIntroduction Page 12 of 24B
Lab 1: Introduction to Measurements with NI ELVIS IISeries Connections in Circuits on a PB and Circuit DiagramsWhen two or more circuit components are connected in series, the same current flowsthrough them all (there is no bypass for the current). The following picture shows anexample of 2 resistors in series.Zoomed-in view of the same picture clearly shows the rows where the wires and resistorsare inserted to ensure the series connection. 2010 A. GanagoIntroduction Page 13 of 2413
14Lab 1: Introduction to Measurements with NI ELVIS IIThe circuit diagram for series connection of 2 resistors is shownhere:Note that the ground, to which the (–) terminal of the powersupply and the “bottom” of resistor R 2 are connected on thediagram, are indeed connected to each other. Also, the groundserves as reference node, which has zero voltage.BBThe rule to remember:All ground nodes are connected to each other, and they all have zero voltage.On the previous 3-D picture of the PB, resistor R 1 is connected to rows 34 and 37;resistor R 2 is connected to rows 37 and 40; row 37 corresponds to the fat dot on thecircuit diagram, where R 1 and R 2 are connected to each other.BBBBBBBBWhen you build circuits with resistors, it does not matter which end of a resistor connectsto the ground and which one goes to the ( ) terminal of the power supply. However,polarity is very important when you build circuits with semiconductor diodes. 2010 A. GanagoIntroduction Page 14 of 24
15Lab 1: Introduction to Measurements with NI ELVIS IICircuits with Semiconductor DiodesThe circuit symbol for a semiconductordiode resembles an arrow or a trianglepointing a crossbar. The diode conductslarge currents when it is forward-biased, inother words, when voltage is applied asshown on this diagram; then the currentflows in the direction of the arrow.On the 3-D pictures on the next few pages,the diode is shown as a cylinder markedwith a band, which corresponds to the crossbar on the circuit symbol.In circuits, a diode must be connected in series with a load resistor; otherwise the currentthrough it might get dangerously high.In the lab, you will build circuits with an LED whose circuit symbol also includes wavyarrows; the polarity requirements are the same as for other diodes.Thus, one can envision 4 various connections for the circuit with anLED, shown below and labeled A, B, C, D from left to right.ABCDOf course, out of the 4 circuits, in only 2 the LED is forward-biased thus it will shine; inthe other 2 circuits, the LED is reverse-biased and it will not shine.The corresponding 3-D pictures of the circuit board are shown on the next pages. 2010 A. GanagoIntroduction Page 15 of 24
16Lab 1: Introduction to Measurements with NI ELVIS IIOne 2010 A. GanagoIntroduction Page 16 of 24
Lab 1: Introduction to Measurements with NI ELVIS IITwo 2010 A. GanagoIntroduction Page 17 of 2417
18Lab 1: Introduction to Measurements with NI ELVIS IIThree 2010 A. GanagoIntroduction Page 18 of 24
Lab 1: Introduction to Measurements with NI ELVIS IIFour 2010 A. GanagoIntroduction Page 19 of 2419
20Lab 1: Introduction to Measurements with NI ELVIS IIVoltage divisionThe circuit shown on this diagram is called a voltagedivider. Its output voltage equals:VOUT VS R2R1 R 2For example,if V S 6 V, R 1 100 Ω and R 2 200 Ω,BBBBBBthenVOUT VS R2200 Ω ( 6 V) 4VR1 R 2(100 Ω) ( 200 Ω)However, the same pair of resistors may be differently connected to the same source andthe output, as shown on the second diagram:Then the output changes to:VOUT VS ( 6 V) R1R1 R 2100 Ω 2V(100 Ω) ( 200 Ω)Make sure to pay attention to all connections when youbuild your circuits in the lab.In DC measurements (when the source voltage is constant), the output voltage ismeasured with a voltmeter whose reference is at the ground node, and the probe is at thenode where the two resistors connect to each other. 2010 A. GanagoIntroduction Page 20 of 24
21Lab 1: Introduction to Measurements with NI ELVIS IIVoltage Division in AC MeasurementsAC measurements are made with voltages that vary withtime. Most often, we use sinusoidal voltagesV(t) Vmax sin(2π f t)or—the same thing—V(t) Vmax sin(2π t)Twhere f is frequency in hertz, and T is period in seconds.In AC measurements, the source on the diagram above is a function generator, whichproduces sine waves at the desired frequency f and peak voltage V max , and the outputvoltage is measured with an oscilloscope. A good oscilloscope has two channels, or twoindependent inputs thus it can measure both V S and V OUT at the same time.BBBBBBOn this screenshot, the green line corresponds to V S and the blue line to V OUT .BBBBThese waveforms were obtained with a voltage divider R 1 100 Ω and R 2 200 Ω. Notethat the formulas for voltage division remain the same as discussed above.B 2010 A. GanagoBIntroduction Page 21 of 24BB
22Lab 1: Introduction to Measurements with NI ELVIS IIWhen the two resistors are swapped, as shown on thisdiagram, the output waveform changes, as you can seeon the screenshot below, which was also obtained withthe NI ELVIS oscilloscope.For comparison between DC measurements (where thesource voltage is constant) and AC measurements(where the source voltage is sinusoidal), you may thinkof an oscilloscope as a voltmeter that can rapidly readvarying signals and is connected to the circuit in exactlythe same way for both types of measurements.Note that the oscilloscope control panel to the right of the plot on the screenshot allowsyou to choose Volts/Div (volts per division on the vertical scale) in Channel 0 and inChannel 1 independently (here, they both equal 500 mV/div). The horizontal scale isdetermined by the choice of Time/Div, the same for both channels.Also note that the NI ELVIS oscilloscope automatically measures and displays theamplitude of signal in each channel in Vp-p, or volts peak-to-peak (Vp-p 2 V max forthe sine wave), and the frequency in hertz (Hz). The readings of frequency on thisscreenshot agree with the 1 kHz setting on the function generator. The displayedamplitudes of the input and output signals allow you to verify the equations for voltagedivision in this experiment.B 2010 A. GanagoIntroduction Page 22 of 24B
Lab 1: Introduction to Measurements with NI ELVIS IIAC Measurements with a Resistor–LED CircuitSince an LED is a nonohmic circuit element, the output voltage is not directlyproportional to the input voltage.According to the offset model, our diode conducts onlywhen the source voltage exceeds V D0 1.7 V. It meansthat, when the source voltage remains negative orpositive but below V D0 , the current does not flowthrough this circuit thus, from Ohm’s law, the voltagemeasured across the load resistor remains R L zero.BBBBBBThe screenshot below shows the output voltagemeasured across the load resistor R L 200 Ω in a circuit with an LED.BBNote that the overall shape of the output waveform agrees with our expectations: whenthe input voltage is negative or positive but below 1.7 V, the output is dead zero; whenthe input exceeds 1.7 V, the output looks like a cropped sine wave, similar toVOUT VIN (1.7 V ) . 2010 A. GanagoIntroduction Page 23 of 2423
24Lab 1: Introduction to Measurements with NI ELVIS IIFrom comparison between the input and output waveforms, one can estimate the value ofthe offset voltage as VD0 VIN, MAX VOUT, MAXThere are at least two ways to determine thenecessary numerical values of VIN, MAX andVOUT, MAX from the lab data:1. Measure the two peak values shownwith the arrows, using the Volts/Divvalue or directly with cursors of theoscilloscope2. Use the numerical readouts of bothpeak-to-peak amplitudes, along withVIN, peak-to-peakthe relationships: VIN, MAX (valid because the input is a sine wave)2and VOUT, MAX VOUT, peak-to-peak (because the output is zero or positive).The effect observed on the screenshot of page 22 is called rectification: the input voltageof alternating polarity is converted to the output voltage of constant polarity.The huge difference between VIN, MAX and VOUT, MAX results from the large V D0 and theBBsmall VIN, MAX . In practical rectifier circuits, VIN, MAX is larger, and V D0 is usually smaller.B 2010 A. GanagoIntroduction Page 24 of 24B
25Lab 1: Introduction to Measurements with NI ELVIS IIPre-LabThe pre-lab includes 6 problems. Make sure to complete them all before the lab.1. Identify which diagram on page 15 for the circuits with a resistor and an LED(repeated here for your convenience) corresponds to each 3-D picture of theprototyping board on pages 16–19. Write a brief explanation of how you foundwhich circuit is which, for diagram C.A 2010 A. GanagoBCPre-Lab Page 1 of 6D
26Lab 1: Introduction to Measurements with NI ELVIS IIPre-Lab (continued)2. This sketch showsconnections for themeasurements ofthe voltage acrossand the currentthrough a resistor.Note that allconnections here arebuilt “in the air”without aprototyping board.On the sketchbelow, show thesame connectionsusing nodes on theprototyping board; specifically, the power supply should be connected to the buslines on the left and the resistor should be connected to individual nodes on theright. Draw connections for the measurements of the voltage across and thecurrent through a resistor. 2010 A. GanagoPre-Lab Page 2 of 6
Lab 1: Introduction to Measurements with NI ELVIS IIPre-Lab (continued)3. Draw connections for the measurements of the voltage across and the currentthrough a forward-biased LED (be careful with the polarity). In this circuit, noload resistor is needed. The power supply should be connected to the bus lines onthe left and the LED should be connected to individual nodes on the right. 2010 A. GanagoPre-Lab Page 3 of 627
28Lab 1: Introduction to Measurements with NI ELVIS IIPre-Lab (continued)4. Draw connections for the circuit with an LED andresistor shown on this diagram. The power supplyshould be connected to the bus lines on the left,the resistor and LED should be connected to theindividual nodes on the right, and the voltmetershould measure the output voltage. 2010 A. GanagoPre-Lab Page 4 of 6
Lab 1: Introduction to Measurements with NI ELVIS IIPre-Lab (continued)5. From the screenshots for voltage division givenon pages 21 and 22, and from the circuits shownon these diagrams, calculate the ratios ofresistances R 1 /R 2 and R 2 /R 1 .BBBBBBBBCompare the results of your calculations with theratios of 100 Ω and 200 Ω resistances in the circuit.Calculate the percentage error:( Measured ) ( Expected ) 100%( Expected)Here, Measured stands for what you obtain fromexperimental data on pages 20 and 21; Expectedstands for what you found from the nominal valuesof 100 Ω and 200 Ω.For your reference, the peak-to peak voltages on thescreenshots are:Page 21Channel 04.270 VChannel 12.848 VPage 22Channel 04.267 VChannel 11.415 V 2010 A. GanagoPre-Lab Page 5 of 629
30Lab 1: Introduction to Measurements with NI ELVIS IIPre-Lab (continued)6. From the screenshot on page 23, obtained with the circuit with a resistor andLED, determine the offset voltage V D0 . Use both methods explained on page 24;discuss their accuracy.BBFor your reference, the peak-to peak voltages on the screenshot of Page 23 are:Channel 04.850 VChannel 1608.74 mVEnd of the pre-lab 2010 A. GanagoPre-Lab Page 6 of 6
Lab 1: Introduction to Measurements with NI ELVIS IIIn-Lab WorkNOTE 1:The
TABLE OF CONTENTS LAB 1 Introduction to Measurements with NI ELVIS II 1 LAB 2 Introduction to Multisim 47 LAB 3 Thevenin Equivalent Circuit; Beyond Parallel and Series 65 LAB 4 Operational Amplifiers (Op Amps) 93 LAB 5 Transient Responses of First-Order RC Circuits 139 LAB 6 Transient Responses of Second-Order RLC Circuits 159 LAB 7 AC Analysis 183
Contemporary Electric Circuits, 2nd ed., Prentice-Hall, 2008 Class Notes Ch. 9 Page 1 Strangeway, Petersen, Gassert, and Lokken CHAPTER 9 Series–Parallel Analysis of AC Circuits Chapter Outline 9.1 AC Series Circuits 9.2 AC Parallel Circuits 9.3 AC Series–Parallel Circuits 9.4 Analysis of Multiple-Source AC Circuits Using Superposition 9.1 AC SERIES CIRCUITS
Under the special circumstances of COVID-19, 7 labs (including Lab-0) from class 11 and 6 labs from class 12 are suggested. Lab-0 is mandatory. From the remaining 12 labs each school can select 5 labs ( 3 labs from class 11 and 2 from class 12 or vice versa ) List of Suggested Labs Class { 11
1 Introduction to RL and RC Circuits Objective In this exercise, the DC steady state response of simple RL and RC circuits is examined. The transient behavior of RC circuits is also tested. Theory Overview The DC steady state response of RL and RC circuits are essential opposite of each other: that is, once steady state is reached, capacitors behave as open circuits while inductors behave as .
/ Voltage Divider Circuits Voltage Divider Circuits AC Electric Circuits Question 1 Don’t just sit there! Build something!! Learning to mathematically analyze circuits requires much study and practice. Typically, students practice by working through lots of samp
circuits, all the current flows through one path. In parallel circuits, current can flow through two or more paths. Investigations for Chapter 9 In this Investigation, you will compare how two kinds of circuits work by building and observing series and parallel circuits. You will explore an application of these circuits by wiring two switches .
Lab Experiment 7 Series-Parallel Circuits and In-circuit resistance measurement Series-Parallel Circuits Most practical circuits in electronics are made up combinations of both series and parallel circuits. These circuits are made up of all sorts of components such as resistors, capacitors, inductors, diodes, transistors and integrated circuits.
TrueVector, ZoneAlarm, Integrity Desktop, Integrity Server, the Zone Labs logo and Zone Labs are . IMsecure from the Windows Start menu. Once launched, Zone Labs IMsecure Pro runs in the background. . If you want to uninstall Zone Labs IMsecure Pro, run the uninstall program included
Next Insurance CoverHound INSHUR INSHUR Next Insurance Next Insurance Next Insurance Slice Labs Slice Labs Zeguro Sure DataCubes Indio Technologies Zeguro CoverWallet CoverWallet Embroker Embroker Slice Labs Slice Labs Slice Labs CoverWallet 35 58 8.5 8.5 35 83 250 11.6 20 5 8 0 0 5 18.5 0 12.2 28 3.9 11.6 20 0 Amount ( , M)
