LABORATORY 3: Bridge Circuits, Superposition, Thevenin .
Alpha LaboratoriesECSE-2010NameLABORATORY 2: Bridge circuits, Superposition, Thevenin Circuits,and Amplifier CircuitsNote: If your partner is no longer in the class, please talk to the instructor.Material covered: Bridge circuits Voltage dividers Superposition Thevenin Circuits Amplifier CircuitsPart A: Resistive Bridge CircuitsVsR1R3RbridgeR2R40Wheatstone BridgeWheatstone Bridge:A Wheatstone Bridge can be used to measure the value of an unknown resistor. Itis a basic type of Ohmmeter. The bridge is shown on the in the above figure. Whenthe bridge is ‘balanced’, no current flows through the Rbridge resistor. If that is thecase, then both the left node and right node for that resistor must have the samevoltage. Additionally, since no current is flowing through Rbridge, the left andright paths can be treated as voltage divider circuits with two resistors in series.Circuit analysis then gives usVLeft R2VSR1 R 2and VRight R4VSR3 R 4Written by J. BraunsteinRensselaer Polytechnic InstituteModified by S. Sawyer Spring 2020: 1/24/2020Troy, New York, USA1
Alpha LaboratoriesECSE-2010NameAgain VLeft VRight, so we can set these two expressions equal, perform somealgebra and obtain a relationship for the resistors when the bridge is balanced (nocurrent through Rbridge) asR1 R3 R2 R4If one of the resistors is unknown, R4 for example, we can then use the bridge tofind that value. Holding R1 and R3 fixed, we can vary R2 until we measure zerovoltage drop (no current) across Rbridge. Once we have found that value for R2,we apply the above expression and determine R4. Thus, we have an Ohmmeter.A1: Wheatstone Bridge and Parametric AnalysisWe will use the Wheatstone bridge to determine the resistance of an unknownresistor. Pick up the unknown resistor on the podium (You can of course measurethe resistor directly so that you can verify your experimental results). In theexperiment, a potentiometer is the variable resistor. By adjusting the potentiometersuch that the voltage across Rbridge is zero, the value of Runknown can bedetermined. In the LTSpice simulation, parametric analysis allows varying resistorvoltages.1) Determine the symbolic expression for Runknown when Vbridge is zero(see laboratory introduction).2) Using values of R1 2.2kΩ, R2 4.7kΩ, Rbridge 100kΩ, and Runknown ?. R3 is a 10K potentiometer. Note: Resistors were renamed by rightclicking the given name like R4 and writing “Runknown.”3) In LTSpice, plot Vbridge vs Rpotentiometer where Rpotentiometer is aparametric value. In the LTpice simulation, follow the procedure to performa parametric analysis (details below). Using the plot and a differentialvoltage marker, identify the Rpotentiometer value that results in Vbridge 0. The LTSpice schematic is shown below.Written by J. BraunsteinRensselaer Polytechnic InstituteModified by S. Sawyer Spring 2020: 1/24/2020Troy, New York, USA2
Alpha LaboratoriesECSE-2010Namea) Parametric analysis: The .step command performs repeatedanalysis while stepping through specified values of a modelparameter, global parameter or independent source.1. Define the component parameter by right clicking theresistor R3 and entering “{X}” for the value of resistance(as shown in the diagram below). Note: Runknown isgiven the arbitrary value of 1k so the simulation can run.2. Add a .step command using a SPICE directive (press “s”)which specifies the steps for a parameterExample: “.step param X 1 10k 1k” steps the parameter Sfrom 1 to 100k in 1k increments.Written by J. BraunsteinRensselaer Polytechnic InstituteModified by S. Sawyer Spring 2020: 1/24/2020Troy, New York, USA3
Alpha LaboratoriesECSE-2010NameYou may change the increments to a value that will giveyou more points.3. Add .op in the SPICE directive. (Click “.op” far right ontoolbar and add .op then place anyway on circuit)4. Run the simulation (click “Running man”) go to “DC oppnt tab” and click “ok”5. Run the simulation again. (click “Running man”). Thesimulation pop up window should show but withouttraces with resistor values as the x axis.6. To specify the differential probes across Rbridge, clickthe node to the left of Rbridge (a red probe shouldappear), hold and click the right (a black probe shouldappear).7. The trace V(N00n, N00nx) should appear (where n issome number label of node).8. Now find the variable resistor value when VRbridge 0V. Use the cursor function by clicking the trace label atthe top of the diagram “V(N00n, N00nx)”. You can dragthe cursor along the curve by clicking and holding wherethe horizontal and vertical lines meet.9. Include the screenshot/plot of the balanced bridge pointwith clear labels in your report.10. Use the equations in the introduction to calculate theRunknown value from a balanced bridge circuit.Written by J. BraunsteinRensselaer Polytechnic InstituteModified by S. Sawyer Spring 2020: 1/24/2020Troy, New York, USA4
Alpha LaboratoriesECSE-2010Name4) Build the physical circuit using a 10kΩ Potentiometer, as shown in thecircuit below. Note, one leg of the potentiometer is floating. Turn thepotentiometer such that the measured Vbridge 0. Once you find that value,use an Ohmmeter to measure the resistance of the potentiometer (they are onthe center table). Be careful not to turn your potentiometer and make sureyou disconnect the circuit so you don’t measure the other resistors. Compareyour result to part 0Compare the LTSpice simulated value to the value obtained from your physicalcircuit. Compare both to your mathematically calculated value.PART A: Proof of Concepts listProve the concept of a balance bridgeInclude a screen shot of your results in your Proof of Concept Report. Proofof Concept example and template can be found herehttps://ecse.rpi.edu/ ssawyer/CircuitsFall2019 all/Labs/Circuits OmegaLabDocs/04 Deliverables/03 ProofofConcepts.docxWritten by J. BraunsteinRensselaer Polytechnic InstituteModified by S. Sawyer Spring 2020: 1/24/2020Troy, New York, USA5
Alpha LaboratoriesECSE-2010NamePSpice – Differential vs Nodal Measurements:In the simulations we have done with LTSpice, we have used nodalmeasurements which provides the voltage at a node relative to thedesignated ground. In order to determine the voltage across a component, wethen found the voltage difference between the two nodes associated with thatcomponent. In practice, measuring the voltage across a component whereneither of the nodes is connected to ground can be problematic. To safelymake those kind of measurements, we use differential probes. Fortunatelyfor us, the Discovery Board only makes differential measurements.Part B: Analog Discovery Board Variable Sources and SuperpositionDiscovery Board – Variable Sources:In the last laboratory, we used the fixed 5V supply. This source isconstant. If we want to vary the source voltage, we need to use thefunction generator channels instead. There are two channels available,labelled W1 (yellow wire) and W2 (yellow striped wire) on theDiscovery Board.To access the software, when you bring up the Waveforms main menua. Select WaveGen, the second item under the Welcome settings.b. We will want to use both Channels at various times during the course.(When we use only one Channel, you can turn off the other one if youwant more space on your Desktop.) To enable both Channels, click on“Channels” pull down menu. Select both Channel 1 (AWG1) andChannel 2 (AWG2) such that there are check marks by both. Yourwindow will probably refresh.c. We will use DC sources for now. Select the straight line from thecolumn of waveform shapes (it should be the first icon).d. Go to the Offset pull down menu and set the DC voltage level.e. To output the voltage on the W1 (AWG1) wire, you need to selectmake sure the Channel is both Enabled and running. In the upper rightof the window, make sure “Enabled” is checked. Click Run.f. Repeat steps c.-f. for AWG2Written by J. BraunsteinRensselaer Polytechnic InstituteModified by S. Sawyer Spring 2020: 1/24/2020Troy, New York, USA6
Alpha LaboratoriesECSE-2010NameB1: Two Sources/SuperpositionConstruct the following circuit. You will need to use both source channels (AWG1and AWG2) on the Discovery Board to build the circuit. Note: The diagram belowwas created in PSpice but please duplicate this in LTSpice.R3R11kV V1R22.2k2.2kV-V201) Analytically, obtain an expression for the voltage across R3 in terms of thevoltages V1 and V2. You should use superposition in your analysis (forpractice). You are looking for an expression of the formVR3 a(V1) b(V2)where a and b are coefficients determined by your circuit analysis.2) Build the circuit using the AWG wires (yellow and striped yellow) for thesources. Set V1 to 2.5 [V] and plot the voltage across R3 as a function of V1for 0 V1 4Volts (pick a few values for V1 in that range and measure R3).3) Repeat with V2 set to -2.5 [V], again plotting the voltage across R3 as afunction of V1 for 0 V1 4Volts.4) For both plots, compare your results with a plot of your expression from part1).PART B: Proof of Concepts listProve the superposition conceptInclude screen shots of your LTSpice, Experimental, and Analyticalresults in your Proof of Concept Report.Written by J. BraunsteinRensselaer Polytechnic InstituteModified by S. Sawyer Spring 2020: 1/24/2020Troy, New York, USA7
Alpha LaboratoriesECSE-2010NamePart C: Amplifier CircuitsOverall notes:TL072CP chip (dual op-amp):The data sheet for the chip can be found online from any number of sites. One isprovided below (it is long and contains several chips)http://www.ti.com/lit/ds/symlink/tl071.pdfA copy of the pin connections is shown belowThere are two op-amps on the chip, indicated by the ‘1’ and the ‘2’ pin labels. Forexample, 1IN is the V and 1IN- is the V- of the first op-amp, with 1OUT beingthe Vout. Power connections are Vcc at pin 8 and –Vcc at pin 4.Written by J. BraunsteinRensselaer Polytechnic InstituteModified by S. Sawyer Spring 2020: 1/24/2020Troy, New York, USA8
Alpha LaboratoriesECSE-2010NameIn LTSpice, you can use the “UniversalOpamp2” component or “opamp”component. The “opamp” component does not have power levels and is assumedideal. It is useful for simplified drawings, but your simulations will not be the sameas the experiments. As such, please use the “UniversalOpamp2” component, withLTSpice details shown below.A summary of the connections for LTSpice “UniversalOpamp2” component: input, - (left), inverting inputinput, (left), non-inverting input-(bottom), V-: Negative power, 9 V (top), V , Positive power, 9VRight node: Vout, output voltageThe DC power sources will be the 9 Volt batteries that you have in your kit. Notethe orientation of the batteries when you connect the leads.Again, for LTSpice simulations, the circuits on the following pages indicate how topower a uA741 op-amp. The input and output connections depend on the circuit.Written by J. BraunsteinRensselaer Polytechnic InstituteModified by S. Sawyer Spring 2020: 1/24/2020Troy, New York, USA9
Alpha LaboratoriesECSE-2010NameAn example of an op-amp reaching saturation is shown below. The input is asinusoidal. If the op-amp was ideal, the output would also be a sinusoid with ascaled amplitude. However, saturation occurs and the output voltage cannot exceed(positive or negative) the source voltages.C1: Amplifier CircuitsBuild the comparator circuit shown above. V and V- will be your inputs and Voutwill be the output. In Analog Discovery experiments, use the TL072CP chip (orWritten by J. BraunsteinRensselaer Polytechnic InstituteModified by S. Sawyer Spring 2020: 1/24/2020Troy, New York, USA10
Alpha LaboratoriesECSE-2010Nameequivalent. You only need one amplifier for this part). In the LTSpice simulationsuse the “UniversalOpamp2” component.1) We will use W1 and W2 for out amplifier inputs. The Voltmeter channelsinputs will act as the RLarge.a. Connect W1 (yellow wire) to the V op-amp input and ground(orange striped wire) to the V- op-amp input.b. Ground the V- op-amp input.c. To compare input voltage to output voltage, use the Voltmeter tomeasure the output voltage (refer to Lab 1).d. Using the Discovery board, set the W1 output voltage to DC modeand check the output voltage of the op-amp for the following inputvoltages (This chart and others below should end up in your Proof ofConcepts report )Vin [V]210-1-2Vout [V]e. Comment on your results and expectations when Vin 0 V.Written by J. BraunsteinRensselaer Polytechnic InstituteModified by S. Sawyer Spring 2020: 1/24/2020Troy, New York, USA11
Alpha LaboratoriesECSE-2010Name2) In LTSpice, build the comparator circuit using a UniveralOpamp2 op-amp.You will need to add a load resistor at the output node since LTSpice doesnot allow nodes to float (be unconnected). A 1E6Ω load is fine (useexponential notation since M in LTspice is 1E-3). Compare the outputvoltages between LTSpice and Analog Discovery. You should see somedifferences, what causes these differences?Vin [V]210-1-2Vout [V]Written by J. BraunsteinRensselaer Polytechnic InstituteModified by S. Sawyer Spring 2020: 1/24/2020Troy, New York, USA12
Alpha LaboratoriesECSE-2010Name3) Remove the ground connection at V- and use AWG2 (W2, yellow stripedwire) to provide a 1.5V input at the V- opamp input. Effectively, your circuitwill behave as if there was a 1V source at the negative input, as shownabove.If you didn’t use AWG2 for the 1.5V input, what type of circuit can you useto produce the 1.5V? (Consider the 5V Discovery board connection fromLab 1.)a. Repeat the output voltage measurements againVin [V]210-1-2Vout [V]Written by J. BraunsteinRensselaer Polytechnic InstituteModified by S. Sawyer Spring 2020: 1/24/2020Troy, New York, USA13
Alpha LaboratoriesECSE-2010Name4) Again, compare your Analog Discovery experiment to the LTSpicesimulation.Vin [V]210-1-2Vout [V]Inverting Op-amp, Non-inverting op-ampBuild and test the following circuits. (Again, this schematic was created in PSpice.Recreate in LTSpice. Remember the power connections. They have been removedto simplify the drawing but they must still be included in the circuit). 0OS22uA741-4OUTOS15Vout61V-VinR1U2V 375) Inverting Op-amp with a gain of -2.5R2a. When considering the saturation voltage, what is the maximum Vinsuch that Vout -2 Vin? Choose appropriate resistors.Vin [V]5310-1-3-5Vout [V]Written by J. BraunsteinRensselaer Polytechnic InstituteModified by S. Sawyer Spring 2020: 1/24/2020Troy, New York, USA14
Alpha LaboratoriesECSE-2010Nameb. Build the circuit in LTSpice and verify that simulation is constantwith experiment (within the limits of the respective saturationvoltages).6) Non-Inverting Op-amp with a gain of 4Build, simulate and test a circuit you create.Come up with a simple chart of inputs and record output.PART C: Proof of Concepts listProve the function of a comparator op amp circuit (0V reference)Prove the function of a comparator op amp circuit (1.5V reference)Prove the function of an inverting op amp circuit (gain -2.5)Prove the function of a non-inverting op amp circuit (gain of 4)Include screen shots of your LTSpice, Experimental, and Analyticalresults in your Proof of Concept Report.Part D: Alpha Laboratories Applications1) You will have an opportunity in class/lab to discuss and design acircuit that includes components learned throughout Unit 1. Drawhigh level design blocks including input and output for each blockbased on the Building Block components Lab Requirements: BuildingBlocks (scroll down to page 10) that include:1. at least one input stage components,2. two Milestone 1 stage components,3. and at least one output stage component.2) Simulate each individual building block and describe how it shouldbehave in your circuit.Each high level design block from 1) should have an associatedschematic created in LTSpice or equivalent. Then the simulationoutput should be shown. Highlight how the output you are showingbecomes the correct input for the next stage. (You do not have toconnect the building blocks into one working simulation, but TRY tosee what happens, comment on this!!!)Written by J. BraunsteinRensselaer Polytechnic InstituteModified by S. Sawyer Spring 2020: 1/24/2020Troy, New York, USA15
Alpha LaboratoriesECSE-2010NamePART D: Proof of Concepts listProve that your individual design blocks with your given input resulted in thecorrect output for the next stage of your design. (You can make assumptionsand replacements for sensors like an LDR is analogous to a potentiometer with avarying resistance).Include screen shots of your LTSpice, Experimental, and Analyticalresults in your Proof of Concept Report. (You do not need to build thiscircuit). Be sure to discuss what happened when you tried to connect yourbuilding blocks. Did it work? Did it not work as expected? If not, speculatewhy it didn’t work?EXTRA CREDIT: Write in your metacognition journal (instructions and templatein the link below, feel free to continue to edit a Google doc throughout the courseto add entries).https://ecse.rpi.edu/ ssawyer/CircuitsFall2019 all/Labs/Circuits OmegaLabDocs/04 Deliverables/05 Circuits Metacognition%20and%20Reflections.docxSUMMARY of ConceptsConcept List that must be accounted for in your Proof of ConceptsPART A:1. Prove the concept of a balance bridgePART B:1. Prove the superposition conceptPART C:1. Prove the function of a comparator op amp circuit (0V reference)2. Prove the function of a comparator op amp circuit (1.5V reference)3. Prove the function of an inverting op amp circuit (gain -2.5)4. Prove the function of a non-inverting op amp circuit (gain of 4)PART D: Alpha Labs Applications1. Prove that your individual design blocks with your given input resulted in thecorrect output for the next stage of your design.Written by J. BraunsteinRensselaer Polytechnic InstituteModified by S. Sawyer Spring 2020: 1/24/2020Troy, New York, USA16
1 LABORATORY 2: Bridge circuits, Superposition, Thevenin Circuits, and Amplifier Circuits Note: If your partner is no longer in the class, please talk to the instructor. Material covered: . experiment, a potentiometer is the variable resistor. By adjusting the potentiometer
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
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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 .
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.
Hammersmith Bridge Suspension Bridge, 2 piers (1887) 210m 13m No, on road only Steps footway/ road Narrow traffic lanes, 20000 veh/day 3,872 1,923 5,795 Barnes Footbridge Deck arch bridge, 2 piers (1895) 124m 2.4m No, foot bridge only Steps Runs alongside railway bridge 1,223 256 1,479 Chiswick Bridge Deck arch bridge, 2 piers (1933) 185m 21m .
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EXPLANATION Simple sound wave Resultant wave C. Waves out of phase Figure 2. - Superposition of simple soundwaves. (Modified from Jeans, 1968.) APPLICATION OF SUPERPOSITION TO A SIMPLE HYDROLOGIC SYSTEM Just as the amplitudes of two simple waves were added together in figure 2 .to obta
FoNS guidelines for writing a final project report July 2012 1 Guidelines for writing a final project report July 2012 FoNS has a strong commitment to disseminating the work of the project teams that we support. Developing and changing practice to improve patient care is complex and we therefore believe it is essential to share the outcomes, learning and experiences of those involved in such .
