28CHAPTER3.ANALYSISTECHNIQUES1.Recalculate thefour node voltages using the nominal resistor valuesand the measured values for Isrei, Isre2, and Vsc. Create a data ta-ble to compare these values with your analytical results in terms ofdifferenceand relative difference.2. Measure and record the five resistances Ri to R4.3. Recalculate the four node voltages using the measured resistor valuesand the measured values for Isrcl, Isrc2, and VsRc. Create a data ta-ble to compare these values with your analytical results in terms ofdifference and relative difference.4. Summarize your results: What level of agreement did you achievebetween the analytical solution and the physical measurements?
28 CHAPTER 3. ANALYSIS TECHNIQUES 1. Recalculate the four node voltages using the nominal resistor values and the measured values for Isrc1, Isrc2, and VSRC. Create a data table to compare these values with your analytical results in terms of difference and relative difference. 2. Measure and record the five resistances R1 to R4. 3. Recalculate the four node voltages using the measured resistor values and the measured values for Isrc1, Isrc2, and VSRC. Create a data table to compare these values with your analytical results in terms of difference and relative difference. 4. Summarize your results: What level of agreement did you achieve between the analytical solution and the physical measurements?
293.2.MESH-CURRENTMETHOD(3-2)3.2Mesh-Current Method (3-2)Apply themesh-current method to determine the mesh currents Ii to I4.From these results determine the voltage across the current source Vi.R4R3R1R27>NsrI3vsrcFigure3.2:Circuit forProblem3.2Use these component values:·IsRC=12.5mA.VsRC=15VR=5.6k2,Rz=2.2k2,R3=3.3k2,andR4=4.7k2NI Multisim MeasurementsEnter thecircuitof Figure3.2intoNIMultisim.Use"MeasurementProbes"and interactive simulation to measure the four mesh currents. Use the mul-timeter or a measurement probeto displaythe voltage acrossthe currentsource.·Place themeasurement probe on wires that carry only a single meshcurrent; remember that many of the resistors carry two mesh currents
3.2. MESH-CURRENT METHOD (3-2) 29 3.2 Mesh-Current Method (3-2) Apply the mesh-current method to determine the mesh currents I1 to I4. From these results determine the voltage across the current source V1. Figure 3.2: Circuit for Problem 3.2 Use these component values: • ISRC = 12.5 mA • VSRC = 15 V • R1 = 5.6 kΩ, R2 = 2.2 kΩ, R3 = 3.3 kΩ, and R4 = 4.7 kΩ NI Multisim Measurements Enter the circuit of Figure 3.2 into NI Multisim. Use “Measurement Probes” and interactive simulation to measure the four mesh currents. Use the multimeter or a measurement probe to display the voltage across the current source. • Place the measurement probe on wires that carry only a single mesh current; remember that many of the resistors carry two mesh currents
30CHAPTER3.ANALYSISTECHNIQUESNIMultisimvideotutorials:: Measure DC mesh current with a measurement probe:http://youtu.be/1KOLcTNroxI? Measure DC node voltage with a measurement probe:http://youtu.be/svNGHA2-uK4·Measure DC voltage with a voltmeter:http://youtu.be/xLyslyikUwsNImyDAQMeasurementsBuild the circuit of Figure 3.2 on the previous page. Use the myDAQ DMM(digital multimeter) as an ammeter to measure each of the four mesh cur-rents; use the DMM voltmeter to measure the voltage across the currentsource..Place the resistors to match the resistor orientations shown in Fig-ure 3.2 on the preceding page. Use 1-inch jumper wires to establishthetopconnectionsbetweentheresistorstofacilitatemeasurementofthe mesh currents.. Implement the voltage source VsRc with the NI myDAQ-15V powersupply.. Implement the current source IsRc according to the circuit diagramof Figure B.4 on page 166. Use a 100 2 resistor for the adjustmentresistor R..Measure IsRc with themyDAQDMM ammeter and confirm that thecurrent is close to 12.5 mA. If you desire more precision, use a 1.0 ks2potentiometer for the adjustment resistor.NI myDAQ video tutorials:. DMM voltmeter:http://decibel.ni.com/content/docs/Doc-12937.DMMammeter:http://decibel.ni.com/content/docs/Doc-12939
30 CHAPTER 3. ANALYSIS TECHNIQUES NI Multisim video tutorials: • Measure DC mesh current with a measurement probe: http://youtu.be/lK0LcTNroXI • Measure DC node voltage with a measurement probe: http://youtu.be/svNGHA2-uK4 • Measure DC voltage with a voltmeter: http://youtu.be/XLyslyikUws NI myDAQ Measurements Build the circuit of Figure 3.2 on the previous page. Use the myDAQ DMM (digital multimeter) as an ammeter to measure each of the four mesh currents; use the DMM voltmeter to measure the voltage across the current source. • Place the resistors to match the resistor orientations shown in Figure 3.2 on the preceding page. Use 1-inch jumper wires to establish the top connections between the resistors to facilitate measurement of the mesh currents. • Implement the voltage source VSRC with the NI myDAQ -15V power supply. • Implement the current source ISRC according to the circuit diagram of Figure B.4 on page 166. Use a 100 Ω resistor for the adjustment resistor R. • Measure ISRC with the myDAQ DMM ammeter and confirm that the current is close to 12.5 mA. If you desire more precision, use a 1.0 kΩ potentiometer for the adjustment resistor. NI myDAQ video tutorials: • DMM voltmeter: http://decibel.ni.com/content/docs/DOC-12937 • DMM ammeter: http://decibel.ni.com/content/docs/DOC-12939
313.2.MESH-CURRENTMETHOD(3-2)FurtherExploration withNImyDAQSome types of digital-to-analog converters require binary-weighted cur-rents that can be selectively summed together. With a slight modification toyour existing circuit topology you can redesign it to produce mesh currentsthat meet your own specifications such as those required by the digital-to-analogconverter1. Consider the modified circuit of Figure 3.3. Apply mesh-current anal.ysis to write a set of equations in terms of the indicated currents andresistorvalues.2.Chooseresistorvaluesthatwill establishthebinary-weighted currentvaluesI2=IsRC/2,I3=IsRC/4,I4=IsRC/8,andI5=IsRC/16,and that will limit the current sourcevoltageVito5volts or less.3. Note: The standard parts list of Appendix A on page 159 includesresistorsthat are closeto the calculated values you need.4.Buildthecircuitand measureall fivemeshcurrentsItoIs5.MeasurethecurrentsourcevoltageVi.6. Evaluate your results to determine how well the circuit produces thedesiredbinary-weighted currents.I2I4I,I,Is≥R2R1R3>R4R5Figure 3.3: Modified circuit for Problem 3.2 to produce binary-weightedcurrents
3.2. MESH-CURRENT METHOD (3-2) 31 Further Exploration with NI myDAQ Some types of digital-to-analog converters require binary-weighted currents that can be selectively summed together. With a slight modification to your existing circuit topology you can redesign it to produce mesh currents that meet your own specifications such as those required by the digital-toanalog converter. 1. Consider the modified circuit of Figure 3.3. Apply mesh-current analysis to write a set of equations in terms of the indicated currents and resistor values. 2. Choose resistor values that will establish the binary-weighted current values I2 = ISRC/2, I3 = ISRC/4, I4 = ISRC/8, and I5 = ISRC/16, and that will limit the current source voltage V1 to 5 volts or less. 3. Note: The standard parts list of Appendix A on page 159 includes resistors that are close to the calculated values you need. 4. Build the circuit and measure all five mesh currents I1 to I5. 5. Measure the current source voltage V1. 6. Evaluate your results to determine how well the circuit produces the desired binary-weighted currents. Figure 3.3: Modified circuit for Problem 3.2 to produce binary-weighted currents
32CHAPTER3.ANALYSISTECHNIQUES3.3Superposition (3-4)1. Apply the superposition method to determine the current I and thevoltage VB,i.e.,find the current IAidueto the current source Ii actingalone, the current IA2 due to the voltage source V2 acting alone, andthe current IA3 due to the voltage source V3 acting alone, and thenevaluate the sum IA = IA1 + IA3 + IA3. Make use of current dividersand voltage dividers as much as possible.2. Use the superposition method to determine the voltage V3.Apply the node-voltage method to find IA and VB,and then comparetheseresultstothoseofthesuperpositionmethod.Ve十R3M>R2R11312Figure3.4:CircuitforProblem3.3Usethesecomponentvalues:I1=1.84mA.V2=3.0Vand V3=4.9V Ri = 1.0 k2, R2 = 2.2 k2, and R3 = 4.7 k2
32 CHAPTER 3. ANALYSIS TECHNIQUES 3.3 Superposition (3-4) 1. Apply the superposition method to determine the current IA and the voltage VB, i.e., find the current IA1 due to the current source I1 acting alone, the current IA2 due to the voltage source V2 acting alone, and the current IA3 due to the voltage source V3 acting alone, and then evaluate the sum IA = IA1 + IA3 + IA3. Make use of current dividers and voltage dividers as much as possible. 2. Use the superposition method to determine the voltage VB. 3. Apply the node-voltage method to find IA and VB, and then compare these results to those of the superposition method. Figure 3.4: Circuit for Problem 3.3 Use these component values: • I1 = 1.84 mA • V2 = 3.0 V and V3 = 4.9 V • R1 = 1.0 kΩ, R2 = 2.2 kΩ, and R3 = 4.7 kΩ