Lab8
.pdf
School
University of California, Davis**We aren't endorsed by this school
Course
EEC 100
Subject
Electrical Engineering
Date
Dec 17, 2024
Pages
7
Uploaded by LieutenantIron15748
Laboratory 8: Laplace Transform Analysis Techniques
Introduction: OverviewIn this lab, you will observe the behavior of a circuit with a switch. More specifically, you will investigatethe initial value, final stable value, minimum value, and the time it takes to reach the minimum value forone of the resistor voltages of the circuit. In the prelab, you will calculate what your expected results shouldbe. In the simulation, you will observe the circuit behavior in ideal circumstances. In the experiment, youwill observe what happens in the real-world after a switching action happens.1Prelab1. Determine V(t) of the circuit shown in Figure 1 fort≥0, given that the switch is opened att= 0 afterhaving been closed for a long time. Use the following component values: Vs= 5V, Rswitch= 270Ω,R1= 470Ω, R2= 100Ω, Rw= 90Ω, C = 1.0 F, and L = 33mH.2. Plot V(t) from 0ms to 5ms using Excel, MatLab or other computer tools (the plot can also be by handon graphing paper if such tools are not available).Figure 1:Prelab Circuit 1.3. Determine the following values for V(t):Initial value V(t) (before the switch opened)Final/Stable value of V(t) (after the switch opened)Minimum value of V(t)Time to reach the minimum value of V(t) from the moment the switch opened.1
2SimulationIn the simulation and measurement parts of this lab, we turn the switch shown in Figure 1 on and offperiodically instead of keeping it closed till t=0 and then opening it. The reason is that if we open it justone time, the measured V(t) would be zero quickly after we open the switch and we would not be able torecord the results. We select the period of ON-OFF switching in simulation and measurement parts longenough to emulate long-term opening and closing behavior of the circuit shown in Figure 1.1. Create a new project.2. Enter the circuit in Figure 3 through schematic editor using the provided values.To emulate theswitching behavior, use “S” component from “analog.olb”.The component is a voltage controlledswitch and it has two control inputs.Once the control input meet certain differential voltage level(Vd=V+−V−), it will close or open the switch (depending on how the component is configured). Wewill be using “S” switch’s following parameters with the specified values,ParameterDescriptionValueVONIfVdis above this value, the switch is closed.5VVOFFIfVdis below this value, the switch is opened.0VRONIfSwitchis closed, the switch is acted as a resistor of this value.270ΩThe capacitor requires time to charge up, to emulate the initial condition, close the switch att= 0msby setting “VPULSE” so thatV1= 0 andV2= 5 with TD=0 (0 delay), this will make V1 = 5V att=0. Set pulse width to 3ms so that “VPULSE” transitions fromV2= 5 toV1= 0 at 3ms later toopen the switch. The voltage response after 3ms and before 6ms(when the switch closes again) is ourdesired transient waveform.2
Figure 2:Simulation Circuit Configuration.3. Create new simulation profile. Make a transient analysis with run time 6 ms and maximum step sizeof 1s. Run the simulation.4. In the “PSpice/AD” window, use voltage probe to measure the input voltage. Verify the step changeat 3ms. Print the plot.5. Under the same plot, use voltage probe to measure the voltage Vs. Find the steady state voltage beforethe switch is opened using cursor. Print the plot and include it in the laboratory report. Explain whythe voltage after the switch is not a perfect square wave right (ie. why is there ringing?).6. Under the same plot, use voltage probe to measure the capacitor voltage Vc. Find the steady statevoltage before the switch is opened using cursor. Verify this value against the theoretical value. Printthe plot and include it in the laboratory report.7. Under the same plot, use differential voltage probe to measure the voltage across R1. Using cursor,find the initial and final voltage across “R1”. Find the minimum voltage across “R1” and also the timeit takes to reach the minima. Print the plot and include it into the laboratory report.3
3Experimentation1. Construct the circuit of Figure 4 using the following components , the power supply, function generator,and oscilloscope:One normally-open Switch 1 contained in the Texas Instruments CD4066B quad analog switchdescribed in Appendix VII. Use it in the place of the switch.Ignore Rswitch in the circuitconnection since it is the on-resistance (Ron) of the CD4066B analog switch (We don’t need toexternally place a Rswitch because it is already included inside chip CD4066B).Figure 3:Pinout of CD4066 chip powered by the DC Power supply.1.0F electrolytic capacitor.33mH inductor. Ignore Rw since it is the internal wire resistance of the inductor(We don’t needto externally place a Rw because it is already included inside the inductor).One 100Ω resistor and one 470Ω resistor.2. Build the circuit of Figure 4 on breadboard.3. Connect Channel 1 of the oscilloscope to the positive side of R2(100Ω) and Channel 2 of the scope tothe negative side of R2. You will use theMathfeature to subtractCh1 - Ch2to display the voltageacross R2, i.e. V(t).This is a tricky measurement to take accurately because the Math feature has poor resolution whenmeasuring tiny (mV) differences in signals when the signals themselves are on the order of Volts(thousands of millivolts).To improve the resolution of the Math waveform, you need to zoom thevertical scale of both channels of the oscilloscope as much as you can, zooming in and adjustingvertical position to focus on the sections of the waves you are interested in measuring.4
4.Use the fine vertical scaling by pushing the scaling knob to switch to Fine mode.Thevertical scaling should bethe samefor both channels and bebetween 76 mV/Div and 180mV/Divfor the best possible resolution on the Math waveform.5. Set theMathScale to50mV. Ask your TA for help with this measurement if you need it.Figure 4:Schematic of switching RLC circuit.6. On the oscilloscope, ensure both channels are DC coupled.7. Keep the output of both the power supply and function generator off until you have setup all parametersand double-checked the wiring against the schematic.8. On function generator, create asquarewaveform to control the switch.a Set the amplitude to be5 Vpp. This generates a square wave that goes from -2.5 V to 2.5 V.b Set the DC offset to be+2.5 V. This shifts the waveform upwards of 2.5 volts. Instead of goingfrom -2.5V to 2.5V, now the waveform goes from 0V to 5V.c Set the frequency to be100 Hz. Set the output load of the function generator toHigh Z.9. Connect the output of function generator to the switch control pin on chip CD4066B.10. Supply5V DCvoltage using the power supply to both VDD= 5V and to the input of Switch 1.11. After checking the connection, turn on power supply and signal generator.12. Display V(t) from 0 to 5 mson the oscilloscope.13. Use the cursor on Scopy to measure the following values for v(t):5
Initial value V(t) (before the switch opened)Final/Stable value of V(t) (after the switch opened)Minimum value of V(t)Time to reach the minimum value of V(t) from the moment the switch opened.6