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Lab 7 Resonance Background Resonance is a characteristic of physical systems to oscillate at greater amplitude for some input frequencies. The frequencies where the output amplitude is the highest are known as resonant frequencies. Although it is possible for a system to have multiple resonant frequencies, our circuit will have only one. There are several excellent articles on Wikipedia about resonance in general and electrical resonance in particular. I would recommend reading the general article first. General: http://en.wikipedia.org/wiki/Resonance Electrical: http://en.wikipedia.org/wiki/Electrical_resonance In the previous lab, we used a resistor and capacitor to build a lowpass filter. In this lab, the resonant circuit will be for a bandpass filter. This could be used as part of a radio to tune to a particular frequency and attenuate signals at other frequencies. By using a variable capacitor, you could change the resonant frequency and tune to a different channel. It is not necessary to become too involved with the math behind resonance. Just understand the concept and how it could be applied. In our case the input signal is coming from the signal generator. We will measure the input signal on channel A and the output (across the resistor) on channel B. Equipment 1 USB Oscilloscope 1 Set of Leads (2 black, 1 gray) 1 Battery 1 Prototype Circuit Board 1 100 ohm Resistor 1 Capacitor 1 Inductor 1 Decade Box 1 Multimeter Wires, as needed Setup Open the Excel Spreadsheet. Obtain your scope from either the lab instructor OR the lab supervisor. Do NOT get it from anywhere else. Connect the scope to the USB cable from the computer. It may take a couple of minutes to add the device driver, so do this as soon as you can. Watch the video to see how to be sure. If it does not add the device successfully or you have an error on startup, please get my attention immediately. Connect the gray lead to the signal generator output of the scope. Connect the black leads to channel A and B of the scope. Start the scope application from the desktop shortcut. Note that there are tips in the spreadsheet for calculating the quantities required. Simply hover the mouse near the red triangle in the upper right of the cell. Furthermore, βxβ means MULTIPLY. Part I. Inductor The object of the first part of this lab is to determine the inductor value. Inductance is measured in Henries. Note that inductors are also called coils. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. Connect the circuit as shown at the front of the lab for the inductor measurement. Set the decade box to 5000 Ohms. Make sure that the other dials are all at 0. Set the multimeter to measure AC Voltage. AC, not DC. Set the signal generator frequency to the first frequency in the datasheet. Setup the voltmeter to measure the voltage across the decade box (as shown in the video). Adjust the amplitude of the signal generator until the voltmeter reads as close to 1 volt as you can obtain. Measure the output voltage of the signal generator. Measure the voltage of the coil. Record all of the voltages on the spreadsheet. Calculate the current (Hint: Ohms Law. You have the voltage across the resistor and the resistance). Calculate the inductive reactance. This is the coil voltage divided by the current. Calculate the inductance. π ππππ‘ππππ πΌπππ’ππ‘ππππ = 2π(πππππ’ππππ¦) Repeat steps 4 through 12 for the remaining frequencies. Average the inductances for your final value. NOTE: There should not be much variation in your inductances. If there is, you did something wrong. Part II. Capacitor 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. This is very similar to the first part, but you will use the second circuit for the capacitor. Set the signal generator frequency to the first frequency in the datasheet (for capacitors). Setup the voltmeter to measure the voltage across the decade box (as shown in the video). Adjust the amplitude of the signal generator until the voltmeter reads as close to 1 volt as you can obtain. Measure the output voltage of the signal generator. Measure the voltage of the capacitor. Record all of the voltages on the spreadsheet. Calculate the current (Hint: Ohms Law. You have the voltage across the resistor and the resistance). Calculate the capacitive reactance. This is the coil voltage divided by the current. Calculate the inductance. 1 πΆππππππ‘ππππ = 2π(π ππππ‘ππππ)(πππππ’ππππ¦) Repeat steps 2 through 10 for the remaining frequencies. Average the capacitances for your final value. NOTE: There should not be much variation in your capacitances. If there is, you did something wrong. Part III. Resonance Measurement 1. Setup the third circuit. Note that R is 100 ohms. 2. 3. 4. 5. Connect the signal generator as shown. Connect channel A of the scope to the output of the signal generator. Connect channel B of the scope to the resistor. Calculate the theoretical resonant frequency and enter it in the datasheet: 1 π ππ ππππππ πΉππππ’ππππ¦ = 2πβπΏπΆ 6. Determine the frequencies where you will take data. The equations for calculating these frequencies are shown in the datasheet. Please note that these are approximate in most cases. As long as you are more than 10 Hz from the resonant frequency, you can round it to the nearest 10 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. Hz or even more β the important point is to get a wide range of frequencies around the resonant frequency and some very close to the resonant frequency. Set the signal generator frequency to the first frequency in the datasheet (for resonance). Adjust the amplitude of the signal generator until channel A measures 1 volt. Watch the video to see how to use the cursors to make this measurement easier. Measure the amplitude of the resistor voltage (Channel B). Record your data and calculate the current. Repeat steps 7 through 10 for the remaining frequencies. Plot the frequency (x) versus the resistor voltage (y) Determine the frequency where your voltage peak occurs β this may require you to estimate between two points. This is the experimental resonant frequency and should be recorded on your datasheet. (Near the theoretical frequency). Calculate the percent difference between your theoretical and experimental resonant frequency. Change the hardware to Network Analyzer mode and re-run your data β but with a small frequency stepsize. Copy and paste your plot from the network analyzer to the datasheet. Part IV. Conclusion 1. Save your data file in dropbox (either in the morning or afternoon folder). The file name should be S[Section]S[Station] Lab 7 Resonance.xls, where [Section] is 1 for the morning and 2 for the afternoon and [Station] is your station number. Make sure that your name is included in the report. 2. Please note that dropbox does not always work. Verify that the instructor has your lab report BEFORE taking apart your circuit or returning your equipment. 3. Return the scope to either the instructor or lab supervisor. Do NOT leave it at the front or on the cart. If you are in the morning class, log off your computer and turn off your monitor. If you are in the afternoon class, shut down your computer and turn off your monitor. 4. Leave. Part V. Troubleshooting 1. No signal on scope: Check ALL of your wires. Make sure the vertical setting for the scope is not too high or too low. If you are using the signal generator, make sure that the signal generator amplitude is not 0 β it should be around 50. 2. Capacitance or Inductance changes with frequency: Usually indicates that you are not measuring voltage correctly β or your formula is wrong. 3. Resonance Circuit: Resistor Voltage does not change with frequency: Usually indicates that you hooked up the circuit or the scope probes wrong.