ET1210: Module 5 Inductance and Resonance

Transcription

1 Part 1 Inductors Theory: When current flows through a coil of wire, a magnetic field is created around the wire. This electromagnetic field accompanies any moving electric charge and is proportional to the magnitude of the current. If the current changes, the electromagnetic field causes a voltage to be induced across the coil, which opposes the change. This property, which creates a voltage to oppose a change in current, is called inductance. Inductance is the electrical equivalent of inertia in a mechanical system. It opposes a change in current in a manner similar to the way capacitance opposes a change in voltage. This property of inductance is described by Lenz's law. According to Lenz's law, an inductor develops a voltage across it that counters the effect of a change in current in the circuit. The induced voltage is equal to the inductance times the rate of change of current. That is, Where ΔI is the change in current, t the time in seconds and L is the inductive properties of the coil. Inductance (L) is measured in Henries. One Henry is defined as the quantity of inductance present when one volt is generated as a result of a current changing at the rate of one ampere per second. Coils that are made to provide a specific amount of inductance are called inductors. When inductors are connected in series, the total inductance is the sum of the individual inductors. This is similar to resistors connected in series. Figure 5-1 1

2 Likewise, the formula for parallel inductors is similar to the formula for parallel resistors. Figure 5-2 Unlike resistors, an additional effect can appear in inductive circuits. This effect is called mutual inductance and is caused by the interaction of the magnetic fields. The total inductance can be either increased or decreased due to mutual inductance. Inductive circuits have a time constant associated with them, just as capacitive circuits do, except the rising exponential curve is a picture of the current in the circuit rather than the voltage as in the case of the capacitive circuit. Unlike the capacitive circuit, if the resistance is greater, the time constant is shorter. The time constant is found from the equation: Where τ represents the time constant in seconds, L is in Henries and R is in Ohms. Inductor Identification There are many types of inductors available with a wide variety of specifications. Inductors are not polarized. However coupled inductors (transformers) have a phase relationship that may be important. The inductance value of an inductor is typically marked on the body of the inductor or indicated by a color code scheme similar to the resistor color code scheme. In this experiment, you will witness the effects of inductor operation and examine the time constant of an RL circuit. Preparation: 1. Obtain the following items from your lab equipment. o mydaq 9V Protoboard 2. Obtain the following items from your lab kit. o 7H Iron Core Inductor (See Image 1 of the ET1210.W 5.Lab.Images PowerPoint for 2

3 greater detail.) ET1210: Module 5 Inductance and Resonance o Neon bulb (NE-2) (See Image 1 of the ET1210.W 5.Lab.Images PowerPoint for greater detail.) o SPST switch o 9V battery (not part of the kit) 3. If the SPST switch doesn't have wires attached, you should solder on some short leads, to plug into the breadboard. 4. Examine the following circuit. Figure 5-3 o When S1 is closed, the +12V will be applied to the Neon bulb and parallel 7H Iron Core inductor. 12V is not enough voltage to light the neon gas, so the bulb will remain dark. o When S1 is suddenly opened, the instantaneous change of current will cause a significant voltage spike. That spike will be large enough to excite the neon gas. The bulb will briefly flash & use up the energy stored in the inductor. 5. Examine the following circuit. Figure Calculate the RL time constant. L / R, record the results in Table Determine the period required to fully flux and then fully unflux the inductor. This requires 5 time 3

4 constants. 8. Calculate the frequency of a square wave that will fully flux and unflux the inductor. Time to Time to LR Flux Unflux Total Time Frequency TC 5xL/R 5xL/R Table 5-1 Wiring Procedure: 1. Use the following schematic to wire the circuit. Figure 5-5 Test Procedure: o See Image 2 of the ET1210.W 5.Lab.Images PowerPoint for greater detail. 1. Turn the switch on and then off again, the neon bulb should flash. Do not leave the switch on for more than a second or you will drain the battery very quickly or burn up the inductor. o Note: You could opt to ignore the switch and just connect and disconnect the +Batt voltage to the circuit. If you hold the leads of the bulb, you may get a "zap". o The fluxed voltage is large enough to excite the neon gas, the bulb will flash on while the energy in the inductor unfluxes through the neon bulb. o Now observe the waveforms of the neon bulb circuit, by building the following circuit in MultiSim, 4

5 2. Open the file ET1210.U5.Lab.Part1.Inductors file. o You should see the following circuit. Figure Open the Oscilloscope and the Function Generator by double-clicking them. They should appear as follows. 4. Start the simulation. Figure 5-7 5

6 5. From the Oscilloscope screen you can see that it takes about 1 milli-second to fully flux and 1 milli- second to unflux the inductor. 6. Make the following changes to the frequency of the frequency generator and describe the result in Table 5-2. Frequency Observations 50Hz 500Hz 5kHz Table For each of the frequencies, determine the value of R that will allow the inductor to fully flux and unflux. Record the value in the Table 5-3. Frequency Value of R to fully flux 50Hz 500Hz 5kHz Table Turn off the simulation and close MultiSim. 9. You should now be able to: o Describe the effect of Lenz's law in a circuit. o Measure the time constant of an LR circuit and test the effects of series and parallel inductances on the time constant. 6

7 Part 2 Inductive Reactance and Series RL Circuits Theory: Inductive Reactance When a sine wave is applied to an inductor, a voltage is induced across the inductor as given by Lenz's law. When the rate of current change is a maximum, the peak induced voltage appears across the inductor. This is illustrated in Figure 5-8. Figure 5-8 Notice that when the current is not changing (at the peaks), the induced voltage is zero. The induced voltage leads the current in the inductor by 1/4 cycle (90 degrees). If we increase the frequency of the sine wave the rate of change of current is increased and the value of the opposing voltage is increased. This results in a net decrease in the amount of current. Thus, the inductive reactance is increased by an increase in frequency. The inductive reactance, in Ohms, is given by the equation This equation reveals that a linear relationship exists between the inductance and the reactance at a constant frequency. Recall that in series, the total inductance is the sum of individual inductors (ignoring mutual inductance). The reactance of series inductors is, therefore, also the sum of the individual reactances. Likewise, in parallel, the reciprocal formula which applies to parallel resistors can be applied to both the inductance and the inductive reactance. Ohm s law can be applied to inductive circuits. The reactance of an inductor can be found by dividing the voltage across the inductor by the current in it. That is, 7

8 Series RL Circuits When a sine wave drives a linear series circuit, the phase relationships between the current and the voltage are determined by the components in the circuit. The current and voltage are always in phase across resistors. With capacitors, the current is always leading the voltage by 90, but for inductors, the voltage always leads the current by 90. (A simple memory aid for this is "ELI the ICE man", where E stands for voltage, I for current, and L and C for inductance and capacitance.) Figure 5-9 shows an RL circuit with its impedance and voltage phasor diagrams plotted. Figure 5-9 As in the series RC circuit, the total impedance is obtained by adding the resistance and inductive reactance using the algebra for complex numbers, or right triangle interpretations. In this example, the current is 1.0 ma, and the total impedance is 5 kω. The current is the same in all components of a series circuit, so the current is drawn as a reference in the direction of the x-axis. If the current is multiplied by the impedance phasor, the voltage phasor is obtained as shown in Figure 5-9 (c). In this experiment, you explore how to make measurements of the phase angle. Your inductors may have parasitic resistance (due tio the coil wire resistance) that affects the ideal phase angle in the circuit. You will add a series resistor that is large compared with the inductorsresistance to mask this error. Preparation: 1. Obtain the following items from your lab equipment. o mydaq o mydaq Test Probes o mydaq analog BNC adaptor o BNC to Hook test leads, two sets 8

9 o Oscilloscope Probe 2. Obtain the following items from your lab kit. o 10kΩ resistor (much larger than the coil's parasitic resistance) o 100mH inductor 3. Connect the mydaq Test Probes to the mydaq. 4. The mydaq analog BNC adaptor must be inserted in the mydaq 5. Select the DMM instrument, set to measure Resistance, Mode to Auto, Run to Run Continuously o Run 6. Measure and record the value of R1. 7. Stop the DMM. 8. Connect the Oscilloscope Probe to the BNC adaptor AI-0 Input port. 9. Connect the BNC to Hook test leads to the BNC adaptor AO-0 Output port. 10. Connect the 2nd BNC to Hook test leads to the BNC adaptor AI-1Input port. Wiring Procedure: 1. Use the following schematic to wire the circuit. Figure 5-10 o The AC signal will be provided by the Function Generator AO-0 Output. 2. Connect the Function Generator BNC to Hook test leads across the two components. o See Image 3 of the ET1210.W 5.Lab.Images PowerPoint for greater detail. 3. Connect the Channel 0 (AI-0) Oscilloscope Probe to measure the voltage on R1 and the Channel 1 (AI-1) Oscilloscope Probe to measure the voltage on C1. o See Image 4 of the ET1210.W 5.Lab.Images PowerPoint for greater detail. Test Procedure: 1. Connect the MyDAQ to the computer using the USB cable. 2. Start the NI ELVISmx Instrument Launcher 3. Select the DMM instrument, set to measure Voltage AC, Mode to Auto, Run to Run Continuously o Run 9

10 4. Select the Function Generator instrument and set its controls as follows: o ac sine waveform o Frequency to 1.6 khz. o Amplitude 3.0 Vpp o DC Offset to 0V o Signal Route to AO 0. o Run 5. Select the Oscilloscope instrument and set its controls as follows: o Channel 0 Settings Source AI 0 Source Enabled Scale Volts/Div to 1V Vertical Position to 0 o Channel 1 Settings Source AI 1 Source Enabled Scale Volts/Div to 1V Vertical Position to 0 o Timebase Time/Div to 1ms o Trigger Type Edge (positive slope) o Run Continuously o Run 6. The circuit is a series circuit, so the current in the resistor is the identical current seen by the inductor. 7. You can find this current easily by applying Ohm s law to the measured resistor value. 8. Measure the rms voltage across the resistor, V R1, using the DMM and record in Table 5-4. Result Measured voltage across R1, V R1 Calculated total current, I Measured voltage across L1, V L1 Calculated inductive reactance, X L Calculated inductance Table

11 9. Compute the current in the circuit by dividing the measured voltage V R1 by the resistance of R1 and enter in Table Measure the rms voltage across the inductor, V L1. Record this voltage in Table Use this voltage to compute the inductive reactance, X L, using Ohm s law and record the value in Table 5-4. Notice X L is about the same value as R1, the circuit is operating near the critical frequency (where R=X L ). 12. Using the inductive reactance found in the previous step, compute the inductance using the equation and record in Table 5-4. o This value should agree with the value marked on the inductor within experimental tolerances. 13. Change the frequency from the Function Generator to 500Hz. 14. For the next steps, you will measure the voltage with a voltmeter and check both voltage and frequency with the Oscilloscope. Record the all results in Table 5-5. Frequency V R rms V L rms I X L V Lpeak 100Hz 500Hz 1600Hz 4000Hz 8000Hz Table Using the DMM, measure the rms voltage across R1, then measure the rms voltage across L Compute the rms current in the circuit by applying Ohm s law to the measured values of V R1 and of the resistor R1: 11

12 17. Since the current is the same throughout a series circuit, this is a simple method for finding the current in both the resistor and the inductor. Compute the inductive reactance, X L, by applying Ohm s law to the capacitor. 18. Use the Oscilloscope to measure the peak voltage dropped across the inductor. 19. Change the frequency of the function generator to the next frequency in the list and repeat the calculations until Table 5-5 is complete. 20. What happens to the value of V L as the frequency increases? 21. What is the relationship between V R1 and V L at the critical frequency? 22. What is the critical frequency of the circuit (where R=X L )? 23. From the data in Table 5-5 and the measured value of R1, draw the impedance phasors and voltage phasors for the circuit at a frequency of 500 Hz. Look at the phasor diagrams when the frequency is 1.6kHz. Plot

13 24. From the data in Table 5-5 and the measured value of R1, draw the impedance phasors and voltage phasors for the circuit at a frequency of 1600 Hz. Plot From the data in Table 5-5 and the measured value of R1, draw the impedance phasors and voltage phasors for the circuit at a frequency of 8000 Hz. Plot The phasor drawings reveal how the impedance and voltage phasors change with frequency. 27. Investigate the frequency effect further by determining the phase angle between the input signal and the voltage dropped across the inductor. 13

14 28. Measure the period, T, of the generator. Record it in Table 5-6. Frequency Period Time θ T difference Δt 100Hz 500Hz 1600Hz 4000Hz 8000Hz Table Set the Oscilloscope to view both channels. 30. Adjust the amplitudes of the signals using the Volts/Div controls until both channels appear to have about the same amplitude as seen on the scope face. 31. Spread the signal horizontally using the Time/Div control until both signals have one full cycle displayed across the screen. 32. Measure the time between the two signals, Δt, by counting the number of divisions along a horizontal graticule of the Oscilloscope and multiplying by the Time/Div setting and record in table The phase angle may now be computed from the equation: 34. Repeat the phase angle measure for each of the frequencies in Table o What happens to the voltage dropped across the inductor as its phase angle increases? Record observation: 35. Stop the instruments, close the DMM instrument and NI ELVISmx Instrument Launcher. 36. Disconnect the mydaq USB cable from the computer. 37. Disconnect the mydaq, disassemble the circuit and put the components away. 38. You should now be able to: o Measure the inductive reactance of an inductor at a specified frequency. o Compare the reactance of inductors connected in series and parallel. o Compute the inductive reactance of an inductor from voltage measurements in a series

15 RL circuit. o Draw the impedance and voltage phasor diagram for the series RL circuit. o Measure the phase angle in a series circuit. 15

16 Part 3 Series Resonance Theory: The reactance of inductors increases with frequency according to the equation On the other hand, the reactance of capacitors decreases with frequency according to the equation Consider the series LC circuit shown in Figure Figure 5-11 In any LC circuit, there is a frequency at which the inductive reactance is equal to the capacitive reactance. The point at which there is equal and opposite reactance is called resonance. By setting X L = X C, substituting the relations given above, and solving for frequency (f), it is easy to show that the resonant frequency of an LC circuit is: Where f r is the resonant frequency. 16

17 Recall that reactance phasors for inductors and capacitors are drawn in opposite directions because of the opposite phase shift that occurs between inductors and capacitors. At series resonance these two phasors are added and cancel each other. This is illustrated in Figure 5-11 (b). The current in the circuit is limited only by the total resistance of the circuit. The current in this example is 5.0 ma. If each of the impedance phasors is multiplied by this current, the result is the voltage phasor diagram as shown in Figure 5-11 (c). Notice that the voltage across the inductor and the capacitor can be greater than the applied voltage! At the resonant frequency, the cancellation of the inductive and capacitive phasors leaves only the resistive phasor to limit the current in the circuit. Therefore, at resonance, the impedance of the circuit is a minimum and the current is a maximum and equal to V Source /R. The phase angle between the source voltage and current is zero (resistors have zero phase angle). If the frequency is lowered, the inductive reactance will be smaller and the capacitive reactance will be larger. The circuit is said to be capacitive because the source current leads the source voltage. If the frequency is raised, the inductive reactance increases, and the capacitive reactance decreases. The circuit is said to be inductive. The selectivity of a resonant circuit describes how the circuit responds to a group of frequencies. A highly selective circuit responds to a narrow group of frequencies and rejects other frequencies. The bandwidth (BW ) of a resonant circuit is the frequency range at which the current is 70.7% of the maximum current. A highly selective circuit thus has a narrow bandwidth (BW). This sharpness of the response to the frequencies is ccalled the circuit Q. The Q for a series resonant circuit is the reactive power in either the coil or capacitor divided by the true power, which is dissipated in the total resistance of the circuit. The bandwidth and resonant frequency can be shown to be related to the circuit Q by the equation Figure 5-12 below illustrates how the bandwidth can change with Q. Responses 1 and 2 have the same resonant frequency, but different bandwidths. The bandwidth for curve 1 is shown. Response curve 2 has a higher Q and a smaller BW. 17

18 Figure 5-12 A useful equation that relates the circuit resistance, capacitance, and inductance to Q is: The value of R in this equation is the total equivalent series resistance in the circuit. Using this equation, the circuit response can be tailored to the application. For a highly selective circuit, the circuit resistance is held to a minimum and the L/C ratio is made high. The Q of a resonant circuit can also be computed from the equation: Where X L is the inductive reactance and R is again the total equivalent series resistance of the circuit. The result is the same if X C is used in the equation, since the values are the same at resonance, but usually X L is shown because the resistance of the inductor is frequently the dominant resistance of the circuit. This experiment examines the characteristics of a series resonant circuit. You will also calculate the Q factor and bandwidth. Preparation: 1. Obtain the following items from your lab equipment. 18

19 o mydaq ET1210: Module 5 Inductance and Resonance o mydaq analog BNC adaptor o BNC to Hook test leads, 2 sets o Oscilloscope Probe 2. Obtain the following items from your lab kit. o 470Ω resistor o 100 mh inductor o 0.1uF capacitor 3. Connect the mydaq Test Probes to the mydaq. 4. The mydaq analog BNC adaptor must be inserted in the mydaq 5. Select the DMM instrument, set to measure Resistance, Mode to Auto, Run to Run Continuously o Run 6. Measure and record the value of R1. R1 = 7. Measure the winding resistance of the inductor and record the value of R W. Rw = 8. Stop the DMM instrument. 9. Connect the Oscilloscope Probe to the BNC adaptor AI-0 Input port. 10. Connect the BNC to Hook test leads to the BNC adaptor AO-0 Output port. 11. Connect the 2nd BNC to Hook test leads to the BNC adaptor AI-1Input port. 12. Examine the following circuit. Figure 5-13 o This is a series RLC circuit. At a certain frequency X L is equal to and cancels X C, and the circuit is resonant. o At resonance, the circuit current will be at maximum and the voltage drop across R S1 will be at maximum. R S1 is the sense resistor (allows monitoring current via Ohm's law, I=V/R). 19

20 13. Calculate the ideal circuit resonant frequency and record in Table 5-7. fr f lower Q f upper BW Table Calculate the ideal circuit quality factor (Q) and record in Table Calculate the ideal circuit bandwidth (BW ) and record in Table Calculate the idea lower and upper cutoff frequencies and record in Table 5-7. Wiring Procedure: 1. Use the following schematic to wire the circuit. Figure 5-14 o The AC signal will be provided by the Function Generator AO-0 Output. 2. Make sure the Function Generator BNC to Hook test leads are connected across the circuit components. o See Image 5 of the ET1210.W 5.Lab.Images PowerPoint for greater detail. 3. Connect the Channel 0 (AI-0) Oscilloscope Probe to measure the voltage on R1 and the Channel 1 (AI-1) Oscilloscope Probe to measure the voltage on R S1. o See Image 6 of the ET1210.W 5.Lab.Images PowerPoint for greater detail. 20

21 Test Procedure: 1. Connect the MyDAQ to the computer using the USB cable. 2. Start the NI ELVISmx Instrument Launcher Practical Resonant Circuit Quality, Bandwidth and Cutoff Frequencies 3. Calculate the practical circuit resonant frequency and record in Table 5-8. fr f lower Q f upper BW Table Calculate the practical circuit quality factor (Q) and record in Table Calculate the practical circuit bandwidth (BW ) and record in Table Calculate the practical lower and upper cutoff frequencies and record in Table Notice that the Q factor is different, subsequently the bandwidth will be different. o The lower and upper cutoff frequencies will also be different. 8. Select the DMM instrument, set to measure Voltage AC, Mode to Auto, Run to Run Continuously o Run 9. Select the Function Generator instrument and set its controls as follows: o Signal Route to AO 0. o ac sine waveform o Frequency to 1.6 khz. o Amplitude 2.0 Vpp o DC Offset to 0V o Run 10. Select the Oscilloscope instrument and set its controls as follows: o Channel 0 Settings Source AI 0 Source Enabled Scale Volts/Div to 200mV 21

22 Vertical Position to 0 o Channel 1 Settings Source AI 1 Source Enabled Scale Volts/Div to 200mV Vertical Position to 0 o Timebase Time/Div to 1ms o Trigger Type Edge (positive slope) o Run Continuously o Run 11. Use the Oscilloscope to measure the voltage across R1. ET1210: Module 5 Inductance and Resonance 12. Adjust the frequency generator until the voltage drop across R1 is at its maximum value. It should be very close to 1Vpeak. o It should be close to 1.59 khz. o Record the resonant frequency in Table 5-9. f lower f r f upper Table Decrease the frequency from the frequency generator until the voltage drop across R1 is 70.7% of its maximum. It should be about.707 volts. o It should be very close to the practical lower cutoff frequency you calculated in a previous step. o Record the lower cutoff frequency in Table Increase the frequency from the frequency generator until the voltage drop across R1 is 70.7% of its maximum. It should be about.707 volts. o It should be very close to the practical upper cutoff frequency you calculated in a previous step. o Record the upper cutoff frequency in Table Adjust the frequency from the frequency generator to 1/10 and 10 times the resonant frequency and observe the voltage drop across R1. Describe your observations below. Observation: 16. Stop the instruments, close the DMM instrument and NI ELVISmx Instrument Launcher. 17. Disconnect the mydaq USB cable from the computer. 22

23 18. Disconnect the mydaq, disassemble the circuit and put the components away. 19. You should now be able to: o Compute the resonant frequency, Q, and bandwidth of a series resonant circuit. o Measure the frequency response of a series resonant circuit. o Explain the factors affecting the selectivity of a series resonant circuit. 23

24 Part 4 Parallel Resonance Theory: In a parallel RLC circuit, the current in each branch is determined by the applied voltage and the impedance of that branch. For an ideal inductor (no resistance), the branch impedance is X L, and for a capacitor the branch impedance is X C. Since X L and X C are functions of frequency, it is apparent that the currents in each branch are also dependent on the frequency. For any given L and C, there is a frequency at which the currents in each are equal and of opposite phase. This frequency is the resonant frequency and is found using the same equation as was used for series resonance: Ideal Parallel RLC Circuits The circuit and phasor diagram for an ideal parallel RLC circuit at resonance is illustrated in the Figure Figure 5-15 Some interesting points to observe are: The total source current at resonance is equal to the current in the resistor. The total current is actually less than the current in either the inductor or the capacitor. This is because of the opposite phase shift which occurs between inductors and capacitors, causing their currents to cancel. Also, the impedance of the circuit is then solely determined by R, as the inductor and capacitor appear to be gone. If th circuit consisted of only L and C, the source current would be Zero, causing the impedance to be infinite! Of course, this does not happen with actual components that do have resistance and other parasitic effects. 24

25 Practical Parallel RLC Circuits In a practical two-branch parallel circuit consisting of only an inductor and a capacitor, the only significant resistance is the winding resistance of the inductor. The Figure 5-15 (a) below illustrates a practical parallel LC circuit containing winding resistance. By network theorems, the practical LC circuit can be converted to an equivalent parallel RLC circuit, as shown in Figure 5-15 (b). Figure 5-16 The equivalent circuit is easier to analyze. The phasor diagram for the ideal parallel RLC circuit can then be applied to the equivalent circuit. The equations to convert the inductance and its winding resistance to an equivalent parallel circuit are: Where R p(eq) represents the parallel equivalent resistance, and R W represents the winding resistance of the inductor. The Q used in the conversion equation is the Q for the inductor: The selectivity of series circuits was discussed in the previous experiment. Parallel resonant circuits also respond to a group of frequencies. In parallel resonant circuits, the impedance as a function of frequency has the same shape as the current versus frequency curve for series resonant circuits. The bandwidth of a parallel resonant circuit is simply the frequency range at which the circuit impedance falls to 70.7% of the maximum impedance. The sharpness of the response to frequencies (width) is again measured by the circuit Q. The circuit Q will be different from the inductor Q when there is additional resistance in the circuit. The parallel resonant circuit Q matches the inductor Q when there is no separate resistor in parallel with L and C. This experiment examines the characteristics of a parallel resonant circuit. You will calculate the Q 25

26 factor and bandwidth. Preparation: 1. Obtain the following items from your lab equipment. o mydaq o mydaq analog BNC adaptor o BNC to Hook test leads, 2 sets o Oscilloscope Probe 2. Obtain the following items from your lab kit. o 1kΩ resistor o 100mH inductor o 0.033uF capacitor 3. Connect the mydaq Test Probes to the mydaq. 4. The mydaq analog BNC adaptor must be inserted in the mydaq 5. Select the DMM instrument, set to measure Resistance, Mode to Auto, Run to Run Continuously o Run 6. Measure and record the value of R1. R1 = 7. Measure the winding resistance of the inductor and record the value of RW. Rw= 8. Stop the DMM instrument. 9. Connect the Oscilloscope Probe to the BNC adaptor AI-0 Input port. 10. Connect the BNC to Hook test leads to the BNC adaptor AO-0 Output port. 11. Connect the 2nd BNC to Hook test leads to the BNC adaptor AI-1Input port. 12. Examine the following circuit. Figure This is a series circuit with a parallel LC (tank) network. At a frequency where X L is equal to X C, the circuit is resonant. 14. For a parallel LC network, when the circuit is at resonance all of the energy is being transferred 26

27 back and forth in the LC tank. No energy will pass to the R S1 resistor. ET1210: Module 5 Inductance and Resonance 15. At resonance, the circuit current will be at minimum and the voltage drop across R S1 will be at minimum. 16. Also, the only resistance in the LC network is the internal resistance of the inductor. o Hence the approximate value of Q is calculated using the following formula. Wiring Procedure: 1. Use the following schematic to wire the circuit. Figure The AC signal will be provided by the Function Generator AO-0 Output. 3. Make sure the Function Generator BNC to Hook test leads are connected across the circuit components. o See Image 7 of the ET1210.W 5.Lab.Images PowerPoint for greater detail. 4. Connect the Channel 0 (AI-0) Oscilloscope Probe to measure the voltage on R1 and the Channel 1 (AI-1) Oscilloscope Probe to measure the voltage on RS1. o See Image 8 of the ET1210.W 5.Lab.Images PowerPoint for greater detail. Test Procedure: 1. Connect the MyDAQ to the computer using the USB cable. 2. Start the NI ELVISmx Instrument Launcher 27

28 3. Calculate the practical circuit resonant frequency and record in table fr f lower Q f upper BW Table Calculate the practical circuit quality factor (Q) and record in Table Calculate the practical circuit bandwidth (BW ) and record in Table Calculate the practical lower and upper cutoff frequencies and record in Table Select the Function Generator instrument and set its controls as follows: o Signal Route to AO 0. o ac sine waveform o Frequency to 1.6 khz. o Amplitude 2.0 Vpp o DC Offset to 0V o Run 8. Select the Oscilloscope instrument and set its controls as follows: o Channel 0 Settings Source AI 0 Source Enabled Scale Volts/Div to 200mV Vertical Position to 0 o Channel 1 Settings Source AI 1 Source Enabled Scale Volts/Div to 200mV Vertical Position to 0 o Timebase Time/Div to 1ms o Trigger Type Edge (positive slope) 28

29 o Run Continuously o Run 9. Use the Oscilloscope to measure the voltage across R Adjust the frequency generator to the calculated resonant frequency. The voltage drop across R1 is at its minimum value. It should be very close to 0Vpeak. o Enter the resonant frequency in Table 5-11 (below). f lower f r f upper Table Decrease the frequency from the frequency generator until the voltage drop across R1 is 70.7% of its maximum. It should be about.707 volts. o It should be very close to the lower cutoff frequency you calculated in a previous step. o Record the lower cutoff frequency in Table Increase the frequency from the frequency generator until the voltage drop across R1 is 70.7% of its maximum. It should be about.707 volts. o It should be very close to the upper cutoff frequency you calculated in a previous step. o Record the upper cutoff frequency in Table Plot Voltage vs. Frequency 13. Calculate an increment frequency using the following formula. 14. Calculate ten increment frequencies and record them in Table Record the test frequencies in the table. Computed Frequency V R1 I Z f r 5f i f r 4f i f r 3f i 29

30 Computed Frequency ET1210: Module 5 Inductance and Resonance V R1 I Z f r 2f i f r 1f i f r + 1f i f r + 2f i f r + 3f i f r + 4f i f r + 5f i Table Adjust the function generator to the first computed frequency; record each result in Table o Measure the peak voltage across resistor R1. o Use Ohm s Law to determine the current through resistor R1. I peak = V R1_peak / R1 o Use Ohm s Law to calculate the impedance of the circuit. Z = V S_peak / I peak 16. Repeat for each of the computed frequencies. 17. Plot the voltage vs. frequency using the data from Table

31 Plot What happens to the output voltage as the frequency increases? o Describe your observations below. Observation: 19. What is the actual bandwidth of the circuit (uses the 70.7% from peak criteria)? 20. Stop the instruments, close the DMM instrument and NI ELVISmx Instrument Launcher. 21. Disconnect the mydaq USB cable from the computer. 22. Disconnect the mydaq, disassemble the circuit and put the components away. 23. You should now be able to: o Compute the resonant frequency, Q, and bandwidth of a parallel resonant circuit. o Use frequency response to determine the bandwidth of a parallel resonant circuit. *Multisim Files are products of National Instruments. (2012). NI Multisim (Version 12) [Software]. Available from: 31