Week 5 Lab 1 Low Pass and High Pass Filters Lab Report

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Defense Acquisition University *

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EET111

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Electrical Engineering

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Jan 9, 2024

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Electric Circuits Lab Instructor: Khalid Taha Low Pass and High Pass Filters Student Name(s): Charles Haskett Honor Pledge: I pledge to support the Honor System of ECPI. I will refrain from any form of academic dishonesty or deception, such as cheating or plagiarism. I am aware that as a member of the academic community, it is my responsibility to turn in all suspected violators of the honor code. I understand that any failure on my part to support the Honor System will be turned over to a Judicial Review Board for determination. I will report to the Judicial Review Board hearing if summoned. Date:
Contents Abstract ....................................................................................................................................................... 3 I ntroduction ................................................................................................................................................ 3 Procedures ................................................................................................................................................... 3 Part I: Series LR Low-pass filter: ............................................................................................................... 3 Part II: Series RC Low-pass filter: .............................................................................................................. 6 Part III: Series RL High-pass filter: ............................................................................................................ 8 Part IV: Series CR High-pass filter: .......................................................................................................... 11 Data Presentation & Analysis .................................................................................................................... 14 Calculations ........................................................................................................................................... 15 Required Screenshots ............................................................................................................................ 17 Conclusion ................................................................................................................................................. 33 References ................................................................................................................................................. 34 2
Abstract Using the Multisim software the student will build and test passive low-pass and high-pass filters. They will learn to calculate the critical frequency of the circuits using F C =1/2πL/R formula for the low-pass filter circuit, and the F C =1/2πRC formula for the high-pass filter circuit. Using the Bode analyzer in the Multisim software the student will verify within (-)3 dB the cutoff frequency that they had calculated using the previous stated formulas. I ntroduction A low-pass filter is a filter that will pass signals with frequencies that are lower than the selected cutoff frequency and will attenuate signals with frequencies that are higher than the cutoff frequency. A high-pass filter is a filter that will pass signals with frequencies higher than the cutoff frequency and will attenuate signals with frequencies that are lower than the cutoff frequency. A cutoff frequency is the frequency that is either above or below the power output of a circuit. The formula F C =1/2πL/R is used to calculate the cutoff frequency for an RL circuit, and to calculate the cutoff frequency for an RC circuit you will use the F C =1/2πRC formula. It is important to ensure that the signal is ± 3 dB because this ensures that the output voltage is down 3 dB from the passband’s amplitude at the cutoff frequency. Procedures Part I: Series LR Low-pass filter: 1. Build the following circuit. VS 1 Vpk 1kHz 0° R1 1.0kΩ L1 100mH Figure 1: Series LR Circuit 2. Calculate the cutoff frequency (f C ) of the above filter using the following equation. Record the result in Table 1 . Cutoff frequency f C = 1 2 π ( L R ) 3. Connect the Bode Plotter as shown in Figure 2 . 3
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Figure 2: Circuit showing Bode Plotter 4. Change the measurement settings on the Bode Plotter as shown in Figure 3 Figure 3. Bode Plotter Settings . 5. Run the simulation and observe the output. The Bode Plot will display the Gain in dB with respect to the Frequency in Hertz . See Figure 4. 4
Figure 4: Series LR circuit low-pass filter Gain response 6. Select the Phase button on the Bode Plotter to observe the phase in degrees with respect to the Frequency in Hertz . See Figure 5 . Note the Vertical settings. Figure 4: Series LR circuit low-pass filter Phase response 7. Measure the cutoff frequency on the Magnitude response . Set the cursor to read the frequency where the Gain (dB) is -3 dB. This will be the cutoff frequency. Record this value in Table 1 . Figure 5: Bode Plotter cursor approximately at -3 dB 8. Switch to the Phase plot. Measure the phase angle at the cutoff frequency determined in step 7. Record this value in Table 1 . 5
9. Repeat steps 1 to 8 by replacing the R and L according to the values shown in Table 1 . Part II: Series RC Low-pass filter: 10. Build the following circuit on the breadboard. Figure 6: Series RC Circuit 11. Calculate the cutoff frequency (f C ) of the above filter using the following equation. Record the result in Table 2 . Cutoff frequency f C = 1 2 π RC 12. Connect the Bode Plotter as shown in Figure 7 . Figure 7: Circuit showing Bode Plotter 13. Change the measurement settings on the Bode Plotter as shown in Figure 8 6
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Figure 8. Bode Plotter Settings . 14. Run the simulation and observe the output. The Bode Plot will display the Gain in dB with respect to the Frequency in Hertz . See Figure 9. Figure 9: Series RC circuit low-pass filter Gain response 15. Select the Phase button on the Bode Plotter to observe the phase in degrees with respect to the Frequency in Hertz . See Figure 10 . Note the Vertical settings. Figure 10: Series LR circuit low-pass filter Phase response 7
16. Measure the cutoff frequency on the Magnitude response. Set the cursor to read the frequency where the Gain (dB) is -3 dB. This will be the cutoff frequency. Record this value in Table 2 . Figure 11: Bode Plotter cursor approximately at -3 dB 17. Switch to the Phase plot. Measure the phase angle at the cutoff frequency determined in step 16. Record this value in Table 2 . 18. Repeat steps 10 to 17 by replacing the R and C according to the values shown in Table 2 . Part III: Series RL High-pass filter: 19. Build the following circuit. Figure 12: Series LR Circuit 20. Calculate the cutoff frequency (f C ) of the above filter using the following equation. Record the result in Table 3 . Cutoff frequency f C = 1 2 π ( L R ) 21. Connect the Bode Plotter as shown in Figure 13 . 8
Figure 13: Circuit showing Bode Plotter 22. Change the measurement settings on the Bode Plotter as shown in Figure 14 . Figure 14. Bode Plotter Settings . 23. Run the simulation and observe the output. The Bode Plot will display the Gain in dB with respect to the Frequency in Hertz . See Figure 15. 9
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Figure 15: Series LR circuit high-pass filter Gain response 24. Select the Phase button on the Bode Plotter to observe the phase in degrees with respect to the Frequency in Hertz . See Figure 16 . Note the Vertical settings. Figure 16: Series LR circuit low-pass filter Phase response 25. Measure the cutoff frequency on the Magnitude response. Set the cursor to read the frequency where the Gain (dB) is -3 dB. This will be the cutoff frequency. Record this value in Table 3 . Figure 17: Bode Plotter cursor approximately at -3 dB 26. Switch to the Phase plot. Measure the phase angle at the cutoff frequency determined in step 25. Record this value in Table 3 . 10
27. Repeat steps 19 to 26 by replacing the R and C according to the values shown in Table 3 . Part IV: Series CR High-pass filter: 28. Build the following circuit. Figure 18: Series RC Circuit 29. Calculate the cutoff frequency (f C ) of the above filter using the following equation. Record the result in Table 4 . Cutoff frequency f C = 1 2 π RC 30. Connect the Bode Plotter as shown in Figure 19 . Figure 19: Circuit showing Bode Plotter 31. Change the measurement settings on the Bode Plotter as shown in Figure 20 11
Figure 20. Bode Plotter Settings . 32. Run the simulation and observe the output. The Bode Plot will display the Gain in dB with respect to the Frequency in Hertz . See Figure 21. Figure 21: Series RC circuit low-pass filter Gain response 33. Select the Phase button on the Bode Plotter to observe the phase in degrees with respect to the Frequency in Hertz . See Figure 22 . Note the Vertical settings. Figure 22: Series LR circuit high-pass filter Phase response 12
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34. Measure the cutoff frequency on the Magnitude response. Set the cursor to read the frequency where the Gain (dB) is -3 dB. This will be the cutoff frequency. Record this value in Table 4 . Figure 23: Bode Plotter cursor approximately at -3 dB 35. Switch to the Phase plot. Measure the phase angle at the cutoff frequency determined in step 34. Record this value in Table 4 . 36. Repeat steps 28 to 35 by replacing the R and C according to the values shown in Table 4 . 13
Data Presentation & Analysis RL combinations Calculated Frequency f C Measured Frequency f C Measured phase R=1 kΩ, L= 100 mH 1,592 Hz 1.611 kHz -45.341 ° R=1 kΩ, L= 150 mH 1,061 Hz 1.074 kHz -45.346 ° R=10 kΩ, L= 100 mH 15,915 Hz 16.012 kHz -45.173 ° R=10 kΩ, L= 150 mH 10,610 Hz 10.676 kHz -45.177 ° Table 1: Calculated and measured values RL combinations Calculated Frequency f C Measured Frequency f C Measured phase R=1 kΩ, C= 2.2 nF 72,343 Hz 72.574 kHz -45.091 ° R=1 kΩ, C= 1 nF 159,155 Hz 160.117 kHz -45.173 ° R=10 kΩ, C= 2.2 nF 7,234 Hz 7.3 kHz -45.26 ° R=10 kΩ, C= 1 nF 15,915 Hz 16.106 kHz -45.341 ° Table 2: Calculated and measured values RL combinations Calculated Frequency f C Measured Frequency f C Measured phase R=1 kΩ, L= 100 mH 1,592 Hz 1.58 kHz 45.212 ° R=1 kΩ, L= 150 mH 1,061 Hz 1.053 kHz 45.207 ° R=10 kΩ, L= 100 mH 15,915 Hz 15.706 kHz 45.38 ° R=10 kΩ, L= 150 mH 10,610 Hz 10.472 kHz 45.375 ° Table 3: Calculated and measured values RL combinations Calculated Frequency f C Measured Frequency f C Measured phase R=1 kΩ, C= 2.2 nF 72,343 Hz 71.456 kHz 45.354 ° R=1 kΩ, C= 1 nF 159,155 Hz 158.037 kHz 45.202 ° R=10 kΩ, C= 2.2 nF 7,234 Hz 7.197 kHz 45.149 ° R=10 kΩ, C= 1 nF 15,915 Hz 15.579 kHz 45.612 ° Table 4: Calculated and measured values 14
Calculations Part 1 Step 2 (4 values): f C = f C = 1/ 2π (L⁄R) = f C = 1/ 2π (100 mH ⁄ 1,000 Ω) = f C = 1/ 2π (0.0001) = f C = 1/ 0.000628318 = 1,591.549431 Hz = 1,592 Hz f C = 1/ 2π (L⁄R) = f C = 1/ 2π (150 mH ⁄ 1,000 Ω) = f C = 1/ 2π (0.00015) = f C = 1/ 0.000942477 = 1,061.032954 Hz = 1,061 Hz f C = 1/ 2π (L⁄R) = f C = 1/ 2π (100 mH ⁄ 10,000 Ω) = f C = 1/ 2π (0.00001) = f C = 1/ 0.000062831 = 15,915.49431 Hz = 15,915 Hz f C = 1/ 2π (L⁄R) = f C = 1/ 2π (150 mH ⁄ 10,000 Ω) = f C = 1/ 2π (0.000015) = f C = 1/ 0.000094247 = 10,610.32954 Hz = 10,610 Hz Part 2 Step 11(4 values): f C = f C = 1/ 2πRC = f C = 1/ 2π (1,000 Ω x 2.2 nF) = f C = 1/ 2π (0.0000022) = f C = 1/ 0.000013823 = 72,343.15595 Hz = 72,343 Hz f C = 1/ 2πRC = f C = 1/ 2π (1,000 Ω x 1 nF) = f C = 1/ 2π (0.000001) = f C = 1/ 0.000006283 = 159,154.9431 Hz = 159,155 Hz f C = 1/ 2πRC = f C = 1/ 2π (10,000 Ω x 2.2 nF) = f C = 1/ 2π (0.000022) = f C = 1/ 0.00013823 = 7,234.315595 Hz = 7,234 Hz f C = 1/ 2πRC = f C = 1/ 2π (10,000 Ω x 1 nF) = f C = 1/ 2π (0.00001) = f C = 1/ 0.000062831 = 15,915.49431 Hz = 15,915 Hz 15
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Part 3 Step 20 (4 values): f C = f C = 1/ 2π (L⁄R) = f C = 1/ 2π (100 mH x 1,000 Ω) = f C = 1/ 2π (0.0001) = f C = 1/ 0.000628318 = 1,591.549431 Hz = 1,592 Hz f C = 1/ 2π (L⁄R) = f C = 1/ 2π (150 mH x 1,000 Ω) = f C = 1/ 2π (0.00015) = f C = 1/ 0.000942477 = 1,061.032954 Hz = 1,061 Hz f C = 1/ 2π (L⁄R) = f C = 1/ 2π (100 mH x 10,000 Ω) = f C = 1/ 2π (0.00001) = f C = 1/ 0.000062831 = 15,915.49431 Hz = 15,915 Hz f C = 1/ 2π (L⁄R) = f C = 1/ 2π (150 mH x 10,000 Ω) = f C = 1/ 2π (0.000015) = f C = 1/ 0.000094247 = 10,610.32954 Hz = 10,610 Hz Part 4 Step 29 (4 values): f C = f C = 1/ 2πRC = f C = 1/ 2π (1,000 Ω x 2.2 nF) = f C = 1/ 2π (0.0000022) = f C = 1/ 0.000013823 = 72,343.15595 Hz = 72,343 Hz f C = 1/ 2πRC = f C = 1/ 2π (1,000 Ω x 1 nF) = f C = 1/ 2π (0.000001) = f C = 1/ 0.000006283 = 159,154.9431 Hz = 159,155 Hz f C = 1/ 2πRC = f C = 1/ 2π (10,000 Ω x 2.2 nF) = f C = 1/ 2π (0.000022) = f C = 1/ 0.00013823 = 7,234.315595 Hz = 7,234 Hz f C = 1/ 2πRC = f C = 1/ 2π (10,000 Ω x 1 nF) = f C = 1/ 2π (0.00001) = f C = 1/ 0.000062831 = 15,915.49431 Hz = 15,915 Hz 16
Required Screenshots Part 1 RL Low Pass Filter Figure 24a. Magnitude Plot at Cutoff Frequency for RL LPF (R = 1 kΩ and L = 100 mH) 17
Figure 24b. Phase Plot at Cutoff Frequency for RL LPF (R = 1 kΩ and L = 100 mH) Figure 25a. Magnitude Plot at Cutoff Frequency for RL LPF (R = 1 kΩ and L = 150 mH) 18
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Figure 25b. Phase Plot at Cutoff Frequency for RL LPF (R = 1 kΩ and L = 150 mH) Figure 26a. Magnitude Plot at Cutoff Frequency for RL LPF (R = 10 kΩ and L = 100 mH) 19
Figure 26b. Phase Plot at Cutoff Frequency for RL LPF (R = 10 kΩ and L = 100 mH) Figure 27a. Magnitude Plot at Cutoff Frequency for RL LPF (R = 10 kΩ and L = 150 mH) 20
Figure 27b. Phase Plot at Cutoff Frequency for RL LPF (R = 10 kΩ and L = 150 mH) Part 2 RC Low Pass Filter Figure 28a. Magnitude Plot at Cutoff Frequency for RC LPF (R = 1 kΩ and C = 2.2 nF) 21
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Figure 28b. Phase Plot at Cutoff Frequency for RC LPF (R = 1 kΩ and C = 2.2 nF) Figure 29a. Magnitude Plot at Cutoff Frequency for RC LPF (R = 1 kΩ and C = 1 nF) 22
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Figure 29b. Phase Plot at Cutoff Frequency for RC LPF (R = 1 kΩ and C = 1 nF) Figure 30a. Magnitude Plot at Cutoff Frequency for RC LPF (R = 10 kΩ and C = 2.2 nF) 23
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Figure 30b. Phase Plot at Cutoff Frequency for RC LPF (R = 10 kΩ and C = 2.2 nF) Figure 31a. Magnitude Plot at Cutoff Frequency for RC LPF (R = 10 kΩ and C = 1 nF) 24
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Figure 31b. Phase Plot at Cutoff Frequency for RC LPF (R = 10 kΩ and C = 1 nF) Part 3 RL High Pass Filter Figure 32a. Magnitude Plot at Cutoff Frequency for RL HPF (R = 1 kΩ and L = 100 mH) 25
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Figure 32b. Phase Plot at Cutoff Frequency for RL HPF (R = 1 kΩ and L = 100 mH) Figure 33a. Magnitude Plot at Cutoff Frequency for RL HPF (R = 1 kΩ and L = 150 mH) 26
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Figure 33b. Phase Plot at Cutoff Frequency for RL HPF (R = 1 kΩ and L = 150 mH) Figure 34a. Magnitude Plot at Cutoff Frequency for RL HPF (R = 10 kΩ and L = 100 mH) 27
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Figure 34b. Phase Plot at Cutoff Frequency for RL HPF (R = 10 kΩ and L = 100 mH) Figure 35a. Magnitude Plot at Cutoff Frequency for RL HPF (R = 10 kΩ and L = 150 mH) 28
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Figure 35b. Phase Plot at Cutoff Frequency for RL HPF (R = 10 kΩ and L = 150 mH) Part 4 RC High Pass Filter Figure 36a. Magnitude Plot at Cutoff Frequency for RC HPF (R = 1 kΩ and C = 2.2 nF) 29
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Figure 36b. Phase Plot at Cutoff Frequency for RC HPF (R = 1 kΩ and C = 2.2 nF) Figure 37a. Magnitude Plot at Cutoff Frequency for RC HPF (R = 1 kΩ and C = 1 nF) 30
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Figure 37b. Phase Plot at Cutoff Frequency for RC HPF (R = 1 kΩ and C = 1 nF) Figure 38a. Magnitude Plot at Cutoff Frequency for RC HPF (R = 10 kΩ and C = 2.2 nF) 31
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Figure 38b. Phase Plot at Cutoff Frequency for RC HPF (R = 10 kΩ and C = 2.2 nF) Figure 39a. Magnitude Plot at Cutoff Frequency for RC HPF (R = 10 kΩ and C = 1 nF) 32
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Figure 39b. Phase Plot at Cutoff Frequency for RC HPF (R = 10 kΩ and C = 1 nF) 33
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Conclusion In this lab my understanding of how to calculate the cutoff frequency for an RL low/high pass filter was re-enforced using the F C =1/2πL/R formula for the low pass and high pass filters, and the F C =1/2πRC formula to calculate the cutoff frequency for the low-pass and high-pass filters of an RC circuit. Using the Multisim software and building either the RL or RC circuit with low- pass or high-pass filters and using the Bode analyzer my calculations of the cutoff frequencies for the circuits were confirmed to be within ±3dB. I did notice that in the low-pass filter circuits the signal began to attenuate after the cutoff frequency, and the signal seemed to continue to rise after the cutoff frequency in the high-pass filter circuits. 33
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References Floyd, T. L. Principles of Electric Circuits. [VitalSource Bookshelf]. Retrieved from https://bookshelf.vitalsource.com/#/books/9780134880068/ Smith, R. Electric Circuits. [VitalSource Bookshelf]. Retrieved from https://bookshelf.vitalsource.com/#/books/9781256056454/ (2017) National Instruments Multisim (V 14.1) [Windows]. Retrieved from http://www.ni.com/multisim/ 34
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