EET221L_Week2_Activity_Stemple

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ECPI University *

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EET221L

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Electrical Engineering

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Jan 9, 2024

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Unit 2 Activity: Active Filters Low-Pass Filter (LPF): 1. Build the following single pole active LPF using Multisim. VCC 15.0V VEE -15.0V U2 741 3 2 4 7 6 5 1 R2 1kΩ R1 3kΩ R3 1kΩ C1 0.022µF V1 1Vpk 1kHz 0° 2. In the above circuit, R 3 & C 1 will form a LPF, the op-amp is a non-inverting amplifier with gain selected by R 1 and R 2 . 3. Calculate the cut-off frequency of the filter using the following formula. The cut-off frequency (fc) is 7.24kHZ Cutoff Frequency f c = 1 2 Π R 3 C 1 4. Calculate the voltage gain of the non-inverting amplifier using the following formula. The voltage gain (Av) is 4 5. We can verify the filter design using Bode-plotter. Connect Bode-plotter as shown below. Note: Bode-plotter can be found from the right side instrument panel on Multisim. LPF A v(NI) = 1+ R 1 R 2

VCC 15.0V VEE -15.0V U2 741 3 2 4 7 6 5 1 R2 1kΩ R1 3kΩ R3 1kΩ C1 0.022µF V1 1Vpk 1kHz 0° XBP1 IN OUT 6. Launch the Bode-plotter by double clicking on it and change it to the following settings. 7. Run the simulation. You should be able to observe the low-pass filter response as shown below. 8. Now move the cursor around the cut-off frequency calculated in step 3. The dB gain value is 8.98DB @7.4KHZ

9. Since we are using Active filter, this dB value is -3 dB below the actual dB gain. 10. Above the cutoff frequency (observe in between the arrows) the gain will be reduced by - 20dB/decade (since it is a single-pole filter) 11. Now modify the circuit as sallen-key two-pole low-pass filter. VCC 15.0V VEE -15.0V U2 741 3 2 4 7 6 5 1 R2 1kΩ R1 586Ω R3 1kΩ C1 0.022µF V1 1Vpk 1kHz 0° XBP1 IN OUT R4 1kΩ C2 0.022µF 12. Run the simulation and observe the Bode-plotter. 13. Now this time observe, above the cutoff frequency (in between the arrows), the roll-off rate is higher and gain is smaller than the single-pole filter. It is -40dB/decade.

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High-Pass Filter (HPF): 14. Build the following sallen-key (two pole) active HPF using Multisim. Observe the location of resistors and capacitors are interchanged from the LPF. VCC 15.0V VEE -15.0V U2 741 3 2 4 7 6 5 1 R2 1kΩ R1 586Ω R3 2.2kΩ C1 0.022µF V1 1Vpk 1kHz 0° XBP1 IN OUT R4 2.2kΩ C2 0.022µF 15. Calculate the cut-off frequency (fc) of the HPF. The cut-off frequency is 3.3kHz C1, R4 and C2, R3 are two HPF’s Cutoff Frequency f c = 1 2 Π √ R 3 R 4 C 1 C 2

16. Calculate the voltage gain of the non-inverting amplifier. The voltage gain is 1.59Av 17. Now run the simulation and observe the Bode-plot. 18. Even though it is a high-pass filter, the plot looks like a band-pass filter with very high bandwidth. Remember all the practical HPF’s are BPF’s. Band-Pass Filter (BPF): 19. A band-pass filter can be constructed using cascaded arrangement of high-pass and low-pass filters. 20. Build the following BPF. VCC 15.0V VEE -15.0V U2 741 3 2 4 7 6 5 1 R2 1kΩ R1 2.2kΩ R3 10kΩ C1 0.022µF V1 1Vpk 1kHz 0° XBP1 IN OUT VEE -15.0V U1 741 3 2 4 7 6 5 1 R4 1kΩ R5 2.2kΩ R6 2.2kΩ C2 0.01µF VCC 15.0V 21. Calculate the lower cutoff frequency of the BPF using C1 and R3 from the HPF. The lower cutoff frequency fc1 is 723.8kHz Lower cutoff Frequency f c1 = 1 2 Π R 3 C 1

22. Calculate the upper cutoff frequency of the BPF using C2 and R6 from the LPF. The upper cutoff frequency fc2 is 3.3kHz Upper cutoff Frequency f c2 = 1 2 Π R 6 C 2 23. Calculate the bandwidth of the BPF. Bandwidth = fc2 – fc1 = 2.6kHz 24. Calculate the center frequency f 0 = √ fc 1 ∗ fc 2 = 1.5kHz 25. Calculate the quality factor Q = f 0 BW = 0.7 26. Now Run the Multisim simulation and observe the bode plotter. 27. Place the cursor at the maximum value of the plot. This will be at the center frequency. The center frequency is f 0 = 2.3kHz and gain in dB is 19.34 28. Now place the cursor on the left side of the plot at 3dB below the maximum gain. This will gives the lower cutoff frequency of the BPF. Lower-cutoff frequency fc1 = 573Hz 29. Now place the cursor on the right side of the plot at 3dB below the maximum gain. This will gives the upper cutoff frequency of the BPF. Upper-cutoff frequency is fc2 = 8.8kHz 30. The measured bandwidth is BW = fc2 – fc1 = 8.23

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