Week 5 Lab 2 Analyses of Series and Parallel Resonant Filters - ELVIS OG

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Electric Circuits Lab Lab 10: Analyses of Series and Parallel Resonant Filters I. Objectives : After completing this lab experiment using, you should be able to: 1. Build and test series resonant band-pass filters. 2. Build and test parallel resonant band-stop filters. 3. Calculate and measure the center frequency and bandwidth of series resonant band- pass filters. 4. Calculate and measure the minimum output voltage for parallel resonant band-stop filters. 5. Use the Bode analyzer to observe and measure the frequency response of the filters. II. Parts List : 1. Resistor (1)10 kΩ, (1)1 kΩ, (1)10 Ω 2. Inductor (1) 33 mH. 3. Capacitor (1) 2.2nF. 4. Connecting wires (as necessary). III. Procedures : 1. Connect the ELVIS workstation to the computer and open NI ELVISmx Instrument Launcher. If not open automatically go-to Start >> All Programs >> National Instruments >> NI ELVISmx for NI ELVIS and NI myDAQ >> NI ELVISmx Instrument Launcher 2. Measure the value of the resistor R and record the results in the table 1 below. 3. Turn the prototyping board power ON. 4. Measure the value of the capacitor and inductor. Record the results in the table 1 below (use DUT+ and DUT- terminals, pins 29 and 30 respectively). Listed value Measured value 1

1 kΩ 10 kΩ Rw – 10Ω C - 2.2 nF L - 33 mH Table 1: Listed and Measured values Part I. Series Resonant Band-Pass Filter 1. Review the solution to Example 18-8 on pages 849-850 in your textbook. 2. Build the following circuit on the bread board. Use the function generator terminal on the prototyping board (pin no 33). Use either of the available grounds (pin 49 or 53). Figure 1: Series Resonant Band Pass Filter 3. According to the circuit above, verify the following calculations for bandwidth from Example 18-8. Calculate the resonant or center frequency, f 0 : f 0 = 1 2 π √ LC = 1 2 π √ ( 33 mH )( 2.2 nF ) = 18.68 kHz Calculate the inductive reactance, X L , at the center frequency f 0 : X L = 2 πfL = 2 π ( 18.68 k Hz ) ( 33 mH ) = 3.87 kΩ 2 GROUND: pin 49 FGEN: pin 33

Calculate the total circuit resistance: R T = R L + R w = 1 kΩ + 10 Ω = 1.01 kΩ Calculate the Q factor: Q = X L R T = 3.87 kΩ 1.01 kΩ = 3.83 Finally, calculate the bandwidth, BW: BW = f 0 Q = 18.68 kHz 3.83 = 4.87 kHz 4. Open the Bode Analyzer from the NI ELVISmx Instrument Launcher . 5. Connect CH0 of the oscilloscope across the Function generator (FGEN). (This would be the Stimulus Channel on the Bode Analyzer) 6. Connect CH1 of the oscilloscope across the load resistor (R L ). (This would be the Response Channel on the Bode Analyzer) 7. Change the Measurement settings on the Bode Analyzer as show below. 8. Run the Bode Analyzer by clicking the Green Run arrow. 9. After few minutes, the Analyzer will plot the Gain in dB (top) and phase in degrees (bottom) with respect to the Frequency in Hertz . 10. Turn On the cursors under the Cursor settings. 11. Place the cursor at the maximum value of the dB gain. Record the frequency in table 2 under measured center frequency (f0). 12. Move the cursor to the left as such that the gain (dB) should be close to -3 dB as shown below. 3 Figure 2: Bode Analyzer settings

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Figure 3: Bode Analyzer with cursor at lower -3 dB 13. Note the frequency value. This will be the lower critical frequency. Record the result in table 2 under lower critical frequency. 14. Move the cursor to the right as such that the gain (dB) should be close to -3 dB as shown below. Figure 4: Bode Analyzer with cursor at upper -3 dB 15. Note the frequency value. This will be the upper critical frequency. Record the result in table 2 under upper critical frequency. 4

16. Now, calculate the bandwidth using the formula below. Record the result in table 2 under measured bandwidth. Band width = Upper critical frequency – Lower critical frequency 17. Repeat steps 7 through 20 using resistance R = 10 kΩ. R Calculated f 0 Calculate d BW Measured Center frequenc y f 0 Upper Critical Frequenc y f 1 Lower Critical Frequenc y f 2 Measured BW f 1 -f 2 1kΩ 18.68 kHz 4.87 kHz 10kΩ Table 2 . Resonant Frequency and Bandwidth for Band-pass filter Part II. Parallel Resonant Band-Stop Filter 1. Review the solution to Example 18-12 on pages 855-856 in your textbook. 2. Construct the circuit shown in Figure 5. V1 1Vpk 1kHz 0° L 33mH RW 10Ω C 2.2nF RL 1kΩ Figure 5. Parallel Resonant Band-Pass Filter 3. Verify the following calculations for bandwidth and minimum output voltage for the example below. The center frequency is: 5

f 0 = 1 2 π √ L∙C = 1 2 π √ ( 33 mH )( 2.2 nF ) = 18.68 kHz At the center or resonant frequency: X L = 2 π f 0 L = 2 π ( 18.68 kHz ) ( 33 mH ) = 3.87 kΩ Q = X L R w = 3.87 kΩ 10 Ω = 387 Z r = R w ( Q 2 + 1 ) = ( 10 Ω ) ( 387 2 + 1 ) = 1.5 MΩ Use voltage-divider to find the minimum output voltage (magnitude only): V out ( min ) = ( R L R L + Z r ) V ¿ = ( 1 kΩ 1 kΩ + 1.5 MΩ ) ( 1 V ) = ( 1 kΩ 1.501 MΩ ) ( 1 ) = 666.22 µV 4. Connect bode analyzer as per steps 9 and 10. Then set to the following settings. Figure 6: Bode Analyzer settings 5. Run the analyzer and you should be able to observe the following plot. 6

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Figure 7. Gain at Resonant Frequency 6. Place the cursor at the lowest point and measure the center or resonant frequency. Record result in table 3 under measured center frequency. 7. Measure the output gain at center frequency in dB V dB = _________. 8. Calculate the minimum output voltage from the definition of voltage gain in decibels (V dB ) (the following calculation shows as per the above figure gain of -41.58 dB. Yours will be different). V dB = 20 log 10 ( V out V ¿ ) V out = ( V ¿ ) ( 10 V dB 20 ) = ( 1 V ) ( 10 − 41.58 20 ) = 8.33 mV Record result in table 3 under measured V out(min) . R L Calculated Center Frequency Measured Center Frequency Calculated V out(min) Measured V out(min) 1 kΩ 18.68 kHz 666.22 µV 10 kΩ Table 3. Calculated and Measured Minimum Output Voltage 9. Repeat steps 3 through 8 using R L = 10 kΩ. IV. References: 7

Floyd, T. L., & Buchla, D. M. (2019). Principles of Electric Circuits (10th Edition). Pearson Education (US). https://bookshelf.vitalsource.com/books/9780134880068 National Instruments. (2019, April 3). Multisim Education Edition Version (14.2.0). 8