EC312 Security Exercise 13 – Low-pass and High-Pass Filters
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EC312 Security Exercise 13 – Low-pass and High-Pass Filters Discussion: The purpose of this lab is to provide you the opportunity to investigate two passive filters, the high pass and low pass RC filters. Also, you will get the chance to become more proficient with your skills in the use of the oscilloscope, function generator, and digital multimeter. II. Equipment • • • Standard Lab Bench setup (We will be using the Function Generator, and the Oscilloscope and cables). One 0.1 µF capacitor One 1 kΩ resistor III. Lab Procedure CIRCUIT # 1 Analysis and Predictions: Before you set up your first circuit (shown in Figure 1), we’ll conduct some analysis and make some predictions based on the theory we learned in class today. FIGURE 1 Question 1. Recall that the impedance for a capacitor is πππΆπΆ = 1 ππ2ππππππ voltage divider equation to write out an expression for ππππππππ /πΈπΈππ . and for a resistor is just πππ π = π π . Use the Question 2. Based on your answer to question 1, at very low frequencies, do you expect ππππππππ /πΈπΈππ to be closer to 0 or closer to 1? How about at very high frequencies? Place either a 0 or a 1 (as approximations) in the first two spaces of the table below. Question 3. For the circuit in Figure 1, if R = 1 kΩ and C = 0.1 µF, calculate the cutoff frequency ππππππ and enter it into the table below. 1 Circuit 1 (Fig. 1) (ππππππππ /πΈπΈππ ) (ππππππππ /πΈπΈππ ) @ very low frequencies @ very high frequencies Cutoff frequency (ππππππ ) Question 4. Based on your answers to the previous questions, what type of filter is this? Question 5. From your answer to question 1, determine an expression for the value of |ππππππππ /πΈπΈππ | in dB, i.e. ππ+ππππ √ππ2 +ππ 2 20 log(|ππππππππ /πΈπΈππ |). Hint: recall that for complex numbers, οΏ½ππ+ππππ οΏ½ = √ππ 2 +ππ2 . Question 6. Using your equation from Question 5, determine the magnitude of the ratio ππππππππ /πΈπΈππ in dB at the specific value ππ = ππππππ . Fill this value in on your answer sheet, and plot the point as a dot or circle on the graph below. Experimental verification: In this section we’ll build the circuit and take measurements to compare experimental implementation to theoretical predictions. Question 7. Measure the actual capacitance of the 0.1 µF capacitor and actual resistance of the 1 kΩ resistor, and record them below. π π 1kΩ = ____________ πΆπΆ1µF = ____________ 2 - Construct the circuit shown in Figure 1 on your quad board. Make the connections to Channel 1 and Channel 2 of the oscilloscope as shown. Don’t forget to connect a wire from the ground of your circuit to the ground of the o-scope. Power on your function generator and set it up to provide a 100 Hz sine wave at an amplitude of 1 Vrms Question 8. Use the MEASURE button on your O-scope to determine the rms voltage for ππππππππ and the rms voltage for πΈπΈπ π , and enter your measurements in the table below. Question 9. Using your measurements from question 8, calculate the magnitude of the ratio |ππππππππ /πΈπΈππ | in dB (i.e. 20 log(|ππππππππ /πΈπΈππ |) ) and enter your answers in the table below. Question 10. Use the cursors to determine the time delay Δπ‘π‘ between the signals in CH1 and CH2 (i.e. between the input πΈπΈππ and the output ππππππππ ) and enter your measurements in the table below. Question 11. Calculate the period T for your input signal and fill it in the table below. Then, using your measurements of time delay from question 10, determine the phase angle between the input πΈπΈππ and the output ππππππππ by making use of the equation for phase angle Δππ = Δπ‘π‘ × 360° / ππ where Δπ‘π‘ is your calculated time delay and T is the period of the signal. Enter your answers in the table below. Question 12. Repeat the steps in questions 8-11 for input frequencies of 1.59 kHz and 20 kHz, and fill out the remainder of the table. NOTE: Dialing these subsequent frequencies on the function generator – as opposed to entering them using the pushbuttons – allows you to observe the changing relationship (both magnitude and phase) between the two sinusoidal waveforms on the o-scope as the frequency is changed. You will need to adjust your horizontal and vertical scales of the o-scope as you increase the frequency of your input signal. Frequency 100 Hz π¬π¬πΊπΊ (rms) π½π½ππππππ (rms) |π½π½ππππππ /π¬π¬πΊπΊ | (dB) 1.59 kHz 20 kHz 3 Period T (sec) π«π«ππ (sec) π«π«π«π« (deg) CIRCUIT # 2 Analysis and Predictions: Now we’ll consider a slightly altered version of our first (shown in Figure 2), again conducting some analysis and making some predictions before setting up the circuit to take measurements. FIGURE 2 Question 13. Use your voltage divider equation to determine an expression for ππππππππ /πΈπΈππ for this circuit. Question 14. Based on your answer to question 13, at very low frequencies, do you expect ππππππππ /πΈπΈππ to be closer to 0 or closer to 1? How about at very high frequencies? Place either a 0 or a 1 (as approximations) in the first two spaces of the table below. Question 15. For the circuit in Figure 2, if R = 1 kΩ and C = 0.1 µF, calculate the cutoff frequency ππππππ and enter it into the table below. Circuit 2 (Fig. 2) (ππππππππ /πΈπΈππ ) (ππππππππ /πΈπΈππ ) @ very low frequencies @ very high frequencies Cutoff frequency (ππππππ ) Question 16. Based on your answers to the previous questions, what type of filter is this? Question 17. From your answer to question 13, determine an expression for the value of |ππππππππ /πΈπΈππ | in dB, i.e. 20 log(|ππππππππ /πΈπΈππ |). 4 Question 18. Using your equation from Question 5, determine the magnitude of the ratio ππππππππ /πΈπΈππ in dB at the specific value ππ = ππππππ . Fill this value in on your answer sheet, and plot the point as a dot or circle on the graph below. Experimental verification: In this section we’ll build the circuit and take measurements to compare experimental implementation to theoretical predictions. - Construct the circuit shown in Figure 2 on your quad board. Question 19. Follow the same steps as described in questions 8-12 to fill out the table below. Frequency 100 Hz π¬π¬πΊπΊ (rms) π½π½ππππππ (rms) |π½π½ππππππ /π¬π¬πΊπΊ | (dB) Period T (sec) π«π«ππ (sec) π«π«π«π« (deg) 1.59 kHz 20 kHz Question 20. If the cut-off frequency is the point at which frequencies change from passing through the filter to not passing through the filter, what range of frequencies will pass through filter in Circuit 1? What range of frequencies will pass through the filter in Circuit 2? (Use “0 Hz” for very low frequencies and “∞ Hz” for very high frequencies.) 5 EC312 Security Exercise 13 Name: __________________________________________________________________________________________ Question 1: __________________________________________________________________________________________ Question 2-3: Circuit 1 Cutoff frequency (ππππππ ) (ππππππππ /πΈπΈππ ) @ very low (ππππππππ /πΈπΈππ ) @ very high frequencies frequencies (Fig. 1) _______________________________________________________________________________________ Question 4: __________________________________________________________________________________________ Question 5: __________________________________________________________________________________________ Question 6: At ππ = ππππππ , |π½π½ππππππ /π¬π¬πΊπΊ | (dB) = __________________________________________________________________________________________ Question 7: π π 1kΩ = ____________ πΆπΆ1µF = ____________ _________________________________________________________________________________________ Question 8-12: |π½π½ππππππ /π¬π¬πΊπΊ | Frequency Period T π¬π¬πΊπΊ (rms) π½π½ππππππ (rms) π«π«ππ (sec) π«π«π«π« (deg) (sec) (dB) 100 Hz 1.59 kHz 20 kHz 6 __________________________________________________________________________________________ Question 13: __________________________________________________________________________________________ Question 14-15: Circuit 2 (Fig. 2) (ππππππππ /πΈπΈππ ) (ππππππππ /πΈπΈππ ) @ very low frequencies @ very high frequencies Cutoff frequency (ππππππ ) __________________________________________________________________________________________ Question 16: __________________________________________________________________________________________ Question 17: __________________________________________________________________________________________ Question 18: At ππ = ππππππ , |π½π½ππππππ /π¬π¬πΊπΊ | (dB) = __________________________________________________________________________________________ Question 19: Frequency 100 Hz π¬π¬πΊπΊ (rms) π½π½ππππππ (rms) |π½π½ππππππ /π¬π¬πΊπΊ | (dB) Period T (sec) π«π«ππ (sec) π«π«π«π« (deg) 1.59 kHz 20 kHz __________________________________________________________________________________________ Question 20: Range of frequencies for Filter in Circuit 1: Range of frequencies for Filter in Circuit 2: 7
