EC312 Security Exercise 14 – Band-Pass Filters
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EC312 Security Exercise 14 – Band-Pass Filters Discussion: In this lab we will investigate the series RLC circuit, which can be used as a band-pass filter. You may remember from previous discussions that this configuration has the property that certain frequencies will pass through the circuit and other frequencies will be stopped by the capacitor and inductor combination. The frequencies that pass through are said to be in the pass-band of the filter. II. Equipment • • • • Standard Lab Bench setup (We will be using the Function Generator, two DMM, and cables). One 0.001 µF capacitor One 47 mH inductor One 1 kΩ resistor III. Lab Procedure Analysis and Predictions: Before you set up your circuit (shown in Figure 1), we’ll conduct some analysis and make some predictions based on the theory we learned in class today. C L VS RLOAD + VOUT − FIGURE 1 The nominal component values for this exercise are: C = .001 µF L = 47 mH RLOAD = 1 kβ¦ 1 Question 1. Recalling that the resonant frequency for an RLC band-pass filter is given by πππ π = 2ππ√πΏπΏπΏπΏ , calculate the resonant frequency for this circuit based on the nominal values given above. Enter your answer into Table 1 below. Question 2. The quality factor Q is related to the selectivity of a filter, with higher Q corresponding to a more ππ 2ππππ πΏπΏ selective filter. Using the equation ππ = π π πΏπΏ = π π π π , calculate the quality factor Q for the circuit in Figure 1 πΏπΏπΏπΏπΏπΏπΏπΏ πΏπΏπΏπΏπΏπΏπΏπΏ based on the nominal values given above, and enter your answer in Table 1. 1 Question 3. The pass-band of the filter extends from a lower cutoff frequency, πππΏπΏ , to an upper cutoff frequency, πππ»π» . These frequencies are also called the half-power frequencies. The difference between the half-power frequencies, πππ»π» − πππΏπΏ , gives the bandwidth, BW, of the filter. Use the relationship πππ π π΅π΅π΅π΅ = ππ to find the bandwidth of the filter, and then find the upper and lower cutoff frequencies by using the fact that the resonant frequency πππ π is the exact midpoint between πππΏπΏ and πππ»π» . Enter your results in Table 1 below. RLC circuit (Based on nominal values) TABLE 1 Q πππΉπΉ [kHz] BW [kHz] πππ³π³ [kHz] πππ―π― [kHz] Experimental verification: In this section we’ll build the circuit and take measurements to compare experimental implementation to theoretical predictions. In the calculations above, we used the nominal values of the components. In addition to having a design tolerance of ± 5% or ± 10%, the values of many components will change as they age, so we should get better correspondence between predicted results and practical results if we use the actual, or measured, values of the components. Therefore, we will first measure the values of the components, using the DMM to measure resistance, and the Sencore meter to measure the inductor and capacitor. Also, since real inductors are made from real wire, there is a resistive component in the inductor which cannot be ignored, so we have to measure the resistance of the inductor as well. Question 4. Measure and enter these values onto the circuit diagram in Figure 2. FIGURE 2 2 Of particular importance is to note that the voltage amplitude value you read on the display of the Function Generator, VDISPLAY , is not the same as the value of VS, the voltage at the terminals. A small but significant voltage is developed across the 50 Ohm output impedance of the Function Generator, making VS a little smaller than VDISPLAY. Therefore, we’ll use the Digital Multimeter to measure actual VS rather than just reading the value off the Function Generator display. Question 5. Using the component values you just measured in question 4, determine revised estimates for πππ π , Q, BW, and the cut-off frequencies πππΏπΏ and πππ»π» , and enter your results in Table 2 below. **NOTE** Use the total circuit resistance (i.e. the sum of every resistor in Figure 2) when calculating Q. RLC circuit (Based on measured values) TABLE 2 Q πππΉπΉ [kHz] BW [kHz] πππ³π³ [kHz] πππ―π― [kHz] TABLE 2 Circuit setup and measurement: • Construct the circuit shown in Figure 3 on your quad board, connecting your two Digital Multi-meters to measure the source voltage and output voltage as shown. Since we are working with AC rather than DC, make sure the multi-meters are set to measure AC voltage (i.e. RMS voltage). FIGURE 3 • Connect your function generator to be the voltage source Vs. Set the frequency to 20 kHz and adjust the output amplitude of the Function Generator until DMM #1 shows an amplitude of 1 Vrms. Question 6. Find the resonant frequency by adjusting the frequency on your function generator until VOUT (i.e. DMM #2) reaches a maximum value, and then record the corresponding frequency in the first column of Table 3 below. 3 • Again adjust the amplitude of your function generator until you measure an amplitude of 1 Vrms for your source voltage (i.e. DMM #1) Question 7. Measure the output voltage of your circuit (i.e. DMM #2) at the resonant frequency and record as “VOUT @ fr” in Table 3 below. Question 8. Since we now know the output voltage VOUT at the resonant frequency πππ π , we can determine what the output voltage should be at the half-power frequencies (i.e. πππΏπΏ and πππ»π» ) , by ππππππππ(@ πΉπΉπ π ) ππππππππ(@ πΉπΉπΏπΏ) = = .707 ∗ ππππππππ(@ πΉπΉπ π ) √2 Determine these values and write them in Table 3 as VOUT under the columns for πππΏπΏ and πππ»π» . Question 9. Now we’ll determine the actual half-power frequencies (i.e. πππΏπΏ and πππ»π» ) by first adjusting the function generator frequency downward until VOUT (i.e. DMM #2) reaches the half-power value determined in Question 8, and then adjusting the frequency upward until VOUT (i.e. DMM #2) again reaches the value determined in Question 8. Record these values as the half-power frequencies under the columns for πππΏπΏ and πππ»π» in Table 3. ππππππππ Question 10. Based on the measurements in the steps above, calculate the actual values for οΏ½ ππππ ππππππππ οΏ½, οΏ½ ππππ dB), Q, and BW, and enter the values in the table below. NOTE: If you are pressed for time, you may want to come back to Question 10 after you have taken all measurements for the entire security exercise. ππ π½π½πΆπΆπΆπΆπΆπΆ π½π½πΊπΊ π½π½πΆπΆπΆπΆπΆπΆ οΏ½ οΏ½ π½π½πΊπΊ π½π½πΆπΆπΆπΆπΆπΆ οΏ½ οΏ½ (π π π π ) π½π½πΊπΊ @ πππΉπΉ 1.0 Vrms ππ π½π½πΆπΆπΆπΆπΆπΆ π½π½πΊπΊ π½π½πΆπΆπΆπΆπΆπΆ οΏ½ οΏ½ π½π½πΊπΊ @ πππ³π³ 1.0 Vrms π½π½πΆπΆπΆπΆπΆπΆ οΏ½ οΏ½ (π π π π ) π½π½πΊπΊ ππ π½π½πΆπΆπΆπΆπΆπΆ π½π½πΊπΊ π½π½πΆπΆπΆπΆπΆπΆ οΏ½ οΏ½ π½π½πΊπΊ π½π½πΆπΆπΆπΆπΆπΆ οΏ½ οΏ½ (π π π π ) π½π½πΊπΊ Q = ______________________ @ πππ―π― BW = ______________________ TABLE 3 4 οΏ½ (in 1.0 Vrms Question 11. Set the function generator to the resonant frequency determined in Question 6, and make sure the source voltage (i.e. DMM #1) still reads 1.0 Vrms . Then adjust the frequency to each of the values listed in Table 4 below. Measure VOUT and calculate the ratios to fill out the rest of the table. 10 kHz 14 kHz 18 kHz 30 kHz 34 kHz 38 kHz π½π½πΆπΆπΆπΆπΆπΆ π½π½πΆπΆπΆπΆπΆπΆ οΏ½ οΏ½ π½π½πΊπΊ π½π½πΆπΆπΆπΆπΆπΆ οΏ½ οΏ½ (π π π π ) π½π½πΊπΊ TABLE 4 π½π½πΆπΆπΆπΆπΆπΆ Question 12. Using the values from Table 3 and Table 4, plot οΏ½ π½π½πΆπΆπΆπΆπΆπΆ 1 below and in οΏ½ π½π½πΊπΊ οΏ½ vs. frequency in dB in Graph 2. GRAPH 1 π½π½πΊπΊ οΏ½ vs. frequency as a unitless ratio in Graph GRAPH 2 5 EC312 Security Exercise 14 Name: __________________________________________________________________________________________ Question 1-3: RLC circuit (Based on nominal values) TABLE 1 Q πππΉπΉ [kHz] BW [kHz] πππ³π³ [kHz] πππ―π― [kHz] _______________________________________________________________________________________ Question 4: __________________________________________________________________________________________ Question 5: RLC circuit Q BW [kHz] πππΉπΉ [kHz] πππ³π³ [kHz] πππ―π― [kHz] (Based on measured values) TABLE 2 __________________________________________________________________________________________ Question 6-10: @ πππΉπΉ @ πππ³π³ @ πππ―π― ππ ππ ππ π½π½πΆπΆπΆπΆπΆπΆ π½π½πΆπΆπΆπΆπΆπΆ π½π½πΆπΆπΆπΆπΆπΆ 1.0 V 1.0 V 1.0 Vrms π½π½πΊπΊ π½π½πΊπΊ π½π½πΊπΊ rms rms π½π½πΆπΆπΆπΆπΆπΆ π½π½πΆπΆπΆπΆπΆπΆ π½π½πΆπΆπΆπΆπΆπΆ οΏ½ οΏ½ οΏ½ οΏ½ οΏ½ οΏ½ π½π½πΊπΊ π½π½πΊπΊ π½π½πΊπΊ π½π½πΆπΆπΆπΆπΆπΆ π½π½πΆπΆπΆπΆπΆπΆ π½π½πΆπΆπΆπΆπΆπΆ οΏ½ οΏ½ (π π π π ) οΏ½ οΏ½ (π π π π ) οΏ½ οΏ½ (π π π π ) π½π½πΊπΊ π½π½πΊπΊ π½π½πΊπΊ Q = ______________________ BW = ______________________ 6 __________________________________________________________________________________________ Question 11: 10 kHz 14 kHz 18 kHz 30 kHz 34 kHz 38 kHz π½π½πΆπΆπΆπΆπΆπΆ π½π½πΆπΆπΆπΆπΆπΆ οΏ½ οΏ½ π½π½πΊπΊ π½π½πΆπΆπΆπΆπΆπΆ οΏ½ οΏ½ (π π π π ) π½π½πΊπΊ _____________________________________________________________________________________ Question 12: 7
