Exercise 2: High-Pass Filters
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1 Exercise 2: High-Pass Filters EXERCISE OBJECTIVE When you have completed this exercise, you will be able to calculate and measure the cutoff frequencies oscilloscope. DISCUSSION of inductors, capacitors, and resistors. In each circuit, a series resistor and a reactive component (L or C) form a voltage divider across the generator (V GEN ). o ) change as the generator frequency (V GEN ) is varied? a. yes b. no C ) is low (compared to the resistance, R) at frequencies above the cutoff frequency (f c ). Most of the input voltage (V i ) appears across the output resistor (R). FACET by Lab-Volt 167
2 AC 2 Fundamentals As the generator frequency decreases below the cutoff frequency (f c ), the capacitive reactance (X C ) increases. As a result, more and more voltage is dropped across C and less appears across output resistor R. I L ) is large (compared to the resistance, R) at high frequencies. Does most of the input voltage (V i ) appear across the resistor (R) or inductor (L) at high frequencies? a. resistor b. inductor As the generator (V GEN ) frequency decreases, X L decreases. As a result, more and more voltage is dropped across R and less appears across output inductor L. 168 FACET by Lab-Volt
3 At the cutoff frequency, the output signal is 3 db down (0.707 x V o ) from the output signal at higher frequencies. c 1 RC CIRCUITS: fc = 2 π RC R RL CIRCUITS: fc = 2 π L PROCEDURE Locate the HIGH PASS FILTER circuit block, and connect the circuit shown. Adjust V GEN for a 15 V pk-pk, 100 khz (10 s) sine wave. FACET by Lab-Volt 169
4 AC 2 Fundamentals While observing the output (V o o ) increase or decrease with a decrease in frequency? a. increase b. decrease Again adjust V GEN for a 15 V pk-pk, 100 khz (10 s) sine wave. o ) across R2. V o(100khz) = V pk-pk (Recall Value 1) 170 FACET by Lab-Volt
5 The value of output voltage at 100 khz ( V pk-pk [Step 5, Recall Value 1]) is used to calculate the 3 db output voltage point (V o( 3dB) ). V o( 3dB) = V o(100khz) x V o( 3dB) = V pk-pk (Step 5, Recall Value 1) x *V o( 3dB) = V pk-pk NOTE: 70.7% (0.707) of V o(100khz) expressed in decibels is 3 db. To determine the voltage level (V o( 3dB) ) at cutoff (f c ), slowly decrease the generator frequency as you observe a decrease in V o. Stop when V o equals ( V pk-pk [Step 5, Recall Value 1] x 0.707) the 3 db point. * Certain calculated answers based on measured Recall Values are not included in the Instructor Guide. The instructor may use Recall Value nominal answers from the Instructor Guide to determine if the calculated answer by the student is within the nominal value range. FACET by Lab-Volt 171
6 AC 2 Fundamentals Determine f c by measuring the period (T) of the ( Vpk-pk [Step 5, Recall Value 1] x 0.707) output signal. f C 1 = T f c = khz (Recall Value 2) Adjust V GEN for a 15 V pk-pk, 5 khz (200 s) sine wave. o(5khz) ). V o(5khz) = V pk-pk (Recall Value 3) 172 FACET by Lab-Volt
7 The db value of the ratio of output voltage (V o(5khz) ) to input voltage (V i ) at 5 khz is determined as shown. V o(5khz) = V pk-pk [Step 10, Recall Value 3]) db = 20 log 10 V V O(5kHz) V O(5kHz) db = 20 log10 15 V pk pk i *db = Compare your value of db at 5 khz calculated in Step 11 ( value at the cutoff frequency ( khz [Step 8, Recall Value 2]). db) with the 3 db Are frequencies smaller than f c essentially passed or greatly reduced in this RC high-pass a. passed b. reduced * Certain calculated answers based on measured Recall Values are not included in the Instructor Guide. The instructor may use Recall Value nominal answers from the Instructor Guide to determine if the calculated answer by the student is within the nominal value range. FACET by Lab-Volt 173
8 AC 2 Fundamentals Connect the RL high-pass circuit shown. Adjust V GEN for a 15 V pk-pk, 100 khz (10 s) sine wave. While observing the output (V o 1000 Hz. Does V o increase or decrease with a decrease in frequency? a. increase b. decrease The f c for this RL high-pass circuit is 23.8 khz. f f C R = 2 π L 1.5 = 6.28 x (10 x 10 ) C -3 f c = 23.8 khz 174 FACET by Lab-Volt
9 If the generator frequency were adjusted for a frequency of 2.38 khz, the attenuation would be a. 3 db. b. 23 db. c. 6 db. CONCLUSION c ). decade. FACET by Lab-Volt 175
10 AC 2 Fundamentals REVIEW QUESTIONS 1. Locate the HIGH PASS FILTER circuit block, and connect the circuit shown. Adjust V GEN for a 15 V pk-pk, 100 khz (10 s) sine wave. Place the CM switch 17 in the ON position to change the value of R2 Slowly decrease the frequency of V GEN as you observe a decrease in V o. Stop when V o equals 10.6 V pk-pk, the 3 db point. Determine the cutoff frequency (f c pk-pk output signal. a. 340 Hz b. 1.1 khz c. 3.4 khz d. 8.1 khz 2. a. lower than the cutoff frequency (f c ). b. greater than f c. c. 6 db lower than f c. d. equal to f c. 176 FACET by Lab-Volt
11 3. c ) of 50 khz. At which frequency is the output voltage greatest? a. 50 khz b. 500 khz c. 5 khz d. 500 Hz 4. As the frequency decreases, X L1 decreases; therefore, V o a. increases. b. peaks. c. remains the same. d. decreases. 5. a. lower than the cutoff frequency (f c ). b. greater than f c. c. 1 db lower than f c. d. equal to f c. NOTE: Make sure all CMs are cleared (turned off) before proceeding to the next section. FACET by Lab-Volt 177
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