BME 3512 Bioelectronics Laboratory Six - Active Filters

Transcription

1 BME 5 Bioelectronics Laboratory Six - Active Filters Learning Objectives: Understand the basic principles of active filters. Describe the differences between active and passive filters. Laboratory Equipment: Agilent Oscilloscope Model 56A Agilent Function Generator Model HP0A Agilent Power Supply Model E6A Multimeter Supplies and Components: Breadboard KΩ esistor.7 KΩ esistor (two each) 0.07 μf capacitor Op-Amp 7 or 58 Pre-Lab Questions. What are the primary differences between active filters and passive filters?. What does the term corner frequency imply?. What does the term Butterworth filter mean? Post-Lab Questions. What are the advantages of active filters over passive filters?. With respect to the ratio of V out / V in, what does + db imply?. List two practical uses of active notch filters.

2 Laboratory Six - Active Filters Laboratory Procedures Previously, we looked at passive filters. When a signal needs to be both amplified and filtered, one can use an op-amp to build an active filter to do the two operations simultaneously. Figure shows an active high-pass filter built around a 7 op-amp. ) Using an op-amp to build an active high-pass filter (filter with gain) =.7K V in = K C = 0.07μF +0V V out V p-p.7k -0V The corner frequency is Figure. An active high-pass filter f 0 = and the gain in the pass band is G = πc +. a) Using the component values, calculate the expected corner frequency and gain. b) Build the circuit according to Figure. The input signal is again a sine wave generated by the Function Generator, and the output is connected to CH of the oscilloscope. The peak-to-peak amplitude of the input signal is V and its frequency changes. c) Set the frequency of the input signal to the following values (unit is Hz): 0, 50, 00, 00, 00, 600, 650, 700, 750, 800, 850, 900, k, k, k, 5k,0k At each frequency, measure the peak-to-peak amplitude of the output signal. d) While maintaining the p-p amplitude of the input signal to be V, adjust the frequency of the input signal until the p-p amplitude of the output signal equals H max * Write down this frequency which is the measured corner frequency. How close are the measured corner frequency and the one determined in a)? e) Based on the measurements in d), calculate the magnitude of the transfer function at each frequency, where V in (f) is V. f) Graph the magnitude of the transfer function as a function of the frequency. Mark the corner frequency on your plot.

3 ) Using an op-amp to build an active low-pass filter Figure shows an active low-pass filter built around a 7 op-amp. C = 0.07μF =.7K V p-p V in = K +0V V out -0V The corner frequency is f 0 Figure. An active low-pass filter = and the gain in the pass band is G = π C. a) Using the component values, calculate the expected corner frequency and gain. b) Build the circuit according to Figure. The input signal is again a sine wave generated by the Function Generator, and the output is connected to CH of the oscilloscope. The peak-topeak amplitude of the input signal is V and its frequency changes. c) Set the frequency of the input signal to the following values (unit is Hz): 0, 50, 00, 00, 00, 600, 650, 700, 750, 800, 850, 900, k, k, k, 5k,0k At each frequency, measure the peak-to-peak amplitude of the output signal. d) While maintaining the p-p amplitude of the input signal to be V, adjust the frequency of the input signal until the p-p amplitude of the output signal equals H max * Write down this frequency which is the measured corner frequency. How close are the measured corner frequency and the one determined in a)? e) Based on the measurements in d), calculate the magnitude of the transfer function at each frequency, where V in (f) is V. f) Graph the magnitude of the transfer function as a function of the frequency. Mark the corner frequency on your plot.

4 Grading ubric: Active Filters (Lab 6) Name: Points Cover Page I) Circuit Diagrams (Circuit Maker Only) a. Experiment Active High Pass Filter b. Experiment Active Low Pass Filter In the circuit diagrams for Experiment and, make sure you label the op-amp with its part number ( LM7CN is the proper name, the common name is 7 or LM7 are acceptable also). Don t forget to label the supply voltages for the op-amp as well as V IN and V OUT. II) Data and esults ) Experiment - Active High Pass Filter / a. All Measured Values of and C b. Equation and Calculation for the Expected Corner (Cutoff) Frequency, f O [Hz] c. Equation and Calculation of the Expected and Actual Amplifier Gain (G) d. Data Table Showing: Input Frequency (f), Input Voltage Magnitude ( V IN ), Output Voltage Magnitude ( V OUT ), and the calculated Transfer Function Magnitude ( H(jw) ). e. Corner Frequency (Measured) When V OUT = (V OUT, MAX ) f. Graph of the Transfer Function Magnitude ( H(jw) ) vs. Frequency (f). ) Experiment - Active Low Pass Filter a. All Measured Values of and C / b. Equation and Calculation for the Expected Corner (Cutoff) Frequency, f O [Hz] c. Equation and Calculation of the Expected and Actual Amplifier Gain (G) d. Data Table Showing: Input Frequency (f), Input Voltage Magnitude ( V IN ), Output Voltage Magnitude ( V OUT ), and the calculated Transfer Function Magnitude ( H(jw) ). e. Corner Frequency (Measured) When V OUT = (V OUT, MAX ) f. Graph of the Transfer Function Magnitude ( H(jw) ) vs. Frequency (f). III) Discussion ) Experiment - Active High Pass Filter a. In lab, you used a closed form equation to calculate the predicted transfer function magnitude for a passive high pass filter based on the measured values. For this lab, we are going to use your understanding of how the active filter affects H(jw). Develop an equation for the predicted H(jw) of the high pass filter only using, C,, and as variables. Then using the measured values of, C,, and, use your own closed form equation to calculate the H(jw) of your filter (using the same frequency points as from lab). b. Plot the predicted H(jw) on the same graph as the experimental H(jw) (making sure that you label y-axis, x-axis, title and legend properly. c. Comment on how the experimental data and the predicated data from the closed form equation are / related.

5 ) Experiment Active Low Pass Filter a. In lab, you used a closed form equation to calculate the predicted transfer function magnitude for a passive low pass filter based on the measured values. For this lab, we are going to use your understanding of how the active filter affects H(jw). Develop an equation for the predicted H(jw) of the low pass filter only using, C,, and as variables. Then using the measured values of, C,, and, use your own closed form equation to calculate the H(jw) of your filter (using the same frequency points as from lab). b. Plot the predicted H(jw) on the same graph as the experimental H(jw) (making sure that you label y-axis, x-axis, title and legend properly. c. Comment on how the experimental data and the predicated data from the closed form equation are related. IV) Post-Lab Questions Post Lab Question #: Hint answer this question first: With respect to the ratio of V OUT /V IN, what does 0 db imply? After answering the hint, proceed to answer the post-lab question. Note: there is an error in the lab manual; lab question should read -db. V) eferences / / 8 / 5