Active Filter Design - Laboratory Experiment 12 | ECE 225, Lab Reports of Electrical Circuit Analysis

Download Active Filter Design - Laboratory Experiment 12 | ECE 225 and more Lab Reports Electrical Circuit Analysis in PDF only on Docsity! Boise State University Department of Electrical and Computer Engineering ECE225L – Circuit Analysis and Design Lab Experiment #12: Active Filter Design 1 Objectives The objectives of this laboratory experiment are to design a second-order active Sallen and Key bandpass filter and to investigate its filtering characteristics. 2 Theory Filters perform different roles in many types of electronic equipment. In power supplies, they are frequently used to attenuate undesirable ripple. In audio circuits, they are used for bass and treble control. In signal processing applications, they are sometimes used to band limit a signal before sampling it. There are four basic types of filters: the low-pass, the high-pass, the bandpass, and the bandstop (or bandreject or notch). Analog filters are classified as either passive or active. Passive filters are designed using only passive components (resistors, inductors, and capacitors). Active filters, on the other hand, are built using passive elements along with active devices such as transistors and op-amps. A circuit derived by amplifying the output of a passive filter using an op-amp cannot be called an active filter! The op-amp must be part of the resonant circuit or feedback loop. Op- amps are generally preferred over transistors in active filters because of their high performance characteristics and low cost. R F R I C 1 + − + − v (t) i v (t) o + − R 2 + − v (t) 3 R 3 2R 1 C Figure 1: Second-Order Sallen and Key Bandpass Filter 1 Typically, an active filter uses combinations of op-amps, resistors, and capacitors to obtain a re- sponse equal to or better than that of a passive filter. For example, in order to obtain a sharp response using a passive filter, several passive stages may have to be cascaded. Each stage would tend to load down the previous stage attenuating not only the undesirable frequencies but also the wanted frequency part of the signal to be filtered. This problem is referred to as insertion loss. Active filters practically eliminate insertion loss due to the high input impedance and low output impedance of an op-amp. Furthermore, with active filtering, we can attenuate unwanted frequencies while amplifying desired ones. Two other advantages of active filters include simplicity of design and ease of tuning. Additionally, active filters usually do not use inductors which are bulky, expensive, and depart substantially from the ideal than capacitors. In this experiment, we will investigate the performance characteristics of a bandpass filter using an active Sallen and Key filter. First, let us review some important parameters of a bandpass filter. Refer to Figure 2 for the physical description of each term. Center Frequency: The center or resonant frequency, fo is the frequency at which the maximum gain of the filter occurs. Maximum Gain: The maximum gain Ho is the ratio of the output amplitude Vo,pp to the input amplitude Vi,pp at the center or resonant frequency fo: Ho = Vo,pp Vi,pp (1) Lower and Upper Cutoff Frequencies: The lower and upper cutoff frequencies (also called half- power frequencies) fL and fH are, respectively, the frequencies below and above the resonant frequency where the filter gain drops to 1/ √ 2 of its maximum value Ho. These frequencies are also called the 3-dB frequencies because their gain is 3 dB lower than the maximum gain Ho in dB. Thus, H1 = H2 = Ho√ 2 or (2) 20 log10 H1 (dB) = 20 log10 H2 (dB) = 20 log10 Ho − 3 (dB) (3) Theoretically, the resonant frequency fo is the geometric mean of the half-power frequencies fL and fH , that is fo = √ fLfH (4) Passband: The passband is the frequency range for the part of the signal that is not attenuated (i.e., the gain is still within 3 dB of the maximum gain). Hence, the frequency range for the passband lies between the lower and upper cutoff frequencies, fL and fH . Bandwidth: The bandwidth, given by β, is closely related to the passband. The bandwidth is essentially a measure of how wide the passband is. That is, the bandwidth is the difference between the upper and lower cutoff frequencies β = fH − fL (5) Quality Factor: The quality factor of a filter is denoted Q. This is a dimensionless quantity expressed as the ratio of the center frequency to the bandwidth Q = fo β (6) 2 4 Procedure Part A: Fourier Series 0 T 2 T 3T 2 2T 5T 2 −2.5 −5.0 2.5 5.0 v(t) (V) t (s) Figure 3: Test Periodic Waveform 1. Program the periodic waveform shown in Figure 3 using the arbitrary function generator and the instructions on pages 103-108. Use N = 12 points and enter the following: Start Point Value End Point Value 00000 0.5000 00001 0.5000 00002 1.0000 00003 1.0000 00004 0.5000 00005 0.5000 00006 -0.5000 00007 -0.5000 00008 -1.0000 00009 -1.0000 00010 -0.5000 00011 -0.5000 2. Set the frequency of the trapezoidal waveform at 1 kHz and display about 40 complete cycles on the scope. Run an FFT magnitude on this waveform. Use the markers to measure the harmonics present. The frequency scale should be at 1 kHz per division. Save a plot of the harmonic spectrum. (What harmonics of the fundamental frequency are either missing or attenuated?) Part B: Transfer Function of an Active Bandpass Filter 1. Select R1 = R2 = RI = 3.3 kΩ, R3 = 2 × 3.3 kΩ, and C1 = C2 = 0.047 µF for the Sallen and Key bandpass filter shown in Figure 1. For RF , use a 10-kΩ potentiometer. Connect a function generator (sine wave, 5-V peak-to-peak, zero offset) to the input and adjust the frequency and the feedback resistor RF until you obtain an output waveform that is 5-V peak-to-peak and in phase with the input waveform. (Use the Lissajous or X-Y feature of the scope.) 2. Apply the arbitrary waveform shown in Figure 3 to the input of the Sallen and Key filter. Adjust the amplitude to 5 V peak-to-peak, the frequency to the resonant frequency fo found above. Submit a plot of this input waveform as well as the output waveform superimposed on each other. 5 Part C: Active Filter Design 1. In this part, you will design an active filter to clean up the output waveform observed in Part B.2. Using the same setup, adjust the frequency and the feedback resistor RF until you obtain an output waveform that is 25-V peak-to-peak and in phase with the input waveform. (Use the Lissajous or X-Y feature of the scope.) 2. Vary the frequency of the input sinusoid on both sides of the resonant frequency and record the amplitude (peak-to-peak) of the input and output sinusoids over a sufficient range to plot the frequency response of the Sallen and Key bandpass filter. Adjust the peak-to-peak amplitude of the input sinusoid at every test frequency if necessary. f (Hz) Vo,pp (V) Vi,pp (V) H = Vo/Vi 7.50 5.00 10.00 5.00 12.50 5.00 15.00 5.00 17.50 5.00 20.00 5.00 22.50 5.00 25.00 5.00 22.50 5.00 20.00 5.00 17.50 5.00 15.00 5.00 12.50 5.00 10.00 5.00 7.50 5.00 3. Apply the arbitrary waveform shown in Figure 3 to the input of the Sallen and Key filter. Adjust the amplitude to 5 V peak-to-peak, the frequency to the resonant frequency fo found above. Submit a plot of this input waveform as well as the output waveform superimposed on each other. 4. Record the exact values of these components using an RLC meter. (Use a test frequency of 1 kHz for the RLC meter.) R1 (kΩ) R2 (kΩ) R3 (kΩ) RI (kΩ) RF (kΩ) C1 (µF) C2 (µF) Nominal 3.3k 3.3k 6.6k 3.3k 4.95k 0.047µ 0.047µ Measured 5. Increase RF until your filter becomes unstable. This instability will manifest itself in a ringing or saturation of the sinusoid as viewed on trace 2 of the oscilloscope at certain or all frequencies. Then, reduce the feedback resistor RF slightly and record its value. Keep below this critical value when designing your filter. 6 5 Report Questions 1. What harmonics of the fundamental frequency are either missing or are attenuated in Part A? 2. Comment on the output of the active filter in Part B.2. 3. Plot the normalized magnitude H/Ho of the frequency response from your results in Part C.2. (Submit two plots: One plot with a linear frequency axis and a linear gain axis, and another plot with a logarithmic frequency axis and a gain axis in decibels (dB). Comment on the shapes of both plots.) 4. Measure the following parameters directly from the plot and compare them to the nominal ones as well as those predicted using the exact measured values in Equations (13) and (15). fo (Hz) fL (Hz) fH (Hz) β = fH − fL (Hz) Ho Q K Nominal 1000 - - 500 5 2 5/2 Measured 5. Comment on the output of the active filter in Part C.3. 7