|Brandeis University||Physics 29a|
|Fall 2017||Kevan Hashemi|
The circuit below is a second-order, single-stage active filter. The ratio R1/(R1+R2) is the gain of the filter. The product RC is its time constant. Look at the Active Filter sheet of our Filter Design Guide spreadsheet, which you will find on the 29A page. You will see example values for the gain and time constant of low-pass filters with cut-off frequency 1 rad/s. The time constant of a filter with cut-off frequency ω rad/s will be ω times smaller than for 1 rad/s. In today's lab, use the TL081 op-amp. You will find its data sheet in the 29A section for Lab 8.
To turn the low-pass active filter into a high-pass active filter, exchange the two resistors with value R with the two capacitors of valuce C. To make a fourth-order, two-stage active filter, connect two of the above circuits in a row.
Whenever you design a filter, you trade off the sharpness of cut-off for uniformity of gain in the pass-band. The Butterworth response is maximally flat in the pass-band. The 3-dB Chebyshev filter allows 30% gain variation in the pass band and has a sharp cut-off. The 0.5-dB Chebyshef filter allows 10% gain variation.
Part 1: Make a second-order, single-stage, active low-pass filter with cut-off frequency 1 kHz. Choose whatever filter response you like. Use the Filter Design Guide spreadsheet to plot the theoretical response of the filter. Measure its gain versus frequency at ten or more points. Does your measurements and perdiction agree?
Part 2: Connect the output of your low-pass filter to the ADC you built for Lab 11. Does the filter prevent aliasing distortion of the digitized waveform?
Part 3: Convert your high-pass filter into a low-pass filter. Measure the gain versus frequency. Is the new cut-off frequency the same as the old?
Part 4: Concatinate two active-filter circuits to make a four-pole 3-dB Chebyshev low-pass filter with cut-off frequency 1 kHz.