EE 212L: Multiple Feedback Topology Band-pass Filter and the
Fourier Series
Objective: The purpose of this lab is to design a band-pass
filter that selects a harmonic of a square or triangle wave to
produce a sinusoid.
Pre-lab:
Calculate the trigonometric Fourier Series of a 1kHz square wave
that varies equally (i.e., 50% duty cycle) between 0V and 2V.
For the Multi Feedback Topology Band-pass Filter circuit shown
in Figure 1 below, confirm the transfer function H(s) given below.
Determine parameters for the MFT BPF such that it will pass only
the first harmonic of the square wave's Trigonometric Fourier
Series, and the output will have an amplitude of one. Values for
resistors should roughly stay within the range of 1kΩ to
100kΩ and values for capacitors should roughly stay within the
range of 1nF to several µF.
Plot the frequency response of the designed filter using values
selected for resistors and capacitors, and the transfer function to
confirm your design. Note you'll be confirming this behavior in
lab, so bring a useful copy of the frequency response.
Laboratory Procedure:
Build the circuit as designed in the pre-lab.
Confirm the filter performs as designed by sketching its
amplitude response (make sure to check key values used in the
design) found through measurements and compare to that
predicted in the pre-lab.
Use the function generator to create a square wave of the type
noted in the pre-lab.
Check that the square wave looks as expected on the
oscilloscope and then use the Fast Fourier Transform (FFT) under the
oscilloscope's Math Options to display the square wave's amplitude
spectrum. How does this amplitude spectrum compare to that of the
trigonometric Fourier Series?
Use the square wave as the input to your filter, and sketch
the input and the output. Is your output the sinusoid (amplitude
and frequency) expected? What would change if a low-pass filter
with the first harmonic in the pass-band was implemented instead
of the band-pass filter?
With same square wave as input, can you change the filter's
middle frequency to view the third (second nonzero) harmonic? This
may be possible by changing one resistor, so give it a try and
comment as to why it did or didn't work.