L303.9.V5
91
Drexel University
Electrical and Computer Engineering Dept.
Electrical Engineering Laboratory III,
ECEL 303
E. L. Gerber
FOURIER
ANALYSIS
and
THIRD_ORDER FILTER DESIGN and ANALYSIS
Object
The object of this experiment is to become familiar with some properties of the Butterworth
thirdorder filter. Then you will design a filter and observe the effect that the filter has on the
frequency content of a periodic signal passing through it. Both computer simulation and real
circuits will be examined.
Theory
Consider the thirdorder low pass filter below. The transfer function of an ideal thirdorder
Butterworth filter (see the Appendix Eqs. 5 and 10) is written in terms of the corner
frequency, C = 2
π
f
c
, rad/sec., and its magnitude is,
H
(
s
)
=
C
3
s
3
+
2
Cs
2
+
2
C
2
s
+
C
3
abs
[
H
(
f
)]
=
1
1
+
(
f
/
f
c
)
6
ThirdOrder Filter #2.
We can determine the output, v
o
(t), of this filter with a unit square wave input, as we
did last week. We can calculate the output voltage at each of the harmonic frequencies of the
Fourier series of the input. The solution to this system is much more complicated than the
firstorder filter that we did last week. So we can use Maple to solve the thirdorder transfer
function H
3
(s) of this filter. Maple can then be used to solve for the output terms as was done
in the firstorder circuit earlier. Use the magnitude expression H(f) to solve for the values of
H at the first ten nonzero terms.
In order to obtain the output waveform from these terms
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L303.9.V5
92
you must sum the various terms with the appropriate phase and frequency. This can be
accomplished in Maple by combining (sum) the magnitude of the transfer function with the
Fourier series terms including the phase of the transfer function. That is, at each frequency
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 Fall '07
 GERBER
 Fourier Series, Square wave, Lowpass filter, Butterworth Filter

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