Design a second order low pass Butterworth filter with a cutoff frequency 300 pi

Question

Design a second order low pass Butterworth filter with a cutoff frequency 300 pi rad/s (see Figure 6.12a, page 307). The input signal is a square wave of magnitude plusminus 1 V as shown in Example 6.6, and with a fundamental frequency of 200 pi rad/s. Assume R_0 = 2 k Ohm and answer the following: Use the butter (N, Wn, 's') command in Matlab to generate the transfer function (Please note that the s variable in Matlab is equivalent to j omega. Find the magnitude and phase spectra of the filter. Use Matlab and Simulink to plot the magnitude spectrum of the input X omega and the output signal Y omega, on the same Figure, and analyze your result. Use Multiuse simulator to check the results in (ii) and to plot the output filtered signal y(t). In the laboratory, fabricate the designed second order low pass Butterworth filter, and show y(t) on the oscilloscope. Use transfer function block in Simulink to model the filter. The pulse generator block can be used to model the source. Attach a Scope to the output of the transfer function block to observe the output signal.

Explanation / Answer

Command Window log:

>> [B A] = butter(2,300*pi,'s')

B =

1.0e+005 *

0 0 8.8826

A =

1.0e+005 *

0.0000 0.0133 8.8826

>> tf(B,A)

Transfer function:
8.883e005
------------------------
s^2 + 1333 s + 8.883e005

>>

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