The next circuit Has the next Transfer Function Hs r3 R4r3

The next circuit Has the next Transfer Function: H(s) = r3 + R4/r3/s^2 (R1R2C1C2) + s (R1C1 + R2C1 + R1C2 (-R4/R3)) + 1 Using MATLAB - SIMULINK - SIMSCAPE (any way will do) Design a low pass filter (Select its cutoff frequency) using this op amp circuit and test it using your computer microphone or an audio file. Show the frequency spectrum of your original signal and the frequency spectrum after the filter. Compare with the filter\'s frequency response.

Solution

A first-order filter, for example, reduces the signal amplitude by half (so power reduces by a factor of 4, or 6 dB), every time the frequency doubles (goes up one octave); more precisely, the power rolloff approaches 20 dB per decade in the limit of high frequency. The magnitude Bode plot for a first-order filter looks like a horizontal line below the cutoff frequency, and a diagonal line above the cutoff frequency. There is also a \"knee curve\" at the boundary between the two, which smoothly transitions between the two straight line regions. If the transfer function of a first-order low-pass filter has a zero as well as a pole, the Bode plot flattens out again, at some maximum attenuation of high frequencies; such an effect is caused for example by a little bit of the input leaking around the one-pole filter; this one-pole–one-zero filter is still a first-order low-pass. See Pole–zero plot and R