Bandpass Filter Design - Maple Help
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Bandpass Filter Design



This transfer function defines the response of a Bandpass filter.

GsR Cs2+sR C+1L C:


The product L C controls the bandpass frequency while R C controls how narrow the passing band is. To build a bandpass filter tuned to the frequency 1 rad/s, set L=C=1 and use R to tune the filter band.


First define a transfer function object.



sysTFTransfer Functioncontinuous1 output(s); 1 input(s)inputvariable=u1soutputvariable=y1s


Now generate a Magnitude plot


As expected, the RLC filter has maximum gain at the frequency 1 rad/s. However, the attenuation is only -10dB half a decade away from this frequency.

To get a narrower passing band, try increasing values of R.

MagnitudePlotsysTF,size=800,400,parameters=R=20, L=1,C=1,background=ColorTools:-ColorRGB,221/255,231/255,240/255,thickness=0

The resistor value R=20 gives a filter narrowly tuned around the target frequency of 1 rad/s.


We can confirm the attenuation properties of the circuit (R=20) by simulating how this filter transforms sine waves with frequency 0.9, 1, and 1.1 rad/s.

Create two response plots for the filter at R=20 with two inputs: sin(0.9 t) and sin(t).

p1ResponsePlotsysTF,sin0.9t,duration=100, parameters=R=20,L=1,C=1:

p2ResponsePlotsysTF,sint,duration=100, parameters=R=20,L=1,C=1,color=black: