Bandpass Filter Design - Maple Programming Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Applications and Example Worksheets : Science and Engineering : applications/BandpassFilter

Bandpass Filter Design

 

restart:

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.

withDynamicSystems:

sysTFTransferFunctionG

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

(1)

Now generate a Magnitude plot

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

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:

plots:-displayp1,p2