Bandpass Filter Design - Maple Programming Help

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Bandpass Filter Design

 > $\mathrm{restart}:$

This transfer function defines the response of a Bandpass filter.

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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.

 > $\mathrm{with}\left(\mathrm{DynamicSystems}\right):$
 > $\mathrm{sysTF}≔\mathrm{TransferFunction}\left(G\right)$
 ${\mathrm{sysTF}}{≔}\left[\begin{array}{c}{\mathbf{Transfer Function}}\\ {\mathrm{continuous}}\\ {\mathrm{1 output\left(s\right); 1 input\left(s\right)}}\\ {\mathrm{inputvariable}}{=}\left[{\mathrm{u1}}\left({s}\right)\right]\\ {\mathrm{outputvariable}}{=}\left[{\mathrm{y1}}\left({s}\right)\right]\end{array}\right$ (1)

Now generate a Magnitude plot

 > $\mathrm{MagnitudePlot}\left(\mathrm{sysTF},\mathrm{size}=\left[800,400\right],\mathrm{parameters}=\left[R=1,L=1,C=1\right],\mathrm{background}=\mathrm{ColorTools}:-\mathrm{Color}\left("RGB",\left[221/255,231/255,240/255\right]\right),\mathrm{thickness}=0\right)$

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.

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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).

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 > $\mathrm{plots}:-\mathrm{display}\left(\mathrm{p1},\mathrm{p2}\right)$

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