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Assume we have an $ RLC $ circuit as described in the picture

enter image description here

This should be a Band-stop filter. But somethings bother me in my calculations. This is my calculations for the frequency response:

Using the impedance of the inductor and the capacitor, and using voltage divider, we conclude:

$$ V_{out}=\frac{\frac{1}{j\omega C}}{\left(j\omega L+\frac{1}{j\omega C}+R\right)}V_{in}=\frac{1}{\left(1-\omega^{2}LC\right)+R}V_{in} $$

Where $$ V_{out},V_{in} $$ represents phasors.

So now the amplitude given by: $$ |\frac{V_{out}}{V_{in}}|=\frac{1}{\sqrt{\left(1-\omega^{2}LC\right)^{2}+\left(\omega RC\right)^{2}}}=\frac{1}{\sqrt{\left(1-4\pi^{2}LCf^{2}\right)^{2}+\left(2\pi RCf\right)^{2}}}$$

And now if I'll try to plot the graph of the amplitude of the frequency response for, say $$ \begin{cases} R=300\varOmega\\ L=84mH\\ C=8.3nF \end{cases} $$

This is what I get by desmos:

enter image description here

Which does not seem like a Band Stop Filter, as we can see here for example: (photo that I found online)

enter image description here

What am I doing wrong?

Thanks in advance. This is very appreciated.

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    \$\begingroup\$ This is not a notch filter - bandstop. \$\endgroup\$ May 3, 2021 at 17:17
  • \$\begingroup\$ @MarkoBuršič Is this a band pass filiter? \$\endgroup\$
    – FreeZe
    May 3, 2021 at 17:21
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    \$\begingroup\$ @FreeZe yes that is true, it is a band-pass. \$\endgroup\$ May 3, 2021 at 17:21
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    \$\begingroup\$ @Jan No. It could be lowpass, but not bandstop or bandpass. \$\endgroup\$ May 3, 2021 at 17:26
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    \$\begingroup\$ This is a lowpass, plain and simple. The transfer function should make it clear that it's of the form 1/(s^2+s+1). \$\endgroup\$ May 3, 2021 at 17:29

1 Answer 1

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It's a low pass filter. At DC the inductor acts like a short circuit and the capacitor acts like an open circuit. Therefore it lets DC pass. This rules it out as being a band-stop filter.

At high frequencies the inductor blocks input signals producing much output signal and the capacitor shunts high frequencies hence, it is a low pass filter: -

enter image description here

Link to LPF calculator.

It can produce a resonance around the natural frequency of the circuit but, it's still a low pass filter.

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