# Band stop filter RLC circuit frequency response

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

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:

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

What am I doing wrong?

Thanks in advance. This is very appreciated.

• This is not a notch filter - bandstop. May 3, 2021 at 17:17
• @MarkoBuršič Is this a band pass filiter? May 3, 2021 at 17:21
• @FreeZe yes that is true, it is a band-pass. May 3, 2021 at 17:21
• @Jan No. It could be lowpass, but not bandstop or bandpass. May 3, 2021 at 17:26
• 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). May 3, 2021 at 17:29