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Comments on Band pass filter given cutoff frequency and bandwidth

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Band pass filter given cutoff frequency and bandwidth

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I have decided to try design a band-pass filter with a cut-off frequency of 10kHz and bandwidth of 2 Hz.

Image alt text

$$ \frac{1}{\sqrt{LC}} = 10001 \rightarrow LC = 1/100020001 sec^{2}$$

$$ \frac{R}{L} = 2Hz$$$$ \frac{1}{RC} = 2Hz$$

Here is what I have done but if I plug the values to WolphramAlpha

it says it doesnt have any solutions.What am I doing wrong?

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4 comment threads

What's the purpose? (4 comments)
Unreadable image deleted. (2 comments)
Equations (1 comment)
"Bandwidth"? (1 comment)
What's the purpose?
a concerned citizen‭ wrote over 2 years ago

Did you mean "center frequency"? If so, even for a 20 dB attenuation at 1000 times the bandwidth in the stopband, I run into numerical issues and can't get such a high order, and thi sis for a Cauer/elliptic filter. You could try a 2nd order, but that would mean a Q of f0/BW=5000. You'll likely need an xtal for that. A 32768 Hz for watches is in the order of tens of thousands. But, before that, can you say what it is for? It sounds like an XY problem.

MissMulan‭ wrote over 2 years ago

No I don't mean center frequency I mean bandwidth of the pass band filter,the range of frequencies at which the attenuation is higher than - 3dB

a concerned citizen‭ wrote over 2 years ago

MissMulan‭ I meant about the 10 kHz part because, as Olin says in his answer, that's not a characteristic of a bandpass filter. But you can define it in terms of center frequency and bandwidth (and attenuations in both pass- and stop-band). You haven't answered, though: what purpose will that filter serve? There may be different, less absurd ways to do it -- because a 2 Hz bandwidth at 10 kHz is absurd. For a 2nd order, the settling time will be 4.6 s for 1%.

MissMulan‭ wrote over 2 years ago

Ya I agree Q will be really high.