Electronics > Beginners
Bandpass Filter Design
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Wimberleytech:

--- Quote from: Yansi on May 02, 2018, 05:32:53 pm ---Replace it with 0ohm. That is what should be there. (Sallen key 2nd order, bessel Q=0.5 fc=1.5kHz, R1=R2=10k, C1=C2=10n)  :-//

--- End quote ---

The reason he is using the modified SK is to compensate for GBW of the opamp.  In one of the earlier posts, he references the TI application note discussing this.
Benta:

--- Quote from: Rigolon on May 02, 2018, 05:50:38 pm ---So if I want a better roll-off isn't better to use the same fc? So I get 80 db/dec roll off?
Or are there any advantages or reasons to use different fc?

--- End quote ---

Refer back to my post #18.
You keep focusing on fc, but this is not relevant for the single filter stages. The only fc that's interesting is the fc of the complete filter cascade. The individual stages will have different fc and often different Q.
This is why you need to use the pole tables for the different responses (Butterworth, Bessel etc.). Each second-order section gets its own set of complex conjugate poles.

Any filter type (Bessel etc., Cauer excepted) will at the end all have the same rolloff depending on filter order, the difference is what happens below and above the cutoff frequency.
Nitrousoxide:

--- Quote from: Rigolon on May 02, 2018, 04:26:27 pm ---In the case where fc is not the same for how do I know fc? Let's say I have a LPF with fc1 = 10kHz and another LPF with  fc2 = 50kHz, the final fc it's equal to the smallest one or is there some kind of equation?

--- End quote ---

I believe you can take the geometric mean of the two cascaded centre frequencies. i.e. sqrt(10*50) = 22.3607.

edit: As mentioned before a bode plot would give you better information.
Wimberleytech:

--- Quote from: Nitrousoxide on May 03, 2018, 11:19:23 am ---
--- Quote from: Rigolon on May 02, 2018, 04:26:27 pm ---In the case where fc is not the same for how do I know fc? Let's say I have a LPF with fc1 = 10kHz and another LPF with  fc2 = 50kHz, the final fc it's equal to the smallest one or is there some kind of equation?

--- End quote ---

I believe you can take the geometric mean of the two cascaded centre frequencies. i.e. sqrt(10*50) = 22.3607.

edit: As mentioned before a bode plot would give you better information.

--- End quote ---

It depends on how fc is defined.  Is it the -3dB point?  That would be typical.  Think about this...
If you have a single pole LP filter with a -3dB point at 10kHz, then cascade it with a single pole LP filter having a -3dB point at 50kHz, will the -3dB frequency increase above 10kHz?

Now, if compare terms of the standard second-order polynomial: s2 + W0/Q S + W02 to s2 + 2W1W2 S + W1W2 then W0 is geometric mean of W1 and W2
Rigolon:

--- Quote ---You keep focusing on fc, but this is not relevant for the single filter stages. The only fc that's interesting is the fc of the complete filter cascade. The individual stages will have different fc and often different Q.
This is why you need to use the pole tables for the different responses (Butterworth, Bessel etc.).

--- End quote ---

I've actually never worked with these tables before, I asked about the fc because I was thinking how to build each stage using the math, but I guess doing this is more to researchers or experts on the matter. Since my goal is to learn about electronics in general and try to work as a developer someday, the best thing I do is to keep more simple and use tools that are already there. It's just that I get excited and want to learn all the details  :-/O.


--- Quote from: Wimberleytech on May 03, 2018, 01:23:52 pm ---
--- Quote from: Nitrousoxide on May 03, 2018, 11:19:23 am ---
--- Quote from: Rigolon on May 02, 2018, 04:26:27 pm ---In the case where fc is not the same for how do I know fc? Let's say I have a LPF with fc1 = 10kHz and another LPF with  fc2 = 50kHz, the final fc it's equal to the smallest one or is there some kind of equation?

--- End quote ---

I believe you can take the geometric mean of the two cascaded centre frequencies. i.e. sqrt(10*50) = 22.3607.

edit: As mentioned before a bode plot would give you better information.

--- End quote ---

It depends on how fc is defined.  Is it the -3dB point?  That would be typical.  Think about this...
If you have a single pole LP filter with a -3dB point at 10kHz, then cascade it with a single pole LP filter having a -3dB point at 50kHz, will the -3dB frequency increase above 10kHz?

Now, if compare terms of the standard second-order polynomial: s2 + W0/Q S + W02 to s2 + 2W1W2 S + W1W2 then W0 is geometric mean of W1 and W2

--- End quote ---

I see.
I thought fc was always the -3dB point, didn't know that are other ways to define it.


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