# How's this filter calculated?

Discussion in 'General Electronics Chat' started by Dawud Beale, Dec 8, 2014.

1. ### Dawud Beale Thread Starter Member

Feb 10, 2012
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Last edited: Dec 8, 2014

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3. ### wmodavis Well-Known Member

Oct 23, 2010
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Enter four values, C1, Minimum Freq, Maximum Freq & Passband Gain then click on the CALCULATE button.

4. ### Dawud Beale Thread Starter Member

Feb 10, 2012
275
7
Thanks Bertus I will take a look.

wmodavis, sorry i should have been a bit clearer, I know how to generate the filter using the calculator, I was wondering what the underlying calculations were that were deriving the filter values

5. ### wmodavis Well-Known Member

Oct 23, 2010
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I believe in clarity.

6. ### MrAl Distinguished Member

Jun 17, 2014
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Hi,

Are you familiar with "Nodal Analysis" ?

7. ### Papabravo Expert

Feb 24, 2006
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The underlying analysis can be found in: Van Valkenburg, Analog Filter Design.
The analysis begins with a derivation of the only transfer function that guarantees a maximally flat response.

Jun 6, 2011
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9. ### MrAl Distinguished Member

Jun 17, 2014
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Hi,

Just in case you are still interested, here is the amplitude response:
Vout=(Vin*w^2*C1^2*R2*R3*R5*R6)/(sqrt((-w^2*C1^2*R1*R2*R3+R2+R1)^2+4*w^2*C1^2*R1^2*R2^2)*sqrt((-w^2*C1^2*R4*R5*R6+R5+R4)^2+4*w^2*C1^2*R4^2*R5^2))

with w=2*pi*f, f=frequency in Hertz.

Sometimes the caps are not made equal to each other (for each stage) and that allows a sharper response when needed.

10. ### t_n_k AAC Fanatic!

Mar 6, 2009
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I suspect there is no simple answer to your question. As Papabravo indicates there is a significant body of knowledge one has to assimilate before gaining a grasp of the subject. One simply has to Google "4th Order Bandpass Active RC Filter Design" to readily appreciate the level of background understanding required & the various technical subtleties involved.

Last edited: Dec 9, 2014
11. ### Papabravo Expert

Feb 24, 2006
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The transfer function of a maximally flat magnitude response leads to a root locus the defines that response. The location of the poles is used to imply the components for a low pass response. The component values for the low pass response are then transformed into components for the bandpass response and the whole thing is scaled to the frequency of interest, the input impedance, and output impedance. If you want the details you'll just have to dig deeper.

You can start here:
http://www.crbond.com/papers/btf2.pdf

12. ### joeyd999 AAC Fanatic!

Jun 6, 2011
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Actually, an MFBP filters are quite easy to calculate. The loop gain for each stage is dependent solely on Q, which is dependent upon bandwidth and f0. An attenuator network is pasted onto the front end of the stage to achieve stage gains less then the Q dependent loop gain (R1 & R2 and R4 & R5 in the OPs web link).

All these calculations are performed in the spreadsheet I wrote and linked to above. It is quite educational.

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13. ### t_n_k AAC Fanatic!

Mar 6, 2009
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No doubt once the correct formulae are at hand there's no issue with entering values for the specific design parameters.
I wondered if OP was perhaps looking for a deeper understanding of the methodology underpinning the number crunching applet. Maybe they were simply looking for the applicable equations. Who knows...
Perhaps they were satisfed with the answers received & moved on - as is often the case.

14. ### Papabravo Expert

Feb 24, 2006
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That is why I suggested the reference that I did. It is the best explanation I have found to the question. Once you understand it for the passive case, the active case comes more quickly into focus. People ignore my advice all the time, but I never(well almost never) take it personally.

Not as good an explanations is the wiki
http://en.wikipedia.org/wiki/Butterworth_filter

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15. ### t_n_k AAC Fanatic!

Mar 6, 2009
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I am always impressed with your insightful contributions - even though I rarely respond. There are many worthy contributions from others that also often come & go unacknowledged most of the time.
If we actually expected the thanks (albeit acknowledgement) we thought due, at least from the perspective of everyday courtesy, we probably wouldn't even bother with contributing. Goes with the territory it seems. Sort of a cargo cult ....
Hopefully it improves the lives & opportunities of others seeking help.

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