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12th July 2010, 12:25 #1
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Re: cutoff frequency of seond order low pass filter
how to calculate the cutoff frequency of seond order low pass filter mathematically?
anyone knows?
Added after 23 minutes:
to be more exact, i mean how to calculate fc (cutoff) from the transfer function, similar to the Q, Wp calculation.

12th July 2010, 12:25

12th July 2010, 12:58 #2
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Re: cutoff frequency of seond order low pass filter
Originally Posted by edafisher
1.) Calcualte the magnitude of the transfer function
2.) Set the magnitude equal to 0.7071 (for 3dB cutoff) and solve for w.
3.) For Chebyshev and elliptic (Cauer) response: Set the magnitude equal to the value at dc and solve for w.
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12th July 2010, 14:16 #3
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cutoff frequency of seond order low pass filter
thank LvW. I also got the answer at
http://www.engin.umich.edu/group/ctm/freq/wbw.html

12th July 2010, 14:16

12th July 2010, 15:31 #4
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Re: cutoff frequency of seond order low pass filter
Originally Posted by edafisher
are you really sure that the above link contains the information you want
(relationship between cutoff and pole frequency for a second order lowpass) ?

12th July 2010, 15:31

12th July 2010, 15:45 #5
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Re: cutoff frequency of seond order low pass filter
hi Lvw,
thanks for your notice. i found the link gives the wrong formula (lacks a coefficient).
I redo the derivation, and gives the right formula in below
W3dB = Wn * sqrt[12ζ^2+sqrt(4ζ^44ζ^2+2)]
where Wn is the pole frequency and ζ is the damping factor (equals 1/(2Q) )

12th July 2010, 16:03 #6
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Re: cutoff frequency of seond order low pass filter
Congratulations! This formula is correct!

12th July 2010, 16:08 #7
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Re: cutoff frequency of seond order low pass filter
Originally Posted by LvW

12th July 2010, 16:14 #8
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Re: cutoff frequency of seond order low pass filter
Just one additional comment (in case you don't know yet):
The formula gives you the 3dB cutoff.
However, for Chebyshev and elliptic (Cauer) responses it is common (also) to use another definition for cutoff (end of pass band):
The frequency where the peak (ripple) in the pass band crosses the transfer function value at w=0.
In most textbooks, this definitin is used to table the pole data.

12th July 2010, 16:14

13th July 2010, 18:27 #9
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cutoff frequency of seond order low pass filter
How do we choose teh natural frequency of a closed loop??
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