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cutoff frequency of seond order low pass filter

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edafisher

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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.
 

edafisher said:
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.

The answer is simple - however the calculation itself can be involved:

1.) Calcualte the magnitude of the transfer function
2.) Set the magnitude equal to 0.7071 (for 3-dB 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.
 

    edafisher

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thank LvW. I also got the answer at
**broken link removed**
 

edafisher said:
thank LvW. I also got the answer at
**broken link removed**

Hi edafisher,

are you really sure that the above link contains the information you want
(relationship between cut-off and pole frequency for a second order lowpass) ?
 

hi Lvw,

thanks for your notice. i found the link gives the wrong formula (lacks a coefficient).

I re-do the derivation, and gives the right formula in below

W-3dB = Wn * sqrt[1-2ζ^2+sqrt(4ζ^4-4ζ^2+2)]

where Wn is the pole frequency and ζ is the damping factor (equals 1/(2Q) )
 

Congratulations! This formula is correct!
 

Just one additional comment (in case you don't know yet):

The formula gives you the 3-dB cut-off.
However, for Chebyshev and elliptic (Cauer) responses it is common (also) to use another definition for cut-off (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.
 

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