Cascading biquad filter- calculating the effective frequency

[aibrahim]

Cascading biquad filter

Hello all,

I'm designing a fourth order filter by designing 2 biquad filters in cascade . can any one tell me how i can calculate the effective frequency band wo of the filter and also the effective quality factor Q based on wo, Q of each biquad section.
If there is any PDF describe this phenomena this will be of a great help.

Best Regards,

 

[LvW]

Re: Cascading biquad filter

Hello all,

I'm designing a fourth order filter by designing 2 biquad filters in cascade . can any one tell me how i can calculate the effective frequency band wo of the filter and also the effective quality factor Q based on wo, Q of each biquad section.
If there is any PDF describe this phenomena this will be of a great help.
Best Regards,

What kind of filter are you speaking of ? Lowpass, highpass, bandpass, notch .....?
What kind of approximation do you want ? (Butterworth, Chebysheff, ...)
What do you mean with "effective frequency band" ?

You see, a general answer is not possible. You need some basics of filter design as well as some tabulated filter parameters (pole Q and pole frequency) for the various approximations. Look for example at
http://www.circuitsage.com/filter.html

Or you can try to become familiar with some filter design programs which you can download for free from the internet.

 

[Kral]

Re: Cascading biquad filter

aibrahim,
You can calculate the effective bandwidth of any number of cascaded sections by doing the following:
Make the substitution s=jw in the transfer function for each section to get the frequency domain response.
.
Multiply the frequency domain responses to get the overall frequency response.
.
Calculate the frequenciesy at which the normalized gain = 1/(Sqrt(2)). The difference between the two frequencies is the bandwidth (BW).
.
Let f0 = the frequency at which the (normalized) gain = 1.
.
Q = BW/f0.
.
Regards,
Kral

 

[LvW]

Re: Cascading biquad filter

Aibrahim,

the procedure as proposed above by KRAL is in general NOT applicable; it may be OK for one or some very specific cases.

Added after 19 minutes:

KRAL, do you really recommend to calculate the magnitude of an 4th order function and to set it equal to 1/sqrt(2) in order to get the 3-dB-frequency ???
Have you done already something similar ? I can´t believe it.

 

[Kral]

Re: Cascading biquad filter

LvW has a point. It helps to have some kind of math package with a solver, such as MathCad. If you can settle for an approximate solution, you can plot the function in a spreadsheet, and solve it graphically.
regards,
Kral