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.
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.
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.
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Multiply the frequency domain responses to get the overall frequency response.
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Calculate the frequenciesy at which the normalized gain = 1/(Sqrt(2)). The difference between the two frequencies is the bandwidth (BW).
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Let f0 = the frequency at which the (normalized) gain = 1.
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Q = BW/f0.
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Regards,
Kral
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.
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