a question about the Q of high order LPF

Since we know that a high order filter can realised by a series of several stages.I am wondering what the exact ralationship between the quality factor of each stage and the quanlity factor of overall.Thank you very much!

davidwx said:

Since we know that a high order filter can realised by a series of several stages.I am wondering what the exact ralationship between the quality factor of each stage and the quanlity factor of overall.Thank you very much!

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1.) It is correct that each stage has a different quality factor; however, the relationship between these different Q values depends on the approximation chosen (Butterworth, Chebyshev, Bessel,...)
2.) An "overall" quality factor can be given only in case of a bandpass. But remember this overall Q has another definition as the pole Q for each stage.
LvW

LvW said:

1.) It is correct that each stage has a different quality factor; however, the relationship between these different Q values depends on the approximation chosen (Butterworth, Chebyshev, Bessel,...)
2.) An "overall" quality factor can be given only in case of a bandpass. But remember this overall Q has another definition as the pole Q for each stage.
LvW

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suppose that i choose Chebyshev II polynomial to approximate the transfer function,what the relationship i could expect.Thank you again!

David, you certainly know that there are several Chebyshev II alternatives depending on
* the degree of the transfer function, and
* the amount of damping in the stop band (zero placement).

More than that, it is not possible to give any relation between the Q values for a selected characteristic. These values result from the transfer function based on the Chebyshev polynoms when it is split into 2nd order expressions.