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Design >> Analog Design >> Definition of Q for lowpass filters
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Message started by fz2101 on Dec 4^th, 2007, 7:57am

Title: Definition of Q for lowpass filters
Post by fz2101 on Dec 4^th, 2007, 7:57am

Hello Everyone,

Is there a general definition of Q for lowpass filters?

For a bandpass filter, there is the definition, Q=wo/bw, where "wo" is the resonant frequency, and "bw" is the
bandwidth.

For second order filters, the filter transfer function has a standard form in its denominator, so Q can
be extracted. For the same reason, each stage of the biquad has a clearly defined Q.

However, what about a third-order filter, e.g., Z21= K/(s^3+2s^2+2s+1), what is its Q, does it have any meaning? Is
there some graphical way of finding it, e.g., amount of peaking, etc?

Thanks

frank

Title: Re: Definition of Q for lowpass filters
Post by ACWWong on Dec 4^th, 2007, 11:46am

For your example i would factorise to yield (s²+s+1)(s+1).
So you have a 2nd order section complex pole pair of Q=1 cascaded with a critically damped (Q=0.5) real pole.
But its true Q or damping factor is only really useful for complex pole pairs.