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Definition of Q for lowpass filters (Read 1578 times)
fz2101
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Definition of Q for lowpass filters
Dec 04th, 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
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ACWWong
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Re: Definition of Q for lowpass filters
Reply #1 - Dec 4th, 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.
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