Critical Q design theory


Paid Member
2007-07-17 2:35 am
Central Berlin, Germany
Well, the engineering terms on this are quite clear. Critical Q, more precisely called filter response with critical characteristic (opposed to any other characteristic with higher Q like Bessel, Butterworth, Chebycheff), is when you have a set of all real and identical poles in the overall acoustical transfer function's denominator. It is not dependent on the construction type and can be had with CB, BR, BP, OB, Horns and what have you.

The specific merits of a highpass of this type (with the highpass variant we deal with in subwoofer design) is that it shows the minimum overshoot in the time domain, when fed a square pulse, which is synonymous with the flattest achievable group delay change. That's what is critical about it, you can't get beyond these barriers. The compromise (if any) is the very gradual transition into the roll-off. Like Linkwitz put it: the merits of a butterworth highpass are no other than to look good.

The simplest way to model it electrically is a buffered(!) cascade of identical first order highpass networks (simple C-R combos). The electrical analogies are also a good starting point for studies, see for example (unfortunately critical filters are not discussed directly by uising that naming -- they call it simple low-pass, but high-pass isn't covered -- , but you can still get the overall concept).

- Klaus
I am fairly sure that what you have described as a critical Q filter is in fact a Bessel filter. A bessel filter is maximally falt in the time domain, i.e there is no peak in the group delay. It has a Q of 0.505 and this is consistant with the information on the sub design.

Personaly I don't think that the Q of 0.5 is the important factor in this type of Sub sounding good. I think it is because it matches the kind of rise you get from the room gain so you are less likely to get a big hump in the response at the bottom end.

Since the acoustic response is what is important in the waveform shape, it is unlikely that this has a Q of 0.505 in room so it is unlikely that the group delay advantage is mantained.

Having said this, when working on a sub design I had the benifit of an adjustable linkwitz transform box and I can definately say that the sub intergrated into the room best at a Q of arround 0.5 so this is what I designed the LT that when in the amp to do.