What is a Linkwitz Transformation ?
The Linkwitz transform was developed by Siegfried Linkwitz. It allows you to take a driver in a sealed enclosure that has an Fc and Qtc for that box and lets you "transform" or simulate a new Fc and Qtc for that driver in that box.

How does it work ?
It works by creating a precise equalisation curve to compensate for any peaking or rolling off that the driver is encountering. By doing this, a new Fc and Qtc can be assigned to that system.

Example:
 Driver specifications: Fs = 33.5 Hz Qts = 0.75 Vas = 46.1 litres (1.647 ft3) We put this driver in a 37.5 litres (1.334 ft3) box. This will us a Qtc of 1.12 This speaker in this box will yield the following results: Fc = 50 Hz F3 = 37.6 Hz Qtc = 1.12 Vb = 37.5 litres (1.334 ft3)

1

You may notice in this graph, there is a 1.4 dB hump before the roll off occurs. While this response is ok for your average listener, we are not satisfied with it.

Wouldn't it be nice if we could simply move the Fc down to say 20 Hz and have the Qtc = 0.707 to get a response that looked more like this...

 Fc = 20.0 Hz F3 = 20.0 Hz Qtc = 0.707

2

This graph shows the compensation that the Linkwitz transform
is using in order to flatten out the response curve of the driver