Theory

The Karlson may be called a broadband-resonator; the resonator in the design is an aircolumn (in an on one side closed pipe). These pipes however have a nasty habit. They not only resonate on a frequency with a wavelength four times the length of the column, but also on the odd harmonics of this frequency. the characteristics are sketched in fig 1-a.
fig 1 a,b,c. Halfopen pipe resonance
 

At frequencies of which the colmumnlength equals half the wavelength or a multitude of that, the reflection at the open end of the pipe is in anti-fase, causing an acoustic shortcircuit, resulting in an almost nihil radiation.
If we now make a cut at the open end of the pipe, then the effect of this is that the pipe doesn't have a distinct length anymore, causing the peeks at odd harmonics to widen. (fig 1b)
If we make the cut stretch up to 2/3 of the pipe, and make the cut exponential in width, the broadband of fig. 1c is the result.

 

Maybe it's hard to find a pipe with an exponential cut in the construction, also because John Karlson added in the bass-reflex principle to increase the radiation at lower frequencies even more. The Karlson can
therefore be seen as a special bass-reflex enclosure, of which the port is loaded with an open pipe that has an exponential cut.
fig2. Karlson design