Dipl.Biol.
ErnstGeorg Beck The KCoupler A New Acoustical Impedance Transformer A loudspeaker is an
electromechanical transformer that, as the name implies,
converts electrical into acoustical signals. In the
simplest case a membrane radiates sound directly into the
surrounding air (direct radiator). Another possibility is
to couple the radiating membrane to the air through a
horn. The KCoupler described here is a special kind of
horn. While looking for an optimal acoustical
impedance transformer the American John E. Karlson took
to a new road. In three patents (1951, 1954 & 1968)
he presented a solution to be noted, which combined the
advantages of the newer acoustical horns, high
efficiency, high bandwidth, and wide horizontal
dispersion, with other properties hitherto not feasible
under high efficiency: the KCoupler. This design (fig 1)
consists of a tube with an exponential cut along the
side. The basic idea is as follows: when a membrane radiates sound in an infinite pipe, it meets constant, frequencyindependent radiation resistance. Finite pipes however present only a small usable radiation resistance. [1] Furthermore, low frequencyreflections arise because of the fixed length of the pipe, causing rough impedance and frequency responses. Such systems create resonances due to the vibrating aircolumn. Sound is only radiated at a pipelength/wavelength fraction of ¼, ¾, 5/4, 7/4 etc. To create more resonances, the pipe can have more openings, as have a lot of wind instruments.
Frequency response and efficiency The frequency response of the KCoupler
is determined by the mathematical function of the cut,
and the length of the pipe. The bottom frequency follows
from the wavelength four times the length of the
KCoupler, dropping by 12dB/octave below that. An upper
frequency can be determined theoretically nor
practically. The mid/high implementation of the
KCoupler, the Tube, yields a flat response up to 20 kHz
using a TAD 2001 driver. Because the radiation resistance above
the bottom frequency coincides with the radiation
resistance of a finite pipe or exponential horn at high
frequencies, values for efficiency are around 50 %.
However, exponential horns can only reach this value in a
small bandwidth. Not the KCoupler, having a high
efficiency from lowest to highest frequency. Distortions Unlike horns, the KCoupler has no
small opening, so no distortion can be caused by one.
Measurements indicated no harmonical or intermodulation
distortion. Auditory tests also indicate no exceptions in
that matter. In comparing the Tube verses various
longthrow, radial and diffraction horns it showed a
good resolution, dynamics and lack of coloration. Radiation Due to the construction of the
KCoupler, sound is projected in another way than with
usual systems. The radiation of sound through the cut is
determined by reflections on the inside of the pipe. This
causes the horizontal radiation of sound to be determined
by the form of the crosssection. A combination of flat
walls causes 'lobes' (polar diagram of multicell horns in
[1]). Elliptical or circular crosssections yield an
almost halfcircular frequencyindependent projection. 
Just that is only approachable with horns. With the Tube a horizontal radiation angle of about 120° was measured. Also, every frequency has its defined point of origin along the cut. Vertically the Tube radiates in a plane which, depending on used compression driver, lies in an angle of about 35° below the length axis of the Tube, and doesn't increase with distance. These projection properties allow the KCoupler to be used as shortthrow mid/high range unit. On the other hand, frequency measurements as used with horns and direct radiators can only be limitedly compared: an SPL measurement at a meter distance yields a nonlinear characteristic depending on angle of measurement. Also important is the fact that, as opposed to horns, the sound level doesn't decrease to a quarter, but to a half with a double distance [3]. 
Practical design of the KCoupler: basshybridenclosure
The oldest
use of the KCoupler idea is in a basshybridenclosure
(fig 2). This construction is mostly a combination of the
KCoupler with bassreflex. The relatively small enclosure
allows a radiation of about 50…900 Hz under high
efficiency. However, the frequency response shows two
constructiondetermined dips, and furthermore the SPL
drops 6 dB above 900 Hz. The dips are caused by the use of parallel walls in the front chamber 1. Chamber 2  behind the speaker  is connected with chamber 1 through opening X. So, the loudspeaker radiates backwards through a system of two chambers, causing flaws in the frequency response. Because of the vertical length of 80 cm, sound is radiated up to 130 Hz. Below this frequency the reflexports start working. The direct radiation of the driver amplifies the upper frequencies. The nonlinear frequency response is furthermore caused by standing waves in the KCoupler and parallel construction. Fig 2: Basshybridenclosure as a combination of bassreflexenclosure and KCoupler. 
This
enclosure has been in the interest of professional audio
since 1980/81. As a bassenclosure for small PAsets and
as an instrumentloudspeaker it has convinced several
musicians, even though it has the mentioned
characteristics. Unfortunately, in the PA market the
emptyenclosure fever has broken out, leaving the
musician with the choice of which driver one uses. This,
in conjunction with financial causes, most of the time
leads to systems that only produce a fraction of the
power that they could produce with the right tuning. This
also goes for the KCoupler.

The
Tube Another KCoupler that was on the
market is the model "The Tube" (pic 3 & 4) 

The special
abilities of the Tube can only be used to full when
drivers with a precisely constructed phasingplug are
used. Midrange drivers, radiating within a range of 500
up to maximally 6000 Hz, like the ones from EV, Fane,
RCF, H+H and Beyma, are therefore unsuitable. On the
other hand, using broadband compression drivers from TAD,
JBL, Altec, Emilar, Coral and Beyma yields good results,
because they reach their upper frequency around 1722
kHz. Fig 3 Using a tube, having an exponential cut along its side, John E. Karlson combined the advantages of acoustical horns with a large bandwidth and high horizontal dispersion. This is a "Tube" midhigh unit.

Perspectives The principally new properties of the
KCoupler offer room for further developments. Especially
the use of the Thiele/Small theory promises an
optimization of the systems so far. Theoretically it is
possible to create a KCoupler for the lowest frequency
range. However, it would have to be 3½ meters long in
order to be able to radiate 30 Hz, posing a limiting
factor for commercial use. Practical solutions therefor
are, like in basshorns, folded systems or combination
with other acoustical principles. Such experiments were
done by BECAudio. Prototypes exist, that yield deep bass
production with high efficiency. Furthermore systems for bass/mid range between 200 and 2000 Hz are thinkable. Unfortunately, only one suitable highperformance speaker (M4, Community, Light + Sound) exists at the moment. The future will show whether the comparably unusual building form and radiation will be accepted, and where the KCoupler idea has possibilities for other systems. 
Pic
4. Complete midhigh unit using "The Tube" from
BECAudio 
Literature [1] Olson, H.F.:
"Acoustical Engineering. Van Nostrand 1957. This article was published in the Fachzeitschrift Funkschau, special #39 (Musik und Elektronik). 