The K-Coupler
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 K-Coupler 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 K-Coupler. 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, frequency-independent radiation resistance. Finite pipes however present only a small usable radiation resistance. [1] Furthermore, low frequency-reflections 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.
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Karlson took this
construction idea all the way, by making
infinitely many in size increasing openings in
the length of the pipe, yielding a cut that
caused infinitely many resonance frequencies.
Along such a cut a uniform sound radiation
exists. The cut can widen following several
mathematical functions. Karlson found an
exponential curve to be the best. Because almost
all sound energy is radiated before the end of
the pipe, reflections are minimal. This causes an
extraordinarily flat radiation impedance,
respectively frequency response. [2] By using a horn (e.g. exponential horn) a smooth transition of the high radiation resistance at the horn entrance into a low radiation resistance at the horn mouth also follows. Finite horns however have an abrupt end, and because of this, have reflections at the horn mouth, like finite pipes (fig 1). This is an important difference between horn designs and the K-Coupler. fig 1. Acoustical Impedance of a finite pipe (top), a finite eponential horn (middle) and a K-Coupler (bottom). ZA1= input impedance, ZA2= output impedance, rA1= real part of ZA1, XA1= Imaginary part of ZA1. |
Frequency response and efficiency
The frequency response of the K-Coupler
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
K-Coupler, dropping by 12dB/octave below that. An upper
frequency can be determined theoretically nor
practically. The mid/high implementation of the
K-Coupler, 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 K-Coupler, having a high
efficiency from lowest to highest frequency.
Distortions
Unlike horns, the K-Coupler 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
K-Coupler, 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 cross-section. A combination of flat
walls causes 'lobes' (polar diagram of multicell horns in
[1]). Elliptical or circular cross-sections yield an
almost half-circular frequency-independent projection.
