Dipl.­Biol. Ernst­Georg Beck

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.

 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.