The Karlson Coupler

An 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 1/4, 1/3, 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.

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.

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 K-Coupler 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 K-Coupler: bass-hybrid-enclosure

The oldest use of the K-Coupler idea is in a bass-hybrid-enclosure (fig 2). This construction is mostly a combination of the K-Coupler with bass-reflex. The relatively small enclosure allows a radiation of about 50-900 Hz under high efficiency. However, the frequency response shows two construction-determined 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 reflex-ports start working. The direct radiation of the driver amplifies the upper frequencies. The nonlinear frequency response is furthermore caused by standing waves in the K-Coupler and parallel construction.

Fig 2: Bass-hybrid-enclosure as a combination of bass-reflex-enclosure and K-Coupler.

This enclosure has been in the interest of professional audio since 1980/81. As a bass-enclosure for small PA-sets and as an instrument-loudspeaker it has convinced several musicians, even though it has the mentioned characteristics. Unfortunately, in the PA market the empty-enclosure 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 K-Coupler.

The Tube

Another K-Coupler that was on the market is the model "The Tube" (pic 3 & 4)
This construction represents the purest form of the K-Coupler for the mid/high range. Only compression drivers are suitable for this type. Because of its size and acoustical behavior this model is a real alternative for all shortthrow horns.

The special abilities of the Tube can only be used to full when drivers with a precisely constructed phasing-plug 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 17-22 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" mid-high unit.

Perspectives

The principally new properties of the K-Coupler 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 K-Coupler for the lowest frequency range. However, it would have to be 3 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 BEC-Audio. 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 high-performance 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 K-Coupler idea has possibilities for other systems.

Pic 4. Complete mid-high unit using "The Tube" from BEC-Audio
Literature

Literature

[1] Olson, H.F.: "Acoustical Engineering. Van Nostrand 1957.
[2] Poppe: "The KCoupler, a new acoustical lmpedance transformer``, EEE Transactions on Audio and Electroacustics, Vol Au 14No 4, 1966, seite 163.
[3] Zintz, W.: Engineering Letter No. s, TPC.
[4] Olson, H.F.: Music, Physics and Engineering, Dover Publications 1967.

This article was published in the Fachzeitschrift Funkschau, special #39 (Musik und Elektronik).