The Performance and Restrictions of High Frecuency Waveguides in Line Arrays

Audio Engineering Society

Convention Paper 6777Presented at the 120th Convention

2006 May 20–23 Paris, France

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The performance and restrictions of high frequency waveguides in line arrays

Dipl. Ing. (FH) Nils Benjamin Schröder1, Dipl. Ing. (FH) Tobias Schwalbe2, and Prof. Dr. Robert Mores3

1 Hamburg University of Applied Sciences [email protected]



ABSTRACT

It is necessary to form a plane coherent wavefront in the hf-section of line arrays. Several different concepts have been applied to reach this goal. We discuss these existing solutions. The different ideas on how to create a cylindrical wavefront will be explained and evaluated. Especially those waveguides which have their weak point in the theoretical design will be criticized. An explanation on how we developed a new waveguide will be given. Finally, we want to give some ideas on how the next generation of waveguides could be designed. Basically, five principles of forming flat wavefront are in use:

1. PRESENTLY APPLIED PRINCIPLES OF FORMING FLAT WAVEFRONTS

The first working solution was Dr.Christian Heil`s DOSC-waveguide as described in 1.3. The aperture that is looked for has to reshape the wavefront emitted by a conventional compression driver into a flat isophasic wavefront needed for a line array. Thereby the curvature of the resulting wavefront has to be less than λ/4 at the highest operating frequency (corresponding to 5 mm at 16 kHz).

1.1. Long Horns

The easiest way to do so is the use of long and narrow conventional horns. These devices flatten the wavefront up to a frequency depending on the horn’s length. For a maximum wavefront-curvature of ¼ of the wavelength corresponding to 16 kHz and an exit slot of the size of a standard 1.5“-driver, the duct had to be approximately 540 mm long. Implementations of this idea often use shorter ducts than that. An additional problem of this solution is, that narrow horns of this dimension produce distortions and resonances. Especially the crossover between the duct and the free field produces a sudden change in the acoustic impedance which can result in comb filter effects due to reflections at this point. In

Schröder et al RESTRICTIONS OF WAVEGUIDES

AES 120th Convention, Paris, France, 2006 May 20–23

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spite of these arguments, systems with long hf-horns often deliver good results, though.

1.2. Acoustical mirrors, reflective waveguides

Several manufacturers reshape the wavefront emitted by compression drivers using reflections. The reflective waveguide is implemented in two ways.

The first variation uses an acoustic mirror to create a wavefront virtually emitted from a source far behind the front of the speaker. This is done by a hyperbolic shaped surface on which a wavefront will be reflected. If it was a parabolic instead of a hyperbolic shaped mirror, it could nearly form a flat wavefront (therefore one had to assume that a compression driver represents a perfect point source). But this version uses a hyperbolic reflector so it does not emit a flat wavefront. It emits a “divergent curved convex wavefront” and therefore is a good compromise considering that most line array modules are used in curved parts of arrays.

Another way of implementing the reflected waveguide is the “double reflective waveguide”. The first reflection creates a virtual pointsource compensating for the fact, that real compression drivers have a certain size, so they are not a true pointsource. This is done by a parabolic reflector. Then, a second reflection on a parabolic surface is supposed to reshape this pointsource into a linesource. However, the dimensions of such waveguides are so small that in the relevant frequency range no reflections will occur but rather diffraction. Such waveguides will work as highly directive horns, so coupling will work up to a certain frequency, but the double reflective mechanism itself will not work.

1.3. The continuous equalisation of pathlengths with the help of „acoustic detours“

Another way to equal the pathlengths is the implementation of indirections. This is done by adding a phaseplug that continuously lengthens the way to the exit of the waveguide.

The accuracy of the coupling depends on how carefully these waveguides are developed. The first working waveguide of this kind is Dr. Christian Heil’s DOSC. It equalizes the pathlengths from the driver’s exit slot to the waveguide’s exit using a cut-off conus, which produces a parabola. The driver is allocated in the

mirrored focal point of this parabola. In this alignment every way from the driver’s exit to the exit of the waveguide has the same length. Apart from the fact, that a driver is no perfect point source, this device is theoretically correct and works in reality. Another waveguide product on the market uses a patented ring-diaphragm driver, and „half“ the DOSC waveguide which will transform the „ring-shaped“ sound wave into a cylindrical one. Such combination should work as well as it uses the same idea as Heil’s Waveguide. Other examples of “detour”geometries are torroids, but there is no proper documentation so it is difficult to evaluate this version.

1.4. Multiplying the source

Related to the idea of ajusting pathlengths is the concept of creating several virtual soundsources out of one. This is done by appending several ducts to the throat of driver. These ducts then follow different curves and end in a vertical alignment where the soundwaves of all the ducts should arrive with the same phase. One manufacturer for example uses four ducts per 1.5“ driver. So the gap between the virtual sources is about 3 cm wide. This will result in a theoretical coupling frequency of 5.7 kHz. Others try to influence the speed of sound in those ducts by filling them with cellular material, accepting the resulting high frequency damping. This way to create a planar wavefront works as well. The frequency up to which the WST-criterias are fulfilled depends on the number of new soundsources that are created. The more sources there are, the more complicated will be the correct model of little “CD-Horns” out of each duct. Implementations of this technology work up to a frequency of 10 kHz to 12 kHz in measurements.

1.5. Ribbon Transducers

There are manufacturers that have managed to develop a ribbon transducer suitable for PA-Systems. They can build an array without further reshaping of the wavefront. They can be seen as perfect finite line arrays. When using such a device, the highest coupling frequency only depends on how close these devices are mounted to each other.

2. A COMBINATION OF THE APPROACHES

The transformation of the wavefront often collides with the needs of CD-horns, which in fact these devices should be, too. So they should also have a defined



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hornshape, no unwanted compression chambers, no internal interference or missmatched acoustic impedance causing an unsuitable frequency response. The waveguide is driven by a state-of-the-art neodym 1”-driver to ensure a maximum package and SPL per height relation.

2.1. Multiplied soundsources and continues pathlength adaptation in one device

We built a waveguide that combines the idea of separate sources with the continuous adaptation of the pathlengths. Six separate ducts per 1“-driver are being used. Their exits are vertically aligned and thus form an array of same size as the physical height of the compression driver. The result is an array of six separate soundsources. The distance between their centres is about 17 mm. Those ducts are shaped like a period of a cosines-wave to avoid discontinuities that would occur if one would for example use semicircles. The cross sectional area of each duct is exponentially increasing along the soundpath to avoid distortions caused by the cross-sectional diameter remaining constant. Inside those ducts we use a stepless adaptation of the pathlengths. For that purpose two sets of parameters for cosines functions are calculated for each duct. One period of these cosines has an arc length equal to the longest path form the exit throat of the driver to the exit of the waveguide. Over these cosines a surface is laid which continuously adapts the way “detours” in the waveguide. These detours are longer for soundpaths located closer to the centre of the waveguide.

Figure 1 Abstract Scheme of the waveguide, dashed: driver’s exit throat, solid: possible ways through the waveguide the straight one above is unchanged, the others follow cosines, solid bold: waveguide’s exit

2.2. Avoiding a pressure chamber

To avoid a pressure chamber between the ducts and the driver, the pathlength equalisation begins 20 mm away

from the driver. The section in between widens a little for gaining space for the necessary catwalks, which would divide the sound into different ducts. Arrangements other than this proposal are likely to cause reflections between the driver and the respective catwalk front sides.

2.3. Vertical Phaseplug

To avoid standing waves along the horizontal axis within the exit mouth of each duct, there is a horizontal phaseplug installed in the last third of the waveguide. Without that phaseplug non-linearity occurs right at the frequency where the respective wavelength corresponds to the horizontal width of the mouth. With the phaseplug this width is halved and the unwanted non-linearity is shifted to double frequency. We have achieved a much smoother frequency response

Figure 2 Waveguide seen from the six exits throats of the ducts, red: phaseplug



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Figure 3 dashed: frequency response without vertical phaseplug, solid: frequency response with vertical

phaseplug

Figure 4 CAD-Drawing of a half waveguide

Figure 5 CAD-Drawing of a half waveguide, the pathlength equalizations begins with the purple part

2.4. Verification of the new waveguide

The output of each of the six waveguide channel is inphase with the other outputs.

Figure 6 impulse response measured at the three different exits of the ducts of the waveguide

The three different outputs are in phase and time aligned. Though the other three are mirrored, only three of the six outputs are shown in figure 6.

Figure 7 vertical directivity pattern of one waveguide, measured on axis, 1m distance

This waveguide works well in the frequency range of 1 kHz to 17 kHz. The isobaric diagram shows a nearly perfect behaviour, very similar to an ideal nonseparated line source. It is implemented in a line array module that also includes carefully modelled directivity patterns in the midrange.



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Figure 8 vertical directivity pattern of eight line array units in one arrangement, 4 m long, each equipped with

the waveguide, measured on axis, 8 m Distance

This figure shows that the devices couple and form a line array without sidelobes up to a frequency of about 17 kHz. (The irregularities are caused by gusts of wind during the measurements).

2.5. Ideas for a future research

There are still some remaining questions:

What kinds of measurement methods are accurate to really determine whether a wavefront is cylindrical? Impulse measurements along the waveguide or the isobar-diagram of the directivity are evidences for that, but perhaps more accurate methods can be found.

What is really happening in complex waveguides? A software based simulation model, or a general “physical model” that would depict what is happening in complex waveguides is still not existent. Which is the optimum shape of the emitted wavefront, planar or perhaps „preemphased“, or even convex like for example Dipl. Ing. Jörg Knieschewski, HK Audio, requests? Another possibility for new developments would be an adjustable waveguide. Its characteristic could be adjusted to the necessities of the curvature the module in the line array has. Our waveguide is just another step to new technologies realising better hf-reproduction with line arrays.

3. ACKNOWLEDGEMENTS

This work was supported by the TOTEC company, Hamburg, where we designed the information first line array implementing the proposed principle. http://www.totec.de http://informationfirst.de

4. REFERENCES

[1] M. Urban, C. Heil, P. Buaman, „Wavefront sculpture Technology“, presented at the 111th AES Convention, New York, USA, September 21-24, 2001

[2] D. Button, “High Frequency Components for High Output Articulated Line Arrays”, presented at the 111th AES Convention, Los Angeles, California, USA, October, 5-8. 2002

[3] G. Noselli, “Outline Butterfly’s Whitepaper”, January 2003, Brescia, Italy

[4] Nexo SA, GEO Technologies, June 17, 2003, Roissy Cedex, France

The Performance and Restrictions of High Frecuency Waveguides in Line Arrays

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