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1、TRAP TRue Array Principle Design Integrating Arrayable Systems with Mathematically Correct Topologies A Renkus-Heinz Engineering White Paper by Ralph D. Heinz, Vice-President, R&D RadioFans.CN 收音机爱 好者资料库 TRAP (True Array Principle) Design Integrating Arrayable Systems with Mathematically Correct Top
2、ologies iiA Renkus-Heinz Engineering White Paper Why Array?Why Array?Why Array?Why Array?Why Array? For the purposes of this discussion we can define a loudspeaker array as “a group of two or more full- range loudspeaker systems, arranged so their enclosures are in contact.” System designers use arr
3、ays of multiple enclosures when a single enclo- sure cannot produce adequate sound pressure levels, when a single enclosure cannot cover the entire listening area, or both. These problems can also be dealt with by distributing single loud- speaker systems around the listening area, but most designer
4、s prefer to use arrays whenever possible because it is easier to maintain intelligibil- ity using a sound source that approximates a point source than by using many widely separated sources. Array Problems and Partial Solutions:Array Problems and Partial Solutions:Array Problems and Partial Solution
5、s:Array Problems and Partial Solutions:Array Problems and Partial Solutions: A Condensed HistoryA Condensed HistoryA Condensed HistoryA Condensed HistoryA Condensed History First-generation portable sound systems designed for music used a very primitive form of array: they simply piled up lots of re
6、ctangular full range speaker systems together, with all sources aimed in the same direction, in order to produce the desired SPL. This type of array produced substantial inter- ference, because each listener heard the output of several speakers, each at a different distance. The difference in arriva
7、l times produced peaks and nulls in the acoustic pressure wave at each loca- tion, and these reinforcements and cancellations varied in frequency depending on the distances involved. So although the system produced the desired SPL, the frequency response was very inconsistent across the coverage are
8、a. Even where adequate high frequency energy was available, intelligibility was compromised by multiple arrivals at each listening location. Second-generation systems incorporated compres- sion drivers and horn-loading techniques derived from cinema sound reinforcement and large-scale speech-only sy
9、stems (the original meaning of “public address”). When these horns were incorpo- rated in a single enclosure with trapezoidal sides that splayed the horns away from each other, the first “arrayable systems” were introduced to the marketplace. These products promised to eliminate lobing and dead spot
10、s (peaks and nulls) and to drastically reduce comb filtering (interference). They did improve performance over the stack of rectan- g u l a r enclosures loaded mainly with d i r e c t r a d i a t i n g cones. But frequency response across the coverage area remained i n c o n s i s t e n t . In addit
11、ion t o t h e midrange and high frequency v a r i a t i o n s across the coverage area of the array, low frequency output varied from t h e f r o n t t o the rear and side to side. Low frequency energy was focused along the longitudinal axis of the array and close to it, producing a “power alley” th
12、at gave the seats with the best views the worst sound. Even when a single enclosure is designed to resemble a point source, multiple enclosures will always interfere with each other when connected to a coherent audio signal. RadioFans.CN 收音机爱 好者资料库 TRAP (True Array Principle) Design Integrating Arra
13、yable Systems with Mathematically Correct Topologies iiiA Renkus-Heinz Engineering White Paper Conventional Array Shortcomings:Conventional Array Shortcomings:Conventional Array Shortcomings:Conventional Array Shortcomings:Conventional Array Shortcomings: Pictorial AnalysisPictorial AnalysisPictoria
14、l AnalysisPictorial AnalysisPictorial Analysis As we said in the first paragraph, the performance advantages of the array (whether horizontal or vertical) derive from its ability to approximate a perfect acoustical point source. But even the smallest arrays typically include three or more loudspeake
15、r enclosures, each with two or three separate acoustic centers of its own. Its easy to appreciate that getting all those discrete sources to behave like a theoretically ideal point source is difficult in practice. Signal processing solutions attempt to compensate for the difference between theory an
16、d reality by sacrificing the coherency of the electronic signal. They apply frequency shading and/or micro-delays to the signals sent to different enclosures, in order to ameliorate the acoustic problems. These approaches are costly, compli- cated and often meet with limited success. CoEntrant topol
17、ogies (US patent #5,526,456) reduce the complexity of the problem by integrat- ing midrange and high frequency transducers into a single acoustic source. A rigorous analysis of the acoustical physics of the multi-enclosure array can point the way toward a practical, physical solution. First, conside
18、r what is probably the most common arrayable system in use today: 60 x 40 horns in enclosures with 15 trapezoidal sides (Fig. 1). Tight-packing three of these systems with their 15 sides touching pro- duces a 30 splay between the horns, for a total included angle of 120. At first glance, this seems
19、like an ideal alignment. But the EASE interference predictions in Fig .2 show the Fig. 1 A very common array uses three 60 x 40 horns in enclosures with 15 trapezoidal sides: tight-packed, this array produces substantial overlap and interference between adjacent horns. Fig. 2Fig. 2Fig. 2Fig. 2Fig. 2
20、 The interference patterns shown above were produced by tight- packing three “arrayable” speakers using 60 x 40 constant directivity horns in enclosures with 15 trapezoidal sides. While this is an improvement over a pile of direct radiating transducers, it is far from the ideal point source array. T
21、RAP (True Array Principle) Design Integrating Arrayable Systems with Mathematically Correct Topologies ivA Renkus-Heinz Engineering White Paper familiar and clearly audible problems with this configuration: significant interference above 1 kHz, with variations of 8 to 9 dB depending on the angle. On
22、 axis, there is about 10 dB of gain at frequencies below 1 kHz. Where maximum SPL is the main consideration, this type of array will deliver acceptable performance. When the front- of-house mix position can be located on the axis of left and right arrays, they can usually be “tweaked” to deliver acc
23、eptable reproduction in this limited area. Other areas of the house, including the “high r o l l e r s e a t s ” u p f r o n t , w i l l s u f f e r . The interference patterns displayed in Fig. 2 can be reduced by widening the splay between cabinets to 30, as illustrated in Fig. 3. This array will
24、not look as pretty as the first, but it does have much more even response across the coverage area (Fig. 4). At 2 kHz and 4 kHz, the individual horns are clearly discernible in the ALS-1 predictions. Also note that the “seams” between the horns become deeper with increasing frequency. Fig. 5 shows w
25、hy there will always be interference with conventional horn arrays (whether they are enclosed in “arrayable” cabinets with trapezoidal sides or mounted in free air). As the wavefronts radiate from points of origin that are separated in space, they will always create some interference at the coverage
26、 boundaries. Fig. 4 ALS-1 interference predictions for a wider splay show reduced interference, but the three horns are clearly apparent at higher frequencies. Fig.3 Widening the splay between horns reduces interference and widens the coverage angle to 180, but reduces forward gain. As always, energ
27、y is conserved. Fig. 5 The acoustic pressure wave expands as a sphere, and multiple spherical sections will always overlap unless they originate from a common center. TRAP (True Array Principle) Design Integrating Arrayable Systems with Mathematically Correct Topologies vA Renkus-Heinz Engineering W
28、hite Paper audible and frequency response across the arrays intended coverage area will become more uniform. Fig. 6 The acoustic ideal - co-locating the acoustic centers of all horns - is not a practical possibility. y For an array in far field, dependence on angle is For a distance to the listening
29、 area very much larger than the array dimensions, let the sound pressurebe the real part of whereis the sound pressure,is the angular frequency, and A( ) is a function of the angle between the array longitudinal axis and the direction of the distant listening point. It gives the ratio of the sound p
30、ressure due to the source as a ratio of its on-axis value at the same distance. For thesource shown in Fig. A, assuming identical sources, the pressure contribution is given by whereis the wavelength,is the frequency andis the speed of sound.is the distance by which the path length from thesource to
31、 the distant point exceeds the distance from the origin to that point. For an array ofsources, the total pressureis given by The square of the pressure amplitude is given by Where= For a circular arc array, the additional path length as shown in Fig. A, for thesource at radius and angleis given by T
32、herefore, the smalleris, the smaller the differences, and the less the interference between sources. Ideally,= 0 for all sources. As approaches 0, the interference will become less SPL( ) = 10logdB?P0 2 P P i kc cS nP SiR RR P P PA Pk S SR ( ) = = A( ) ( ) =( ) ( ) = cos() + ( )sin ( ) =cos() ? ? ?
33、? ? ? ? ? ? ? ? ? ? i i i th th ii ii i ii jkSi njkSi () 22 ? ? ? 0 A( ) ( )() ( )(). ? ? ? ? ? ? ? ? ? jkSi jkSijn nn () () 2 ? ? ? ? ? ? ? ? ? i th ii iiiii ii ii ? ? A AAk S AA RS i i Conventional Array Shortcomings: Mathematical Analysis TRAP (True Array Principle) Design Integrating Arrayable S
34、ystems with Mathematically Correct Topologies viA Renkus-Heinz Engineering White Paper Fig.7 Because drivers and enclosures are physical objects, the acoustic centers of TRAP horns are not perfectly co- incident - but they are close enough to achieve measurable and audible reductions in interference
35、. Coincident Acoustical Centers: The key toCoincident Acoustical Centers: The key toCoincident Acoustical Centers: The key toCoincident Acoustical Centers: The key toCoincident Acoustical Centers: The key to true arrayabilitytrue arrayabilitytrue arrayabilitytrue arrayabilitytrue arrayability Clearl
36、y, the ideal solution is to colocate all the acoustic points of origin, as shown in Fig. 6. We could achieve this by stacking the horns vertically, but this would solve the problem in the horizontal plane by creating a worse situation in the vertical (front to back of the listening area) direction.
37、Fig. 7 shows a more realistic approximation that takes into account the physical constraints of loud- speaker design (the dimensions of the transducers, horns, enclosure walls, etc.). Because the acoustic sources are real physical objects, we cannot reduce Ri to 0. But we can get close enough to mak
38、e measurable, audible improvements in the perfor- mance of the multi-enclosure array. TRAP horns: a new approachTRAP horns: a new approachTRAP horns: a new approachTRAP horns: a new approachTRAP horns: a new approach Fig. 7 implies that the way to minimize R i and the resultant interference - is to
39、move the acoustic centers as far to the rear of the enclosure as possible. We can attempt to minimize the size of the drivers, for instance by using high-output magnetic materials such as neodymium. But the biggest obstacle to coincident acoustic centers is the horn itself. This is because typical c
40、onstant directivity horns exhibit “astigmatism:” their appar- ent points of origin are different in the horizontal and vertical planes. In order to create a wider coverage pattern in the horizontal plane, the apparent apex is moved forward, while the vertical apex is farther to the rear because its
41、coverage pattern is usually narrower. This is certainly the case with the most popular horn patterns in use today: 60 x 40 and 90 x 40. One approach to a solution, then, is to use the vertical apex for the horizontal plane as well. This is the basic innova- tion behind TRue Array Principle designs:
42、moving the acoustic origin as far the rear of the cabinet as possible, first by using the vertical apex as the horizontal apex instead of locating the horizontal origin far forward within the enclosure. Subsequent refinements to the horn flare itself have been awarded US Patent #5,750,943. This “Arr
43、ayguide” topology goes even farther in locating the apparent acoustic origin toward the rear of the enclosure. To repeat, moving the acoustic centers to the rear Fig. 8 TRAP design produces truly arrayable systems with minimal destructive interference in the horns passband. TRAP (True Array Principl
44、e) Design Integrating Arrayable Systems with Mathematically Correct Topologies viiA Renkus-Heinz Engineering White Paper minimizes R, the distance between acoustic points of origin within the array, and the resulting interfer- ence between array elements. Fig. 8 shows the ALS-1 predictions for the f
45、irst generation of TRAP horns. It is clear that interfer- ence has almost disappeared. Fig. 9 shows measured EASE data for a three- wide array of TRAP40 enclosures. Frequency response is consistent in both vertical and horizontal planes within 4 dB. This is an “out of the box” array, using no freque
46、ncy shading or micro-delay to improve performance. Measured results dont track the predictions 100% because the actual pattern of the horns varies somewhat with frequency: first genera- tion TRAP horns maintain nominal coverage 10 from 1 kHz to 4 kHz. TRAP PerformanceTRAP PerformanceTRAP Performance
47、TRAP PerformanceTRAP Performance TRAP is a method for optimizing the mutual cou- pling between adjacent horns in an array. As such, the TRue Array Principle operates over the pattern bandwidth of the horns (the frequency range over which their coverage varies less than a defined amount, for instance
48、 10). CoEntrant topology extends the pattern bandwidth of the horns (and therefore the effectiveness of TRAP design) in two ways: by integrating midrange and high frequency transducers so that the horn is loading a broad- band acoustical source, and by permitting the designer to use a single large h
49、orn instead of two smaller ones. Fig. 10 TRAP arrays can be quite small: however, the size of the horns will determine the lower frequency limit at which the TRue Array Principle ceases to operate. Fig.9Fig.9Fig.9Fig.9Fig.9 The TRAP array produces almost no measurable interference from a tight-packed three-wide cluster. This is because the three spherical wave- fronts produced by the three horns originate from a common acoustical center. Therefore they behave as a single acoustic unit, without overlap or interference. TRAP (True Array Principle) Design In
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