Full System Optimization of Pair-Wise Symmetric Multi-Way Loudspeaker Arrays
These articles have recently interested me.
"Application of Linear-Phase Digital Crossover Filters to Pair-Wise Symmetric Multi-Way Loudspeakers Part 2: Control of Beamwidth and Polar Shape"
AES E-Library: Application of Linear-Phase Digital Crossover Filters to Pair-Wise Symmetric Multi-Way Loudspeakers Part 2: Control of Beamwidth and Polar Shape
"Application of Linear-Phase Digital Crossover Filters to Pair-Wise Symmetric Multi-Way Loudspeakers Part 1: Control of Off-Axis Frequency Response"
AES E-Library: Application of Linear-Phase Digital Crossover Filters to Pair-Wise Symmetric Multi-Way Loudspeakers Part 1: Control of Off-Axis Frequency Response
It appears we may be able to maintain an essentially constant vertical lobe by summing a large array of drivers. Bandwidth control will be limited by the effective length of the line (LF) and inter-driver spacing (HF).
I'd like to investigate the design of a pair-wise symmetric multi-way loudspeaker utilizing some of the drivers I have available.
I currently have
-4x Aurasound NS15
-2x AE TD15M Apollo
-2x Beyma TPL150
A WWMTMWW (NS15 <--> TD15M <--> midrange <--> TPL150 <--> midrange <--> TD15M <--> NS15)
A WMTMW (TD15M <--> midrange <--> TPL150 <--> midrange <--> TD15M) + distributed LF (4x NS15)
Either of the aforementioned alignments would appear to embarass most systems exceeding $100k.
I would simply have to purchase 4x midrange drivers and an additional pair of TD15M Apollo drivers.
Topics for discussion:
-Driver considerations / layout.
Inter-driver spacing will define the upper limit on vertical directivity control. I would assume the upper limit to be a distance of 1 wavelength between radiating drivers. If we assume a tweeter height of 160mm, a midrange diameter of 150mm and separation distances of 12mm, we’ll arrive at ~1khz.
I believe the TPL150 is maximally effective down to 1.5khz. A compromise must then be admitted between the uniformity of off-axis response and distortion response. What level of off-axis response error is considered acceptable?
Should the midranges be crossed higher (~1.5khz) or lower (~1khz)?
AE TD6? (Is this ever going to get released?)
The TPL150 already possesses a rear enclosure. Alternatively, the rear chamber could be removed and allowed to operate in a heavily damped transmission line (response may approach that of an infinite baffle). Has anyone experimented with this before?
A heavily damped transmission line would appear to provide a maximally linear response (response may approach that of an infinite baffle). Maximum absorption occurs when the line exceeds 1/4 wavelength of the desired frequency. A ~24" line should suffice for >150hz.
A bass-reflex alignment (65-75hz tuning @ 3-5 cu.ft) would restrict linear excursion (<3mm P < -- > P) and maximize output. Would the group delay inherent to such an alignment be audible?
The enclosure volume will possess resonances, which will degrade the response. I believe a damping material can be used to reduce these resonances to negligible levels. However, an excess of material will damp the response of the port. How do you determine how much stuffing is effective to simply damp the enclosure resonances and not the port?
I am aware that midrange energy is able to pass through the enclosure ports. The ports will also possess Helmholtz resonances, which may be excited and degrade the response. A passive radiator would appear to minimize both of these errors. Has anyone ever experimented with passive radiators at high tunings (65-75hz)?
A sealed alignment will avoid the aforementioned errors of the bass-reflex alignment, albeit without the efficiency and output gains. Would this be the lesser of two evils?
If implemented correctly, a bipole should minimize diffraction as the front and rear waves will support each other. However, I do not have the funds for a bipole alignment. As a result, I must deal with diffraction effects.
How much significance should be given to diffraction effects? As far as I understand, there are two primary approaches:
1) ignore them as they do not contribute significantly to the total response and equalization may result in a spectral imbalance.
2) equalize them to maintain a maximally flat response
How should I approach optimization of the enclosure shape?
I believe the driver choice will define the constraints for the optimum geometry. Maximum width will be defined by the LF drivers and minimum width will be defined by the HF driver. Intuitively I would assume, the minimum diffraction design would possess a baffle whose width decreased as one approached the center.
If we assume a constant depth, we might define the front and rear baffles as planes. This will allow us to define functions (baffle width “X” as a function of height “Y”) for each plane, which we may optimize. We might define the enclosure shape as a surface (baffle width “X” as a function of height “Y” and depth “Z”), which intersects both planes.
What would be the optimum function defining the planes? We might reach a higher resolution by defining the maximum “X” and minimum “X” (X=width) values for the function.
The maximum baffle width will be defined by the LF driver (ex. X=18”) and the minimum baffle width will be defined by the HF driver (ex. X=5”). Would an exponential hyperbolic function which passes through these points approach optimum?
We should seek to maximize the LF enclosure volume. As a result, the maximum baffle width will be defined by the width of the front baffle (X<front baffle). We might place further constraints by defining the optimum enclosure volume and minimizing the rear baffle width which achieves our target volume goal. Assuming the HF driver already possesses a rear chamber, enclosure volume is not a consideration. Additionally, I believe the teardrop shape possesses a minimum of diffraction. The minimum flat baffle width will then be zero. We will thus have two curves which define the upper and lower flat sections of the rear baffle since the center width will equal 0 over a finite range of Y values.
I believe the minimum diffraction design would minimize surface curvature and approach a constant rate of curvature. If we allowed the surface to pass through a curve defined by holding X constant at a maximum width value “A” (X=”A”, Y=?, Z=?) which is orthogonal to the front plane, I believe we would maximize the effective roundover radius. Intuitively, maximizing the radius would minimize the curvature (ex. Smaller circles exhibit higher curvature than larger circles). In addition, this will allow us to place another constraint allowing us to further simplify the optimization process. The maximum width “A” will be defined by the maximum width of the front baffle (ex. X=18”). If we minimized the curvature of the surface which intersects the front and rear planes and the curve defined by holding X constant at the maximum width value “A” (X=”A”, Y=?, Z=?), would we achieve minimum diffraction?
Surface treatments? I am aware of a large variety of materials used for treating diffraction (ex. Foam, felt). What materials are most effective? How would you approach optimizing the placement of surface treatments? Can this be separated from enclosure shape optimization?
Above the upper limit defined by inter-driver spacing, vertically directivity will be defined solely by the HF driver. Perhaps foam wedges affixed to the front baffle (covering a finite portion of the driver) could be used to extend directivity control higher in frequency (ex. RAAL 140-15D). How could we calculate the optimum spacing between the foam wedges? How could we calculate the optimum wedge geometry?
Intuitively, the most effective way of minimizing the influence of resonances would be to place them beyond the bandwidth of the loudspeaker. However, this is simply unrealistic as the audio bandwidth is quite large. All enclosures will possess resonance. If we coupled individual drivers to individual enclosures and decoupled them from each other (instead of coupling all of the drivers to a single enclosure), we might achieve a higher fidelity response. The enclosures could be optimized for a specific bandwidth.
HF enclosure (>1khz)? I believe maximizing the stiffness of the enclosure would be an exercise in futility as a fundamental enclosure resonance (J=0) which exceeds 20khz is unrealistic. Intuitively, maximizing damping should result in the optimum response. Would maximizing the mass approach optimum over this bandwidth?
How would you achieve this?
MF enclosure (200hz/300hz < -- > 1000hz/1500hz)? An enclosure resonance is inevitable over the coupled drivers bandwidth. Would maximizing stiffness and minimizing mass approach optimum over this bandwidth?
How would you achieve this?
LF enclosure (<300/500hz)? It may be possible to achieve a fundamental enclosure resonance (J=0) which exceeds the bandwidth of the coupled driver. I assume that maximizing the stiffness and minimizing the mass of the enclosure would approach optimum over this bandwidth.
How would you achieve this?
How to create a minimum diffraction surface? The only cost effective means of achieving a complex surface geometry that I’m aware of would involve fiberglass. The front and rear baffles could be machined out of wood or plastic. The surface connecting the two planes could be segmented into horizontal sections (X=?, Y=constant, Z=?) that approximate the surface which are machined out of wood or plastic. The fabric could then be wrapped around the structure (front and rear baffles + horizontal sections) to form a continuous surface.
Any other ideas?
Affordable manufacturing methods will place a constraint on possible surface geometries. Any ideas on how one would incorporate these constraints into the surface geometry optimization process?
How would you approach crossover optimization? Intuitively I would assume it would be a matter of building the enclosure and measuring each pair of drivers (full-range) individually over a range of spatial points. This data could then be imported into a computer to calculate the total combined response assuming a given filter function for each pair of drivers.
Assuming this method is effective, how would you define the number and location of the spatial points?
Assuming this data is available, how would you approach calculation of the optimum filter functions for each pair of drivers which results in an essentially constant vertical lobe vs frequency over a maximum bandwidth?
The source's interaction with the room will vary considerably with frequency (LF is dominated by modal acoustics, HF is dominated by ray acoustics). Would the optimum beamwidth be dependent on frequency?
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