| Baffle spacing, phase angles and time alignment, revisited [message #41352] |
Tue, 13 May 2003 23:56  |
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Wayne Parham
Messages: 18785
Registered: January 2001
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Illuminati (33rd Degree) |
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In this post, I'd like to revisit the issues of baffle spacing, phase angles and time alignment. It's been a while since we talked about this, and I think it would be good to come at it from a different angle.
Bad pun. Sorry.
There's no way to make two sound sources be phase-aligned at all points in space and at all frequencies. Not even an infinitely powerful DSP algorithm on an infinitely powerful computer can accomplish phase correction of two or more sound sources at all points and all frequencies simultaneously. But a designer can pick their target locations and range of frequencies and align for them. The better products are those that have design choices that limit dispersion and crossover overlap such that anomalous conditions are only present outside the dispersion window, and so are not developed by the loudspeaker at all, or at a highly suppressed level.
The reason for this is simple. When there are two points in space generating a wave, there can be path length differences between the observer/listener and each source. If those path length differences are at odd multiples of a half wavelength, then cancellation results. So there are positions and frequencies that will cancel, resulting in nulls.
The most common solution is to align sources vertically, so that movement on the horizontal plane results in no change to the distances between the observer/listener and each source. That means that the problem will only present itself at certain positions along the vertical plane. I'll provide some illustrations below, which are from the AES Journal paper called "Improvements in Monitor Loudspeaker Systems."
The illustration above shows the window of locations where response will be good for this loudspeaker. Generally, if the crossover region is narrow, one can assume that both subsystems will be online only over a very small band of frequencies around the crossover frequency. Frequencies above or below this region will be generated by only one sound source, but in the crossover region, there will be two sound sources that are separated by space and time (phase). Where the angles between sound sources cause path length differences at odd multiples of a half wavelength, interference nulls are formed. Really clever designs have these nulls positioned at the edge of the coverage pattern, where they actually become useful, serving to abbreviate pattern cutoff.
The normal listening room is wider than it is tall, so the ideal coverage pattern is too. One problem that presents itself is a flare angle that is wider than it is tall terminates in a mouth that is also wider than it is tall. This means either the horizontal flare must be oversized to allow the vertical flare to develop enough to get pattern control, or the horn can be made smaller but it will sacrifice vertical control. However, if the adjacent drivers are stacked vertically, then interference nulls are formed at angles above and below, with the angle determined by the positions of the sound sources. If carefully placed, these nulls will act to reinforce pattern control, by providing it at low frequencies where the undersized horn is not able to provide vertical control solely by its dimensions.
A Theater Series four π loudspeaker is one that is relatively large, and the spacing between the tweeter and midwoofer is somewhat distant for aesthetic reasons. It wouldn't look good to have a large box with two drivers stuck closely together. But there is also some reasoning behind the choices, as is shown by the analysis below.
Using Linkwitz formula, the Theater Series four π speaker's asymmetrical 1600Hz crossover and tweeter-midwoofer spacing of 13.25" yields
d1 = 0.33m (13.25") between the tweeter center and the midwoofer center
λc = 0.22m (8.5") wavelength of 1600Hz
a = 19° or 2a = 38° (arc between nulls)
This is equal to the vertical dispersion of the HF horn. The nulls are set at the edge where HF dispersion falls off.
This is my favorite implementation, and why I prefer asymmetric horns to round or square ones. Not only is the target listening area asymmetric, but the vertical placement of sound sources tends to work in your favor if you choose such a pattern. I like a consistent radiation pattern in both horizontal and vertical planes, or at least a uniformly collapsing one. But with vertically stacked sound sources, one must pay attention to coverage angle and driver placement in order to avoid having an off-axis null right in the middle of the pattern. In my opinion, the best way to handle this is to limit the vertical pattern to the location of the first null.
The bottom line is that there are a handful of things to consider when bringing two subsystems together as a loudspeaker system. The slope of the crossover sets the phase relationships of the motors and the overlap frequency region. The directionality, position and orientation of the radiators sets the acoustic phase relationship in space as well as the amount of energy delivered to that space. So if the two radiators are nearly matched in directivity and output in the crossover range, then the transition will be seamless and the reverberent field will be uniform, resulting in the most natural sound.
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| Re: Baffle spacing, phase angles and time alignment, revisited [message #41360 is a reply to message #41352] |
Wed, 14 May 2003 04:22  |
spkrman57
Messages: 522
Registered: May 2009
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Illuminati (1st Degree) |
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Wayne,
Good explanations there, I will admit that I do more skimming of information like this than I actually do understand it. I do catch the general theory if not the math involved. I have found some of these things out the hard way(I am old-school trial and error student), so get many of the same results, just takes me longer to get there.
I have found that using Martinelli horns(current setup), I have to extend the front of the horn about 1" in front of the woofer board. That gets me the 7 1/4" half wave length in regards to the woofer VC. I am close to the "horn-to-woofer" distance of 13 1/4" spacing you mentioned. I have experimented with different spacing between the woof/tweet and have noticed much interference in the sound around the upper midrange. I have also noticed that if I place the woofer too high off the ground(closer to ear level), I pick up too much unwanted sounds from the woofer.
Thanks for the furthering education !!!!! Ron
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| Re: Baffle spacing, phase angles and time alignment, revisited [message #41362 is a reply to message #41352] |
Wed, 14 May 2003 04:50 |
DRC
Messages: 169
Registered: May 2009
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Master |
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Holy cow, Wayne! I'm gonna have to have my morning coffee and try this again. I'm constantly amazed at the way you wade (swim, Scuba?) into the depths on these design considerations for the benefit of the forum folk. I feel like the least I can do is try to get a handle on the issues at hand. Now, where's my coffee mug . . .
Keep your ears and your mind open.
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| The $64,000 guestion, how do you determine how much tilt you have?? [message #41386 is a reply to message #41352] |
Thu, 15 May 2003 07:25 |
Robert Hamel
Messages: 93
Registered: May 2009
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Viscount |
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Let's say you get it down to figuring out the delay is phase from the crossover and the actual path length because of the voice coil offsets at crossover or the overlap range where both driver have significant output. My intuition says its simple geometry but how do you do it?? Second question if you know you slopes, I use 24db how much overlap or what frequencies above and below crossover would you be interested in. How do you determine this based on your slopes??? Thanks
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