I have recently done some modeling of crossovers, looking at phase related issues. I decided to share some of my findings by writing up a white paper. The attached pdf,
can be downloaded from my web site by clicking on the title above.
I used a point-source model of a two driver (e.g. midwoofer and tweeter) loudspeaker. The drivers are described by their vertical (y-coordinate) offset in the baffle plane, and the difference their horizontal (z-coordinate) offset, of their acoustic centers. Each driver is modeled as a second order high-pass filter, e.g. a driver in a sealed box.
The influence of the offsets, and some aspects of analog delay design are covered. The influence of the tweeter phase in the crossover region, and how to fix the response problems that this can create, are covered at the end of the paper.
This is just a limited study, but brings up some interesting issues. I hope that this is informative, and starts some discussion of the topic.
-Charlie
can be downloaded from my web site by clicking on the title above.
I used a point-source model of a two driver (e.g. midwoofer and tweeter) loudspeaker. The drivers are described by their vertical (y-coordinate) offset in the baffle plane, and the difference their horizontal (z-coordinate) offset, of their acoustic centers. Each driver is modeled as a second order high-pass filter, e.g. a driver in a sealed box.
The influence of the offsets, and some aspects of analog delay design are covered. The influence of the tweeter phase in the crossover region, and how to fix the response problems that this can create, are covered at the end of the paper.
This is just a limited study, but brings up some interesting issues. I hope that this is informative, and starts some discussion of the topic.
-Charlie
Impressive work Charlie,
I just took a quick look Charlie I have to take more time to get a overview. I hoped to see a concrete conclusion about what outcome is best filter solution.
I haven't read the paper yet, but as further info, you may want to read this paper, and especially reference 7 in the references cited at the end of the paper.
http://users.ece.gatech.edu/~mleach/papers/LinkRyl.pdf
http://users.ece.gatech.edu/~mleach/papers/LinkRyl.pdf
Ah, it seems that one can not do work that hasn't already been done before when it comes to loudspeakers! Thanks for bringing that Leach paper to my attention. It addresses some of the same things that I do, with respect to the driver's phase response and integrating the driver response in to the crossover. I know that is not a new concept, and I wasn't trying to make that case, but I wasn't aware of Leach's work. I will look in to REF#7 as well.
-Charlie
Correct Time-Alignment
You forgot to mention the optimum mitigation - Achieve Correct Mechanical Time-Alignment.
You forgot to mention the optimum mitigation - Achieve Correct Mechanical Time-Alignment.
If what you mean is physically aligning the driver by tilting the baffle, setting back parts of the cabinet (e.g. for the tweeter) and so on, this often causes other even more problems (IMHO).
Perhaps the only system that I have seen where this might have been pulled off in an OK way is shown here:
-Charlie
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It has been my experience that the improvements in overall sound character that result from correct mechanical alignment of all drivers far outweighs any minor response anomolies that might occur. The sound character that results from no alignment and use of phase-shift time-correction circuits sounds peculiar and veiled.
I based my 4th year EE project on exactly this concept, back in the 80s, except I generalized it for all all-pass xover, not just LR (which is Butterworth derived). Looked at on axis, off axis, acoustic power response, impedance and group delay.
Bottom line is that including the tweeter xover phase function as a phase eq branch results in reduced rolloff of one of the orders (HP or LP). You can determine which order is lower, by how you derive LP and HP from the all pass function. ie the derived one is lower order. In my sims, found best tradeoff between off axis control and group delay was with a biquad where the poles were placed between Bessel and Butterworth.
The xfer function requires zeroes, so it has to be active. Knocked it up in LM833s back then (good stuff at the time) and it all measures/works as advertised.
IME the only potentially advantageous application of this is if you xover very close to tweeter resonance. However, the tweeter must be very robust and I don't know that this xover makes sense for any real world domes out there, unless maybe if they're heavily waveguide loaded for the extra power handling. Even then, its more a theoretical advantage than real world because there are simpler ways to get very nearly the same effect, with standard all-pole filters.
Dave
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I've recently done similar investigations using quasi-optimal Brooke / Le Cleac'h crossovers which minimize group delay.
The following link shows some of them, it is is french but there are some pictures which may help to understand the stuff.
Filtres compensés
I explored another way from Linkwitz to implement transforms, I called it Breden's, whose the idea comes from. My three ways system is based on it.
Some details on all this can be found here :
http://www.diyaudio.com/forums/anal...s-self-wants-your-opinions-7.html#post2428507
.
The following link shows some of them, it is is french but there are some pictures which may help to understand the stuff.
Filtres compensés
I explored another way from Linkwitz to implement transforms, I called it Breden's, whose the idea comes from. My three ways system is based on it.
Some details on all this can be found here :
http://www.diyaudio.com/forums/anal...s-self-wants-your-opinions-7.html#post2428507
.
If what you mean is physically aligning the driver by tilting the baffle, setting back parts of the cabinet (e.g. for the tweeter) and so on, this often causes other even more problems (IMHO).
Perhaps the only system that I have seen where this might have been pulled off in an OK way is shown here:
-Charlie
Hi Charlie,
If you have the right tweeter, with a slightly rising on axis response, a tilted baffle works extremely well. In fact, since the "on axis" is now ~ 15 degrees off axis from the woofer, a smooth on axis results in a smoother power response averaged over the 30 degree window, since you are using the driver right in the "average" of this 30 degree window.
Done right, the "tilt" also results in a diffraction signature closer to the 30 deg window average, on axis.
Win win!
Dave
I wasn't trying to completely throw away the idea of doing time alignment by offsetting drivers physically. This can work well and you also mention some good points about power response that I hadn't thought about.
But in terms of "more problems", I was thinking of some designs that I have seen for which the diffraction signature must be horrible, because of sharp edges near the tweeter or midrange. For instance, something along these lines:
There examples of good designs, too, like this:
One problem I see is that you need to have the tweeter moved back say about 1-2 inches from the midwoofer, but they should be positioned as close together as possible to keep the off axis response smooth around the crossover. The typical 15 deg sloped baffle can't create enough offset with closely spaced M and T.
-Charlie
Hi Charlie,
I was able to align the drivers in the attached with 13 degrees, mounted very close together, with a 24" stand (stand height matters as well). On axis is as flat as I want it to be (easily +-0.5 dB but I give it some downward tilt) and excess phase is flat (drivers are aligned)
Totally agree about the steps in a baffle, these step reflections land very close in time to teh direct sound and colour the tonal balance.
I say a JonMarsh deign once where he used a lesser tilt and therefore a very large driver spacing, but for me I think the resultant lobing wouldn't be worth the tilt benefit.
The key is using a tweeter response that matches the design need, and there are a few excellent soft domes out there that fit the bill, without extensive passive xover eq. For the average tweeter, you're probably right that this would be a difficult trade off.
Dave
I was able to align the drivers in the attached with 13 degrees, mounted very close together, with a 24" stand (stand height matters as well). On axis is as flat as I want it to be (easily +-0.5 dB but I give it some downward tilt) and excess phase is flat (drivers are aligned)
Totally agree about the steps in a baffle, these step reflections land very close in time to teh direct sound and colour the tonal balance.
I say a JonMarsh deign once where he used a lesser tilt and therefore a very large driver spacing, but for me I think the resultant lobing wouldn't be worth the tilt benefit.
The key is using a tweeter response that matches the design need, and there are a few excellent soft domes out there that fit the bill, without extensive passive xover eq. For the average tweeter, you're probably right that this would be a difficult trade off.
Dave
Attachments
The problem with offsets and delays for aligning acoustic centers is that it only applied to the axis on which the driver is measured. Measure the driver at 30 degrees off axis and the AC is somewhere else and where is not clear. the AC is a measurement dependent position, not a unique point along the driver's axis. It is a fictitious point in space which, relative to the observation point, is the point of the sound source, assuming the source is a minimum phase, point source.
While that's true, an improvement can still be made by targeting alignment eq at a position which is an average of the differential delay in the listening window. When I said "align", it would have been more complete if I said "align on axis".
But as you say, and LipVan showed analytically in their paper in the 80s, it's impossible to use offset and elec phase eq to get true coincidence. A pretty self evident result today, but not back then.
Dave
While I agree with the basic premise, within a reasonable listening angle the change may not be significant. It also probably depends on the kind of driver. The change with axis of a midrange is, I suspect, much less than for a larger midwoofer as well. The difference at 3K LR2 with the 12m/4631 and OW1 is practically nil for fairly large axis changes when measured.
If there are significant diffraction differences with axis, it probably doesn't matter nearly as much. Tilting a flat baffle probably helps in this aspect as well. I'm in DDF's camp on this one.
One thing about the offset I used on the 12m is that on a 3/4" mdf offset, the 12m was actually a very small bit in front of the tweeter. That offset plus the natural high end roll of the 12m and its added delay combined rather well.
It is possible to deal with the stepped baffle diffraction, of course.
Dave
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Nicely done article
While I've come across most of the information before it's nice to see it put together concisely with informative graphs.
However at risk of making a fool of myself I think you have a mistake, or at least an ambiguity in your Butterworth 3rd order results and graphs.
In the first Butterworth 3 "drivers in phase" graph you show that the notch occurs at 30 degrees, while the 3 dB hump occurs at -30 degrees.
However, you don't state at all (unless I missed it) whether this was calculated with the tweeter above or below the woofer, and this will obviously reverse the result, since the relative change in phase with vertical off axis movement will be opposite. With an even order filter it doesn't matter, but with an odd order it does.
Lets assume for the moment you meant for it to be with the tweeter above the woofer, the most common situation.
The next slight ambiguity is that you don't state explicitly whether positive degrees off the vertical axis (in your graphs) represents a listening point which is higher than the equi-distant design axis.
Again I would assume so as it makes sense to me to use positive angles for listening positions above the design axis, and negative values for listening distances below the design axis.
If we make both assumptions - positive off axis angles represent a higher listening position, and the tweeter is above, you seem to have your graphs back to front. A higher tweeter and a positive phasing between drivers should give the 3dB hump above the design axis, and the notch below the design axis.
Consider the relative phase shift of the drivers on the design axis for in phase connection - at the crossover frequency (-3dB point) the woofer has -135 degrees phase shift (lag) while the tweeter has +135 degrees phase shift. (lead)
Therefore the tweeter is +270 degrees ahead of the woofer, or another way of looking at it is -90 degrees behind. 90 degree relative phase shift summed together gives a gain of 3dB thus resulting in flat on axis response.
If we now move the listening position vertically up the distance to the woofer increases more than the the distance to the tweeter, thus more phase lag is added to the woofers response relative to the tweeter.
If we normalize the phase change between the two drivers (since only their relative phase matters in working out how they sum) then at some positive vertical angle (which also depends on distance) the Woofer lag will be -180 degrees, while the tweeter lead has increased to 180 degrees, total phase shift is now 360 degrees or 0 degrees, so there will be a 3dB hump.
Reversing the phase of one driver will swap the notch to be present in the positive angle range and the hump at negative angles. Reversing the physical position of the tweeter and woofer will also reverse the positions of the hump and notch, so both reversed drivers and reversed phase will bring us back to the first situation.
Am I wrong ?
I'm interested to know what you used to generate the graphs too, they look a bit like excel graphs ? Did you write your own custom formulas to generate them ?
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DDf wrote” “it's impossible to use offset and elec phase eq to get true coincidence. A pretty self evident result today, but not back then.”
Well it is a daunting task on a flat baffle, it is too hard to get the drivers close enough together to be less than a quarter wavelength apart.
It is entirely possible using a horn however .
Somewhere here in the archives is here an old post asking about reproducing square waves and then showing some from an SH-50..
That horn system can reproduce a square wave from very good to fair looking, from abut 250Hz to 2700Hz, a span covering both crossovers (which have no apparent phase shift when acoustic phase is viewed). The waveshape fidelity changes some with position left right / up down, but does not loose the shape.
If you examine the phase or 24Khz impulse in the white P, you can see, it is a single acoustic source even though it has three ranges and 7 drivers. Similarly, in the polar plots and 3d balloon, one can see there are no lobes and null one would get when drivers are farther apart.
The square wave reproduction is not an important thing in commercial sound but it is a side effect of coherent addition of the drivers and coupling into a single source.
Bottom line, if you can place all the sources less than a quarter wavelength apart (at the highest frequency they are both on), they add coherently.
If farther, they produce an interference pattern and when greater than ½ wl spacing is reached, reversing one source does not produce any appreciable cancellation and only re-arranges the interference pattern.
I am absolutely convinced that if one can make the low mids and highs come from exactly the same place with no interference, the result is the clues the speaker radiates so far as physical depth are greatly reduced and this makes a large difference in stereo.
Earlier in this thread is an example of something that does a similar thing, a single full range driver on a large baffle, it radiates as a single source over a wide band (I presume the other driver is a woofer). The closest thing I have heard to the SH-50 at a low level was a small fostex full range on a large flat baffle and a Manger, both of which radiate a simple partial spherical pattern over much of their range..
Best,
Tom Danley
Danley Sound Labs
Well it is a daunting task on a flat baffle, it is too hard to get the drivers close enough together to be less than a quarter wavelength apart.
It is entirely possible using a horn however .
Somewhere here in the archives is here an old post asking about reproducing square waves and then showing some from an SH-50..
That horn system can reproduce a square wave from very good to fair looking, from abut 250Hz to 2700Hz, a span covering both crossovers (which have no apparent phase shift when acoustic phase is viewed). The waveshape fidelity changes some with position left right / up down, but does not loose the shape.
If you examine the phase or 24Khz impulse in the white P, you can see, it is a single acoustic source even though it has three ranges and 7 drivers. Similarly, in the polar plots and 3d balloon, one can see there are no lobes and null one would get when drivers are farther apart.
The square wave reproduction is not an important thing in commercial sound but it is a side effect of coherent addition of the drivers and coupling into a single source.
Bottom line, if you can place all the sources less than a quarter wavelength apart (at the highest frequency they are both on), they add coherently.
If farther, they produce an interference pattern and when greater than ½ wl spacing is reached, reversing one source does not produce any appreciable cancellation and only re-arranges the interference pattern.
I am absolutely convinced that if one can make the low mids and highs come from exactly the same place with no interference, the result is the clues the speaker radiates so far as physical depth are greatly reduced and this makes a large difference in stereo.
Earlier in this thread is an example of something that does a similar thing, a single full range driver on a large baffle, it radiates as a single source over a wide band (I presume the other driver is a woofer). The closest thing I have heard to the SH-50 at a low level was a small fostex full range on a large flat baffle and a Manger, both of which radiate a simple partial spherical pattern over much of their range..
Best,
Tom Danley
Danley Sound Labs
Some valid points. I think we can agree that DDF's point about "true coincidence" has very little practical use. Factually, if one carries the analysis to an extreme, most high frequency drivers exhibit "non point source behavior" at their upper limit due to the size of their radiating area and constructive/destructive interference that results from phase differences at very short wavelength output. Blanket rule statements tell us very little about what matters in loudspeaker design. In fact, the issue of "coincidence" is really no more complicated than the phase situation you have described. DLR is quite correct as well here. What truly matters is the combination of the listening position and its angle relative to the acoustic centers of the drivers being used (which establishes the sound wavefront's time of flight), the crossover frequency (establishing the quarter wavelength), and the steepness of the crossover which limits the effect of lobing outside the immediate crossover region. "True coincidence" has never been a requirement for good, accurate sound reproduction. And strictly speaking, "true coincidence" is to some extent a fictional term since the only truly "coincident" sound generator would have to be a point source and point source transducers are about as real and commonplace as unicorns.