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Author Topic: Black Hole Sum, and limiting  (Read 2410 times)

Mark Wilkinson

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Black Hole Sum, and limiting
« on: May 15, 2016, 01:09:54 pm »

A sub topic in a recent thread brought up this link http://www.prosoundtraining.com/site/synaudcon-library/black-hole-sum/#more-5044   (Thx Jay, Alex)

Great article, and if I understand it correctly.....
It says when two low frequency drivers are opposite in polarity, where they are cancelling each other's acoustic output .......
.....that conservation of energy rules, and that the energy still has to go somewhere...
It says that the 'somewhere' is voice coil heat...

The article references low frequency drivers, but shouldn't it apply to drivers of any frequency?

I mean, take a coaxial compression driver crossing over at 6300 hz.  If acoustic polarity is opposite at 6300, won't there be cancellation the same as was for low frequency, that has to result in heat in the voice coils?

And isn't the magnitude of the acoustic cancellation, or voice coil heat, just the bottom half of the familiar phase summation wheel? 
Throughout the crossover region, frequency by frequency....wherever phase implies negative summation?


Once more, if I understood the article...
It says the reason the acoustic cancellation energy turns into voice coil heat is because total driver impedance decreases during cancellation (due to a reduction in acoustic impedance). 
And since voltage to the driver is constant, lower impedance means more current through the voice coil, which of course means more heat.

OK. So how does either RMS or peak voltage limiting do anything to protect for this?
Doesn't this mean true power limiting is the only fail-safe method for out of polarity or badly out of phase regions?

Seems like it might be pretty easy to blow up the upper driver (6300hz up) in the coax example, at high levels with a polarity reversal...even with voltage limiting properly set?

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Keith Broughton

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Re: Black Hole Sum, and limiting
« Reply #1 on: May 15, 2016, 01:30:25 pm »

I would say that the wavelenght of the low frequency driver makes for a more complete "coupling" of the drivers and the subsequent result.
At the high frequency of your example, effective coupling of the drivers would not be possible.
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Mark Wilkinson

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Re: Black Hole Sum, and limiting
« Reply #2 on: May 15, 2016, 02:25:07 pm »

I would say that the wavelenght of the low frequency driver makes for a more complete "coupling" of the drivers and the subsequent result.
At the high frequency of your example, effective coupling of the drivers would not be possible.

Hi Keith, at first I thought yeah, that makes sense........., but then,  isn't a major speaker design goal to space drivers physically so that acoustic coupling does occur?

Take the coaxial compression example ... at its 6300hz crossover, wavelength (2.1") still exceeds exit dia (1.25") for the combined unit.
Or the coupling that's supposed to occur between mid cone and compression driver?
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Ivan Beaver

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Re: Black Hole Sum, and limiting
« Reply #3 on: May 15, 2016, 02:51:23 pm »



Seems like it might be pretty easy to blow up the upper driver (6300hz up) in the coax example, at high levels with a polarity reversal...even with voltage limiting properly set?

2 subs run out of polarity is a completely different thing than a coax HF.

Actually it is very common to run the HF out of polarity as compared to the woofer-but not all the time.

It all depends on the crossover-the phase relationship between the low and high drivers and so forth.

The low and high drivers are only operating over the same freq band at the same level for a limited freq range.

What you want them to do is to couple.  No matter what the polarity is, it is the PHASE relationship that is important.

In most cases (not all) if you have a properly designed crossover and you flip the polarity of either driver you will introduce a notch in the response.

I know of one case that if you do that, the wiggles just change around crossover a little.  However the phase response takes a 180* dive.

As usual, there is no "one size fits all" answer.

But I would not be concerned with burning up the driver in a coax, no matter the polarity.  Unless something else is wrong.

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Tom Danley

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Re: Black Hole Sum, and limiting
« Reply #4 on: May 15, 2016, 03:19:56 pm »

A sub topic in a recent thread brought up this link http://www.prosoundtraining.com/site/synaudcon-library/black-hole-sum/#more-5044   (Thx Jay, Alex)

Great article, and if I understand it correctly.....
It says when two low frequency drivers are opposite in polarity, where they are cancelling each other's acoustic output .......
.....that conservation of energy rules, and that the energy still has to go somewhere...
It says that the 'somewhere' is voice coil heat...

The article references low frequency drivers, but shouldn't it apply to drivers of any frequency?

I mean, take a coaxial compression driver crossing over at 6300 hz.  If acoustic polarity is opposite at 6300, won't there be cancellation the same as was for low frequency, that has to result in heat in the voice coils?

And isn't the magnitude of the acoustic cancellation, or voice coil heat, just the bottom half of the familiar phase summation wheel? 
Throughout the crossover region, frequency by frequency....wherever phase implies negative summation?


Once more, if I understood the article...
It says the reason the acoustic cancellation energy turns into voice coil heat is because total driver impedance decreases during cancellation (due to a reduction in acoustic impedance). 
And since voltage to the driver is constant, lower impedance means more current through the voice coil, which of course means more heat.

OK. So how does either RMS or peak voltage limiting do anything to protect for this?
Doesn't this mean true power limiting is the only fail-safe method for out of polarity or badly out of phase regions?

Seems like it might be pretty easy to blow up the upper driver (6300hz up) in the coax example, at high levels with a polarity reversal...even with voltage limiting properly set?

ďThe article references low frequency drivers, but shouldn't it apply to drivers of any frequency?Ē

Yes..But complete / unilateral cancelation or for that matter unilateral (coherent) addition only happens when the drivers are less than ľ wavelength apart.   Once the spacing is Ĺ wl or greater, they radiate as independent acoustic sources and do not feel each otherís radiation resistance as they do when closer.

This is true for all frequencies, any drivers even where that ľ wavelength transition is impractical to deal with. 
 Wavelength = the speed of sound divided by the frequency.

So far as the coaxial driver, there is usually a significant acoustic discontinuity at the transition between the inner horn and cone body which imposes an amplitude and phase issues in addition to the driver and the rest of the acoustic path and the hf driver is located in a different location front to back, a different place in time (although that can be dealt with sometimes even passively).   
The thing is, youíre stuck with a starting point with the magnitude and phase of the hf driver and the magnitude and phase of the woofer so youíre not starting with a resistorís response and for a passive crossover youíre load isnít a resistor itís the impedance curve and phase for both drivers.

The Crux of the Biscuit to paraphrase Frank is that with a complex mag and phase as a starting point, it may well be that electrically you have a driver inverted from red dot indications.

Yes acoustic cancelation can increase VC heating BUT only to the degree the acoustic load is a significant factor in the drivers impedance.  For instance in an efficient horn, the radiation resistance (appears in series) and is a visible part of the load and so removing it will lower the impedance and for the same Voltage draw more Current and then the heating is the Current squared times load resistance = more heat.
Hope that helps
Tom
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Mark Wilkinson

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Re: Black Hole Sum, and limiting
« Reply #5 on: May 15, 2016, 03:21:21 pm »

2 subs run out of polarity is a completely different thing than a coax HF.

Actually it is very common to run the HF out of polarity as compared to the woofer-but not all the time.

It all depends on the crossover-the phase relationship between the low and high drivers and so forth.

The low and high drivers are only operating over the same freq band at the same level for a limited freq range.

What you want them to do is to couple.  No matter what the polarity is, it is the PHASE relationship that is important.

In most cases (not all) if you have a properly designed crossover and you flip the polarity of either driver you will introduce a notch in the response.

I know of one case that if you do that, the wiggles just change around crossover a little.  However the phase response takes a 180* dive.

As usual, there is no "one size fits all" answer.

But I would not be concerned with burning up the driver in a coax, no matter the polarity.  Unless something else is wrong.

Sure Ivan, all that makes sense...

Particularly where you said it's relative phase that matters.
That's what I'm pondering.... take the coax compression driver alone...just consider the phase relationship between the HF driver and the VHF driver. If there is phase alignment between the two drivers we get good summation through crossover, right?  If not, we get the notch.  Isn't the notch just cancellation energy, and doesn't that energy have to be accounted for somewhere just like in black hole sum for subs article ?  I just don't see how freq makes a difference...seems it should be the same physics whether low freq or high.
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Mark Wilkinson

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Re: Black Hole Sum, and limiting
« Reply #6 on: May 15, 2016, 03:39:22 pm »

ďThe article references low frequency drivers, but shouldn't it apply to drivers of any frequency?Ē

Yes..But complete / unilateral cancelation or for that matter unilateral (coherent) addition only happens when the drivers are less than ľ wavelength apart.   Once the spacing is Ĺ wl or greater, they radiate as independent acoustic sources and do not feel each otherís radiation resistance as they do when closer.

This is true for all frequencies, any drivers even where that ľ wavelength transition is impractical to deal with. 
 Wavelength = the speed of sound divided by the frequency.

So far as the coaxial driver, there is usually a significant acoustic discontinuity at the transition between the inner horn and cone body which imposes an amplitude and phase issues in addition to the driver and the rest of the acoustic path and the hf driver is located in a different location front to back, a different place in time (although that can be dealt with sometimes even passively).   
The thing is, youíre stuck with a starting point with the magnitude and phase of the hf driver and the magnitude and phase of the woofer so youíre not starting with a resistorís response and for a passive crossover youíre load isnít a resistor itís the impedance curve and phase for both drivers.

The Crux of the Biscuit to paraphrase Frank is that with a complex mag and phase as a starting point, it may well be that electrically you have a driver inverted from red dot indications.

Yes acoustic cancelation can increase VC heating BUT only to the degree the acoustic load is a significant factor in the drivers impedance.  For instance in an efficient horn, the radiation resistance (appears in series) and is a visible part of the load and so removing it will lower the impedance and for the same Voltage draw more Current and then the heating is the Current squared times load resistance = more heat.
Hope that helps
Tom

Thanks Tom, that does help, particularly the part about wavelength spacing.
But I guess then, here's my question....if I invert polarity between any two adjacent drivers where I measure smooth response before inversion (by adjacent, I mean adjacent in frequency such as mid to high, or the 2 drivers in the compression coax example) and then after inversion I measure a notch or trough through crossover region, isn't that simple evidence in and of itself that black hole sum exists?

The part about VC heating only to degree of acoustic load helped too... I guess I was stressing my Labhorns (thanks again for those) much more than I realized playing with how they could totally cancel sine waves when out of polarity  yikes lol
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Ivan Beaver

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Re: Black Hole Sum, and limiting
« Reply #7 on: May 15, 2016, 04:43:44 pm »

Sure Ivan, all that makes sense...

Particularly where you said it's relative phase that matters.
That's what I'm pondering.... take the coax compression driver alone...just consider the phase relationship between the HF driver and the VHF driver. If there is phase alignment between the two drivers we get good summation through crossover, right?  If not, we get the notch.  Isn't the notch just cancellation energy, and doesn't that energy have to be accounted for somewhere just like in black hole sum for subs article ?  I just don't see how freq makes a difference...seems it should be the same physics whether low freq or high.
There is a difference between good amplitude summation and flat phase.

Sometimes you can get both, other times you have to choose between flat amplitude and a phase shift or flat phase and a notch in the amplitude response.

So-as usual-it depends.

This is when dealing with passive crossovers.  If you have time (delay) that you can use, this can help.

It also matters how well the drivers overlap amplitude response.

Sometimes it can take quite a bit of "futzing" to get it where you want it.  And sometimes you can only get close.

The difference the freq makes is the wavelength.  With higher freq, small differences in physical location can make a big difference (hence the reason it is so hard to get HF drivers to combine well).

With subs, there is a lot more "play room" because the wavelengths are so much longer.

As Tom says-1/4 wavelength is the goal.  So for your example of 6.3Khz, that is about 1/2 inch or 1.2cm.

For 50Hz that is 56" or 1.4M

BIG difference is how you can move things around-depending on freq.
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Mark Wilkinson

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Re: Black Hole Sum, and limiting
« Reply #8 on: May 15, 2016, 08:04:28 pm »

There is a difference between good amplitude summation and flat phase.

Sometimes you can get both, other times you have to choose between flat amplitude and a phase shift or flat phase and a notch in the amplitude response.

So-as usual-it depends.

This is when dealing with passive crossovers.  If you have time (delay) that you can use, this can help.

It also matters how well the drivers overlap amplitude response.

Sometimes it can take quite a bit of "futzing" to get it where you want it.  And sometimes you can only get close.

The difference the freq makes is the wavelength.  With higher freq, small differences in physical location can make a big difference (hence the reason it is so hard to get HF drivers to combine well).

With subs, there is a lot more "play room" because the wavelengths are so much longer.

As Tom says-1/4 wavelength is the goal.  So for your example of 6.3Khz, that is about 1/2 inch or 1.2cm.

For 50Hz that is 56" or 1.4M

BIG difference is how you can move things around-depending on freq.

Thx Ivan, all you say makes sense....

I've been playing around with eliminating alot of the "depends on" speaker tuning variables, by temporarily saying screw latency, let's see how things work with flat phase. 
IOW, lots of FIR, ....level individual driver response, flat wide overlap, level summation, flat phase through it all.

Ironically, not having to deal with most of the issues you list above, is letting me understand those issues even better....as well as see things like basic summation even clearer.

I may be nuts, and it damn well may not matter, but it still seems like where there is the potential for acoustic summation, there also has to be the potential for acoustic cancellation....and that black hole sum should apply.

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