Hi everybody,
This topic aims to answer a simple theoretical question.
A "friend" of mine (well, not really a friend in fact - a quite knowledgeable person when it comes to audio theory, but a person that I appreciate much less as a human being - God, I hope he comes across this topic and reads this
), has written this :
IMHO, the optimal BR tuning is the one that gives the best transient response, even if this means a F-3dB a bit higher.
From this point of view, the optimal tuning is generally close to Fb = Fs with n = 4.
In fact, the best transient response is obtained when Fb/Fs is between 0,9 and 1, with a consistent Vb.
Unfortunately, the person who has written this hasn't even bothered about trying to justify it (he probably thought whe should just take His Word for it and praise Him for that ). While I strongly disagree with this kind of attitude, I think that he still may be right (like I said, the guy has some audio knowledge when it comes to theory).
So here are my questions :
1/ Can someone explain in cartesian terms why Fb/Fs between 0,9 and 1 gives the best transient response ?
2/ What happens if we lower Fb (Fb/Fs = 0,8 for example) ?
3/ Is digital active crossover (e.g. Izotope Ozone) really capable of actually correcting the transient response ? How, and what's the price to pay ? (I have some trouble understanding this point - sorry).
Thanks in advance.
This topic aims to answer a simple theoretical question.
A "friend" of mine (well, not really a friend in fact - a quite knowledgeable person when it comes to audio theory, but a person that I appreciate much less as a human being - God, I hope he comes across this topic and reads this
), has written this :IMHO, the optimal BR tuning is the one that gives the best transient response, even if this means a F-3dB a bit higher.
From this point of view, the optimal tuning is generally close to Fb = Fs with n = 4.
In fact, the best transient response is obtained when Fb/Fs is between 0,9 and 1, with a consistent Vb.
Unfortunately, the person who has written this hasn't even bothered about trying to justify it (he probably thought whe should just take His Word for it and praise Him for that
). While I strongly disagree with this kind of attitude, I think that he still may be right (like I said, the guy has some audio knowledge when it comes to theory).So here are my questions :
1/ Can someone explain in cartesian terms why Fb/Fs between 0,9 and 1 gives the best transient response ?
2/ What happens if we lower Fb (Fb/Fs = 0,8 for example) ?
3/ Is digital active crossover (e.g. Izotope Ozone) really capable of actually correcting the transient response ? How, and what's the price to pay ? (I have some trouble understanding this point - sorry).
Thanks in advance.
A BR is a closed box with a resonance to increase the bass output. But this resonance will also delay the bass signal around the resonance. Therefore you will get the best impulse responce if you make the port resonance as low as possible (but the you are loosing the wanted increase of the bass level). Actually the best impulse responce is if you tune the port to zero herts...a closed box.
So, it is always a tradeoff between bass output and impulse responce (and maybe other things like distortion).
Fb/Fs between 0,9 and 1 might be a good compromise but you should really do a simulation for your application. Or better do some real life tests!!
DSP or a digital crossover can compensate for the delay but the delay can change at different bass levels making the compensation incorrect at high levels.
So, it is always a tradeoff between bass output and impulse responce (and maybe other things like distortion).
Fb/Fs between 0,9 and 1 might be a good compromise but you should really do a simulation for your application. Or better do some real life tests!!
DSP or a digital crossover can compensate for the delay but the delay can change at different bass levels making the compensation incorrect at high levels.
Hi Dylan, thanks.
BTW, the bass level is not an issue here, since we're talking about qualitative criteria (impulse response), not about SPL.
Of course I agree with you. I have made lots of simulations, and they all seem to prove the benefits of a very low tuning, in order to approach the behaviour of a closed box (impulse response, low group delay) while keeping the benefits of the bass reflex (keeping the excursion below Xmax and lower it around Fb).
But all this would mean that "the lower the Fb, the better the impulse response", plain and simple. And this is not exactly what my "friend" said. Thus my two questions : in your opinion, why only between 0,9 and 1, and what can happen if we go below 0,9 ?
BTW, let's remain on a theoretical basis, because the aim of this topic is only to understand and to try to demonstrate, not to experiment.
Thanks again.
BTW, the bass level is not an issue here, since we're talking about qualitative criteria (impulse response), not about SPL.
Of course I agree with you. I have made lots of simulations, and they all seem to prove the benefits of a very low tuning, in order to approach the behaviour of a closed box (impulse response, low group delay) while keeping the benefits of the bass reflex (keeping the excursion below Xmax and lower it around Fb).
But all this would mean that "the lower the Fb, the better the impulse response", plain and simple. And this is not exactly what my "friend" said. Thus my two questions : in your opinion, why only between 0,9 and 1, and what can happen if we go below 0,9 ?
BTW, let's remain on a theoretical basis, because the aim of this topic is only to understand and to try to demonstrate, not to experiment.
Thanks again.
Impulse response and the shape of the cutoff region (analogous to Q, which properly speaking is only a parameter used in second order) are related 1:1. So, if you start off by saying , "A Q of 0.9 is the best," then the impulse response has already been defined. Can't change one without the other.
Now what Q is "best?" Clearly, that depends on what you're trying to do in the design. There is no one correct answer, with all due respect to your friend. Likewise, the ratio of the box tuning frequency to the driver resonance defines the Q.
Now what Q is "best?" Clearly, that depends on what you're trying to do in the design. There is no one correct answer, with all due respect to your friend. Likewise, the ratio of the box tuning frequency to the driver resonance defines the Q.
No many are third order or intermediate order too.
Quite right. Adding one more remark: The Bessel alignment is only valid for discrete values of Qts in a close range i.e. it exists only for one particular value of Qts at a time with all other parameters locked to specific values.
If Ql is chosen to the common value of 7 and fb/fs is set to = 0.97(35) and a box is made with a volume of Vas /1.91 (1.9076) then a driver with Qts= 0.33(12) is necessary, f-3dB will be about =1.49(42) x fs.
Obviously If Qts slightly off i.e. preferably lower like 0.32 a new Ql value must be re-calculated and so on.
For nearly 35 years ago I used drivers like Kef B110 (SP1057) Qts=0.33 and by measuring the Ql in the box with real + virtual volume magnification from the stuffing giving a equivalent volume about 12.37 L it was possible to come very close to a true acoustic Bessel transfer function.
Many designers overstuffed the boxes at that time so a common recommendation was to design for a real volume of at least 9 L but not over 10 L before stuffing was added.
My opinion at that time was, that the B110 in a Bessel box used below 1 kHz was superior to other BR boxes using similar driver sizes, as they mostly were cutting off higher.
The B110 reached below (60 Hz) avoiding the very critical area about 70 Hz where at and above many BR drivers had cut-off not reaching enough fidelity with respect to male voices.
Fb/fs> about 0.97 and higher gives the best transfer function, TF.
Peaky response.
Yes but also as well use analogue design like the LT or any positive feedback system but only if a closed box is used. Has Izotope Ozone a built in digital active crossover too?
Bad transient response is usually a peaky response having a certain TF and when multiplied with a correcting TF the new TF can be chosen arbitrarily. The resulting TF is the only that matters.
You have to pay for the need of added electronics, added complexity when active design is used and not to forget all the power losses involved.
b
Thanks everyone for your answers. I think I see more clearly now.
Some comments on bjorno's answer :
Some comments on bjorno's answer :
bjorno said:Fb/fs> about 0.97 and higher gives the best transfer function, TF.
[...]
Peaky response.
I understand. Well, in my case I guess that shouldn't be a problem, because I am using digital active crossover (my source being of course a dedicated audio PC). So if I understand well, the transfer function & peaky response thing will only be a real problem for people who don't use digital active xover. Am I right ?
Has Izotope Ozone a built in digital active crossover too?
Of course. See for yourself, you might even like it
You have to pay for the need of added electronics, added complexity when active design is used and not to forget all the power losses involved.
Of course : active design means more complexity (but also more control), and flattening the response (Ozone has a very good "matching" function for that) involves power losses. But hey, that's a reasonable price to pay IMHO given the benefits. Thanks again.
I checked the Bessel (BL4) alignment in the R. H. Small article in JAES 1973 October issue (Vented-Box Loudspeaker Systems - Part IV.: Appendices). Not taking Ql into account, the ideal Qts is 0.316, Vb = Vas / 2.33, f3 = 1.5 * fs. Quite close to your figures with a more realistic Ql.bjorno said:
I always tune my closed mid bass boxes enclosures to Bessel Qtc=1/sqrt (3) but for the lowest octaves more towards the critical damping of 0.5.
Crossing over to a sub is then only a matter of FR smoothness and in the reality it’s difficult to get good flatness from a Bessel tuned mid-bass crossed over to a sub, move the speakers and any fine-tuned FR will be lost.
My opinion and more important is that the group delay should stay below about 0.75/f for mid-bass but can be relaxed below about 40 Hz where it’s better trying to achieve an even FR in the room with a minimum power input to the sub driver which often is the main distortion source in the chain.
b
The question is poorly formed and cannot be answered. Transient response depends on more than just Fb/Fs, it also depends on alpha = Vas/Vb and damping parameters of leakage, absorption and port losses...
There is one JAES article that claims the SC4 filter has the best impulse response - and SC4 has Fb/Fs greater than 1 in all cases. I would be inclined to believe that article before your nameless "technical friends".
BTW, maximally flat delay is just that, it is not "optimized for transient response"; although it is better than many of the other alignments, it is not the best.
Bass enclosure design is a set of tradeoffs. If you were to optimize for transient response, you might find that the actual optimum requires a very large box with a very low tuning - and then what you basically have is a leaky infinite baffle.
To get the practical optimum, you need to give more constraints. An example: Say you wanted to design a dissolving pill that is disc shaped and dissolves quickest. The "optimum" would be a disc one molecule thick, but that wouldn't fit in the cup of water - so you need to add constraints like maximum dimensions, then consider packaging cost, manufacturing costs, etc.... and you end up with a pill that dissolves fast and is inexpensive to make....
There is one JAES article that claims the SC4 filter has the best impulse response - and SC4 has Fb/Fs greater than 1 in all cases. I would be inclined to believe that article before your nameless "technical friends".
BTW, maximally flat delay is just that, it is not "optimized for transient response"; although it is better than many of the other alignments, it is not the best.
Bass enclosure design is a set of tradeoffs. If you were to optimize for transient response, you might find that the actual optimum requires a very large box with a very low tuning - and then what you basically have is a leaky infinite baffle.
To get the practical optimum, you need to give more constraints. An example: Say you wanted to design a dissolving pill that is disc shaped and dissolves quickest. The "optimum" would be a disc one molecule thick, but that wouldn't fit in the cup of water - so you need to add constraints like maximum dimensions, then consider packaging cost, manufacturing costs, etc.... and you end up with a pill that dissolves fast and is inexpensive to make....
Hi Ron. I'm not sure I agree with that. I have looked a bit into this subject since the beginning of this topic, and I've found some information about s. To sum it up, s is to Bass Reflex what Qtc is to sealed enclosures. s = Vb / (Vas x Qts^2). The smaller s is, the better the transient response becomes.Ron E said:
Just FYI :
- s = 5,7 => flat response,
- s = 4,8 => SBB4,
- s = 4,5 => Bessel,
- s = 4,3 => tuning that optimizes Group Delay.
The thing is, for a given speaker, Vas and Qts are constants.
So, for a given speaker, the smaller Vb is, the better the transient response becomes.
Of course there's a tradeoff to make, because Vb can't become too small. But basically, with a small Vb we'll have a good transient response, and with a big Vb we'll have more SPL but a bad transient response.
BTW, a low tuning is always good, because it optimizes group delay. The only tradeoff here will be the size of the ports and the air speed @ max SPL. But if ports size is not a problem, then a low tuning is best, because we come closer to the behaviour of a sealed box, with the advantages of the Bass Reflex. Best of both worlds.
I guess you are in the market for low Q drivers, as that has the greatest effect on S Your magic number S doesn't say much, in my opinion. What's your reference for it?
All of the following are "flat" alignments, very close to QB3 and C4. B4 occurs at the intersection of QB3 and C4 at Qts=0.4048 for a simple model with Ql=7. The table below is calculated with Vb/Vas = 20*Qts^3.3...
Qts Vb/Vas S
0.100 0.01 1
0.125 0.02 1.34
0.150 0.04 1.7
0.175 0.06 2.07
0.200 0.1 2.47
0.225 0.15 2.88
0.250 0.21 3.3
0.275 0.28 3.73
0.300 0.38 4.18
0.325 0.49 4.64
0.350 0.63 5.11
0.375 0.79 5.59
0.400 0.97 6.08
0.425 1.19 6.58
0.450 1.43 7.08
0.475 1.71 7.6
0.500 2.03 8.12
0.525 2.39 8.65
0.550 2.78 9.19
0.575 3.22 9.74
0.600 3.71 10.3
0.625 4.24 10.86
0.650 4.83 11.42
0.675 5.47 12
0.700 6.16 12.58
Your magic number S doesn't say much, in my opinion. What's your reference for it?All of the following are "flat" alignments, very close to QB3 and C4. B4 occurs at the intersection of QB3 and C4 at Qts=0.4048 for a simple model with Ql=7. The table below is calculated with Vb/Vas = 20*Qts^3.3...
Qts Vb/Vas S
0.100 0.01 1
0.125 0.02 1.34
0.150 0.04 1.7
0.175 0.06 2.07
0.200 0.1 2.47
0.225 0.15 2.88
0.250 0.21 3.3
0.275 0.28 3.73
0.300 0.38 4.18
0.325 0.49 4.64
0.350 0.63 5.11
0.375 0.79 5.59
0.400 0.97 6.08
0.425 1.19 6.58
0.450 1.43 7.08
0.475 1.71 7.6
0.500 2.03 8.12
0.525 2.39 8.65
0.550 2.78 9.19
0.575 3.22 9.74
0.600 3.71 10.3
0.625 4.24 10.86
0.650 4.83 11.42
0.675 5.47 12
0.700 6.16 12.58
Hi Ron, thanks for your reply.
: http://francis.audio.monsite.wanadoo.fr/page3.html
I realize I've made a small mistake : I didn't say that the S values given by myself (4,7, etc.) were of course calculated for a given speaker (the Beyma 18LX60 - Vas = 500, Qts = 0,37).
I don't know if S is relevant to compare different drivers. However, what remains true (IMHO) is that for a given driver, the lower S (or the lower Vb), the better impulse response. It's up to us to decide what exactly a "low S" is (trade-off time here ). In fact what I really meant is, if we want a good impulse response, then Vb can't be too high. In other words, real big enclosures are good for higher SPL but not for impulse response / group delay. What do you think ?
As for the flat alignments, I think they can be interesting when using passive xover, but not really when using digital active xover, because in this case you'll probably don't care much about the precise shape of the frequency response because you'll just equalize it in the end and make it almost perfectly flat in a lossless way, with professional software like IZotope Ozone (at least that's what I try to do ).
Well, I'm afraid my "reference" is in french, sorryRon E said:I guess you are in the market for low Q drivers, as that has the greatest effect on S
: http://francis.audio.monsite.wanadoo.fr/page3.htmlI realize I've made a small mistake : I didn't say that the S values given by myself (4,7, etc.) were of course calculated for a given speaker (the Beyma 18LX60 - Vas = 500, Qts = 0,37).
I don't know if S is relevant to compare different drivers. However, what remains true (IMHO) is that for a given driver, the lower S (or the lower Vb), the better impulse response. It's up to us to decide what exactly a "low S" is (trade-off time here
). In fact what I really meant is, if we want a good impulse response, then Vb can't be too high. In other words, real big enclosures are good for higher SPL but not for impulse response / group delay. What do you think ?As for the flat alignments, I think they can be interesting when using passive xover, but not really when using digital active xover, because in this case you'll probably don't care much about the precise shape of the frequency response because you'll just equalize it in the end and make it almost perfectly flat in a lossless way, with professional software like IZotope Ozone (at least that's what I try to do
).
Well, french translates amazingly well using babelfish, so I got a so-so look at your reference. I think you are reading too much into what has been developed there. Much of the treatment involves the use of cookbook formulas, although there is discussion later using more technical language.
The Patrick Snyder document is missing.
I find little justification from the treatment that the curve FB2 represents optimum transient response. I doubt that the transient response of that alignment is significantly better than other alignments.
Your reference does not appear to claim that Fb/Fs is 0.9 to 1, rather:
Fb=0,345 Fs/Qts^0,937
Vb=7,45 Vas.Qts^2,4
F-3=0,44 Fs/Qts^1,1.
IMO, if your priority is transient response, a vented box is not the way to go.
The Patrick Snyder document is missing.
I find little justification from the treatment that the curve FB2 represents optimum transient response. I doubt that the transient response of that alignment is significantly better than other alignments.
Your reference does not appear to claim that Fb/Fs is 0.9 to 1, rather:
Fb=0,345 Fs/Qts^0,937
Vb=7,45 Vas.Qts^2,4
F-3=0,44 Fs/Qts^1,1.
IMO, if your priority is transient response, a vented box is not the way to go.
Thanks for taking a look and thanks for the reference information.
And of course the drivers in a vented box can go down to 20Hz @ 102dB with minimal excursion at all frequencies, while the same drivers in a sealed box just get over Xmax at 40Hz.
Last but not least, air speed in the ports remains acceptable (9m/s @ 20Hz/102dB while the first limit is at 17m/s), so there's no risk of actually "hearing the ports")...
You're right, I also do find little justification about lots of things. That's one of the problems with this guy : he doesn't bother trying to really demonstrate what he says.Ron E said:
Well, in fact he has actually claimed several times that best Fb/Fs is 0.9 to 1... but not in that site. Anyway, I don't agree with him anymore so now I don't have any problems with having Fb/Fs much lower than 0.9...Ron E said:
Yes, I know that (a sealed box with Qtc = 0,5 to 0,56 would be best), but transient response is not the only priority here. Distorsion, thus cone excursion, is a key priority too, and here vented boxes are good, especially below 40Hz. A BR box, with 2x15" drivers in //, a moderate volume and a very low tuning, represents the best compromise IMHO. I've managed to keep group delay just identical to the one of a silent box over 60Hz, below 6-7ms between 60 and 40Hz, and it reaches only 9-10ms @ 20Hz. That's very good IMHO. A sealed box is best of course, with a quite constant group delay of about 5ms all the way down to 20Hz, but the difference is completely unhearable : at 20Hz we'd need much more than 10ms to actually hear something.Ron E said:
And of course the drivers in a vented box can go down to 20Hz @ 102dB with minimal excursion at all frequencies, while the same drivers in a sealed box just get over Xmax at 40Hz.
Last but not least, air speed in the ports remains acceptable (9m/s @ 20Hz/102dB while the first limit is at 17m/s), so there's no risk of actually "hearing the ports")...
Jose Hidalgo said:
Probably more like 50-100ms.
One cycle at 20Hz is 50ms, less than a one cycle delay of lower frequencies in a complex tone is not likely audible at all. All this fuss over group delay is much ado about nothing, IMO. If you do your design properly and make a box with a response that doesn't have peaks, your bass should be just fine.
Just so you get a feel for the complexity of the issue:
The actual value of group delay means nothing without knowledge of the system cutoff frequency (tuning frequency for Vented boxes). A system with 50ms delay and a 100Hz Fb would be bad, a system with 50ms and a 20Hz Fb would be much better.
My suggestion when comparing group delay values is to take the value of group delay and divide by tuning frequency when comparing group delay curves, then normalize the graph in frequency so that Fb=1 in each case. This new graph would have a much more fair comparison.
....but step or impulse responses give a much better idea...
Ron, I definitely agree with you.
Thanks !
FYI, there are people out there who claim that, at 20-30ms you begin to hear, or rather, to "feel" the difference even for the very low frequencies (below 40Hz). They might be wrong... or not. Group delay tresholds are very difficult to evaluate at lower frequencies. That's why the Blauert & Laws table is incomplete : http://en.wikipedia.org/wiki/Group_delay_and_phase_delay (see the end of the page)Ron E said:
Yep, I knew that.Ron E said:
Of course. Well, it's not that simple because the shape of the "group delay treshold vs. frequency" graph is probably not exactly linear in the low frequencies. But your suggestion is probably very close to the Truth, and it would be unreasonable to try to be more accurate anyway IMHO.Ron E said:
Thanks !
Jose Hidalgo said:
These are people who feel there must be some special significance to group delay because it is related to that other hard to understand word "phase", and because delay seems like "slow". Also, since software calculates it, it must be significant, right?
These people would probably shudder if they knew what their room and crossover are doing to their transient response....
A while ago I created an Excel table for calculating/visualizing the speaker/box parameters to frequency and phase response relationship. I believe it can be used without Babelfish...
(hangszóró = speaker, doboz = box, jellemzõk = parameters, származtatott = calculated)
http://tube.fw.hu/Speaker_impedance.xls
Laszlo
(hangszóró = speaker, doboz = box, jellemzõk = parameters, származtatott = calculated)
http://tube.fw.hu/Speaker_impedance.xls
Laszlo
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