DG is simply a comparison of the amplifier's output impedance to the nominal impedance of the speaker. For example, if the amplifier has a rated DF of 50 for a nominal impedance of 8 ohms, its output impedance is 8/50 = 0.16 ohms. HornResp actually provides a means of simulating the impact of an amplifier's DF, but you've got to enter it as an output impedance (Rg), rather than as a ratio.
As expected, once you start to model the impact of varying Rg a HornResp sim, you'd see that an effective DF above 50 or so has barely any effect at all on the FR. DF between 50 and about 30 might cause some tiny differences, but it's debatable IMO if these would be audible. However, start dropping below that, and the differences start to get a little more pronounced, and at different frequencies too, as a subwoofer's impedance does not remain constant as frequency changes. A reduction in "tight bass" for example could show up as a drop in upper bass output in the corresponding sim. Hmm... maybe that's one of the reasons why commercial subwoofer cabs seem to have a rising passband response - to compensate a bit for the use of long cable runs and therefore low DF?
Yes, I'm not doubting Hornresp, and i'm not doubting you either. I'm just not familiar with the conversion from Pa to PSI, so I can't confirm or deny that 165 lbs is correct, but I'm not arguing Hornresp's prediction of 6kPa.
Hope that makes it more clear.
If you say so, I have no reason not to believe you, but like I said I'm not familiar with the conversion.
Yes, this is exactly why sometimes cones fail in horn loaded applications. And it's why weltersys reported unusable amounts of distortion when using the light cone Eminence driver in his Keystone tapped horn, while the B&C driver had no problems. In fact the Eminence was so bad he didn't even bother to measure it, just discarded it and moved on.
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But it's not simply high compression ratios that cause this - your horn has a very high 4:1 compression ratio, yet has extraordinarily low pressure on the cone. As simulated, the TH18 I showed has a lower compression ratio (3:1) but almost 4x more pressure. And that's absolute pressure too, not accounting for the fact that you horn has more than 2x more cone area with the 5 drivers.
There's a lot more going on than just compression ratio, although compression ratio is definitely a factor.
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The units of Bl are [Newton/Ampere]. Multiply the Bl value with the input current (in Ampere) and the result is given in Newton. F = Bl * I Newton = (Newton/Ampere) * Ampere
It is about as simple as algebra gets
I feel really dumb.. . . .
I remember BL having the units of Tesla-meters. But I failed to recognize one Tesla as being equal to one newton, per amp-meter.
Thus you are absolutely right. Amperes times BL, provides raw newtons of force.
Question: is this relationship only applicable with the cone at mid-position? How does the BL value change as you approach Xmax? Is the manufacturing design goal to maintain BL as close to constant as possible, all the way to Xmax?
Depends on the design and the particular driver. The XBL design was meant to keep the Bl constant for as long as possible but other types of coil and motor design taper off gradually.
This opens up a whole new world of topics, how xmax is defined. It's mainly based on distortion and Klippel has come up with a way to rate it based on Bl, suspension and Le linearity.
Here's a Klippel report of a "picture perfect" B&C driver, you can see each of the Bl, Cms and Le measurements that the xmax is based on.
http://circuitcellar.com/wp-content...kasonTBench_BCSpeakerReprintedwPermission.pdf
If you want to know how to read these charts and determine xmax on your own, here's the klippel definitions.
https://www.klippel.de/fileadmin/_migrated/content_uploads/AN_05_Displacement_Limits.pdf
Basically, for woofers, mids and tweeters the xmax spec is based on the 10 percent threshold of THD, whether THD is actually measured by itself, or if the Bl, Cms and Le are measured independently and the THD = 10 percent is met in the first (lowest performing) of these three categories.
For subwoofers the acceptable THD has been raised to 20 percent.
But there are different ways of specifying xmax too, the old way was geometric measurement considering gap depth and coil length. And sometimes the marketing dept just prints whatever figure they pull out of a hat.
Different companies have different ways of making the number larger, B&C for instance publishes xmax (geometric) and Xvar (50 percent reduction in Bl and/or suspension from resting position). And there are numerous variations on all this.
Basically though, to answer your question, there's a Bl curve (Bl vs stroke) of a VERY good driver in the first link.
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Yes, the worthwhile ones. Here's something I dug up from TD about they TH118 woofers.
Ok, I see (or at least I think I see) an inherent problem. . . .
In post #68 to this thread, just-a-guy modeled a horn with 18” driver. Hornresp indicated pressures upwards of 6 kPa will be expected at the cone. Seems reasonable.
6 kPa over a 1225 SD cone, generates a linear-force of 165 pounds. At 1000 watts (11.18 amperes into an 8 Ohm coil), the motor-structure of this driver (BL of 25.77), will generate only 65 pounds of linear force.
If the pressure on the cone generates 165 pounds of force, and the speaker’s motor structure can only generate 65 pounds of force, then the horn would be driving the speaker – not the speaker driving the horn. Isn't this a mechanical impossibility?
What am I missing?
There must be some sort of impulse-momentum phenomenon happening here. . . right?
In post #68 to this thread, just-a-guy modeled a horn with 18” driver. Hornresp indicated pressures upwards of 6 kPa will be expected at the cone. Seems reasonable.
6 kPa over a 1225 SD cone, generates a linear-force of 165 pounds. At 1000 watts (11.18 amperes into an 8 Ohm coil), the motor-structure of this driver (BL of 25.77), will generate only 65 pounds of linear force.
If the pressure on the cone generates 165 pounds of force, and the speaker’s motor structure can only generate 65 pounds of force, then the horn would be driving the speaker – not the speaker driving the horn. Isn't this a mechanical impossibility?
What am I missing?
There must be some sort of impulse-momentum phenomenon happening here. . . right?
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This is an area I have not studied, as I said I've only delved into relative pressures of different designs, not absolute pressure or unit conversions or calculating the force a driver is capable of. All I can tell you is that the sim I posted is a real horn that people have built and used to great satisfaction and success. It performs as the sim would indicate.
Most people use a different driver than I showed, but the difference is academic.
This is also a very close incarnation of a commercial design, the Danley TH118.
Most people use a different driver than I showed, but the difference is academic.
This is also a very close incarnation of a commercial design, the Danley TH118.
Anyway, the sim in post 68 was shown at well over 1000 watts - here's the driver power graph for that sim.
An externally hosted image should be here but it was not working when we last tested it.
Also note that that particular sim is a bit of an exaggeration - it's shown well past the driver's rated power handling and a few mm past xmax.
This was just a sim from my records, copied from someone else who was showing it at this power level. I didn't have the presence of mind to lower the power a bit to show this sim but I should have.
At the power level shown in post 68, the driver is past xmax, so Bl is dropping hard, the suspension is likely becoming much more restrictive, the driver is heating up so Re is rising and not pulling as much power as expected, there are losses from power compression, etc.
This isn't really a practical example for those reasons, but lowering the power by half would still result in tremendous pressure on the cone. Here's the same sim showing cone total pressure at 70.71V (1000 watts referenced to the 5 ohm Re). At 4kPa it's still more than twice as high as your horn pressure.
This was just a sim from my records, copied from someone else who was showing it at this power level. I didn't have the presence of mind to lower the power a bit to show this sim but I should have.
At the power level shown in post 68, the driver is past xmax, so Bl is dropping hard, the suspension is likely becoming much more restrictive, the driver is heating up so Re is rising and not pulling as much power as expected, there are losses from power compression, etc.
This isn't really a practical example for those reasons, but lowering the power by half would still result in tremendous pressure on the cone. Here's the same sim showing cone total pressure at 70.71V (1000 watts referenced to the 5 ohm Re). At 4kPa it's still more than twice as high as your horn pressure.
An externally hosted image should be here but it was not working when we last tested it.
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1) A loudspeaker's magnetic system converts the electrical energy into newtons of force, which will generally be most efficient at mid-position.
2) It will reduce, depending on the design it may be within 70%at Xmax, or it may be less. Many B&C woofers have exceptionally linear BL response, as is borne out by Klipple testing. The B&C18SW115 has some of the best looking (and sounding) BL curves of any driver, at any price (at least
3) Yes, and to not "drop like a rock" past Xmax. B&C lists both Xmax, the maximum linear excursion as is typically measured according to the AES2-1984 standard, corresponding to a maximum of 10% total harmonic distortion (THD) with a sinusoidal signal, though most manufacturers, including B&C, typically provide data for Linear Mathematical Xmax, not measured Xmax.
The main limit of this measurement is that it looks at the output signal instead of the physical features of the driver itself. On the contrary, the most up-to-date Klipple instruments can measure the variations in loudspeaker parameters when they are fed with high-level signals. In this way, an excursion limit can be fixed, beyond which the parameter’s variation becomes excessive.
The “Xvar” value reported in B&C's data indicates the excursion limit, when the magnetic field seen by the voice coil, or the total suspension compliance, or both, drops to less than 50% of their small signal value, producing high distortion levels, strong variations from small signal behavior and power compression. Some of their drivers have a larger Xvar than Xmax, I have found the Xvar figure to be very usable excursion.
As far as your conversion resulting in a 165 pounds of force distributed around the cone in the simulation, that seems about right empirically to me, I know a B&C18SW115 could easily launch my butt out of a chair, and can do a good job throwing golf balls, etc. great distance, as well as kicking up rooster tails of sawdust.
I think JAG may have recalled Tom Danley talking about the fiberglass re-inforced 15" cones used in the SDL-7, which could withstand someone standing on them, I did not attempt that when I owned a pair of 18SW115.
However, I just did a little experiment, a push up with my hands spread around the dust-cap of a B&C 18TBW100-4, which has a 15mm smaller voice coil and slightly less MMS than the 18SW115 . My push up exerts 98 pounds on the bathroom scale, it seemed that was pushing the cone to Xlim (near as I could tell looking down) which is a one way deflection of 27mm. The TBW is less "stiff" than the SW115, concurrent with handling less power.
These drivers are designed to be relatively "bullet proof", the suspension gets progressively harder to push as the BL product becomes less at extreme excursions, it would be more likely to burn out the voice coil than it to suffer mechanical damage, unless you had an amp capable of way more peak power than the "continuous" rating, 3000 W for the TBW100.
Art
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Here's the B&C 18tbw100 Klippel Bl graph, for those that didn't click the link.
An externally hosted image should be here but it was not working when we last tested it.
Do you have a link to B&C 18SW115 Klippels? Love to see it.
This is a massively undersized back loaded horn using a fullrange driver and it's completely impotent at subwoofer frequencies, it's about as relevant to this discussion as a link to IMDB. Why did you post it?
This is a small can of worms and is where you need to depart from some of the simulation results to pick apart the differences.
Example, wedging a horn mouth into the intersection of two walls in a corner so that radiation takes place like a quartered orange, is a fairly substantial method of applying quarter space loading. To some degree this will tend toward allowing quartering of the entire horn along its axis.
However an expanding type horn (as opposed to a waveguide) is not intended to have straight sides (although it can), and this is the source of the discrepancy. In some respects it can be overlooked. At the end of the day such an expanding horn is going to expect free radiation to be possible in at least one dimension.
Another example, placing a horn mouth on the floor can emulate half space loading, but there is a right way to do it. Otherwise the discrepancy can be frequency (and directionally) dependent.
All the while the loading of the individual driver is a consideration. You want to find a way to bring together the compromises so they work.
There are no worms here and the sim is correct, in that it assumes the boundary is infinitely rigid and will create a perfect mirror image.
There is no discrepancy. If you build half a round horn and place it on a perfectly rigid boundary, the boundary will act as a mirror image and result in a full horn.
This is the basis of the theory which is probably at least 100 years old, it's the concept that simulators use, and measurements bear this out.
The way to do it is to make a horn that is one half of a full horn and use the boundary to mirror image the other half. The theory and simulators assume the full horn is round, so you theoretically have to make half of a round horn. But in practice it doesn't have to be completely round, but you can't place a line of subs side by side in a long row and expect it to act like a round horn, you have to stack them to simulate half of a whole round horn.
Gee Just, for someone who appears to agree with me you have an interesting way of going about it.
The sim isn't wrong, but it is specific. This makes it incomplete unless these specifics are followed. This means they must be understood and manually taken into account if you deviate.
My reply was with regards to the way to divide the radiation space for a horn that is supposed to expand continuously and which is expected to terminate onto free space. My allusion was: is there a perfect way to terminate (or constrain, ie partially terminate) such a horn? and especially when the available tools are planar room walls?
The answer to this is it goes beyond the specific limitations of the sim.
It is not beyond the limitations of a simulator. I'm not sure why you think it is. Between Hornresp and the various diffraction and boundary simulators you can simulate pretty much any boundary effect you can think of (as long as the sound source is round or close to round). The fact that the ground or a wall is flat is exactly what the simulator counts on. What happens beyond the mouth is not part of the horn, it's part of the radiation angle.
To give some examples of the differences, if an expanding horn was on the floor and parallel to it and beaming at some frequency, the primary result of the floor image would be the off-axis diffraction, as the listener would be out of the beam of the floor image, so the virtual array is lobing.
Another, fitting the mouth into quarter space makes the horn one quarter of a radial horn (the type that radiates 360 degrees around over a horizontal plane with the horn expansion expressed vertically. Here, (assuming the room walls have been incorporated properly) the vertical horn walls become the sole determinant of the level of support of said walls at a given frequency. Here they ought to support, direct, and load the driver.
Another, fitting the mouth into quarter space makes the horn one quarter of a radial horn (the type that radiates 360 degrees around over a horizontal plane with the horn expansion expressed vertically. Here, (assuming the room walls have been incorporated properly) the vertical horn walls become the sole determinant of the level of support of said walls at a given frequency. Here they ought to support, direct, and load the driver.
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I would need pictures to follow what you are saying as I can't picture what you are describing.
It's easy enough to simulate boundary reflections and lobing. Have you played with a passive crossover designer before? Bagby's suite of spreadsheets can simulate boundary loading and lobing issues. Simply place 2 identical drivers on a baffle (or use .frd and .zma files from a measured horn), this is the same thing as one driver (or horn) being boundary loaded. At any listener position you can simulate the directivity (based on cone size vs frequency), summed response and lobing. This is pretty basic and any competent passive crossover designer spreadsheet or program can do this.
I'm fully aware that there are situations where people build things that are radically different than what they simulated, but that doesn't mean that you can't do an accurate simulation if you know what you are doing.
It's easy enough to simulate boundary reflections and lobing. Have you played with a passive crossover designer before? Bagby's suite of spreadsheets can simulate boundary loading and lobing issues. Simply place 2 identical drivers on a baffle (or use .frd and .zma files from a measured horn), this is the same thing as one driver (or horn) being boundary loaded. At any listener position you can simulate the directivity (based on cone size vs frequency), summed response and lobing. This is pretty basic and any competent passive crossover designer spreadsheet or program can do this.
I'm fully aware that there are situations where people build things that are radically different than what they simulated, but that doesn't mean that you can't do an accurate simulation if you know what you are doing.
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