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Old 8th October 2003, 12:58 AM   #1
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Default TL Power handling

I've finally gotten a grip on Xmax.
Thanks, guys, 'preciate it.
So I can predict it pretty easily in my sim. for some designs, but what about TLs? Supposedly you can get responce all the way down to Fs, but what about small drivers with low Fs like the Dayton 6 1/2" papercone woofer (#295-305)? It has an Xmax of 3.15mm. Can I really get 33Hz out of that on more than a couple of watts? That would make a halfway-decent Sub! Can you really do that with a 6 1/2" driver? This guy claims to get 25Hz!! out of the thing, with room gain. Is this possible?!?

Rhetorically speaking....
Can you always get significant responce all the way down to Fs with a TL, or is this only a rule of thumb appling most of the time?

Fully anticipating the dashing of my hopes,
-fortyquid
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Old 8th October 2003, 02:16 AM   #2
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First-how much air does your speaker move? You have a linear Xmax of 3.15mm. I hope that is Ī 3.15. A 6Ĺ" speaker had a cone area of about 24 in≤. Since 3.15 is approx 1/8", you have a total displacement of about 3 in≥.

The more air you can move, the higher your bass output, (SPL). If you double the air you move, your bass output goes up 6 dB.

i have done some work with Martin King's calculations-I haven't got it all down yet. However, I did notice that TL's seem to add about 6 dB to the total SPL over what the cone generates. In other words, a Transmission Line, with a cone moving 1/8", will generate around the same bass output as a sealed box with the cone moving about 1/4".

Understand so far?

This link gives you the air that must be moved for achieving certain SPL's at certain bass frequencies. There are two charts-one normal measurements, one Metric. Since we are dealing with inches, let's take the normal chart.
Volume Displacement For SPL Chart

The charts only apply for sealed boxes. But since we know that a Transmission Line achieves 6 dB over the sealed box reading, we can use this chart.

How much can we get from this driver at, say, 30 Hz? Well, the chart says a sealed box achieves 85 dB SPL @ 30 Hz. We know the Transmission Line adds about 6 dB, so that brings it up to 91 dB. If you have a pair of them, it goes up another 6 dB, so you are at 97 dB. Room gain might bring it up another 2 dB, so that is 99 dB. And if you stick both speakers in corners, you can go up perhaps another 6 dB. That is 105 dB.

That would be pretty good, I suppose, but everything would have to "break" right for you. The room you are in might deaden the sound as well as enhance it. And so forth.

I would say you are probably stretching things, but you might get some decent output at 30 Hz if you stick these things in a corner. Otherwise, I would say that you are reaching a little too far.
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Old 9th October 2003, 03:16 PM   #3
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Thanks, KW!
But am I going to have to put a big fat ol' HP filter @ 28 Hz to keep the thing from over-excurding? From what I have been discovering about X-max HP is essential, rendering a shallow roll-off impossible; is this actually the case? Or does the TL evidence a shallower roll-off in Pe as well as FR?
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Old 9th October 2003, 07:50 PM   #4
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You guys are missing something really important about excursion and both TL's and BR's. While you gain significant SPL at Fc (or what ever you want to call the system resonance), you run out of excursion an octave ABOVE Fc. Typically, at least what I design for, with F3 of 40Hz, you will run out of excursion at 80Hz. This is why my full-ranger ML-TL's are best for the more civilized genre, acoustic jazz and classical, but aren't real good for head banging, acid rock.

Check this out with MJK's worksheets or Unibox.

Bob
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Old 10th October 2003, 04:49 AM   #5
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Bob:

It is true that you run out of excursion relief when you are one octave above Fb.

But then a frequency one octave above another only requires ľ the excursion to produce the lower note does.

For instance, to achieve an SPL of 112 dB @ 100 Hz requires 6 in≥. To achieve an SPL of 112 dB @ 50 Hz requires 25 in≥.

So if your speaker, at Xmax, can only produce 6 in≥, then it can only produce 112 dB @ 100 Hz in a sealed box, or 112 dB @ 50 Hz in a ported box.

After the excursion relief from the port ends at 100 Hz, the speaker can still produce 112 dB @ 100 Hz on it's own.

So it's no problem with the ported box.

In a Transmission Line, the excursion relief is only 6 dB, but that only means that the speaker can't play as loud in the low range, not the midbass range.
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Old 10th October 2003, 05:06 AM   #6
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Not being much a TL guy I could be mistaken, but I believe the early TL designs attempted to completely unload the driver (like an infinite baffle design). This would be accomplished by making the TL long enough that when filled with sound absorbing material, it would disipate the rear radiation completely. In this case f3 = fs an cone excursion is that of a speaker in an open baffle.
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Old 10th October 2003, 01:29 PM   #7
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kelticwizard,

The point I was trying to make is that, coming down in frequency, you are power limited until an octave above f3, then you are excursion limited, until f3 where you are power limited, then you are excursion limited again when the pipe/box unloads.

At f3, of course, excusion is near zero, since all of the energy is transfered to the pipe/box.

roddyama,

Right. The classic TL is, in practice, a form of infinite baffle. You wind up with a little gain simply because the absorption isn't perfect. Given the size of a bass TL, true infinite baffle, using another room or an attic/celler is the way to go.

Bob
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Old 11th October 2003, 09:58 PM   #8
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[QUOTE]Originally posted by kelticwizard
[B]First-how much air does your speaker move? The more air you can move, the higher your bass output, (SPL).

But I thought that TL performance was determined comepletely by Fs.....? Can't you always get good overall performance all the way down? I was under the impression that I could predict, approximately, the performance of any woofer in a TL configuration based entirely upon its Fs, which would make subwoofer design a breeze; if I want my sub to reach 20Hz, I just find the smallest driver with that spec., caculate 1/4 wave and Sd, construct my, admittedly, massive enclosure and fool with the stuffing 'til I like it. Not so easy?
Also....
I don't see lots of designs for these beasties around and I wonder why. Its a relatively easy thing to find a decent prosound driver with high sensitivity and low Fs. Why don't people stick them in Tls? If my assumptions are correct then they could add a good octave or so to their low end and when you consider the size of some of the horns they use already its hard to think they would balk at the size.


"i have done some work with Martin King's calculations-I haven't got it all down yet. However, I did notice that TL's seem to add about 6 dB to the total SPL over what the cone generates. In other words, a Transmission Line, with a cone moving 1/8", will generate around the same bass output as a sealed box with the cone moving about 1/4"."

But I thought it was about Fs {where the speaker resonates} not "what the cone generates" {how much air it can move}

"How much can we get from this driver at, say, 30 Hz? Well, the chart says a sealed box achieves 85 dB SPL @ 30 Hz."

Is this chart an "Iron Law" or can it be bent?

"We know the Transmission Line adds about 6 dB, so that brings it up to 91 dB."

Then may I conclude that TL responce is determined by sealed box response rather than Fs as I have been hitherto impressed?

And thanks for the advice.
-fortyquid
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Old 12th October 2003, 12:29 AM   #9
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The relationship between the port and the driver in a TL works exactly the same as it does for a bass reflex box. The resonant mechanism is different, the TL is a quarter-wave resonator while the BR is a Helmholtz resonator, but the end result is the same. The box and the driver form a doubly tuned system. The driver is a second order high-pass filter and the box is a second order band-pass filter. You get "additional" bass by tuning the box below the driver, allowing the port to pick up the output as the driver rolls off. If you set the box too low, you get a saddle in the output with peaky, boomy, one-note bass. You can see this graphically with MJK's worksheets (TL's) and with Unibox (BR's).

A TL will always be shorter than the calculated 1/4 wave-length, because the pipe will always be inductively loaded below Fp. Tapering the pipe and adding a port (in the BR sense) increase the inductive loading and further shorten the pipe. Increasing the cross-sectional area, and hence the volume of the pipe increases the pipe output, decreases Fp, and increases the pipe Q. Again, you can see this with MJK's worksheets. It becomes second nature after you run a few simulations.

Hoffmann's Iron Law is not violated because, while you gain additional output, you also increase the high-pass rolloff. To determine the maximum SPL that a TL can deliver, look at the excursion plot on the MJK worksheet. While this graph is calculated only for 2.83 volts into Re (I think -- Martin?), you can scale your results. Doubling power increases SPL by 3dB and increases excursion by the square root of 2. When you exceed either Xmax OR the driver max power, you are at max SPL.

Bob
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Old 13th October 2003, 12:18 AM   #10
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Quote:
Hoffmann's Iron Law is not violated because, while you gain additional output, you also increase the high-pass rolloff. To determine the maximum SPL that a TL can deliver, look at the excursion plot on the MJK worksheet. While this graph is calculated only for 2.83 volts into Re (I think -- Martin?), you can scale your results. Doubling power increases SPL by 3dB and increases excursion by the square root of 2. When you exceed either Xmax OR the driver max power, you are at max SPL.
Hi Bob,

You are correc the input voltage is set at 2.83 volts. Remember that this is a RMS value and that all of the plotted data is also RMS values includign Xmax.

I don't get to hung up on Xmax plots. If I was listening to sine waves at specific frequencies then this plot would be applicable. But when listening to music ,which is the sum of many different frequencies, then Xmax can be exceeded at one individual frequency while the sum is still less then Xmax.

For example, consider a square wave with a unit magnitude. The magnitude of the fundamental is greater then unity. The sum of all the terms in the series is exactly unity. If I were to base my design only on the magnitude of the fundamental, then I would be very conservative on my estimated power handling capability.
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