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Old 20th March 2004, 12:07 AM   #1
Mudge is offline Mudge  United Kingdom
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Default Interesting TL Result

As part of my desire to find a good use for the rear wave, I've been looking at transmission line theory from the bottom upwards. Actually I've been looking at the physics behind loudspeakers, as opposed to the number juggling of Thiele-Small parameters and enclosure alignments.

Anyway, I worked out what kind of pressurisation is produced by a cone at maximum excursion in a sealed box of appropriate size to get Qtc to 0.707. I was using the TS parameters of the Volt RV3143 (as used by PMC in their second largest TL monitor). As you might guess, this is a fairly large number, about 6304 Pascals.

Anyway, the end result is that to get the equivalent acoustic resistance to maximum excursion from an unstuffed TL, I needed a line CSA about 1/10th Sd

The numbers tally up for any extension, since there is only one variable, the cone excursion.


Now, either everyone has been building totally underdamped transmission lines, or I've got my maths for the confinement of the port wrong (about a 50/50 chance of that).
What seems mathematically obvious to me is that if you set the line CSA equal to the Sd of the driver, it behaves as if it was in free space, except that the rear wave is now in phase with the front wave, increasing acoustic output.
This is ignoring flow effects of course, it's likely if you wanted dipole style bass from a TL you'd need a bigger than Sd line.
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Old 20th March 2004, 01:46 AM   #2
MJK is offline MJK  United States
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Hi Mark,

I have to admit that I am having trouble following your logic and arriving at the conclusion you have drawn. My experience simulating, building, and testing a few TLs does not seem to lead me down the path you are following. Could you provide a few more details on how you think a TL works so I can understand what you are concluding.

Thanks in advance,
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Old 20th March 2004, 02:14 AM   #3
Mudge is offline Mudge  United Kingdom
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Martin,
My results are from an unstuffed line, effectively a straight continuous line of a fixed CSA.
Anyway, you have the standard transmission line behaviour which is well explained. Then you have the behaviour in the throat of the line. If the line csa is above the Sd of the driver then there is no restorative force on the driver, as in an open baffle loudspeaker.
If you reduce the csa to below the Sd of the driver, then some work must be done on the air in the throat of the line, in order to force it down the line. As a result of this there would be an opposing force on the driver, analogous to a sealed box.
Using this restorative force to control driver motion, as in an acoustic suspension design, requires a value of Sline much lower than anyone seems to use. It's a tradeoff for someone who greatly prefers the high quality of sealed box bass to the loose flabby stuff you get from a conventional ported box. Anyway my results with a Sline below Sd follow the behaviour of a normal TL quite well, that is they have Qts (for the driver) values (and those I've heard sound like) a sealed box of very low Qts (0.4-0.6).

Have you ever built a TL with such a low Sline?
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Old 20th March 2004, 10:09 AM   #4
Mudge is offline Mudge  United Kingdom
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My intention is to build a compact Linkwitz transform sub, but exploiting the 6dB/Octave as opposed to 12dB/Octave roll off to reduce the power requirements by 4x.

Anyway I'm going to give it a go, hopefully pics and graphs to follow
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Old 20th March 2004, 11:58 AM   #5
MJK is offline MJK  United States
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Hi Mark,

Quote:
Have you ever built a TL with such a low Sline?
No I have never built a low cross-sectional area TL. I have found that the bigger the cross-sectional area the better the low bass performance up to some point at which the returns become small for additional area. Typically for a straight constant area line my designs approach 3 x Sd.
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Old 20th March 2004, 12:33 PM   #6
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Martin,
that seems fairly logical and consistent. I must admit I'm somewhat in awe of your work on TL theory.

I shall have to get busy building my short narrow line and see how the results diverge from the underlying physical model.
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Old 20th March 2004, 11:43 PM   #7
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Hmm, I use T/S because they work quite well. You are right though, if you use sealed 0.707 as a reference Vb, then for a 1/4WL pipe, its cross sectional area will be considerably < Sd in most cases, but Vas, Qts will vary it quite a bit.

Yes, TLs are underdamped to start with, then are stuffed to lower it to somewhat < 0.707 normally.

Don't know about the math, but no way, no how does a 1/4WL pipe allow the driver to perform as if in free space with CSA = Sd. This will require the pipe Vb to be 4-10x Vas depending on the driver's specs, so this is the range that CSA should be derived from. Normally though, the Vb of a T/S max flat for the desired Fb works well enough as a balance between LF extension, gain, and ripple in the passband.

WRT adding a filter chamber to the Sline, this is what was once called an acoustic labrynith and now a Daline, i.e. a bandpass with a very long, well damped vent.

GM
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Old 21st March 2004, 10:23 AM   #8
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Exactly what physical effect do you think causes Vline to have any relation to Vas? If you build a 100m line with the appropriate CSA, then it will have the same Vline as one of 4xSd, but I guarrantee that the behaviour of the driver will be somewhat different.

Vline is irrelevant, there are two parameters, one is the restorative force on a driver, which is a function of the impedance of the line, which is harder to calculate when the line is stuffed and the other is the frequency of the 1st standing wave in the line.
If the flow impedance of the stuffed line is 40x that of the empty line, then of course the CSA of the line should be 4x Sd, if the line impedance, as determined by the TS parameters (by a rather complex set of equations as yet) requires an unstuffed line of CSA 1/10 Sd.
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Old 21st March 2004, 07:36 PM   #9
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Quote:
No I have never built a low cross-sectional area TL. I have found that the bigger the cross-sectional area the better the low bass performance up to some point at which the returns become small for additional area. Typically for a straight constant area line my designs approach 3 x Sd.
so, for any finished strait TL design, if you increase the cross sectional area it will improve the low end response?? Will that change the length of the line or the amount of stuffing? btw im not exactly sure what sd is
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Old 21st March 2004, 07:59 PM   #10
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The less you load the driver with it's own rear wave, the lower the resonant frequency of the driver and consequently the more output you will get at low frequencies for the correct line length.
Once you unload the driver completely, it's resonant frequency becomes Fs and any gains from this point on will be minimal.

Sd is the surface area of the driver.
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