Transmission line bass roll-off

[bcodemz]

I'm trying to understand transmission line enclosures and how it augments bass. It seems like people think transmission lines are better and louder than ported. I understand why it provides better sound quality than ported. However, I keep seeing that transmission lines roll off at 6dB/octave below tuning, but I don't see how that's possible. If that's true, then wouldn't that be more desirable than every other enclosure out there that rolls off at 24dB/octave? Even sealed enclosures roll off at 12dB/octave.

[Pete Schumacher]

Re: Transmission line bass roll-off

I'm trying to understand transmission line enclosures and how it augments bass. It seems like people think transmission lines are better and louder than ported. I understand why it provides better sound quality than ported. However, I keep seeing that transmission lines roll off at 6dB/octave below tuning, but I don't see how that's possible. If that's true, then wouldn't that be more desirable than every other enclosure out there that rolls off at 24dB/octave? Even sealed enclosures roll off at 12dB/octave.

Open ended transmission lines behave exactly like regular vented enclosures below tuning. Both roll off at a 4th order rate. Sealed enclosures roll off with a 12dB/octave slope, the same as a driver on an infinite baffle. Tuned resonators, like TLs and Helmholtz enclosures add another 12dB/octave to the roll off.

The biggest advantage transmission lines offer over standard vented enclosures is much better control of resonances above the quarter wave resonance. The use of stuffing between the driver and terminus audibly reduces midrange coloration.

[Jeff B.]

Re: Transmission line bass roll-off

Pete's answer is exactly right, but to clarify a bit, in a nutshell a transmission line will use very long port to take advantage of the quarter wave resonance and use it help extend the response. The downside to this is that this kind of transmission line is usually a lot larger than a standard vented box. Depending on how you load the line you can get initial roll-offs at varying rates, but below a certain frequency it will drop at 24 dB / Oct. Whoever told you that they roll-off at 6 dB doesn't understand transmission lines.

[charlielaub]

Re: Transmission line bass roll-off

I'm trying to understand transmission line enclosures and how it augments bass. It seems like people think transmission lines are better and louder than ported. I understand why it provides better sound quality than ported. However, I keep seeing that transmission lines roll off at 6dB/octave below tuning, but I don't see how that's possible. If that's true, then wouldn't that be more desirable than every other enclosure out there that rolls off at 24dB/octave? Even sealed enclosures roll off at 12dB/octave.

I believe that the reason behind the stated 6dB/oct rolloff is that the initial rolloff is 6dB/octave until you reach the point where both the output of the line and the driver resonance frequency (usually set about the same) occur, and then you transition to the ultimate rolloff of 24dB/oct.

Like Jeff mentions, a transmission line and a vented box can be thought of as variations on a theme. The output of the port can be used to augment the driver output. In a TL, the tuning is made low, on the order of the driver Fs (which is actually lowered by the line's back loading of the driver) and the line is made to be on the order of the driver's Sd (simplifying here).

Here is a good overview of TLs (and other pages on this site):

http://www.t-linespeakers.org/design/classic.html

Bob Brines, who frequents this site, is pretty highly knowledgeable about TLs:

http://brinesacoustics.com

[philthien]

Re: Transmission line bass roll-off

Pete's answer is exactly right, but to clarify a bit, in a nutshell a transmission line will use very long port to take advantage of the quarter wave resonance and use it help extend the response. The downside to this is that this kind of transmission line is usually a lot larger than a standard vented box. Depending on how you load the line you can get initial roll-offs at varying rates, but below a certain frequency it will drop at 24 dB / Oct. Whoever told you that they roll-off at 6 dB doesn't understand transmission lines.

In that case, can one model a transmission line like a ported enclosure with a port of a substantially larger cross-section?

[Jeff B.]

Re: Transmission line bass roll-off

In that case, can one model a transmission line like a ported enclosure with a port of a substantially larger cross-section?

Yes, but you have to account for pipe resonance modes and accurately define the damping characteristics in the model. This is the part that box models don't often do very well.

[philthien]

Re: Transmission line bass roll-off

Yes, but you have to account for pipe resonance modes and accurately define the damping characteristics in the model. This is the part that box models don't often do very well.

That is a completely new way for me to look at t-lines, thanks!

[Pete Schumacher]

Re: Transmission line bass roll-off

I believe that the reason behind the stated 6dB/oct rolloff is that the initial rolloff is 6dB/octave until you reach the point where both the output of the line and the driver resonance frequency (usually set about the same) occur, and then you transition to the ultimate rolloff of 24dB/oct.

That's not quite true either Charlie. You can make a vented enclosure roll off with a 6dB/octave slope and transition to the 24dB slope below tuning. It's certainly not unique to TLs, or even exhibited by TLs unless designed to do so.

Here's an example of a 4 cubic foot enclosure, same woofer, one version vented, one sealed. You can see the shallower slope of the vented enclosure above tuning.

[DDF]

Re: Transmission line bass roll-off

In that case, can one model a transmission line like a ported enclosure with a port of a substantially larger cross-section?

Martin King has probably analyzed T-Lines more than anyone and from his work, there's much more to them than the standard vented model or even a vented model+pipe resonance/damping.

Martin used a closed form solution of the 1D wave equation to help arrive not only at pipe resonance modes, but also revised tuning outcomes. This is very different than any vented model, which is lumped parameter and assumes all cabinet dimensions are much smaller than the wavelengths being modeled. His model also shows how tapering the line lowers tuning frequency, something you won't get from a vented+pipe resonance/damping view of the cabinet. For example, many (many many) moons ago I wrote a Basic program that modeled a T-Line like a vented + pipe resonances/damping, and it was no where near as accurate as Martin's model (1D wave equation<> pipe resonance model).

Martin also spent significant time modelling fiber stuffing and showed the standard theory (Bradbury) isn't that accurate, and came up with his own stuffing model. His model showed that at max stuffing there was about a 10% reduction in speed of sound through the line at some frequencies, which also affects the tuning outcome, again, something you won't get in any vented model. He also used a frequency dependent impedance at the open end to get much more accurate outcomes from the damping model at higher frequencies (this is something you'd see in a horn modeling package, but not a vented model). Again, these are effects very much not in any vented model.

So I guess you could model it sort of like a vented but you may not get close depending on the design. To get a much more accurate outcome, Martin found he needed to add all the above to the standard theory.

Martin also found that TLs have another advantage you won't get from a vented. According to him, if the TL's termination area is greater than the driver's, the TL will behave more like velocity source than a pressure source below tuning and should excite less room modes and not see as much room gain. For reference, a dipole is also a velocity source though the radiation is obviously different.

Martin has achieved really good measure to model correlation as well.

Edit: I forgot to mention there are also "mass loaded" transmission lines where the output of the line is terminated in a port (which is an acoustic mass). This allows shorter lines for the same tuning frequency as a TL without the port, and it also helps roll off port resonances above the first quarter wave resonance. These are again very different outcomes and models than a standard vented model.

Dave

[philthien]

Re: Transmission line bass roll-off

Thank you for the differences between ported and optimal TL designs, Dave, it is very helpful.

[Pete Schumacher]

Re: Transmission line bass roll-off

Martin King has probably analyzed T-Lines more than anyone and from his work, there's much more to them than the standard vented model or even a vented model+pipe resonance/damping.

Martin used a closed form solution of the 1D wave equation to help arrive not only at pipe resonance modes, but also revised tuning outcomes. This is very different than any vented model, which is lumped parameter and assumes all cabinet dimensions are much smaller than the wavelengths being modeled. His model also shows how tapering the line lowers tuning frequency, something you won't get from a vented+pipe resonance/damping view of the cabinet. For example, many (many many) moons ago I wrote a Basic program that modeled a T-Line like a vented + pipe resonances/damping, and it was no where near as accurate as Martin's model (1D wave equation<> pipe resonance model).

Martin also spent significant time modelling fiber stuffing and showed the standard theory (Bradbury) isn't that accurate, and came up with his own stuffing model. His model showed that at max stuffing there was about a 10% reduction in speed of sound through the line at some frequencies, which also affects the tuning outcome, again, something you won't get in any vented model. He also used a frequency dependent impedance at the open end to get much more accurate outcomes from the damping model at higher frequencies (this is something you'd see in a horn modeling package, but not a vented model). Again, these are effects very much not in any vented model.

So I guess you could model it sort of like a vented but you may not get close depending on the design. To get a much more accurate outcome, Martin found he needed to add all the above to the standard theory.

Martin also found that TLs have another advantage you won't get from a vented. According to him, if the TL's termination area is greater than the driver's, the TL will behave more like velocity source than a pressure source below tuning and should excite less room modes and not see as much room gain. For reference, a dipole is also a velocity source though the radiation is obviously different.

Martin has achieved really good measure to model correlation as well.

Edit: I forgot to mention there are also "mass loaded" transmission lines where the output of the line is terminated in a port (which is an acoustic mass). This allows shorter lines for the same tuning frequency as a TL without the port, and it also helps roll off port resonances above the first quarter wave resonance. These are again very different outcomes and models than a standard vented model.

Dave

To add to all these very salient points I would say that after playing around with Martin's worksheets for a long time that I did come to a conclusion that seem to hold true for most lines.

For similar tuning and low end cut off, vented and tapered TLs require very nearly the same internal volumes. Using box calculators like WinISD to come up with F3 and box volume will give you a very close estimate of what's required for a comparable performing TL. What you will need from Martin's worksheets is the taper ratio and line length to get you the tuning you desire. You don't necessarily need a larger enclosure for a tapered TL.

[philthien]

Re: Transmission line bass roll-off

Thanks Pete.

Do t-line designs have to use a tapered line in order to be considered a true t-line? What about a single full-range driver mounted in the end of a pipe with (one-end capped and the other open), is that considered something other than a t-line?

[Pete Schumacher]

Re: Transmission line bass roll-off

Thanks Pete.

Do t-line designs have to use a tapered line in order to be considered a true t-line? What about a single full-range driver mounted in the end of a pipe with (one-end capped and the other open), is that considered something other than a t-line?

That is a T-line, but one that would be considered far from optimal.

Tapered lines with taper ratios of 10:1 or higher behave better above the quarter wave resonance with easier to control resonances using stuffing. Also, the position of the driver along the line is very important in controlling the resonances. Placing the driver 1/5th the way down the line from the closed end produces the smoothest response in the midrange. Placing the driver at the closed end produces a much lumpier response in the midrange, which would be a problem with full range drivers but not so much with subs.

[DDF]

Re: Transmission line bass roll-off

Pete
Thanks for sharing those outcomes, very interesting

[philthien]

Re: Transmission line bass roll-off

That is a T-line, but one that would be considered far from optimal.

Good to know, thank you.