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Old 16th June 2005, 03:57 PM   #1
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Default technical transmission line questions

I have a surprisingly beefy little 4" woofer from an old ported computer subwoofer. Right now it's in a transmission line test enclosure I made out of cardboard. It's only good down to 90 Hz or so, but I imagine I'm getting a good deal more extension than that from all the stuffing I put in. It has an interesting sound to it, especially when corner loaded. My Eagles CD sounds nice just with this design. However, I'd like to build a more optimized, extended transmission line as a bass module for a tiny casual-listening sub/sat system. I'm trying to think about how to get the most output from this woofer, so I have some technical questions about transmission line enclosures in general:

1. What is the mechanism by which the transmission line can increase the output of the woofer over that of a sealed box? How can one design a line for maximum output?

2. What is the mechanism by which the stuffing can decrease the apparent "boomyness" of the transmission line? Does it have to do with the stuffing absorbing higher frequencies which might bounce around inside the line? By what factor is it possible to increase the apparent length of the line with stuffing?

3. In which case might someone design a transmission line that increases in size such that it has a terminus that is larger than the initial cross-sectional area? (Other than a horn, that is)

4. If this woofer came out of a vented enclosure, is it reasonable that I could design an okay-sounding transmission line for this woofer?

5. What happens if the 1/4-wave frequency of a transmission line is less than the woofer's Fs?

I'm interested to hear if this will be a viable option for this woofer. I don't want to just throw it away. The amplifier on the computer speakers pooped out and I think this is a nice little gem of a 4" woofer.
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Old 16th June 2005, 04:33 PM   #2
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Well, I learned that stuffing increases the apparent line length of the enclosure by up to a factor of 2, and that I need to try to get tuning as close to Fs as possible, but the other questions are still open. Also, if I manage to approximate the woofer's Fs within 5 Hz, do you think that would be acceptable?
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Old 16th June 2005, 04:52 PM   #3
MJK is offline MJK  United States
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BAM

1. What is the mechanism by which the transmission line can increase the output of the woofer over that of a sealed box? How can one design a line for maximum output?

A TL performs the same function as a proted box at low frequencies, bass is added by eciting the fundamnetla resonance of the TL. Most of the same bass performance trade-offs between the closed and aproted box are still applicable with the exception that a stuffed TL has more damping and less ringing (tighter bass).


2. What is the mechanism by which the stuffing can decrease the apparent "boomyness" of the transmission line? Does it have to do with the stuffing absorbing higher frequencies which might bounce around inside the line? By what factor is it possible to increase the apparent length of the line with stuffing?

Stuffing damps the ringing of the enclosure resonance(s) leading to tighter bass. Stuffing does not slow the speed of sound so the line cannot be made shorter by adding stuffing. No apparent line length increase due to stuffing, that was a mistake made many years ago.


3. In which case might someone design a transmission line that increases in size such that it has a terminus that is larger than the initial cross-sectional area? (Other than a horn, that is)

It is one option although the TL will become longer. I argue that most back loaded horn designs are really behaving as TL's that transition to horn behavior at higher frequencies.


4. If this woofer came out of a vented enclosure, is it reasonable that I could design an okay-sounding transmission line for this woofer?

Yes


5. What happens if the 1/4-wave frequency of a transmission line is less than the woofer's Fs?

Without knowing the T/S parameters for the driver it is hard to say. My take on TL design is coverd on my website along with a set of alignment talbes and some modeling software. You might like to do some further reading and try these tools.

Hope that helps,
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Old 18th June 2005, 03:26 AM   #4
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Would I be okay if the tuning frequency of the line is within +/-5 Hz of the driver's Fs? I think this driver may have a highish Qts, around 0.6 or so. I'm just wondering if the tolerances with this design are as close as they are with a bass reflex design, which I wouldn't attempt without T/S parameters..
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Old 18th June 2005, 11:30 AM   #5
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Without T/S parameters you are really just guessing and hoping your design works out. If you would not try a bass reflex without T/S parameters, why would you try a TL? If you don't have reliable T/S parameters (measured or from a reputable manufacturer) in my opinion you are wasting your time. Your guess at an optimum TL design is as good mine.
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Old 18th June 2005, 03:50 PM   #6
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Well, I guess it's a good excuse to try something with this beefy little driver:

http://www.madisound.com/cgi-bin/ind....6546&pid=1707

While the expert on transmission lines is helping me figure stuff out, I have a question about the basic nature of operation of a transmission line. At certain frequencies, the back wave of the driver comes through the terminus and cancels out the output of the driver, creating a comb-filtering effect. I seem to remember that the undulations in the frequency response are broad at the low end and narrow at the upper end. In a narrow-bandwidth application like a bass module or subwoofer, do these undulations create a big problem or is the width of each hump at the lower frequencies wide enough such that only one or two undulations fit within the bandwidth? The intended bandwidth for my application is between 50 and 150 Hz.
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Old 18th June 2005, 05:20 PM   #7
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BAM,

"At certain frequencies, the back wave of the driver comes through the terminus and cancels out the output of the driver, creating a comb-filtering effect."

(MJK) Actually, at the line's resonant frequencies (1/4 wavelength, 3/4 wavelength, 5/4 wavelength, ...) the output from the open end of a TL is +/- 90 degrees out of phase with the driver. The only cancellation of driver output is due to the back pressure acting on the driver causing the driver's motion to be greatly reduced, just like in a bass relfex design at fb. From the driver displacement viewpoint, you could think of the TL as a series of bass reflex designs, acting on the back of the driver cone with tuning frequencies fb, 3 x fb, 5 x fb, ... .


"I seem to remember that the undulations in the frequency response are broad at the low end and narrow at the upper end."

(MJK) I think that most of this is due to the visual of plotting SPL on a log frequency scale. For a straight TL with the driver at the closed end, if you changed the frequency scale to be linear the peaks and nulls would look almost the same and be spaced at equal increments of frequency.


"In a narrow-bandwidth application like a bass module or subwoofer, do these undulations create a big problem or is the width of each hump at the lower frequencies wide enough such that only one or two undulations fit within the bandwidth? The intended bandwidth for my application is between 50 and 150 Hz."

If you are looking at a limited bandwidth, you might consider a tapered TL (S0 > 5 x SL) tuned to approximately 50 Hz so that the next harmonic (3/4 wavelength) would be well above 150 Hz. With a steep cut-off filter you probably could get away with a minimum amount of stuffing and have maximum bass efficiency at 50 Hz. The natural roll-off below 50 Hz would be 24 dB/octave. My alignment tables would help you get a starting point for this design.

Hope that helps,
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Old 18th June 2005, 06:01 PM   #8
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Thanks. I was actually considering designing towards the AuraSound NS4's Fs of 57 Hz, now that I'm considering the Aura driver. So does tapering the TL simply decrease the necessary physical length of the line? Specifically I am wondering what I would lose or gain if I did not taper the line, because I hate dealing with angled pieces. I can accomodate the necessary line for 57 Hz. It will just be placed lengthwise along the wall.

I am looking to mate this to a pair of small satellites with a woofer 3" or less. That's why the extended upper bass response to 150 Hz is an engineering goal for this sub. I like the sound of the cardboard TL box I made for the computer sub driver. The plate amp I'm using to test the concept has 5dB of boost at 35 Hz, though, so a lot of the bass response is probably artificial. Dr. Bose would be proud.
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Old 18th June 2005, 06:29 PM   #9
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I'm trying to think about how to get the most output from this woofer...
Using the specs from the AURA 4" that you posted, and using Rick Shultz' AlphaTL spreadsheet...

Qts: .39
Vas: .133 ft^3 (3.78 L)
Fs: 57
Fb: 40 (~.7*Fs)

Line length would be 5.7 ft
Inner pipe diameter would be 5.15" (6" PVC pipe should be ok)
Fibreglass stuffing -- 1/3 lb per ft^3

According to GM you don't want to go below .7 * Fs -- especially with such a small driver (although the Acoustic Cannon and EBS throw that out the window, as you know).

I prototyped my 20 ft acoustic cannon with a 6ft x 6" pvc pipe and a KEFB110 4" driver. Like you, at normal listening levels it was encouraging enough to build the 20 footer.

WARNING -- If overdriven, I got a nasty CLACK CLACK CLACK (driver slap-back)...
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Old 18th June 2005, 06:35 PM   #10
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Quote:
So does tapering the TL simply decrease the necessary physical length of the line? Specifically I am wondering what I would lose or gain if I did not taper the line, because I hate dealing with angled pieces.
Yes, a tapered line will be shorter for the same tuning frequency.

The advantages of a tapered line are reduce length, probably smaller enclosure, and a big separation between the 1/4 wavelength mode and the 3/4 wavelength mode. This separation would be a big advantage in your situation of only using the TL from 50 to 150 Hz. Disadvantage is the angled cuts in the more complex enclosure.
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