Transmission Line Questions

[Solid Snake]

1. Why is it necessary for the line's area to be equal to or greater than the driver's Sd?

2. How can such an enclosure be considered linear when the the frequency response should be an increasingly frequent sine wave (since the speaker and line's output's phase depend on frequency)?

[GM]

Drivers are no different from people in that they want to 'feel' a certain amount of air pressure around them based on their physical attributes to perform properly. For decades it's been equated with Sd, but it's really about Vas and its relationship to Qts, just like any other box design.

I don't quite follow the second Q, but when properly done, a TL is damped at both ends, like a horn, providing a linear response.

GM

[MadMax]

While most TL's have line area = to sd or more Iam not sure that this is the only way to go, although the line needs to be close to sd at start it could taper down from there depending on what suits driver, stuffing the line is a bit like make it smaller as well. Iam not an expert on TL's but have a test sub at the moment which has a smaller line than sd and although Iam still at the tuning stage I think its going to work ok I to would be intrested in what others think on this.
Cheers Mark

[MJK]

Hello Solid Snake,

1. Why is it necessary for the line's area to be equal to or greater than the driver's Sd?

(MJK) The acoustic impedance and resonant frequencies of a transmission line are functions of line length, cross-sectional area, taper ratio (or straight, or expansion ratio), and fiber filling type and density. The acoustic impedance of the transmission line is what the back of the driver "feels".

The length and taper ratio set the resonant frequencies of the line. The fiber damps the resonances. The cross-sectional area controls the magnitude of the acoustic impedance. You have to adjust all of these parameters to achieve an optimum acoustic impedance for any particular driver.

Assuming that the line is of an appropriate length and taper ratio to produce a first resonance at or near the driver's fs, adjusting the cross-sectional area will change the amount of bass response produced by the open end of the transmission line. In almost every transmission line I have built or simulated, the cross-sectional area of the line needs to be much larger then just Sd. If the cross-sectional area is about Sd, in general the bass output is "strangled" and the speaker has disappointing bass performance.


2. How can such an enclosure be considered linear when the the frequency response should be an increasingly frequent sine wave (since the speaker and line's output's phase depend on frequency)?

(MJK) I am not sure I understand what this question is asking, so I will give a variety of answers for you to choose from.

a. A transmission line speaker is a linear system in the same way as a closed or ported box is a linear system. Mathematical models can be used to simulate the response and these models are linear in nature. If the input doubles so does the output. All modeling elements are linear and not a function of input magnitude.

b. At each of the transmission line resonant frequencies, a standing wave is excited that produces output from the open end while at the same time attenuating the driver's motion. This is the exact same thing that happens in a ported box at the tuning frequency. The difference is that a transmission line has a fundamental tuning frequency and then odd harmonics above this frequency.

c. In reality, closed and ported boxes do have the potential to excite standing waves inside the enclosure which will produce "ripples" in the SPL response. Most simple design programs do not include this phenominon so the user is lead to believe that the response will be nice and flat above the tuning frequency. In my opinion, if you start with a general quarter wavelength model you can make simplifying assumptions to reduce the model to a horn enclosure, a transmission line enclosure, a ported enclosure, or a closed enclosure. The math will be the same for each style of enclosure.

Hope that helps,

[GM]

Iam not an expert on TL's but have a test sub at the moment which has a smaller line than sd and although Iam still at the tuning stage I think its going to work ok I to would be intrested in what others think on this.

Just like in a sealed or BR, too small a Vb in a TL results in an underdamped (ringing) alignment so if you want good transient response you have to stuff it enough to damp it, attenuating the LF extension you normally design a sub for. Not a design I would normally recommend.

Still, the design goal is a speaker that suits your listening needs/room, so there's no such thing as a bad alignment, only a less than optimally performing one.

GM

[Solid Snake]

What I meant with my second question is that a line of a certain length will shift the phase of certain frequencies certain ways. When the line gets out of phase with the driver, the output may cancel itself out. Does anyone have any formulas on how the taper and length affect the output? I know how the length alone affects it. I've heard there are no formulas that really do a good job at predicting response.

[MJK]

What I meant with my second question is that a line of a certain length will shift the phase of certain frequencies certain ways. When the line gets out of phase with the driver, the output may cancel itself out.

(MJK) The only time the output from the line produces significant SPL is in the frequency range near the quarter wavelength resonances. In this frequency range the output from the line is 90 degrees out of phase with the driver output. In addition, the driver output in this narrow frequency range will be significantly attenuated. Between these special frequencies the output from the line is typically not significant and is damped by the fibers.


Does anyone have any formulas on how the taper and length affect the output? I know how the length alone affects it. I've heard there are no formulas that really do a good job at predicting response.

(MJK) I have not found any formulas that accurately predict the frequencies of tapered or expanding TL's, they may exist. The equation f = c / (4 x L) is fairly accurate for a straight TL if you correct for the open end boundary condition. Today you can model TL's using the MathCad worksheets on my website and get a very accurate estimate of a design. In the coming month, I hope to release a comprehensive set of TL alignment tables that will cover the following parameters :

0.3 < Qts < 0.5 recommended but not restricted to this range of values
20 Hz < tuning frequency < 70 Hz but could be extrapolated to other frequency values
10 < S0 / SL < 0.1 area ratio which covers a wide range of expansion and taper geometries

The alignment tables will give you a physical length, a driver offset, and a cross-sectional area to produce a reasonably flat response down to the tuning frequency. The calculations required are minimal. The derived parameters could be used to build a design or as input into my MathCad worksheets for final tuning. I am hoping to have this released in the next month, so far everything checks out.

Hope that helps,

[MadMax]

Has anyone built 1/2 wave or is this not a good idea apart from size. I have a very understanding LOL.
Mark

[MJK]

The only way to have a 1/2 wave transmission line is if it is closed at the far end, like a long skinny closed box enclosure. If it is open at the far end, it has to be a 1/4 wave transmission line. That is the basic physics of the problem.

[MadMax]

Is this because a 1/2 wave would cancel main output ie. 180 deg. out of phase.
Is there a taper ratio which seams best and sd x ? which seams best for subs.
I downloaded the mathcad worksheats but as I dont have mathcad I dont think they will work, do I have to buy mathcad to use them.
Thanks Mark

Ps I stuffed the line and while in goes lower than in small sealed box I had to stuff it real tight to get response to level out. If I understand correctly if I build proper line I can get more LF output and better transieint response with less stuffing.