Some Considerations and Tips
Looking back at some of the TLs of the past with today’s knowledge, it is surprising to see that designs based on wrong assumptions sounded pretty good anyway. If a poorly designed bass-reflex can sound really annoying, a transmission line seems to forgive even large deviations from ideal specifications. With the model it is possible to verify that even considerable variations in the diameter and length of the line, even if they penalize the emission of low frequencies by the opening, do not dramatically affect the performance of the woofer. Probably this is one of the reasons that has made this system, indeed rather difficult to design correctly, so popular among DIYers.
Some purists prefer a “classic” and a bit extreme approach to the design of TLs, sometimes a remnant of obsolete general rules, which provides a duct filled with high density fibrous material and behaviour similar to that of an over-damped closed box (e.g. a pneumatic suspension with Q=0.5) with the only advantage, compared to the latter, of lower coloration due to resonances inside the box. The price to pay is a much bigger (and more challenging to build) cabinet, and this might make you prefer a simple closed box. Moreover, with this solution we would not benefit from the considerable contribution of low frequencies coming from the opening and from the other advantages of a transmission line that we could define “modern”. From the similarity between the latter type of TL and the bass-reflex it can be deduced that a driver suitable for the first system will generally be suitable for the second. In this case a Qts value between 0.35 and 0.45 is commonly indicated as ideal. In general, high qts values lead to tune the TL at frequencies below fs and vice versa.
A good starting point for the dimensioning of the TL is to set the section of the line equal to the surface of the loudspeaker and eventually add a coupling chamber with volume not exceeding 1/3 of the total. It may be necessary to increase or decrease the total volume and this can be done by maintaining the proportions indicated above. A small mounting offset along the line, usually made inevitable by the shape we intend to give the speaker, helps to attenuate the first dip in system response. The maximum effect is at 1/5 of the total length, but it would be better not to exceed this value.
Once we have sketched the design we need to verify that our system is able to produce the desired SPL while remaining within the maximum linear excursion limits of the loudspeaker. You can do this by increasing the input power until you reach the limit imposed by the maximum power applicable to the woofer or, probably before, its linear excursion limit.
In the case of TL with a very small section with respect to the cone surface it would also be advisable to check that the air velocity at the opening does not exceed 3% of the speed of sound. In SPICE you can obtain a graphic display of the measurement simply by dividing the volume speed at the opening (the intensity of the electric current) by the diameter of the same. I have setted up a test point for this measurement that returns the velocity value (m/s) in volt.
With regard to the damping material, I am convinced that polyurethane foam, due to its intrinsic characteristics, is a more than recommendable choice in the development of a modern transmission line. Compared to fibre, foam has the great advantage that it can be glued to the duct walls. With fibre, especially in large TL, it is more difficult to keep the material in position and, in the case of TL with a decreasing (or increasing) section, there is the additional difficulty of keeping the filling density constant along the whole length. In addition, once a design has been developed, the foam can be previously cut to the desired size and this is particularly convenient for mass production.This is probably one of the reasons why prestigious TL manufacturers in the past, such as IMF and TDL, and nowadays, such as PMC, have used or are using polyurethane foam. Added to these practical reasons is the possibility to achieve equal performance in a small space and to overcome (or at least contain) the main limit of TL compared to other loading systems, i.e. larger dimensions.