A First Design
The low frequency performance of the Dayton Audio RS100-4, mounted on the test line, particularly impressed me and I decided to use it in a small nearfield monitor. This is a 4 inch full-range driver (though it would be more correct to call it wide-band or extended-range) and therefore perfect for a single-driver design. The combination of wideband and TL is particularly appreciated by DIYers and is often associated with the use of high sensitivity drivers: light cone, large magnetic motor and very often a second cone (whizzer) near the dust dome to linearize the response at higher frequencies. These drivers, while having an excellent transient response, are penalized in the extension towards the low frequencies: the acoustic pressure is directly proportional to the acceleration of the cone, but, to obtain a good acceleration, you have to make very light cones that characterize the driver with a high resonance frequency. This last parameter affects the balance of the system very much, just think that the efficiency (closely related to sensitivity, to the point of often being confused with it) is directly proportional to the cube of the resonance frequency. This premise certainly does not want to denigrate the qualities of high sensitivity loudspeakers, which find interesting applications in particular contexts, but only serves to underline that, in this case, the loudspeaker used has a low-mid sensitivity of about 87 dB (2.83V-1m). Since the ideal driver does not yet exist, as we have seen above, to improve one parameter you inevitably have to sacrifice another one by making a compromise between frequency extension, moving mass and transient response. In this case the short cover was pulled in the direction that is increasingly being taken in the development of modern high-excursion drivers and which allows a cone with an effective diameter of just 6.7 cm to have a resonance frequency of 87 Hz.
This design was complementary to the development of the computer model and proved indispensable to test its flexibility. In fact, a real transmission line cabinet almost never coincides with the classic straight tube with a constant cross-section (and identical to that of the driver cone) and a valid model must provide equally valid results when the TL geometry changes.
As mentioned above, the HADO design, the small monitors that I’m going to illustrate, has developed in parallel with that of the software. To tell the truth, the former served to complete the latter more than the opposite is true. The idea was to build, starting from the data collected with the test line, a constant section TL lined with polyurethane foam. The tuning frequency, to limit the excursion of the cone at low frequencies, coincides with the fs of the driver. This is obtained simply by sizing the length with the following equation:
where fp is the frequency of the first resonance mode. I then reduced the length by a factor of 0.73 given by the ratio between the speed of sound in the lined TL (with 50% of volume occupied by foam) and the speed of sound in air. The lenght development of the HADO is therefore 73 cm (note that the test line, 1 meter long, is accidentally tuned at the resonance frequency of the speaker). The total volume is 4.5 litres and, from a first simulation, should allow an f3 of at least 65 Hz.
The small offset needed to mount the driver on the front panel, even if only a few centimeters, helps to control the resonance of the second harmonic (3fp), and mitigates the first dip in the system response, without practically affecting the low frequency contribution of the opening.
I added a small coupling chamber, equal to one third of the total volume, to observe the impact this would have on the TL’s behaviour. The data collected were fundamental to integrate the coupling chamber into the simulation model. It turned out that the best way to represent the compliance of this additional volume of air is a simple parallel capacitor, with the only care taken to place it correctly along the line at a distance equivalent to that of the driver offset. In our 73 cm long line each of the 50 sections is worth about 1.5 cm; in the HADO the driver is mounted with about 6 cm offset, so the capacitor should be replace the one in the fourth RLC section.
The model already contains the directives that automatically determine the capacitor value by simply inserting the volume of the coupling chamber (VCC).
Figure 13. SPL opening. a) With coupling chamber. b) Without coupling chamber.
Figure 14. SPL of the system with coupling chamber. a) Measurement. b) Simulation.
The effect of the coupling chamber on the port output is visible in the simulations in Figure 13. Since at mid frequencies the impedance of the TL becomes substantially resistive, the acoustic compliance of the additional air volume gives rise to an acoustic RC filter whose low-pass function adds another 6 dB/oct to the slope of the duct response towards the high frequencies. Also note the lowering of the tuning frequency of the system. The frequency response of the system and its simulation can be seen in Figure 14. Note the f3 at about 60 Hz.