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More on the subject by David Haigner: Since the rise of the PC, the advance in loudspeaker design was mostly software-driven. The impact of software like LEAP, LMS and MLSSA during the 1980s (providing excellent crossover circuit simulation and pseudo-anechoic measurements from 1kHz up within small laboratories) led towards rapid progress from the mid frequencies upwards. But just like a 4ms time-windowed frequency response doesn't tell much about what happens below 1kHz, many simulation programs tend to over simplify the design of bass cabinets.

Since the beginning of the 1960s, the design of bass reflex cabinets can be done without tedious trial-and-error iterations using the results of the work from Thiele, Novak, Nomura, Small and many others. The behavior of the bass reflex system is modelled by comparing its acoustical response with the voltage response of an analog electrical filter with similar high-pass characteristics. Modelling real world systems mostly involves some simplification in the form of parameters that are considered less significant. These parameters are sometimes ignored or lumped together with similar ones to result into a simple and easy-to-process model of the system. Flow loss and other damping effects around the reflex port are particularly hard-to-quantify, heavily nonlinear parameters and very often described by a simple damping coefficient - if they are described at all.

If, as usual today, someone now uses such a model nested inside the code of a speaker enclosure simulation software without knowledge of these simplifications, the simulation results might become questionable. A 2nd order high-pass filter like the closed box is much more stable in case of parameter variations than the 4th order bass reflex. A 20% variation of the driver unit "total Q" (Qts) will produce 2 to 4dB variations around the tuning frequency. So we may well assume that even small deviations between the bass reflex model and the real thing could become significant.

And, we should not forget, our hearing is very sensitive to low-frequency SPL variations. Look at the Fletcher and Munson curves. They come closer together at LF. A 10dB step from 60 to 70dB SPL results in the impression of a 20dB loudness difference at 30Hz (of course, per definition, only a 10dB loudness difference at 1kHz). The usually strong room acoustics influence will only partially mask this sensitivity. Let me show you a somewhat less known influence of the reflex port itself by doing a short design study of a reflex cabinet for a typical 8-inch driver with 22g of moving mass.

First, let's do what everyone else does: Typing the driver parameters into any simulation software promptly results in "optimum" cabinet volume and tuning frequency proposals, the two basic variables of the HR cabinet. So we settle for a 60-liter cabinet. To show the effects of different HR frequencies, let us try 3 different tuning frequencies via port length variation (30-50cm) for our 60 liter cabinet and 100cm² port area.

This graphs shows the influence on frequency response of these 3 alignments plus the closed box response for comparison. Since no damping of any kind is assumed in this simulation, I would start our design with a 40cm port length because damping will have the most influence on the low-end side and eliminate the slight response peak around 40Hz. Now lets check the impedance plots with the same shape (and therefore phase response) for all port lengths, just the tuning frequency is varied (minimum between the two peaks), all having the same minimum impedance of 7 ohms.

But our frequency response simulation shows something else: port resonance. When the half wavelength approximately equates the port length, a resonance occurs just like the quarter wave resonance problem in horn designs. (Reflex ports have two open ends versa only one for front-loaded horns - hence 1/2 versa 1/4 wave resonance.) Longer ports have lower resonances that come closer towards the bandwidth of the port and show heavier influence on frequency response. This is mostly well known behavior and better software will show the effect. Damping material inside the enclosure can reduce the problem.

Port area is another issue. Small ports will start chuffing at lower volumes than larger ones. This is usually shown by better software packages, too. During the 1990s, many papers were written about this. Most of them recommend the use of flared port ends similar to horn mouth openings. Today many programs will tell you the difference between various port areas in terms of dynamic compression (for cylindrical ports only) but there is something else about port size. Let us have another look at our design, varying the port area while keeping the HR frequency constant (this should result into the same bass reflex 'alignment' though many programs will show no differences here at low SPL).

This now shows significant differences for 3 variants (20, 50 and 100cm², length adjusted for constant HR frequency). Obviously the 20cm² port's performance is not adequate. Why do traditional simulations not show these large differences? Lumping together diverse parameters and completely ignoring others ... well, see above. I cannot say for sure what is the dominant factor here but the difference between this simulation and more commonly used cabinet design software lies in the detailed calculation of port radiation resistance and the coupling of the port to the driver via the cabinet volume. Larger port area -> larger radiation resistance and tighter coupling -> better damping properties. As you can see, better damping also helps to smooth the impedance, nice for SE amp users. The worst case minimum impedance is as low as 4 ohms, not what I would like to see with 8-ohm loudspeakers.

In the quite magnified response graph (1 versus the usual 5dB/div) you can also see that the larger port area results into slightly larger bandwidth -> better impulse response. Just for comparison, two graphs to document what we achieve by simply damping the cabinet:

This shows a well-rounded LF roll-off (B50 - damping the whole cabinet lightly| B20 - leaving out areas close to port and driver) and smoother impedance (lower phase angles and higher minimum Z) for higher damping. But of course, we gain neither bandwidth nor sensitivity, losing about 2.5dB below 35Hz (3dB = half output power - you need twice the amplifier power to equalize this).

Summarized, I recommend detailed analysis of flared port systems similar to horn design, in order to optimize both dynamic and steady-state behavior of bass reflex designs. Like a proper horn design, the correct port flare will also smooth out the port's standing wave (1/2 wave pipe resonance). Finally, non-symmetric port flares can help to reduce asymmetrical volume flow of outward versa inward port action.

Of course I had to use simple means to provide an economic solution for these port design issues with the Rho but I do think it works nice - and I hope your listening confirms that I hit the target. There are a whole lot of other interesting things to cover. We did not consider standing waves and other enclosure resonance effects; the differences between various damping materials and their placement inside the cabinet; high level driver parameter variations and their interaction with port compression; and so on.