Effect of Variations of Theile/Small Parameters


This curiosity reared its head a few weeks after purchasing the Satori MR16P-8 (8Ω) drivers for use as mid-range units covering the range from 300hz.  They do quite well up to about 17khz so a tweeter was considered unnecessary.  Another attraction to them was the Egyptian papyrus cone although no remarkable difference in their sound was noticed.  Spectrum analyses were performed on the papyrus cones and a wood cone driver of the same size but the page containing these results has yet to be completed mainly due to not having similar data on a small driver with a paper cone.  That page is still listed in the loudspeaker index but no link is associated therewith.

Several days later when the CLIO was purchased, the papyrus cone was used to familiarize myself with the CLIO since the speaker is small and easy to handle.  It was quite a surprise to find that the measured T/S parameters differed a lot from those given by the manufacturer.  Admittedly, the Satoris have a few dozen hours of playing time but the effect of such playing would seem to have little effect on, especially, Fs simply because the speaker was second order filtered at 300hz.  As can be seen, that parameter has differed by about 3hz.  Unfortunately, no measurement of the T/S parameters was made shortly after acquisition on the LMS system, a computer board purchased from Linear-X Systems in 1994 at a cost of $1200, about $2200 in 2021.  It still works.

There were several tests performed  in Sept. 2019 using the LMS. One of notoriety was break-in and its effect on Fs.    Initially, the speaker checked in at Fs=34.5hz with an impedance at the frequency of 109.4Ω.  After an hour or so of break-in with a 10hz signal strong enough to drive the cone to about 3mm in either direction, Fs dropped to 33.2hz with an impedance at that frequency of 109.6Ω,.  The rise in impedance was attributed to the increased temperature of the voice coil, which was high enough to slightly darken the enamel on the wire.  The change in Fs was attributed to the spider rather than the annulus as the latter is a very soft half roll rubber.  Further tests showed no damage to the speaker as a result of the heated voice coil other than the aforementioned slight darkening.  The driver uses an exposed coil; the spider is mounted on another ring above the top plate.  This is thought to have contributed to heat dissipation.

In short, the Fs was 34.5hz when new and 33.2hz after break-in. That was Sept. 11, 2019.  Here it is Feb. 18, 2021 and those speakers have had dozens of hours of playing time and Fs is still at 35hz.  Some of the difference is attributed to the accuracy of the test equipment used; they are not precision laboratory devices.  The point here is to try to show that slight differences in the T/S parameters make little to no difference in the outcome.

The speaker is manufactured in Indonesia by SB Acoustics    











Parameter Manufacturer Feb. 4, 2021 Feb. 18, 2021
Fs  Hz 32 35.89 35.16
Re  Ohms 6.2 6.4 6.3
Sd  cm^2-in^2 119/18.45 118.8/18.42 118.8/18.42
Qms 5.11 6.77 7.18
Qes 0.32 0.43 0.43
Qts 0.30 0.40 0.41
Cms  mm-N 2.3 1.403 1.5551
Mms  g 10.6 14.0167 13.1784
Rms (mechanical loss in ohms-kg/s, includes air load) 0.40 0.47 0.41
BL  T/M (also N/A) 6.5 6.86 6.5
Sensitivity  dB (1w1m) 88 86.76 86.91
Z(min) nominal  ohms 8.0 6.79 6.82
L (1khz-10khz) mH 0.11 (Freq. not specified 0.15/0.06 0.16/0.06
Vas L/in^3 44.3/2703.2 27.6618/1687.9 30.7514/1876.5




Here is a set of six designs by BassBox Pro, ver.6.  The three at the left are for optimum sealed box while the three at the right are for optimum vented box.  The vents are normalized for 1.5" diameter being slightly larger than that of a minimum size vent for Xmax.  They were enlarged to reduce vent air velocity and also to be sized for the closest standard hole saw.

The more important parts of this data here is the Box Properties.  The so-called ideal Q for a closed box is 0.707 whereas that of a vented box is accepted as 7.  These are, like most things, compromises.  They refer to a box of moderate size but no definition of moderate is given.  For a sealed box, leakage can be critical but leakage in a vented box seems open to discussion considering the comparatively large size of a vent as compared to a leak around the driver or among the panels.




Below are the nine parameters as calculated by BassBox Pro, version 6.  The curves are colour coded to match the six tables above.  The most radical difference is between the closed box vs the vented box.  The differences among the three sets of parameters for the closed boxes are insignificant; similarly for the vented boxes with one exception.  The parameters designated by the manufacturer result in quite different response curves.  Note the RED and LIGHT GREEN curves. for closed and vented, respectively.












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