Mini-Onken – Jacques Mahul, L’Audiophile 1982

This is an English version of the article from L’Audiophile no.26. december 1982.

Translated using source scans from:

Mini ONKEN article scan in french at Onken.info

Mini ONKEN article scan in french from http://6bm8.lab.free.fr

Original text © By Jacques Mahul
L’Audiophile

The Onken enclosure, equipped with the 38 cm Altec Lansing 416-8A and described in issue no. 2 of L’Audiophile, has been widely discussed. It nevertheless remains, for many, a very difficult realisation, given a volume larger than one would reasonably consider for such a project outside professional use. It nonetheless remains a hope of perfection for many. Jean Hiraga has given it renewed momentum among numerous audiophiles disappointed at having no alternative other than to undertake its construction themselves, by describing the “Petite Onken”, of much smaller dimensions, whose low-frequency performance is comparable in many respects, although with a reduction in efficiency of approximately 4 dB. The difference in efficiency between the two loudspeakers, the 416 and the 414, is over the entire audio band of about 4 dB. It is of course not possible to use the HD 17 HR 37 Audax and the T925 Foster in a passive configuration with the filter described in issue no. 18 of L’Audiophile. The use of a smaller diameter loudspeaker with a powerful motor (30 cm instead of 38 cm) makes it easier to avoid room-related phenomena, placement constraints within the same rooms, and also to improve transient response.

This alternative does not, however, solve all problems. The internal volume of 192 litres (vents included), even though it represents a significant reduction compared with an Onken of around 350 litres, nevertheless remains substantial. Moreover, one cannot really speak of a reduction in cost compared with the original, since the 414 is more expensive than the 416.

It was therefore logical and interesting to imagine the creation of an alternative of a volume less than half that of the Petite Onken, whose low-frequency performance would be of high level and which would thus be a sort of Mini-Onken that could be associated with a specific midrange–treble unit using passive filtering or with currently available midrange–treble units using active filtering. This reduction in volume compared with the Petite Onken would necessarily be accompanied by a reduction in efficiency, which would only be compensated by the use of a smaller-diameter loudspeaker.

Is the Onken enclosure a properly tuned classic bass-reflex system?

Not knowing the exact parameters of the 416-8B or 416-8A after ageing, we nevertheless recommend proceeding with respect to the original Onken enclosure of 337 litres by using a method approaching the Thiele calculation, refined by Small and Snyder.

Let us not lose sight of the fact that Mr. Koizumi’s realisation predates the development of this method based on the calculation of a bass-reflex enclosure from loudspeaker parameters.

However, the article in issue no. 25 provides the essential data for calculating the bass-reflex associated with the 414-8B and thus verifying what type of tuning is associated with the Petite Onken and which coefficient n Mr. Koizumi refers to in his various calculations.

Let us therefore take these values for the 414-8B:

Resonance frequency	fs = 28.5 Hz
Total quality factor	Qts = 0.254
Equivalent mass	Mmd = 35.6 g
Active radius	r = 13.3 cm

The choice of this alignment therefore results in a very slight over-damping in the extreme low frequencies relative to perfect linearity.

One can then estimate the theoretical −3 dB low-frequency cutoff with 155 litres and n = 6.34, therefore:

and the tuning frequency of the bass-reflex:

One thus finds, using a classic calculation, a value very close to that announced by Mr. Koizumi, within 0.06 Hz. The latter in fact advanced a value of:

which he had rounded to 45 Hz. The agreement is therefore satisfactory.

Let us now move on to the calculation of the vent dimensions, still using the classical method, and the compliance of the enclosure for 155 litres, with V_b in m³:

And the acoustic mass of the vent will be:

Let us choose the same vent surface as that of the Petite Onken, namely four vents of a width of 3.8 cm and a height of 18 cm.
This gives a total vent surface of:

corresponding approximately to the effective radiating surface of the 414-8B.
For such a surface, the ideal vent length is:

By applying the end corrections, which are important in the present case, the actual length becomes:

The length chosen by Mr. Koizumi is 36.5 cm, that is to say 1.2 cm, or 3%, less than the calculated value. We can therefore conclude that there is a perfect identity between the two approaches.

The calculation having been established by the designer using the perfect Helmholtz–Small–Snyder calculation model, there is identity between the coefficient and the theoretical calculation and we can have no doubt that only Mr. Koizumi’s performance, which we must not forget, predates the establishment of this calculation model.

In conclusion, we can state that the Onken enclosure, derived in its design from the Jensen baffle, is in fact a bass-reflex enclosure perfectly tuned according to the most rigorous laws of fourth-order systems.

The calculations we evoke here are a formalisation of the work of Snyder, which he himself resumed, and of the work of Thiele and Keele by weighting new parameters. These Snyder studies are based on a simple observation: one notices that there is a fairly large dispersion of characteristics and parameters of loudspeakers of the same model within a production series. However, these variations had only a minimal effect on the acoustic performance of bass-reflex enclosures tuned using them.

In conclusion, the performance of loudspeaker systems is currently determined by one or more variable parameters of the woofers. This is thus what allows one to extract parameters such as V_as, Q_ts , f_s, which make it possible to predict response curves and volume optimisations.

The Onken enclosure is a fourth-order tuned system with Q_ts = 0.254 and an alignment n = 6.34.

This verification having been carried out, we now have new insight for possible extensions of this type of enclosure toward more compact systems, which constitutes the object of our study.

An Onken enclosure with the Focal 10C01

All that we have discussed previously does not take into account the extremely delicate positioning of the bass loudspeaker within the enclosure. This positioning has a capital importance for the very shape of the response curve in the lower midrange and for the establishment of internal standing-wave modes. Research here therefore becomes more subjective and is also closely linked to experience.

The starting idea is therefore an Onken enclosure equipped with the 10C01, with an alignment n = 6.34 and with a vent surface close to the active surface of the 10C01, namely 343 cm². The construction will be made of 25 mm particle board. We will not resort to special woods such as Nantex or others, for the good reason that the panel surface areas are much smaller and that the construction remains the same, with eight vents and two internal levels. The problems of rigidity are therefore less acute. Only the presence of a batten of 30 × 30 mm, starting from the bottom of the enclosure to reach the top panel, is required.

The Focal 10C01 woofer testifies to a difference compared with the two Onken enclosures already known. This batten makes it possible to eliminate any secondary vibration of the motor on the baffle, by bracing it against the front wall of the enclosure, while further reinforcing the rigidity of the enclosure in the direction of the cast frame.

All calculations and all optimisations of volume and vent dimensions were carried out with the original Q_ts of the Focal 10C01. We did not take into account a possible increase in this value after adding a series resistance from an inductor. Why such a choice? First of all, we place ourselves under the same conditions as for the two previous Onken enclosures equipped with the 416-8A and the 414-8B, which facilitates comparisons. Next, it would be necessary to see a minimum of two different enclosures, one in volume rather than vent length, one for active filtering, the other for passive filtering. Depending on the values of the series resistances of the inductors used with the 10C01, there may be considerable deviations, fifteen to twenty litres in the present case, for the same alignment and thus the same optimisation. It is not possible to pass from the larger volume (passive version) to the smaller one (active version), since the vent lengths will also be different.

The formula for calculating the optimal volume for a given choice of alignment is:

This clearly shows the importance of a variation in Q_ts, since the latter is squared. This variation, which is an increase in Q_ts of the loudspeaker after adding a series inductor, is attributable to the increase in Q_es and not to Q_ms, which remains unchanged.

Q_ms is always much greater than Q_es, which amounts to assimilating the denominator
(Q_es + Q_ms) to Q_ms alone.

It follows that the increase in Qₜₛ is almost proportional to that of Qₑₛ.

The new Qₑₛ, which we may call Qₑₛ′, is in fact increased by the factor:

where Rcc is the DC resistance of the loudspeaker voice coil and Rs the resistance of the series inductor.

Thus:

Let us take the example of the 10C01, whose most recent parameters are as follows:

f_s = 25.7 Hz
Q_ms = 2.054
Q_es = 0.222
Q_ts = 0.2
V_as = 288 l
with Sd = 3.43 × 10⁻² m²

The active version is calculated as follows:

with Q_ts = 0.2 and n = 6.34

Here is therefore a calculation which confirms the importance of the value of the series inductor resistance in our definitive choice of volume.

The volumes thus increase from 73.04 l to 95.75 l, passing through 79.75 l.
The cutoff frequencies are successively 51 Hz, 44.5 Hz and 48.8 Hz for these three volumes, the shapes of the three response curves being identical.

The volume differences are considerable, especially between the first and second versions. Vent lengths and vent surface areas are also different. The higher the resistance, the larger the volume and the lower the cutoff frequency for the same type of optimisation and the same curve shape.

In certain cases, the presence of a resistive inductor can be a valuable aid, especially when Q_ts is low and the resonance frequency high, since it then allows lowering the cutoff frequency without, however, creating excessive over-damping in the bass, with an alignment of at least 8, which would be detrimental to linearity and to listening quality.

Let us recall the formula for the −3 dB cutoff frequency:

At constant n, the higher Q_ts becomes, the lower f₃ decreases.

In conclusion, a passive version of our Onken system equipped with the Focal 10C01 does not exhibit a reference value if the resistance value of the future series inductor is not specified. Or, the resistance of an inductor is linked to its value. Everything suggests that it will be between 2 mH and 4 mH in the case of future passive coupling with its midrange–treble unit.

If we must respond to the greatest needs of our readers, we opt for the first solution: V_b = 73 l, f₃ = 51 Hz, which has the merit of being directly usable with all current midrange–treble units in active filtering. Moreover, this solution is the most elegant from a technical standpoint, as it is the most compact (73 l for 51 Hz at −3 dB, 95 dB efficiency — a small performance).

When we couple this enclosure by means of a passive filter to our future midrange–treble unit, all our attention will be focused on the choice of an inductor with very low resistance, which in all cases is the most logical approach, as it avoids overdamping the 10C01.

The intervention of this future inductor will very little modify the performance of the system, and optimisation would then logically require reconsidering the volumes and vent lengths, which would differ by only a few percent from the chosen values. These variations will remain below the tolerances given by calculations estimated at ±10%.

The influence of the value of the inductor resistance (or of the inductors, in the case of third-order filtering) on the tuning of the bass-reflex enclosure is therefore decisive.
The tuning of a bass-reflex enclosure or of a closed enclosure is not sufficiently taken into account and remains an important source of error.

Evolution of the parameters of the 10C01

The 26 cm Focal previously had the following parameters:

f_s = 29 Hz
Q_ts = 0.178
V_AS = 247.1 l

Without taking into account any series resistance with the voice coil, we obtain a volume:

V_b = 62.5 l and a cutoff frequency f₋3 = 58 Hz, with an alignment n = 8, that is to say a slight over-damping in the extreme low frequencies.

In the case of an Onken-type enclosure with an alignment n = 6.34, the volume would be:

V_b = 49.6 l and the cutoff frequency f₃ = 64.7 Hz.
If the volume is effectively reduced (less than 50 l), the cutoff frequency becomes manifestly too high.

In the case of a larger volume, for example V_b = 62.5 l, the cutoff frequency becomes acceptable but the over-damping risks becoming somewhat annoying in listening. Moreover, we will no longer generate the alignments realised on the Onken enclosures, and only the external appearance would allow one to refer to this type of realisation.

Thus, the 10C01 was slightly modified in its parameters in order to allow perfect use in an Onken-type enclosure. The cone was slightly increased in diameter, the active surface thus being slightly increased by 2 mm added to the radius. The efficiency of the 10C01 then reaches 95 dB/W/1 m. The active surface is 343 cm² instead of the previous 330 cm². The compliance of the suspension was also slightly modified, from 1.75 × 10⁻³ m/N previously to 1.78 × 10⁻³ m/N. The weight of the moving assembly was slightly increased, rising to 21.9 g, whereas in the previous version it was 17 g. The resonance frequency then drops to 25.7 Hz, the equivalent compliance volume becomes 288 l, and Q_ts becomes 0.2.

The active surface is greater than the average of the 250 mm loudspeakers currently available on the market, but obviously remains lower than that of the Altec 414-8B with its 310 mm diameter.

The increase in Q_ts and the decrease in the resonance frequency f_s make it possible to reduce the cutoff frequency for the same alignment, but at the price of an increase in volume. These new parameters thus allow the realisation of a small Onken of less than 75 litres of useful internal volume (without the volume of the vents), with the same response curve shape and an excellent −3 dB cutoff frequency close to 50 Hz.

The final volume, calculation of the vents

It is obviously very difficult to arrive exactly at an internal volume of 73.04 l. Experience has nevertheless shown that it was preferable to provide for a slightly larger volume.

The external dimensions of the enclosure, 700 mm in height, 476 mm in width and 400 mm in depth, result both from the required internal volume of 75 l, from positioning criteria of the loudspeaker within the enclosure, from criteria of air flow in the vents, and from enclosure shapes allowing the best establishment of internal standing waves.

The internal volume thus results at 75.8 l, from which must be subtracted the volume of the bracing: 0.17 l, the volume of the rear corner blocks: 0.4 l, the volume of the loudspeaker basket, diaphragm and motor: 0.3 l, giving a final internal volume of 74.9 l.

If we take a vent surface of 3.40 cm², we obtain a final width which leaves only little opening between the end of the vent and the bottom. It would then be necessary to increase the depth of the vent, which is not desirable for all the other criteria previously mentioned.

With a total surface of 305 cm², the vent length will be:

By applying the end corrections, the length becomes:

We will reduce this value to 33 cm, since it is necessary to take into account the acoustic braking constituted by the entrance of the vent, shaped with a width of 45 mm (between the end of the vent and the rear wall).

Thus:

Each vent will have a width of 26.5 cm. They are separated from one another by mini-partitions 25 mm thick. The entire enclosure is intended to be made of 25 mm particle board.

Construction

The construction is very simple; all panels will be glued and screwed. Choose a high-density particle board, such as melamine-faced board for example. The front baffle is not designed to be removable, since the mounting of the 10C01 will be done from the front and not from the rear, as is the case with the two Onken enclosures mentioned above. A removable front panel would require vertical and horizontal battens that would reduce the internal volume and would only increase the risk of air leaks and vibrations.

This rear opening will have to accept a cable of 2.5 mm² cross-section. Place this rear terminal sufficiently high on the back panel so as to reduce the external cable length for a possible passive filter.

The internal lining consists of felt 10 mm thick, reference JDM 10 manufactured by EREM. Glue several pieces of felt to the bottom, the top, the sides, and the internal partitions forming the vents. Do not place anything at the bottom of the vents. It is unnecessary to place felt on the front baffle behind the loudspeaker; it will be well isolated from the floor by an intermediary base of dense wood approximately 30 to 40 mm thick.

It will be preferable to wire the 10C01 to the rear terminal using heavy-gauge cable.

Future perspectives

A midrange–treble unit is currently under development to complement this enclosure. We cannot reveal anything further at present, as this is only a new midrange under study.

Editorial note
Mathematical notation follows the conventions used in L’Audiophile at the time of publication. In several places, inverse quantities are expressed using negative exponents rather than fractional notation. The equations have been faithfully preserved, with modern typographical rendering for clarity.