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The Story Of The Fermat

Quite a number of customers asked for a loudspeaker with sufficient bass and a high efficiency. To choose the right components wasn't difficult. After we had used 25 cm bass drivers for the kits listed in our previous newsletters, we this time went for a 20 cm driver. Then we added a tweeter with high efficiency and without any sharpness: the Alcone AC 15.

First we had to discuss how best to achieve the required efficiency of more than 90 dB (2.83V/1m). The easiest solution would be to use two bass drivers in parallel since, at a given voltage, 3 dB will be gained due to the doubled output. And if both are in phase (you might remember the Theory on our discussion pages) you'll gain even 6 dB. In other words, the efficiency will double.

How to arrange the drivers? A d'Appolito design is surely not suitable when using bass drivers of that size; this would strain the tweeter unnecessarily since it would have to kick in at a low frequency.

A three way design is also not a solution: the two bass drivers won't be allowed to operate together, meaning that the required 3 dB resp. 6 dB are not achieved.

Therefore we chose a 2 1/2 way design where midrange and bass drivers are working together over most of their frequency range.

But now the linearity of the AC 8 HE's frequency response gave us some headaches since this driver has a similar output over the entire utilised range. This causes the efficiency in the midrange, where only one AC 8 HE operates, to be insufficient.

The picture below shows the frequency response of a AC 8 HE that is cut-off at 2.2 kHz in purple; in blue the AC 8 HE cut-off at 1.4 kHz. The green line indicates the tweeter's frequency response. The overlapping drivers are represented by the red, higher positioned curve.

When only one driver is operating the red line drops down to the level of just on driver (over the entire high frequency range). If only the midrange driver is playing and the frequency range is wider, then the sound pressure level drops down to the purple line.

The frequency range where only the midrange is playing should, therefore, not be too narrow or, in other words: the bass driver should reach almost up to the tweeter, otherwise the output in the overlapping area would drop too much. Fermat
Picture 1: the Fermat's individual and total frequency responses.

At first, the high cut-off frequency of the bass driver gave rise for plenty discussions. In comparison with other speakers, however, no drawbacks were audible or noticeable.

The crossover

Picture 2: the Fermat's crossover

The fermat's crossover was designed and simulated with Clio and measured using the finished speaker.Fermat

Absolutely mandatory was that all drivers were in phase within their individual frequency ranges. Two drivers at a time had to have a 6 dB higher output at their intersections compared to the individual driver - phase response is then ideal.

The cabinet

The cabinet should be braced adequately to suppress unwanted vibration.

Each bracing panel ought to have 4 cut-outs to ensure free airflow, still providing adequate reinforcement.

The two bracing panels required should be placed with slightly different spacing to avoid standing waves.
Further information is available on the following pages:
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Copyright © Iris Strassacker 2006. All rights reserved.