Histoires de filtres...

[jerome69]

crazyhub> Oui j'ai la même réponse de simulation que toi mais je n'interprète pas pareil
J'ai une réponse de Marc mais j'attends son autorisation pour poster sa réponse complète. J'ai compris qu'il travaille à group delay constant, énergie constante (phase pas aligné) entre le boomer et le médium. C'est un classique LR2 entre médium et tweeter.

[crazyhub]

crazyhub> Oui j'ai la même réponse de simulation que toi mais je n'interprète pas pareil

et t'interprètes comment alors? Pour moi:
- entre mid et bass: à fx (225hz) le mid est à 100° et le bass à 155° (soit 55° d'écart).
- entre mid et tweet, c'est pire encore: à fx (2250hz) le mid est à -115° et le tweet à -180° (soit 65° d'écart).
Le creux atteignant 5db entre 2 et 7Khz est bien là aussi! Je vois pas ce qu'il compense ici sachant que ces hps ne distordent nullement à ces fr.

J'ai compris qu'il travaille à group delay constant, énergie constante (phase pas aligné) entre le boomer et le médium.

J'attends qu'il t'autorise la publication de son explication pour vraiment comprendre...because la constance du temps de propagation de groupe suppose une phase linéaire en fonction de la fréquence; en ce sens j'accepte l'idée d'un décalage des phases des différents hps, mais ce décalage doit donc obligatoirement rester constant sur une plage de fréquences la plus large possible...hors on sait bien que c'est loin d'^tre réalisable à cause des différences de dimension physique des surfaces émissives. Et "énergie constante" pour l'instant je vois pas ce qu'il veut dire par là!?

[jerome69]

Ci dessous la réponse de Marc

Below Marc response

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Dear forum members,
Jerome69 referred to these forum pages because of some confusion on the theoretical back-up of the new Milestones filters. Unfortunately, my French is not so well (my education has been 25 years ago), so I have to write my message in English. As I'm not a member on this forum, I've asked Jerome to post this message (thx!).

I'll split it into two parts. The first one some theoretical backgrounds. The second one about the Milestones filters.

Best regards,
Marc


Chers Membres du forum,

Jerome69 a référé ces pages de forum à cause de quelques confusions sur la théorie sous jacente des nouveaux filtres du Milestone. Malheureusement mon français n'est plus si bon (j'ai quitté les études il y a 25 ans), alors je dois écrire mes messages en anglais. Comme je suis pas un membre du forum, j'ai demandé à Jérome de poster ce message (Merci !)

Je l'ai séparé en deux parties. La première partie quelques bases théorique. La deuxième partie à propos des filtres Milestones.

Salutations distinguées,
Marc




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Part 1, Speakers and radiation patterns

Let me first make some observations, before digging into the filters themselves. In the scientific papers, you'll find a lot of text on different types of filters, the most famous ones Butterworth and Linkwitz-Riley. They both are time-aligned in the sense that the group delay of the units is the same (i.e. the steepness of the acoustic phase curves is the same). In case of Butterworth filters (which are odd-order filters), the phase difference between the units is 90 degrees, whereas for Linkwitz-Riley ilters (which are even-order filters) the phase difference is 0 degrees (or 180 degrees with reversed unit polarities).
The consequence is that these filters have a difference in the way they radiate off-axis.
Both odd-order Butherworth and even-order Linkwitz-Riley filters are flat on-axis. If you measure both of them under angles in a horizontal direction, and if the acoustic centre of the units is aligned on a straight vertical line (e.g. by means of a tilted baffle), the directivity of the units will cause a similar decay for both filters in the higher frequencies. The main difference is the way the speakers radiate in the vertical direction.

A Butterworth filter radiation pattern looks as follows (kindly borrowed from http://www.rane.com/note160.html ). Please keep in mind that the picture is only valid for one frequency only (the crossover frequency), and will change shape for other frequencies.

[jerome69]

Although on-axis flat, due to the fact that depending on the position the relative distances between the speaker units changes, the relative phase will differ, and hence the way the acoustic output of both units will be added. This is reflected by the following pictures (from the B&W 802 manuals).

[jerome69]

One can see that at crossover, the magnitude is +3dB higher. But also at other frequencies one can see peaks and cancellations. In the Journal of Audio Engineering Society 1982, Bank and Hathaway in their article "Three dimensional energy plots in the frequency domain" showed a nice plot of such a system under different angles:

[jerome69]

In a reflective room, one can see that "flat-on-axis" is not really a useful measure to describe the characteristics of a loudspeaker.

Linkwitz-Riley wanted to improve the radiation of the speaker, by making the peak radiate to the front, and avoid it to peak with +3dB. He did it with a nice trick, essentially concatenating two Butterworth filters (resulting in aligned phases). This results in the following radiation pattern:

[jerome69]

Please keep in mind that LR-filters doesn't change the fact there are peaks and cancellations, the LR filter changes the directivity, and the magnitude.
The figure underneath gives the 3D radiation plot of a 4th-order LR filter. It shows less significant peaks and cancellations, than the 1st order case drawn above.

[jerome69]

In general, the magnitude and amount of peaks and cancellations will become less when:
- Drivers are mounted closer to each other.
- The order of the filter is higher.

In general, the directivity and position relative to the on-axis level will be determined by:
- The relative phase between the units.

Besides on-axis and off-axis response on a given position, another way to look at loudspeakers, is to look at their power response. Basically, the power response of a speaker is given by measuring a speaker at all positions around the speaker. In echoic rooms, one would like to have a flat power response (as is the case with a one-driver system - excluding high-frequency directivity due to unit bundling of course).
Butterworth filters show a flat power response, because their peaks and cancellations "even out". In the case of LR filters, a 3dB dip in the power response is caused. In reflective rooms this may cause a perceptive "dip" in the timbre of the speaker.

Not creating a filter that is not strictly a Butterworth or LR filter, will create
something that is "in-between" these characteristics. I.e., with a phase difference of 60 degrees, the power response will dip a bit, and the peak will be directed a bit more horizontal than in the case of a Butterworth filter.

In my opinion, the power response at lower frequencies is more important than at higher frequencies. At low frequencies (say up to 300Hz), one will have reflections in any room, and the perceived timbre is significantly defined by the listening room, hence a dip in the power response will be audible. At higher frequencies (> 700Hz), speakers start to bundle, and the on-axis response in a room with some decoration will start to dominate more and more if one goes higher in frequency.

[jerome69]

Part 2, the Milestones filters

The filter under discussion looks roughly as follows (still experimenting with it). I came to this result, because the previous filter was a bit "hard" in the upper midrange and treble. It was "too analytical" for my taste, still emphasizing the characteristics of the Thiel units to much.

[jerome69]

The magnitude response is pretty flat. The tweeter peaks and dips, but that's part of its response, and because of the fact I'm not using felt anymore. I'm using a first-order circuit with the tweeter, as any circuit that induces a bit of electrical resonance in the electrical circuit, immediately imposes harshness to its sound. The woofer follows a first-order response (dotted line). (BTW, the unit curves are new measurements after some acoustical treatments to the cabinet, at 1.8m inside an anechoic room).

[jerome69]

The phase response of tweeter and midrange are sufficiently aligned. The woofer and mid have roughly a similar group delay up to 300Hz, and the woofer is slowly drifting away from that point (partly due to the compensation circuitry). It has not an exact constant 90 degrees shift, and drifts away. The objection against it is that the woofer is becoming subtracting (on-axis!) from the midrange from 500Hz onwards, as its phase shift becomes larger than 90 degrees.

[jerome69]

One can align the group delay response better by increasing C5 (e.g. to 330uF). It creates a nice 90 degrees difference between the woofer and midrange over a wider range. The audible results are not so good, the sound becomes "muffled" and "undefined", and is getting less transparent.

[jerome69]

If one strives for aligned phases, decrease C5 to 54uF, and increase C6 to 168uF, leave out R3/C3/L3, increase R5 to 3.9Ohm, and R2 to 12 Ohm. One can also align mid and tweeter more by changing the 3.3uF to 2.2uF.

[jerome69]

In my opinion, it takes away the "life-like" performance out of the speaker, the bass becomes more muddy with this large capacitive load, and the whole sounds "shut-in". This is a general observation when either making C3 (6.8uF) or C5 too high.

My current experiments are more towards the following alternative.

[jerome69]

It has exactly the same on-axis response as the first filter above (thin lines), but it sounds completely different: