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Old 7th December 2002, 07:35 PM   #1
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Question Q Qonfusion

Guys,

I'm trying to understand the various Q parameters,
(Qes, Qms, Qts)
Can anybody give me a breif summary of their significance
(effects on suitability for type of enclosure, effects on sonics),
or point me to somewhere on the www where I might find such info?

Thanks,
Pete McK
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Old 7th December 2002, 07:56 PM   #2
Wizard of Kelts
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Cannot help you much with Qes or Qms, not too sure of them myself. Only thing I can tell you is:
Qts = (Qes times Qms)/ Qes + Qms. Qts is the really important number. You can figure bass response with the Qts and not know the others. The other numbers have significance, but nowhere near as much for closed and ported boxes.

All speakers reach a point below which they play progressively softer and softer compared to their "midpoint".

The following measurements, called "Thiele-Small parameters", are usually given by manufacturers in brochures and websites. You can also measure them.

Fs-resonance of speaker in free air-unenclosed
Qts-explaining that now
Vas-volume of box where the air in the box is just as "springy" as the speaker's suspension.
SPL-the volume, at one watt, that the speaker usually plays at. Also called the "midpoint".

The F3-the frequency where the speakers response will be 3 dB down from the normal SPL level-is determined by Fs, Qts and Vas.

Qts determines what the speaker's response looks like in the bass region. As you will see in a couple of minutes, it can get very very irregular.

Closed Box.

Put a speaker with a certain Fs and Qts in a closed box, and both will go up, unless the box is huge. Fc is what Fs gets raised to when speaker is put into a closed box, Qtc is what Qts is raised to when put into a closed box.

The following formula gives the ration of Fs, Vas, and Qts when put into a closed box.
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File Type: gif formula qtc, fc.gif (3.8 KB, 269 views)
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Old 7th December 2002, 08:01 PM   #3
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As a worked example, if a speaker with a Qts of .5 is put into a box whose volume is one third of the speaker's Vas, it will end up with a Qtc of 1.0. Similarly, if the speaker's Fs-it's unenclosed resonance-was 30 Hz, then it ends up with an Fc of 60 Hz.

Now you can arrive at the same Fc and Qtc with two different speakers. For instance, a speaker with a very low Fs but a large Vas can have the same Fc and Qtc as a different speaker with a higher Fs but a smaller Vas.

However they arrive at it, the following chart gives you the response curves for Closed Boxes with various values of Qtc. Remember that Fc is the Fs of the unenclosed speaker that is raised when put into a box.

Note: Not to confuse you, but the responses don't matter if it is Qts or Qtc. In other words. Suppose we have an unenclosed speaker, with a Qts of 1.0, that we mount, without an enclosure, into a great big wall 100 feet high and 100 feet wide. It will measure the same as a speaker in an enclosure with a Qtc of 1.0 that we put against the same big wall.

However you arrive at your final Q, those are the responses you get.

I'll summarize ported boxes when you let me know if you understand this so far.
Attached Images
File Type: gif responses of qtc and fs in closed box-small.gif (30.1 KB, 265 views)
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Old 7th December 2002, 08:12 PM   #4
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Default Re: Q Qonfusion

Kelticwizard,

I knew you'd beat me here on this one.
Quote:
Originally posted by PeteMcK
I'm trying to understand the various Q parameters,
(Qes, Qms, Qts)
Can anybody give me a breif summary of their significance
(effects on suitability for type of enclosure, effects on sonics),
or point me to somewhere on the www where I might find such info?
The problem is the understanding of the various Q factors is not easily summarized. It is a mixture of many different mechanical and electrical parameters that are all interdependent.

Here is a link to the Audio Xpress. There you can get a copy of The Loudspeaker Design Cookbook, by Vance Dickason. It's not the beat-all-end-all, but it is a must have if your interested in understanding the ins and outs of loudspeaker building.
http://www.audioxpress.com/bksprods/bookindexl.htm

Always have fun,
Rodd Yamashita
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Old 7th December 2002, 10:49 PM   #5
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Default Q Query

Hi Keltic Wiz,

Thanks for the explaination. However, I was thinking of how to judge a speaker before getting it anywhere near a box (drooling over catalogues & so on). I think mechanical Q may have something to do with the stiffness of the suspension.

From what you said above, it would seem that Q by itself is probably not that helpful, a ratio of Q with something else (Fc, Vas?) may be more helpful.

In fact I recall seeing some such ratio being used to determine the type of box the speaker should go into, but what exactly it was escapes me at the moment.

I suppose really there's no way to avoid plugging the numbers in to a box calculation program & seeing what the possibilities are.

Cheers,
Pete McK
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Old 7th December 2002, 11:25 PM   #6
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You might play with the program winisd that is available
at www.linearteam.dk/ it's free .....
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Old 8th December 2002, 11:40 AM   #7
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Default Re: Q Query

Quote:
Originally posted by PeteMcK
In fact I recall seeing some such ratio being used to determine the type of box the speaker should go into, but what exactly it was escapes me at the moment.
Hi,

EBP (Efficiency -Bandwidth Product) = Fs / Qes

If EBP < 55 than driver is better in sealed box.
If EBP > 55 than driver is better in vented box.

In addition, drivers with Qts > 0.45 are not suitable for hi-quality vented applications, because they give generally unwanted Chebishev alignment.

Drivers with Qts > 0.7 are not suitable at all for hi-quality applications, even in a sealed boxes, because of high ripple above system resonance, and thus, acousticly "boombox sound".



Definitions of Q's are:


Qts (and Qtc in box) factor is the ratio between the total amount of enegry stored in the system and energy dissipated by looses.

Qes (and Qec in box) is the ratio between total energy stored in the moving system vs energy dissipated by electrical looses (in the resistance of voice coil).

Qms (and Qmc in box) is the ratio between total energy stored in the system vs energy dissipated by mechanical looses (in the driver suspension, and box stuffing for Qmc).



I hope this helps.
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Old 8th December 2002, 06:53 PM   #8
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Default Q

Namotvi,

Yep, thats the ratio I was thinking of, and your definitions do help.

It's just that usually EBP is usually quoted as gospel, with no reasons given for why sealed is better <55, & ported better at >55. Obviously it's to do with the resulting alignments (another reason to play with a box modelling program).

Of course, this doesn't take in to account other enclosure types, such as horns, open baffles etc.

Thanks for your help,
Pete McK
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Old 8th December 2002, 07:34 PM   #9
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Well, you must realize that, determining enclosure type from Fs/Qes value is NOT unbreakable rule, and it only stands for a quick guide.

I like much more a simple rule that every driver which has Qts over 0.45 cannot go in vented box, and below that, sealed and vented will perform both well.

For vented applications you should know that alignment is ALWAYS dependend upon driver's Qts, and B4 (Butterworth, 4th order) alignment is only possible if Qts=0.4. For Qts<0.4 you cannot get B4 any more, but QB3 (Quasy-Butterworth, 3rd order) alignment (still very good, maybe even better than B4), and for Qts>0.4 you get ONLY C4 (Chebishev, 4th order), which is unfortunately bad. Also, vented box will be very big for that driver, which further has lot of drawbacks...

For closed boxes, there are little different rules, but every resulting Q of realized system that exceed 0.707 has ripple in bass, which is unwanted. So, to get a resonable box sizes (and thus good performance), you can use drivers with Qts up to 0.5 or 0.6, but not over that. If your driver has Qts=0.7 or more, no matter how big box is, Qtc is always bigger, and system has ripple over it's resonance.

Following that rules you cannot make mistake. And finally to say, Qts can never be too low, for both enclosure types.

For other enclosure types, analizes is much more complicated, and cannot be shown without lot of additional details.
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Old 8th December 2002, 08:08 PM   #10
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For higher Q drivers you can explore quarterwave or aperiodic enclosures. A Q of 0.4 to 0.7 is ideal, but well done examples of these kind of enclosures have been executed with Qt <0.3 (mass loaded Fostex FE208 TL) and Qts=0.2 (PEARL PR-2 aperiodic enclosure).

I have had good success making resonable sounding speakers with high Q >0.7 with aperiodic loading. These drivers are most suited to open baffle use, where the high Q can help counter the dipole roll-off (the woofers in the Carver dipole had a Q of something like 2-3)

A driver with Q of <0.25 is usually considered suitable for horn loading.

dave
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