Qb and Vb in acoustic suspension systems - diyAudio
 Qb and Vb in acoustic suspension systems
 User Name Stay logged in? Password
 Home Forums Rules Articles diyAudio Store Gallery Wiki Blogs Register Donations FAQ Calendar Search Today's Posts Mark Forums Read Search

 Multi-Way Conventional loudspeakers with crossovers

 Please consider donating to help us continue to serve you. Ads on/off / Custom Title / More PMs / More album space / Advanced printing & mass image saving
 21st February 2004, 09:31 PM #1 diyAudio Member     Join Date: Jan 2004 Location: Houston Qb and Vb in acoustic suspension systems The volume Vb of an acoustic suspension system in terms of its damping factor Qb is typically given by: Vb = Vas / [(Qb^2/Qts^2) - 1] Division by zero results in an undefined quantity, so [(Qb^2/Qts^2) - 1] cannot be zero. Thus (Qb^2/Qts^2) cannot be 1. In turn, Qb^2 cannot equal Qts^2, so Qb cannot equal Qts. Also, if Qb < Qts, Vb is negative, which cannot be so in reality. For practical use we must restrict the above equation to values of Qb in which Qb > Qts. So we never see a driver with Qts equal to or greater than 0.707. In a sealed box, such a driver will never be able to attain a "flat" response! For drivers with a very high Qts, say 0.68, we can never achieve a Qb of less than that value in a "real" enclosure. So how do we get slightly lean bass response (the result of a Qb less than 0.707)? Never! Comments? __________________ KTK. Kool To the Kore.
 21st February 2004, 09:47 PM #2 diyAudio Member     Join Date: Nov 2002 Location: Netherlands Your'e right Qb cannot be lower than Qt of the speaker. When you want Qb == Qt you'll need an infinite box volume. So use a very, very big box or better an open baffle. The only other option is to use horn loading or a LW transform.
diyAudio Member

Join Date: Feb 2004
Location: Stockholm
Re: Qb and Vb in acoustic suspension systems

Quote:
 Originally posted by coolkhoa So how do we get slightly lean bass response (the result of a Qb less than 0.707)? Never! Comments?
Lower Qts by a negative series resistance or by stuffing in the box (in the case of a closed box).
__________________
Simulate loudspeakers: Basta!
Simulate the baffle step: The Edge

diyAudio Member

Join Date: Jan 2004
Location: Houston
Quote:
 Originally posted by Pjotr Your'e right Qb cannot be lower than Qt of the speaker. When you want Qb == Qt you'll need an infinite box volume. So use a very, very big box or better an open baffle. The only other option is to use horn loading or a LW transform.

In practice, that's all we can do. The volume provided by an open baffle is theoretically "infinite," but take into consideration the dimensions of the surrounding space (i.e. room) and it is no longer. Of course, one can always take his open-baffle speaker outside, where the volume of air is truly infinite.
__________________
KTK. Kool To the Kore.

diyAudio Member RIP

Join Date: Nov 2003
Location: Brighton UK
Re: Qb and Vb in acoustic suspension systems

Quote:
 Originally posted by coolkhoa The volume Vb of an acoustic suspension system in terms of its damping factor Qb is typically given by: Vb = Vas / [(Qb^2/Qts^2) - 1] Division by zero results in an undefined quantity, so [(Qb^2/Qts^2) - 1] cannot be zero. Thus (Qb^2/Qts^2) cannot be 1. In turn, Qb^2 cannot equal Qts^2, so Qb cannot equal Qts. Also, if Qb < Qts, Vb is negative, which cannot be so in reality. For practical use we must restrict the above equation to values of Qb in which Qb > Qts. So we never see a driver with Qts equal to or greater than 0.707. In a sealed box, such a driver will never be able to attain a "flat" response! For drivers with a very high Qts, say 0.68, we can never achieve a Qb of less than that value in a "real" enclosure. So how do we get slightly lean bass response (the result of a Qb less than 0.707)? Never! Comments?
Qb is always greater than Qts.

Your other suppositions are entirely incorrect,
because for a start your equation is wrong :

Qb/Qts = root (Vas/Vb+1)

(Qb/Qts)^2 = Vas/Vb +1
Vas/Vb = (Qb/Qts)^2 - 1
Vb= Vas/ [(Qb/Qts)^2- 1]

the first equation tells you :
for Vb = Vas Qb = 1.414Qts
for Vb = 1/3 Vas Qb = 2Qts.

the other rearrangements tell you the same thing in reverse.

There are no restrictions on the value of Qts,
which in practise can vary between 0.1 and 2,
Though for bass units the range is usually 0.20
to impractically high values above 0.7 up to 1.
(unless open baffle or car free air mounting)

sreten.

Wizard of Kelts
diyAudio Moderator Emeritus

Join Date: Sep 2001
Location: Connecticut, The Nutmeg State
Not sure about this discussion. What do you mean by Qb? Do you mean a speaker with Qts put into a closed box to yield Qtc?

If that is the case, I just thought I would post the formula for how we arrive at Qtc. Hope this helps.
Attached Images
 formula for closed box speaker.gif (4.4 KB, 248 views)
__________________
-Anonymous

Wizard of Kelts
diyAudio Moderator Emeritus

Join Date: Sep 2001
Location: Connecticut, The Nutmeg State
Re: Re: Qb and Vb in acoustic suspension systems

Quote:
 Originally posted by sreten There are no restrictions on the value of Qts, which in practise can vary between 0.1 and 2,

I am guessing that when KBK said that, he was assuming that it was understood that we were not interested in speaker/box combos that did not yield absolutely flat response. That "acoustic suspension" system implied flat response.

My understanding is the "classic acoustic suspension " system is as follows:

Qts = 0.38
Vb = 1/3 Vas

Since that time, I believe "acoustic suspension" system has broadened a little to mean a sealed box where the box is appreciably smaller than Vas.
__________________
-Anonymous

diyAudio Member

Join Date: Feb 2004
Location: Stockholm
Re: Re: Qb and Vb in acoustic suspension systems

Quote:
 Originally posted by sreten Vb= Vas/ [(Qb/Qts)^2- 1] the first equation tells you : for Vb = Vas Qb = 1.414Qts for Vb = 1/3 Vas Qb = 2Qts.
Errh... How did you get from

Vb= Vas/ [(Qb/Qts)^2- 1]
to
Vb = Vas Qb = 1.414Qts ??

Quote:
 Originally posted by sreten There are no restrictions on the value of Qts, which in practise can vary between 0.1 and 2, Though for bass units the range is usually 0.20 to impractically high values above 0.7 up to 1. (unless open baffle or car free air mounting) sreten.
I think coolkhoa assumed butterworth response and closed box. In that case, since Qb>Qts Qts cannot be larger than 0.7, unless Qts is altered with negative resistance or stuffing in the box.
__________________
Simulate loudspeakers: Basta!
Simulate the baffle step: The Edge

diyAudio Member RIP

Join Date: Nov 2003
Location: Brighton UK
Re: Re: Re: Qb and Vb in acoustic suspension systems

Quote:
 Originally posted by Svante Errh... How did you get from Vb= Vas/ [(Qb/Qts)^2- 1] to Vb = Vas Qb = 1.414Qts ?? I think coolkhoa assumed butterworth response and closed box. In that case, since Qb>Qts Qts cannot be larger than 0.7, unless Qts is altered with negative resistance or stuffing in the box.
For a Butterworth alignment Qb=0.707, end of story.
It is a maximally flat alignment with no peaking.

Other Q's give other alignments.

The first equation :

Qb/Qts=root(Vas/Vb-1)

If Vb=Vas, then Qb = root2 x Qts.

This is the equation repeated by KW
with the helful addition of :

Fb/Fs= root(Vas/Vb-1)

For sealed boxes alignments range from Qb = 0.5 to Qb =1.1,
though most are between 0.6 and 0.9, with the 0.7 Butterworth
being the most common for builders.

For a sealed Butterworth alignment any driver with Qts
below 0.7 can be used though Vb gets silly with Qts
near 0.7 and Fb gets silly with very low Qts values.

A Qts of 0.35 indicates for Qb = 0.7, Vb = Vas/3.
A Qts of 0.50 indicates for Qb = 0.7, Vb = Vas.

sreten.

 22nd February 2004, 09:36 AM #10 diyAudio Member RIP   Join Date: Nov 2003 Location: Brighton UK coolkhoa, I now see what you where describing, apologies..... simply put : if the design target is an inbox Qb of 0.7, a sealed Butterworth alignment, Qts must be less than 0.7. A driver with Qts > 0.7 cannot be used by definition. Drivers with Qts near 0.7 will give silly box volumes. sreten.

 Posting Rules You may not post new threads You may not post replies You may not post attachments You may not edit your posts BB code is On Smilies are On [IMG] code is On HTML code is OffTrackbacks are Off Pingbacks are Off Refbacks are Off Forum Rules

 Similar Threads Thread Thread Starter Forum Replies Last Post Cal Weldon Multi-Way 26 19th December 2005 04:46 AM BAM Multi-Way 4 23rd October 2003 03:38 PM

 New To Site? Need Help?

All times are GMT. The time now is 09:05 PM.