Not as such but it´s related to the cone area and
the cone area to efficiency.
The acoustical output of a dynamic speaker is defined as:
Pa=v^2*A^2*((w^2*p)/(PI*c))
v=effective cone velocity
A=effective cone area
w=circle frequency
p=density of air
c=speed of sound in air
So if you look at those two speakers as one combined
speaker, A is doubled resulting in Pa doubled - this
gives you 3 dB.
If you wire this two speakers in paralell and drive
them with the same voltage (rather than the same
power) e.g. 2.83 V (corresponding to 1W/8 Ohms) they
will draw twice the current compared to one speaker
resulting in 2W instead of one - this are the
other 3 dB.
You can imagine this two speakers in paralell like
one speaker with half the impedance and Vas
doubled while all other parameters remain unchanged.
I'm not seeing Vas there. You aren't confusing it with the terms V (velocity) and a (area) are you?
Vas is the stiffness or compliance of a woofer expressed as an equivalent volume of air. Put the woofer in a box with volume Vas and you will have doubled its stiffness. Resonance would go to 1.414 x its free air resonance.
As I said, you can make the Vas of a given woofer as large as possible, cut off the suspension and let it flap in the breeze. It may void your warrantly but it won't change efficiency.
In the orriginal equation Vas and Qes are interacting and hiding the real terms of efficiency that are (Bl) squared over Re (magnetic motor force) and moving mass Mms. Those two terms and cone area are all that determine mid band efficiency.
Oh, in your two woofers case, wouldn't it be Vas halved?
David S.
I´m not confusing anything. The math is correct, look it up if you don´t believe me.
And if you double the cone area with all other parameters unchanged Vas will double,
just calculate it through.
And if you double the cone area with all other parameters unchanged Vas will double,
just calculate it through.
This is a complete different thing than paralelling two drivers. In your example the cone area is unchanged.
The single shared box works in theory. The only practical issues I have found with it are when the woofers suffer from DC offset or "jump" problems. This is where a woofer tends to drift in or drift out when fed the right LF signal. The problem is that if one woofer wants to drift in, the second woofer is then happy to drift out and the box offers no restraint. If your woofers are well behaved then sharing the same volume is fine.
You can use two of the same port that you had in the single box, or you can merge the two ports into one of twice the area (1.414 x the diameter).
I've series connected and series parallel connected lots of woofers and seldom had a problem. The issue of woofers having different parameters doesn't seem to be a big deal in practice. If resonances are within 10% or so you tend to get a combined performance of a woofer with midling characteristics.
Some programs will let you specify the number of woofers. If you need to synthesize a single "merged" woofer I think it goes like this:
Mms' = 2 Mms
Sd' = 2 x Sd (Area doubles but diameter goes up by sqrt of 2)
Cms' = 1/2 Cms (stiffness doubles but compliance halves)
Bl squared /Re is doubled. For series connected B is fixed, L is doubled and Re is doubled. For parallel connected B is fixed, L is fixed and Re is halved.
Vas' I'll have to think about it. Anybody??
Regards,
David S.
Dave, you seem to be saying that the suspension stiffness has no effect on efficiency, but I'm having trouble visualising that. It would seem that for a given motor force, increasing the stiffness would reduce the cone travel, and that has to mean less output for the given input, no?
Hi Keriwena,
Stiffness definitely has an effect for low frequencies and increasing it will raise resonance and Q. In that regard it will increase output of frequencies at and above resonance and decrease output below resonance. But when we define driver efficiency we are strictly talking about the asymptotic midrange level in the middle of the drivers range. This is in the so called "mass controlled region" where nothing matters but mass, motor strength and area.
Regards,
David
Stiffness definitely has an effect for low frequencies and increasing it will raise resonance and Q. In that regard it will increase output of frequencies at and above resonance and decrease output below resonance. But when we define driver efficiency we are strictly talking about the asymptotic midrange level in the middle of the drivers range. This is in the so called "mass controlled region" where nothing matters but mass, motor strength and area.
Regards,
David
Wikipedia has a nice summary:
Thiele/Small - Wikipedia, the free encyclopedia
Look for "Other parameters" and there the 4th formula given.
It includes Vas BTW...
Thiele/Small - Wikipedia, the free encyclopedia
Look for "Other parameters" and there the 4th formula given.
It includes Vas BTW...
Yes, I saw that. The third formula is better in that it is defined by the physical parameters of mass, Bl, Re, Sd, etc.
The 4th formula redefines it with derived parameters and obscures the relationships. You may think that it implies a relationship between Vas and efficiency but you are,of course, incorrect.
Plug in any numbers, then double Vas, at the same time Understand that Fs sqrd will half. This leaves the term Fs over Qes. Understand that Fs/Qes is constant with changes of resonance and, WHOA, a change in Vas had no change in efficiency!
David
"Fs sqrd will half" - if you change other parameters too you can arrive at any efficency you want. If your new speaker has different Vas while _all_ other parameters the same you will have different efficency. In our original case here we do have exactly that, Fs of the two drivers in paralell does _not_ change, but Sd and therefore Vas does.
Just found this link:
Technical and Reference Information - DIY Audio, Speakers, Electronics
They have the papers from Thiele and Small online.
Technical and Reference Information - DIY Audio, Speakers, Electronics
They have the papers from Thiele and Small online.
Sd is required to calculate Vas, but it is really another way to look at compliance (Cms).
Again Vas has nothing to do with driver efficiency. Mms, Bl, Re and Sd do.
Again Vas has nothing to do with driver efficiency. Mms, Bl, Re and Sd do.
We run in circles here. Changed Sd results in changed Vas, ok ? Changed Sd results in changed efficiency, ok ? Yet "Vas has nothing to do with driver efficiency" ?
The math is very clear defined how the various paramaters relate to each other,
this is not matter of "another way to look at".
If I have a definded mathematical relation between terms I can use substituton when solving a equation, what´s wrong with that ?
The math is very clear defined how the various paramaters relate to each other,
this is not matter of "another way to look at".
If I have a definded mathematical relation between terms I can use substituton when solving a equation, what´s wrong with that ?
Dave
It's just two different ways of looking at the same formula written in a different form. Happy my point at last came across that you don't need to resort to radiation pattern, mutual coupling or whatever to explain the 6dB increase when doubling the number of drivers. Just the basic formula's (in their different shapes) for loudspeaker efficiency do explain this phenomena.
Vac
It's just two different ways of looking at the same formula written in a different form. Happy my point at last came across that you don't need to resort to radiation pattern, mutual coupling or whatever to explain the 6dB increase when doubling the number of drivers. Just the basic formula's (in their different shapes) for loudspeaker efficiency do explain this phenomena.
Vac
I know this is hard to grasp the first time through, but you have found an equation for efficiency that has a term for Vas and said, Aha! Vas controls efficiency. What I am saying is that you can't, in the context of that equation, adjust Vas alone. While you were adjusting Vas in a real woofer, you would see that Qes and Fs would automatically change as well. In the end the changes in those two terms would balance out the Vas change and efficiency would be unaffected.
This is a fact and underlines what I and others have been telling you: Vas has no effect on efficiency.
Let me explain in straightforward physics. A woofer in simplest terms is a second order resonant system. It has fundamental parameters of mass, compliance or stiffness, and damping drag. These are fundamental parameters in that you can measure them directly. For example you can cut out a cone and voice coil and weigh it to find Mms.
Now, these three parameters determine the fundamental resonance of the woofer. Below resonance stiffness dominates, above resonance mass dominates and only at resonance do we worry about damping. Yes, above resonance only mass matters. The other parameters still exist but are of such low magnitude that we can ignore them. Since mass dominates we have constant acceleration from constant input for all frequencies above resonance. It is through a quirk of the physics that the resistive load of air isn't flat but rises, so that when mass controls motion we have constant acceleration and response is flat.
This is physical fact, that above resonance mass matters and compliance (or Vas) does not. Equation 4 of that section of the Wiki post has the direct equation and it includes the primary 3 factors: force shown as Bl sqrd/Re, the air load as Sd sqrd, and mass Mms.
Note that this equation answers our initial question about +3 or +6 in that the Sd sqrd term means 2 times the area leads to 4 times the efficiency, i.e. +6.
David
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Yes, thats true. It doesn't necessarily solve the conundrum that bringing two woofers together doubles their efficiency, but it does give the right numbers. You still have to explain why efficiency goes up as Sd squared rather than just Sd, if you want to understand it.
Good points. I never like the efficiency formula using Vas.
What may be sharply precised is that the formula gives a reference efficiency sometimes called nominal efficiency. It does not tell anything about the shape of the response and the global efficiency, which, for a closed box, is maximal for Qtc value equal to 1.1.