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EBP - but why?

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jan.i.am View Drop Down
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Post Options Post Options   Thanks (0) Thanks(0)   Quote jan.i.am Quote  Post ReplyReply Direct Link To This Post Topic: EBP - but why?
    Posted: 14 July 2021 at 2:37pm
So I'm wondering about the EBP rule introduced by Mr.Small. This rule of thumb determines if a speaker is more suitable for a closed or vented design. An EBP of more than 100 indicates that a speaker is best suited for vented enclosure and so on.. All good. But why? EBP is defined through the parameters fs and Qes. in which way can those parameters define the enclosure of a speaker?
I'm writing a thesis so I have to be specific..Wink

Thanks for your help!
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Post Options Post Options   Thanks (1) Thanks(1)   Quote toastyghost Quote  Post ReplyReply Direct Link To This Post Posted: 14 July 2021 at 4:09pm
Chapter 40 of Handbook for Sound Engineers, 2015, Davis & Patronis JR Sound System Engineering, and Eargle's Loudspeaker Handbook are good places to start

https://www.eminence.com/support/understanding-loudspeaker-data/ is an overview of all the Thiele-Small parameters, which also mentions that EBP is a rule of thumb.

I assume you've already reviewed Small's classic papers like this one? https://www.aes.org/e-lib/online/browse.cfm?elib=10256

Edited by toastyghost - 14 July 2021 at 4:30pm
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jan.i.am View Drop Down
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Post Options Post Options   Thanks (0) Thanks(0)   Quote jan.i.am Quote  Post ReplyReply Direct Link To This Post Posted: 14 July 2021 at 7:06pm
Thank you for your reply.
Those are all good books, thanks for the advice. But I've searched for EBP in all 3 books and didn't find anything.
Yes I've read the paper of Small, but it doesn't explain exactly about the meaning of EBP.

So, I'm still searching for an answer.


Edited by jan.i.am - 14 July 2021 at 7:10pm
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Post Options Post Options   Thanks (1) Thanks(1)   Quote citizensc Quote  Post ReplyReply Direct Link To This Post Posted: 14 July 2021 at 10:54pm
I am not an engineer and very much consider my self a student when it comes to speaker design so I would look for supporting evidence if you were to quote any of this in an academic setting. I am also open to being fact checked on any of it. Just another opportunity to learn. 

T/S Parameters are a bit funny in that they are emergent properties, they are not fundamental to a loud speaker. Sd is the area of the diaphragm, Mms is combined mass of the diaphragm, VC and radiating mass, Cms is the compliance (stiffness) of the suspension. These properties are what they are, they are not derived from other properties eg. they are fundamental. 

T/S Parameters like Fs are far more abstract, from memory Fs is the frequency where the mass reactance of the moving mass is equal to to the negative reactance of the suspension, someone may want to check me on this. As you can see this is an emergent property resulting from interactions happening with in the driver when it is operating.

The reason T/S Parameters were developed as far as I understand is as simple as they are 'easy to measure' and as far as I understand simulation software like hornresp just converts T/S parameters back in to fundamental parameters before performing further calculations. 

EBP seems even more abstract as it is commonly derived from T/S parameters but what it actually describes is the 'relationship between the strength of motor system compared to the moving mass'. It can actually be expressed in terms of fundamental parameters. The angular EBP can be expressed as Rme/Mmd where Rme = (Bl^2)/Re. To convert to frequency, just multiply it by 1/pi. 

For me the practical use of EBP is just to ball park drivers and what they may be good for, I think reading parameters like Qts and Fs on their own and thinking 'yeah, I think it would be good in x enclosure because it has a Qts of 0.26' can be very misleading and ignores the fact that a loud speaker is a complex system of interacting parameters, it can not be defined or summed up like that. EBP I think is the closest you will get to ball parking a driver with a single value but I would still be very careful doing this. The 15DS115 and 12NDL88 have similar EBP, are they for similar purposes? Absolutely not. 


Hope this helps, or at the very least stimulates some interesting discussion. 
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Post Options Post Options   Thanks (0) Thanks(0)   Quote Contour Quote  Post ReplyReply Direct Link To This Post Posted: 15 July 2021 at 7:59am
Fs is the resonance frequency of the mass/spring system. 
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Post Options Post Options   Thanks (0) Thanks(0)   Quote citizensc Quote  Post ReplyReply Direct Link To This Post Posted: 15 July 2021 at 8:30am
Originally posted by Contour Contour wrote:

Fs is the resonance frequency of the mass/spring system. 


Yes, and if the spring and mass were not able to store energy, eg. they had no reactance, they would not be able to resonate. This is why changing the stiffness of the spring or the mass of the moving mass will change resonant frequency, because they affect the reactance at a given frequency. 

The point I was trying to make is that resonant frequency can seem simple if you just read a number and say 'that's where it resonates'; but this resonance is the result of complex interactions between multiple components within the system. The compliance of the suspension is not, its just a measure of how compliant the suspension is when you apply a force to it. Just trying to create a juxtaposition between T/S parameters and fundamental parameters. 
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Post Options Post Options   Thanks (0) Thanks(0)   Quote toastyghost Quote  Post ReplyReply Direct Link To This Post Posted: 15 July 2021 at 11:44am
It’s also very important to recognise that they’re small-signal parameters, and they don’t necessarily hold true for real-world levels of drive voltage or current, or when non-linear behaviour is considered.

I think the books and papers I referenced cover the fundamentals that make up a metric like EBP and how it relates to cabinet design goals pretty well, so if you don’t feel they explain the concept of EBP I would suggest you go back and read them again.

You won’t likely find a simple ‘EBP is’ statement because the equations and their variables do that job. If the section on EBP in the Small paper for LF horns doesn’t cover it, then look further into the components of the equations. Keep digging and doing that until you hit some fundamentals.

A good place to start from the other end is basics of how a loudspeaker driver works, and the theoretical design parameters for a sealed enclosure, which is also covered in those books.

Edited by toastyghost - 15 July 2021 at 11:46am
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Post Options Post Options   Thanks (0) Thanks(0)   Quote toastyghost Quote  Post ReplyReply Direct Link To This Post Posted: 15 July 2021 at 12:06pm
Originally posted by citizensc citizensc wrote:


The point I was trying to make is that resonant frequency can seem simple if you just read a number and say 'that's where it resonates'; but this resonance is the result of complex interactions between multiple components within the system. The compliance of the suspension is not, its just a measure of how compliant the suspension is when you apply a force to it. Just trying to create a juxtaposition between T/S parameters and fundamental parameters. 


Like you, I am very much ‘not an expert’ but I have studied this stuff a bunch.

Fs is the term presented on the T/S table for a driver, but the term used in the lumped element modelling that the T/S spec is derived from is Qfa. That might be a useful thing to look for in the text books.

You also need the total stiffness (K prime) and total moving mass (M prime). Then you can find the frequency with maximal velocity:


And then determine the bandwidth of that peak, set by the quality factor:


There’s similar equations to determine the on axis pressure for a driver, and then add that to compliance and such to determine the optimal (sealed) enclosure volume for the driver to have maximally flat response. Again, the textbooks cover that. If you plug some numbers in and experiment, you can begin to correlate the derived EBP values to an ‘end product’ result.

If the OP wants to dig in properly, the quality factor - which sets Qes - is one the most misunderstood aspects of a driver. That could be a good topic for a thesis investigation, depending on the original goals and proposal. It might also be worth checking the Klippel papers - there’s a lot - and contacting someone there, or at B&C, Faital or Eighteen Sound to ask for a moment of their time. All of those companies are involved in research and have student engagement history.

Edited by toastyghost - 15 July 2021 at 12:10pm
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Post Options Post Options   Thanks (0) Thanks(0)   Quote smoore Quote  Post ReplyReply Direct Link To This Post Posted: 16 July 2021 at 6:45pm
I think this sums it up fairly nicely...



Efficiency and bandwidth


These two parameters are inversely related. For maximum possibly efficiency, the bandwidth must be narrow. For maximum possible bandwidth, the efficiency then becomes less. Due to the assistance of the vent, a vented driver can have higher efficiency. Many pro woofers will reach 40 Hz with a vented box with around 95 db 1w1m. To achieve this with a sealed box requires an fs one octave lower (20 Hz), and in a 12" size this would be a subwoofer driver with about 85 db 1w1m.
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Post Options Post Options   Thanks (0) Thanks(0)   Quote smoore Quote  Post ReplyReply Direct Link To This Post Posted: 16 July 2021 at 6:49pm
There is further examples of how this works in practice on the link. Also, +1 on what CitizenSC wrote. I think thats a good explanation of loosely how it works (as I understand things anyway..)
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Post Options Post Options   Thanks (0) Thanks(0)   Quote toastyghost Quote  Post ReplyReply Direct Link To This Post Posted: 16 July 2021 at 7:41pm
Originally posted by smoore smoore wrote:

<span style="color: rgb51, 51, 51; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: large;">I think this sums it up fairly nicely...</span>

<span style="color: rgb51, 51, 51; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: large;">


Efficiency and bandwidth</span><br style="color: rgb51, 51, 51; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.85px;"><br style="color: rgb51, 51, 51; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.85px;"><span style="color: rgb51, 51, 51; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 14.85px;">These two parameters are inversely related. For maximum possibly efficiency, the bandwidth must be narrow. For maximum possible bandwidth, the efficiency then becomes less. Due to the assistance of the vent, a vented driver can have higher efficiency. Many pro woofers will reach 40 Hz with a vented box with around 95 db 1w1m. To achieve this with a sealed box requires an fs one octave lower (20 Hz), and in a 12" size this would be a subwoofer driver with about 85 db 1w1m.</span>


That’s also covered in quite a lot of detail in the Small paper I mentioned
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Post Options Post Options   Thanks (1) Thanks(1)   Quote John Boom Quote  Post ReplyReply Direct Link To This Post Posted: 19 July 2021 at 7:37pm
In electronics, you've got this thing called "gain bandwidth product". See https://en.wikipedia.org/wiki/Gain%E2%80%93bandwidth_product. Basically, when you apply negative feedback to an amplifier, the gain drops but the bandwidth rises (it also gets more linear, but that's another story).

Since gain and bandwidth are in trade-off with each other (you can increase one by sacrificing the other), a figure of merit is desired which describes how good your gain is for a given bandwidth. This lets you compare different amplifier types before you've even decided how much feedback to use.

It would appear, although I can't prove this, that Small et all have borrowed from this idea in their definition of an efficiency bandwidth product (the EBP of the topic name). One important difference, however, is that amplification and feedback are not involved at all with EBP.

Instead, think about the throat of a horn flare. This will be an idealised horn flare whose throat loads the driver restively. This acoustic resistance adds on to the actual mechanical resistance of the driver as well as the effective resistance resulting from the electrical circuit seen through the motor (=magnet/voice coil system). As such the driver appears to be more damped than it would be in free air. If you now progressively narrow the throat, you'll increase this total acoustic resistance further and increase the damping further.

One effect of increasing the damping in this way is to increase the frequency at which resistance-limited behaviour gives way to mass-limited behaviour. If (and this is an assumption) you reckon that entering mass-limited behavior will cause a roll-off, then this frequency is at least in the ball-park of your system upper frequency limit, aka bandwidth.

Another effect of increasing the damping in this way is to change the impedance ratio between driver and horn throat, either for better or worse. If you keep increasing the throat resistance, you'll go past a perfect match and the impedance match will then only get worse, and then the efficiency will fall.

At least for throat resistances somewhat higher than driver source resistance, we discover a straightforward trade-off between efficiency (=how much noise can I make for given power) and bandwidth (=how high up can I play before mass-limited mode kicks in). The trade-off must have reminded Small of the gain-bandwith product which was established theory in electronics at the time.

The actual EBP (our figure of merit) is then defined as the transition from resistive to mass limited behaviour for the driver without any horn throat present. Thus, if the efficiency to bandwidth tradeoff is important to you, you'll look for high EBPs.

As a side note, there was a time when people were very worried about this tradeoff - it was central to the design of old public address systems for example. Now we can all buy comps that give 30% efficiency up to around 20KHz, and even if we do have efficiency/bandwidth problems (eg because we scaled them up in size to get more power, mass rose and EBP dropped) we can simply "pop in a supertweeter".

EBP still matters for low-mid and bass however. Low-mid horns are driven by cone drivers with EBPs usually under 500Hz. Getting up to say 3KHz may require "heavy" loading of the driver which will pull down sensitivity. However, the problem is only one of many that must be solved when designing such horns, and may not always be the most critical.

As for bass, port/cavity resonators (aka Helmholtz resonators) get hard to design when their resonance is near or above the EBP, when the driver is in mass-limited mode and therefore behaving as a mass-like source. It's much easier to control these resonant systems in the velocity-limited mode below EBP where the driver looks (to the cabinet) like a resistive source.

Hence the figure of 100Hz for ported boxes. This figure is assuming you want to cut off somewhere typical like 30-50Hz. EBP of 100+ ensures the reflex chamber and port can in principle be tuned in such as way as to obtain the bass extension. OTOH if not using a port, and you want a 40Hz -3dB cutoff, and EBP is over 100Hz, you've got a problem - what Fc and Qtc to use? I'll leave it to you to figure out why that won't work out well (hint: for a sealed box, EBP is roughly Fc/Qtc, to a first order approximation).

On a final note, EBP is also crucial for bandpass designs: similar to the above, multi chamber resonant enclosures also struggle to be controlled by the driver above EBP (and even near it). So if a bandpass bass system is going to stretch up to 150Hz+ (and it may need to in order to properly meet tops) the EBP should be >=150Hz, and this can rule out otherwise suitable looking drivers. The difference is, with bandpasses you don't get to "buy" the bandwidth you need by sacrificing efficiency - you just simply can't go above EBP. Well, not by much, unless you're really good Wink
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