The Heresy of the T/S Parameter Bl

[smowry]

Please note folks, that in ALL of @Lars Risbo discussions, he never even mentioned Bl (Tm). If the amplifier is a voltage source, we don't need Bl and obviously β is not just helpful, it is critical to understanding transducer and loudspeaker design. Yet, the only company that I can identify, that specifies β in their Data Sheets et al. is Peerless by Tymphany. Many people that viewed this thread had never even heard the term β previously. Shame on the Loudspeaker Industry! Going forward, I would LIKE to see the Loudspeaker Industry adopt the use of the term β for the industry's sake. However, this thread is not about what people like; it's about β (N^2/W).

Lars has inadvertently touched upon another Heresy, the 2.83 Voltage Sensitivity. Let's go back to my previous example.

https://ptt.purifi-audio.com/shop/ptt10-0x04-nab-01-ptt10-0x04-nab-01-2043/document/583

Transducer A
Bl = 12.8 Tm
Re = 3.9 Ω
β = 42.0 N^2/W
SPL (1W@1m) = 85.7 dB
SPL (2.83V@1m) = 88.0 dB An imaginary 2.3 dB gain in sensitivity.

https://ptt.purifi-audio.com/shop/ptt10-0x08-nab-01-ptt10-0x08-nab-01-2566/document/454

Transducer B
Bl = 15.7 Tm
Re = 6.4 Ω
β = 38.5 N^2/W
SPL (1W@1m) = 83.9 dB
SPL (2.83V@1m) = 83.9 dB

So with regards to 2.83 Voltage Sensitivity, Transducer A is 4.1 dB more sensitive than Transducer B. Simply because of the difference in the Nominal Impedance and not performance. The actual difference in sensitivity is 1.8 dB based on performance. SPL (2.83V@1m) allows manufacturers to overstate the true sensitivity, SPL (1W@1m). Whereas, SPL (1W@1m) allows us to compare and evaluate transducer sensitivity regardless of Nominal Impedance. Could the intention be to confuse and or mislead the consumer? Most transducers today are 4 Ω Nominal. Years ago, most transducers were 8 Ω Nominal, where power in is (u^2)/Z = (2.83)^2/8 = 1.0 (W). Today's power amplifiers have greater current capacity, some of the better amplifiers like Purifi and yes even the Fosi V3 Mono can drive 2 Ω loads. So when 2 Ω transducer manufacturers specify SPL (2.83V@1m), they will be allowed to overstate sensitivity by another 3 dB.

Whose responsible for Bl and SPL (2.83V@1m) ? Well it's Neville Thiele and Richard Small but their AES papers were published 50 years ago! I hoped that Dr. Klippel would help and although he has done much to advance the industry especially by moving us away from small signal analysis, he's actually part of the problem. He chose to make Bl(x) a large signal parameter while ignoring β(x) as the true motor large signal parameter. These are but other examples that confirm the Loudspeaker Industry is decades behind the other A/V Industries such as Video and Electronics and Digital Audio. However, the Patents of claimed inventions keep on coming! The metaphor here is that the Loudspeaker Industry takes "Baby Inventive Steps".

Dr. Small told me that the moving coil audio transducer was mature. I realize now that in fact the Loudspeaker Industry is immature in their funding of R&D. This is what Dr. Small said to me in 2006, 20 years ago. "I’m not a seer. Moving-coil technology (including planar printed coils) is pretty “mature.” Shots in the arm like neodymium magnets don’t come along too often, but steady improvements with new materials will continue. Personally, I think that of all the conventional driver components, suspensions are the one still in a primitive stage. I am amazed that designers are still content to use bits of paper and fabric with properties that vary wildly with the environment. It would be nice to have a break through here that would give us at least the same kind of environmental stability that magnets, coils, and cones achieve. Note that most manufacturers are still using ferrite magnets. Hear that Lars. You advanced the surround technology but how is the spider R&D at Purifi coming along? Dr. Small used the term "primitive" 20 years ago! Ironically, the first spiders were metal and not continuous discs. Rather they had radial legs like a spider. https://pearl-hifi.com/06_Lit_Archive/14_Books_Tech_Papers/Mowry_Steve/Myra_on_Spiders.pdf Please note that I posted a concept that eliminates the spider and I claim that the best spider is no spider.

 

[smowry]

Hi @Lars Risbo

Okay, I get it now but I am still struggling with units.

1/Qts = 1/Qes + 1/Qms

1/Qts = β / (2πfs Mms) + Rms / (2πfs Mms)

Multiply both sides by 2πfs and combine.

2πfs / Qts = (β + Rms) / Mms Bingo!

or Qts = 2πfs Mms / (β + Rms)

Can anyone help with the unit derivation? N^2/W must equate with kg/s.

 

[NTK]

Can anyone help with the unit derivation? N^2/W must equate with kg/s.

 

[smowry]

https://ptt.purifi-audio.com/shop/ptt10-0x04-nab-01-ptt10-0x04-nab-01-2043/document/583

Transducer A

Bl = 12.8 Tm

Re = 3.9 Ω

β = 42.0 N^2/W

SPL (1W@1m) = 85.7 dB

SPL (2.83V@1m) = 88.0 dB An imaginary 2.3 dB gain in sensitivity.


https://ptt.purifi-audio.com/shop/ptt10-0x08-nab-01-ptt10-0x08-nab-01-2566/document/454

Transducer B

Bl = 15.7 Tm

Re = 6.4 Ω

β = 38.5 N^2/W

SPL (1W@1m) = 83.9 dB

SPL (2.83V@1m) = 83.9 dB

There's one guy on this forum that just will not quit. He keeps posting F = Bli (N) and making claims that N, the number of wire turns for the same magnetic gap and volume of conductor will increase SPL. Where l = NπDiameter (m). He has even gone so far as to claim that changing wire material from Cu to Al will only change Re. I believe that this guy has a PhD. This is frustrating because I have derived and proven over and over that this is not the case and in fact the opposite is the case. For the same magnetic gap to increase the number of turns, N reduces packing factor and thus the volume of conductor in the gap. So I will again utilize the Purifi 10 inch 4 Ω and 8 Ω woofers to disprove his claims.


Which transducer has the most turns, N, where l = NπDiameter, A or B? Both transducers have the same diameter voice coil, wind height, and magnetic gaps. The gap dimensions will not be different due to the hard-part gauges.


Well Re = lA/(SAσ) Where S is the cross-section of the voice coil wire and σ is the conductivity of the voice coil wire.

3.9 = lA/(SAσ)

3.9 = NAπD/(SAσ)

3.9 ∝ NA/SA

6.4 = lB/(SBσ)

6.4 = NBπD/(SBσ)

6.4 ∝ NB/SB

6,4/3.9 = NB/SB/(NA/SA)

1.64 = NB/SB/(NA/SA)

But the wind heights are equal.

Then NB > NA and SB < SA



SPLA @1m) = 85.7 dB(1W

SPLB (1W@1m) = 83.9 dB

SPLB < SPLA but NB > NA Why?

SPL(1W@1m) ∝ β (Lars)

β = (B^2)(Vσ)

Where V is the volume of conductor (m^3). Then I will make the claim that SPL(1W@1m) is not related to N or l. Regardless with what ANYONE claims.

SPL(1W@1m) ∝ Volume of conductor, V


Do you give up Jose?


Note that I keep asking you for proof of claims but you just keep posting Bli.

 

[KSTR]

He has even gone so far as to claim that changing wire material from Cu to Al will only change Re.

In case you are talking about me (not sure about that, though), what I said in the other thread is when you change a VC conductor material from Al to Cu or vice versa and compensate the resistance difference with an external resistor, the total behavior of that modified transducer does not change, and yes, exactly so because Re has not changed.
Same would apply to a dual VC driver with only one coil in use but the total Re being compensated.

In other words, resistance of the VC is a parasitic, one can model a VC as superconducting and embody the resistance as an external resistor. This example was used to prove the point that conductivity distribution along a VC (with no other changes, of course) does not matter as long as the current is the same.

The original idea presented was that when you have a VC with a variable pitch design that leads to some unfilled volume that come with standard techniques being used, one could bring down Re (with all consequences that will follow, notably increased ß) when the unfilled volume is filled with turns paralleled to the existing ones in those areas, it will not affect the action of the variable pitch design.
Partial paralleling effectively is the same as changing the conductivity locally, and that leads to the conclusion that a special wire design that changes cross section (rectangular wire with constant width but variable height) one could optimize a variable pitch VC to fully exploit all of a given volume available for the VC, with slightly changed paramteers of course.

 

[smowry]

See what I mean!

Show me the proof by math model, simulation or build and test, If I use superposition, I get the same results. The input is one current going to the coil, i. Parallel connects will simply facilitate current division. We see that with dual voice coils. Series vs. Parallel has no effect on SPL(1W@1m). If the amplifier is a voltage source. SPL(1W@1m) goes as the volume of conductor. Have I not proved that? At least, you didn't post Bli his time and claim that as proof. The reason why you will not post any Math Model, Simulation, or empirical test results is because you don't have any. You cannot prove your claim; you only argue. Thus I claim that you are argumentative.

Kindly, be advised that I reported your post from above. Your unsupported claims are counter to what I am trying to do in this thread. That being to grow and support the knowledge base of younger engineers. So let's see what Rick wants to do but most likely he will simply close and lock the thread. If that happens, I will claim that you disruptive. The only equation that you have posted is F = Bli. I presented detailed derivations and models and you reply with technical rhetoric. I claim that you are dangerous and potentially harmful for younger engineers.

What you have posted is no help to anyone but yourself. I asked Jack to help out but he did not stop by. Maybe @Lars Risbo could help clear this up. What more can I do?

 

[Lars Risbo]

In case you are talking about me (not sure about that, though), what I said in the other thread is when you change a VC conductor material from Al to Cu or vice versa and compensate the resistance difference with an external resistor, the total behavior of that modified transducer does not change, and yes, exactly so because Re has not changed.
Same would apply to a dual VC driver with only one coil in use but the total Re being compensated.

In other words, resistance of the VC is a parasitic, one can model a VC as superconducting and embody the resistance as an external resistor. This example was used to prove the point that conductivity distribution along a VC (with no other changes, of course) does not matter as long as the current is the same.

The original idea presented was that when you have a VC with a variable pitch design that leads to some unfilled volume that come with standard techniques being used, one could bring down Re (with all consequences that will follow, notably increased ß) when the unfilled volume is filled with turns paralleled to the existing ones in those areas, it will not affect the action of the variable pitch design.
Partial paralleling effectively is the same as changing the conductivity locally, and that leads to the conclusion that a special wire design that changes cross section (rectangular wire with constant width but variable height) one could optimize a variable pitch VC to fully exploit all of a given volume available for the VC, with slightly changed paramteers of course.

i find the above correct but also fail to see what conflict there is?

one warning about paralleling coils: if they have different winding profiles (in particular number of windings ) then when the coil is in motion there may be induced local current running through the coils which burns energy. This amounts to a mechanical loss.

This was not meant to argue against the variable cross section winding where windings conceptually locally are paralleled.

 

[smowry]

@Lars Risbo "i find the above correct but also fail to see what conflict there is?"

Thank you for chiming in. Ironically, within this discussion, an example previously used was the variable pitch winding of the "Purifi" voice coil! KSTR wants to fill in the spaces and make the OD constant with variable wire cross=section, S (m^2).

The other example used was TC Sounds LMS voice coil.

Both voice coils vary the OD vs. position. Then based on β(x) = (B(x)^2)(Vσ) (kg/s)*, which I have simulated 100's of times with VF OPERA and my command file (beta.comi) where the coil's ID and OD were constant, β(x) varies with position because B(x) varies with position but V is constant. However, for your coil and Thilo's coil, we can write β = (B(x)^2)(V(x)σ) where and we can see again that β goes as the effective volume of conductor V(x) and by increasing the volume of conductor locally to compliment the reductions in B(0) as |x| varies, linearity can be improved. So, the claim is that that is how the coils above linearizes β(x) is by varying the effective V(x) with changes in position |x|. In practice, I would use linear superposition and sweep several coils, βn(x) = (B(x)^2)(Vnσ) with constant volume within the same DC FEA simulation and then sum the results. Each coil would have it's respective ID and OD and wind height.

KSTR disputes my claim and my math models. He claims that he can linearize the β(x) by varying l(x), the effective length of conductor vs. position locally but keeping the coil ID and OD constant globally. Additionally, he wants to add parallel connections which inherently decrease l(x) locally. Where turns in parallel are halved. The proof of claim that he presents for this is Bl(x)i. So in the limit his claim could be correct, but his proof is invalid. That is the theme of this thread. Then I could be wrong but someone needs to show that my proof of claim is invalid.

In this thread, I have shown by example using the Purifi 10 inch woofers, that increasing N but keeping the coil ID and OD and wind height constant, actually reduces β!


* I learned something from @NTK. I plan to replace N^2/W with kg/s. "When one shares they learn."

 

[Salt]

I think, just a dozen people here on ASR can 'follow' literally this thread and two or three of them are interested or involved.
(Btw. replacing an 'universally' applicable N by a only locally (om earth) usable kg might become obsolete (on Mars or Moon) in the future)

 

[smowry]

I think, just a dozen people here on ASR can 'follow' literally this thread and two or three of them are interested or involved.
(Btw. replacing an 'universally' applicable N by a only locally (om earth) usable kg might become obsolete (on Mars or Moon) in the future)

It was not I that introduced the crazy stuff. KSTR posted the following. I felt that his posts were potentially detrimental to young engineers and thus I needed to challenge the posts. Note Lars said he is correct! I invited Dr. Jack but I think he's busy.

Figure to better explain things, cross-section of packing of the VC with variable pitch

"From left to right the winding topology evolves:" Note that nobody understands the above.



For example sake only, I posted the following. My claim was that if volume is constant then conductivity must change to linearize β.

Where volume is constant but conductivity changes with position, σ(x). Again based on the same equation, β = (B(x)^2)Vσ(x). In practice this is not manufacturable and is for example only.

Then KSTR posted the following, " The local conductivity of the wire does not matter, nor does its distribution along the total wire length." His proof being Bli (N). Then I told Rick that he was becoming dangerous. This thread is not about people; it is about Beta and Bl.

 

[smowry]

Controversy follows me. ED Dell, the owner of Voice Coil magazine refused to publish my discussion of Bogusium and Deceptium in 2009. So I posted it online and it went viral. Then Ed Dell fired me. He could not handle the "Truth". Subsequently Brush Wellman offered to make me a Be sales representative. In 2009, one tweeter Be dome cost US$30 - US$40 wholesale! I still have a few hanging around.

Loading…

pearl-hifi.com

 

[Lars Risbo]

maybe i see the disagreement now. I think that for a uniform winding, we get that beta is proportional with the wire volume or mass.

If the wire is nonuniform, gets a lower cross section in some sections and higher in other, then the total resistance increases compared to the uniform wire of the same length and volume.

the higher resistance will lower beta.

if we moreover concentrate windings at the ends where B(x) is reduced to linearise Bl(x) then Bl drops compared to the inform and we further reduce beta.

Hence, linearisation of Bl(x) costs in beta for the same winding height and thickness.

Having winding gaps further reduces beta.

 

[smowry]

maybe i see the disagreement now. I think that for a uniform winding, we get that beta is proportional with the wire volume or mass.

If the wire is nonuniform, gets a lower cross section in some sections and higher in other, then the total resistance increases compared to the uniform wire of the same length and volume.

the higher resistance will lower beta.

if we moreover concentrate windings at the ends where B(x) is reduced to linearise Bl(x) then Bl drops compared to the inform and we further reduce beta.

Hence, linearisation of Bl(x) costs in beta for the same winding height and thickness.

Having winding gaps further reduces beta.

Thank you Lars. You are always kind and respectful.

Yes I agree. We can write β(x) = (B(x)^2)(l(x)S(x)σ) kg/s
Where l is the wire length and S is the wire cross section.
However, how is F(x) = Bli(x) helpful?

 

[smowry]

It has been 30 years since I studied Calculus but I think this is how it goes. The voice coil is a flux integrator.

β = ∫(B^2)Sσ dl kg/s

@NTK can you help me out?

 

[NTK]

It has been 30 years since I studied Calculus but I think this how it goes. The voice coil is a flux integrator.

β = ∫(B^2)Sσ dl kg/s

@NTK can you help me out?

I'll try. I'll need to understand what exactly the problem is.

 

[smowry]

I'll try. I'll need to understand what exactly the problem is.

The problem is a voice coil moving through a magnetic gap from z to -z (the displacement limits).
Where r (m) is the radius and S (m^2) is the cross-section of the wire and B is the DC Magnetic Flux Density (Tm).

However, this might require cylindrical coordinates, r, z, θ .
For 2D assume θ = 2π.
Note that 2πr is the circumference and N is the number of turns

What do you think?

 

[smowry]

The above might work for a constant winding density and with constant ID and OD but for variable pitch voice coils the model seems to break down, In the DC magnetic model, B(z) changes with position, z; however, the magnetic gap flux distribution does not change and is independent of the respective voice coil(s). Then we can segment the voice coil and use linear supervision.

If we use the Purifi voice coil for an example, there appears to be 4-layers. Then the first three layers could be coil #1. Then the next layer seems to contain 5 spaced segments. That's a fancy voice coil,

Then summing:
β = β1 + β2 + β3 + β4 + β5 + β6

 

[NTK]

The problem is a voice coil moving through a magnetic gap from z to -z (the displacement limits).
Where r (m) is the radius and S (m^2) is the cross-section of the wire and B is the DC Magnetic Flux Density (Tm).

However, this might require cylindrical coordinates, r, z, θ .
For 2D assume θ = 2π.
Note that 2πr is the circumference and N is the number of turns
View attachment 505732
What do you think?

Right now, I can think of 2 ways to formulate the problem. I also think we shouldn't need more than 1 spatial dimension (no need to use a 2-D or 3-D cylindrical coordinate system, since we shouldn't have, or want, any of the parameters to have dependencies on r or θ, and only on z).

The first way is to uncoil (straighten) the voicecoil. The function for the magnetic flux density B will need to be expressed as a function of the location along the length of the voice coil, x.

The second way is to have a "varying current density" along the voice coil along the height (or z) direction. Since current is constant along the voice coil wire, "current density" means the same as how densely the coils are packed.

I borrow from the picture from the paper by Bezzola and Brunet.
https://www.researchgate.net/public..._Simulations_of_Loudspeaker_Transducer_Motors

 

[smowry]

@NTK

Thank you so much and there is a bunch of good stuff but I have some questions. I see somethings that I was doing wrong.

1. The solution of interest is Beta not Force.
2. The model I am looking for is static and i = 0.
3. If a current is applied, i(t), then there will be an AC magnet field also, Total Flux density(x,t) = BDC(x) + BAC(x,t)
4. For the Purifi coil rc is not a constant and the OD changes as in and out steps.
5. FEA simulation starts with a static DC model and Beta and/or Bl is acquired with a command file. Then an AC current density is applied with frequency, f.
6. Empirical motor evaluation, typically manually sweeps the coil from -x to x and dlambda/dx = Beta is returned. Below is my command file but this will not work with the Purifi coil due to the OD steps. I would need to sweep several command files and sum the results. I had previously simulated the TC Sounds LMS motor like that.

/date: 21/10/09
/author: steve mowry
/notes: this comi file will create a beta sweep of the motor and
/ place the results in a file called "beta.dat".
/
/ length in mm
/
$comi mode=off
/
/$para #n number of turns
/$para #lc coil height
/$para #bt bobbin foil thickness
/$para #cid coil id
/$para #cod coil od
/$para #fpc center of face plate height in model
/$para #i loop parameter
/$cons #np number of points to collect
/$cons #d step size
/$cons #offs coil starting offset
/
$para #n 28.8
$para #lc 2.0
$para #bt 0.05
$para #cid 19.4
$para #cod 20.03
$para #fpc -0.25
$cons #np 101
$cons #d 0.05
$cons #offs -2.5
/
/
/ this command file erases any existing model data before running
$os rm beta.dat
/ open the file beta.dat to write output to
$open 1 beta.dat write
/ define a blank string
$form 1 string string=' '
/ define a format for the file beta.dat
$form 2 exp 0
/ assign output format, coil position, space, beta
$assign 2 1 2
/
/ data collection loop
$para #i 1
$do #i 1 #np
$cons #dx #d*(#i-1)+#offs
/
/ data collection section
$para #rc #cid/2+#bt+(#cod-#cid)/4
$comi mode=off
point meth=cart comp=2*3.1415*#rc*POT xp=#rc yp=#fpc+#dx+#lc/2
$comi mode=off
$cons #phit comp
point meth=cart comp=2*3.1415*#rc*POT xp=#rc yp=#fpc+#dx-#lc/2
$cons #phib comp
$cons #phis #phib-#phit
$comi mode=off
$cons #dldx #n*#phis/#lc
$para #beta (#dldx)


I need to study your reply and get back to you; however, you have identified somethings that I had WRONG. Note that POT is the magnetic vector potential and (2πr)POT is the magnetic flux.

 

[smowry]

@NTK you are the best!

Static DC Model

Note that the above is a 1D model in cylindrical coordinates.
r = rc
z = z
θ = 2π