Started by June 2, 2012
```"Phil Hobbs" <pcdhSpamMeSenseless@electrooptical.net> wrote in message
news:4FCBC491.7CF52A7@electrooptical.net...
> If L = alpha * N**2, then alpha has units of henries per turn squared.
> (Of course a turn isn't really a unit, just as a radian and a steradian
> aren't, but it sure isn't per square root turn.)

Indeed.  The common symbol is A_L.  I call it "inductivity", with reference
to a given core material and geometry.  (It can be a fickle measure because,
for example, the inductivity of a long rod core varies by 50% from center to
end -- as Bill said, a useful definition depends on k --> 1, which depends
on nearly-closed loop, high permeability cores.)

Theorem: it further stands to reason that permeability is actually in units
of H / (m * t) (t = turn).

Proof:

A. For a continuous core of effective permeability mu, cross sectional core
area A_e and average core path length l_e,
A_L = mu * A_e / l_e
Options for throwing around the factor of t^-2:
1. mu: -2, A_e: 0, l_e: 0
2. mu: -1, A_e: -1, l_e: 0
3. mu: -1, A_e: 0, l_e: 1
4. mu: 0, A_e: -1, l_e: 1
It doesn't really make sense to ascribe a factor of t^-2 for A_e or t^2 for
l_e, so those options aren't listed.  I would prefer to avoid 3 and 4,
because it's less intuitive to count the path length multiple times (though
equally valid).

B. The flux per turn you can apply to a core:
Phi_pk / N = B_pk * A_e
Options for throwing around the factor of t^-1:
1. B_pk: -1, A_e: 0
2. B_pk: 0, A_e: -1

C. Field strength vs. flux density:
H = N*I / l_e
B = mu * H
H is in units of A / m, but engineering sources typically define it as A * t
/ m, so we have a good excuse to leave it alone.  That means either:
1. B: -1, mu: 0
2. B: 0, mu: -1

C excludes A1, without making things uglier.  B1 and C1 are inconsistent
with A, when the l_e: 2 option is excluded.  This leaves A2, B2 and C2.
Thus, core area is also per turn.

Note: "Unit" given if the SI specifies a proper name.

Name     | Symbol  | Unit |       Equation        | Derived Units
-------------+---------+------+-----------------------+---------------
Inductance   |  L      |  H   |  L = A_L * N^2        |  Wb / A
Inductivity  |  A_L    |  -   |  A_L = mu * A_e / l_e |  H / t^2
Permeability |  mu     |  -   |  mu = mu_r * mu_0     |  H / (m * t)
MFD*         |  B      |  T   |  B = mu * H           |  Wb / m^2
MFI**        |  H      |  -   |  H = N*I / l_e        |  A * t / m
Core Flux    |  Phi/N  |  -   |  Phi/N = B * A_e      |  Wb / t
Flux         |  Phi    |  Wb  |  Phi = (Phi/N) * N    |  V * s
Core Area    |  A_e    |  -   |  -                    |  m^2 / t
Core Length  |  l_e    |  m   |  -                    |  m

* Magnetic Flux Density, or just Flux Density
** Magnetic Field Intensity; sometimes called Magnetization, though
strictly, this refers to the permanent magnetization term in Maxwell's
equations (integral form).

Engineering units useful to switching design:
Phi in uWb
B in uWb / (mm)^2
H in A / mm
mu_0 ~= 1.256 nH / mm
A_e in (mm)^2
l_e in mm
A_L in nH/t^2
Most manufacturers specify their core properties in mm or cm, which are easy
to use or convert by eye.

Incidentally, notice inductance is ohm * s and capacitance is s / ohm.  This
can be handy when, e.g., tracking an algebra mistake in an unwieldy transfer
function.

Tim

--
Deep Friar: a very philosophical monk.
Website: http://webpages.charter.net/dawill/tmoranwms

```
```Bill Sloman wrote:
> On Jun 3, 1:50 pm, Robert Baer<robertb...@localnet.com>  wrote:
>> Bill Sloman wrote:
>>> On Jun 2, 6:07 am, Robert Baer<robertb...@localnet.com>    wrote:
>>>>      NO transformers.
>>
>>> Use coupled inductors - K1 L1 L2 L3 0.99 tells the program that L1, L2
>>> and L3 are windings on a single transforemr with a coupling
>>> coefficient of 0.99
>>
>>>>      NO saturable inductors.
>>
>>> The John Chan model represents real, hysteretic inductors pretty
>>> accurately, if my limited experience is anything to go by.
>>
>>>>      NO selection of ferrite core materials.
>>
>>> The John Chan model allows you to do that
>>
>>>>      NO selection of ferrite core sizes or shapes.
>>
>>> The John Chan model allows you to do that.
>>
>>> Go to "Help" and section L.Inductor.
>>
>>>>      WTF??
>>
>>> There's not a lot wrong with the program, but you do have to work out
>>> how to get the most out of it.
>>
>>> --
>>> Bill Sloman, Nijmegen
>>
>>     So i can pick a 2N2222 or a 2N3904 or a LT1026 or LT1105 or a 2W 110
>> ohm resistor or a 1uF 10V TDK X5R capacitor as if off the shelf.
>>     BUT.
>>     Transformers? Ferroxcube pot cores? Then accidentally overdrive them?
>>     Nope.
>>     You say i need to \$pend \$2,000 to IEEE to look at some paper i never
>> heard about and that few others heard about if i want to know more than
>> what is disclosed in that help section.
>>     Nobody gives the K or M of their transformers; i have to guess - and
>> the numbers will most likely be wrong no matter what i pick.
>>     And.. nobody mentions that those values are non-linear and what
>> changes them.
>
> The K for most ungapped ferrtie cored transformers is in the 0.99 to
> 0.999 range - anything in that range is usually close enough to model
> what is going on.
>
> We've just measured a coupling of 0.98 in a gapped RM14 core - EPCOS
> gapped it down from 6000uH/root turn for an ungapped pair to 630nH per
> root turn by grinding back the centre pillar by 0.4mm,
>
> http://www.farnell.com/datasheets/486650.pdf
>
> M is K.square root L1.L2 IIRR
>
> The transformer equations are
>
> V1= L1.dI1/dt + M.dI2/dt
>
> V2= M.dI1/dt + L2.dI2/dt
>
> The John Chan model explicitly deals with the non-linear elements -
> though it leaves coupling severely alone. Coupling does decline
> dramatically if you saturate the ferrite, but real circuits blow up if
> you saturate the ferrite. Ferrite permeability does rise with field at
> low field values, but not all that much, and you can usually get away
> with ignoring the effect on coupling - which usually isn't a critical
> parameter.
>
> --
> Bill Sloman, Nijmegen
>
Well, what i have in mind is purposely overdriving driving saturable
inductors in a PFN and fiddling with the parameters to see (a) how few
stages one needs to get a reasonable effect, and (b) see how much of a
speedup one can get on the rise time of a traveling pulse.
Now, some ferrites have a rather nasty nonlinear permeability
starting with almost flat, then goes up to a high hill and then drops
off like a cliff; would be interesting if that "hill" is of use.

Then there is this other case where i have a transformer where the
coupling is a bit frequency dependent, the mutual inductance ditto etc &
etc with no specs as how it was wound (only Zin and Zout at 1KHz) or
what the core was (prolly silicon steel thin laminations as it is for
audio use).
Plan to singe someones eyeteeth with that..

```
```Martin Riddle wrote:
> "Robert Baer"<robertbaer@localnet.com>  wrote in message
> news:xqydnWyQzY_6HlTSnZ2dnUVZ_g-dnZ2d@posted.localnet...
>>    NO transformers.
>>    NO saturable inductors.
>>    NO selection of ferrite core materials.
>>    NO selection of ferrite core sizes or shapes.
>>    WTF??
>
> Here's a pretty good modeling example for transformers.
> Transformers are sort of a black art, it's rare to design one perfectly
> the first time around.
> <http://fmtt.com/Transformer%20SPICE%20Model%202-14-08.pdf>
>
> Cheers
>
>
>
NOW we are getting somewhere!
Thanks!

```
```Bill Sloman wrote:
>
> On Jun 3, 10:09 pm, Phil Hobbs
> <pcdhSpamMeSensel...@electrooptical.net> wrote:
> > Bill Sloman wrote:
> >
> > > On Jun 3, 9:02 pm, Fred Abse <excretatau...@invalid.invalid> wrote:
> > > > On Sun, 03 Jun 2012 05:11:52 -0700,BillSlomanwrote:
> > > > > We've just measured a coupling of 0.98 in a gapped RM14 core - EPCOS
> > > > > gapped it down from 6000uH/root turn for an ungapped pair to 630nH per
> > > > > root turn by grinding back the centre pillar by 0.4mm,
> >
> > > > I think that should be "per turn squared".
> >
> > > Wrong. Inductance is proportional to the square of the number of
> > > turns, as long as they are closely coupled.
> >
> > >http://en.wikipedia.org/wiki/Inductor
> >
> > If L = alpha * N**2, then alpha has units of henries per turn squared.
> > (Of course a turn isn't really a unit, just as a radian and a steradian
> > aren't, but it sure isn't per square root turn.)
>
> Applying dimensional analysis to a manufacturer's design fudge factor
> is the sort of thing that physicists do.

Whereas chemists get it wrong at the top of their lungs?

>
> It's not a particularly useful activity. Reminding junior engineers at
> every possible opportunity that inductance is proportional to the
> square of the number of turns in a winding is an extremely useful
> activity, and saves loads of time at design reviews.

Bill, why is it so hard for you to say, "Oops, quite right."?  It really
wouldn't kill you, and you'd probably find that you got on better all
round.

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC
Optics, Electro-optics, Photonics, Analog Electronics

Briarcliff Manor NY 10510
845-480-2058

hobbs at electrooptical dot net
http://electrooptical.net
```
```boB wrote:
> On Sun, 03 Jun 2012 03:24:10 -0800, Robert Baer
> <robertbaer@localnet.com>  wrote:
>
>> Charles wrote:
>>>
>>>
>>> "Robert Baer" wrote in message
>>> news:xqydnWyQzY_6HlTSnZ2dnUVZ_g-dnZ2d@posted.localnet...
>>>
>>> NO transformers.
>>> NO saturable inductors.
>>> NO selection of ferrite core materials.
>>> NO selection of ferrite core sizes or shapes.
>>> WTF??
>>>
>>>
>>> WTF don't you understand?
>>    Yawn..NOT one word concerning what i mentioned.
>>    2 megs wasted, "covering" a quickie SPICE "review".
>
>
> use google and the vast amount of information on the web
> about LTspice and how to model circuits with core models.
> It's still spice and isn't perfect and you are going to still
> tweak things to get it to run right.
>
> http://ltwiki.org/index.php5?title=Transformers
>
>
Interesting.  Thanks.

```
```On Sun, 3 Jun 2012 17:58:36 -0700 (PDT), Bill Sloman
<bill.sloman@ieee.org> wrote:

>On Jun 3, 10:09&#2013266080;pm, Phil Hobbs
><pcdhSpamMeSensel...@electrooptical.net> wrote:
>> Bill Sloman wrote:
>>
>> > On Jun 3, 9:02 pm, Fred Abse <excretatau...@invalid.invalid> wrote:
>> > > On Sun, 03 Jun 2012 05:11:52 -0700,BillSlomanwrote:
>> > > > We've just measured a coupling of 0.98 in a gapped RM14 core - EPCOS
>> > > > gapped it down from 6000uH/root turn for an ungapped pair to 630nH per
>> > > > root turn by grinding back the centre pillar by 0.4mm,
>>
>> > > I think that should be "per turn squared".
>>
>> > Wrong. Inductance is proportional to the square of the number of
>> > turns, as long as they are closely coupled.
>>
>> >http://en.wikipedia.org/wiki/Inductor
>>
>> If L = alpha * N**2, then alpha has units of henries per turn squared.
>> (Of course a turn isn't really a unit, just as a radian and a steradian
>> aren't, but it sure isn't per square root turn.)
>
>Applying dimensional analysis to a manufacturer's design fudge factor
>is the sort of thing that physicists do.

Engineers, too. My first engineering course at Tulane, first semister
freshman year, was an introduction to units and dimensional analysis.
It was taught by Dr Johnson, the Dean of the Engineering School, who
thought it was important.

Random noise increases as the square root of bandwidth, so we specify
it as volts per root Hz.

Inductance increases with turns squared, so we spec a core Al as
henries per turn squared.

See the difference?

>
>It's not a particularly useful activity. Reminding junior engineers at
>every possible opportunity that inductance is proportional to the
>square of the number of turns in a winding is an extremely useful
>activity, and saves loads of time at design reviews.

They were probably polite enough to laugh at you after you left the
room.

--

John Larkin                  Highland Technology Inc
www.highlandtechnology.com   jlarkin at highlandtechnology dot com

Precision electronic instrumentation
Picosecond-resolution Digital Delay and Pulse generators
Custom timing and laser controllers
Photonics and fiberoptic TTL data links
VME  analog, thermocouple, LVDT, synchro, tachometer
Multichannel arbitrary waveform generators
```
```On Jun 4, 4:47=A0am, Phil Hobbs <pcdhSpamMeSensel...@electrooptical.net>
wrote:
> BillSlomanwrote:
>
> > On Jun 3, 10:09 pm, Phil Hobbs
> > <pcdhSpamMeSensel...@electrooptical.net> wrote:
> > >BillSlomanwrote:
>
> > > > On Jun 3, 9:02 pm, Fred Abse <excretatau...@invalid.invalid> wrote:
> > > > > On Sun, 03 Jun 2012 05:11:52 -0700,BillSlomanwrote:
> > > > > > We've just measured a coupling of 0.98 in a gapped RM14 core - =
EPCOS
> > > > > > gapped it down from 6000uH/root turn for an ungapped pair to 63=
0nH per
> > > > > > root turn by grinding back the centre pillar by 0.4mm,
>
> > > > > I think that should be "per turn squared".
>
> > > > Wrong. Inductance is proportional to the square of the number of
> > > > turns, as long as they are closely coupled.
>
> > > >http://en.wikipedia.org/wiki/Inductor
>
> > > If L =3D alpha * N**2, then alpha has units of henries per turn squar=
ed.
> > > (Of course a turn isn't really a unit, just as a radian and a steradi=
an
> > > aren't, but it sure isn't per square root turn.)
>
> > Applying dimensional analysis to a manufacturer's design fudge factor
> > is the sort of thing that physicists do.
>
> Whereas chemists get it wrong at the top of their lungs?
>
> > It's not a particularly useful activity. Reminding junior engineers at
> > every possible opportunity that inductance is proportional to the
> > square of the number of turns in a winding is an extremely useful
> > activity, and saves loads of time at design reviews.
>
> Bill, why is it so hard for you to say, "Oops, quite right."? =A0It reall=
y
> wouldn't kill you, and you'd probably find that you got on better all
> round.

I don't find it difficult at all, but I've been using the term Henrys
per root turn for many years, and it has taken a while for the logic
to penetrate my brain. I don't think straight in the wee small hours,
when I should have gone to bed, rather than hanging around waiting to
see if my current simulation is going in the right direction.

You are right, and the units ought to Henry per turn^-2 - possibly
Henry per radian^-2. All we've got to do now is to submit your
reasoning to the General Conference on Weights and Measures (CGPM,
Conf=E9rence G=E9n=E9rale des Poids et Mesures). You'd need to go through

The U.S. member of the CIPM is Dr. Willie E. May, Director of the NIST
Chemical Science and Technology Laboratory. The current NIST delegate
to the CCU is Dr. Ambler Thompson of the NIST Technology Services.
Questions concerning the more fundamental aspects of the SI and subtle
aspects of proper SI usage may be directed to him at the following

Dr. Ambler Thompson
NIST, Bldg. 222, Rm. B243
100 Bureau Drive, Stop 2600
Gaithersburg, MD 20899-2601

Telephone: 301-975-2333
email: ambler@nist.gov

--
Bill Sloman, Nijmegen
```
```On Jun 4, 6:00=A0am, John Larkin
<jjlar...@highNOTlandTHIStechnologyPART.com> wrote:
> On Sun, 3 Jun 2012 17:58:36 -0700 (PDT),BillSloman
>
>
>
>
>
>
>
>
>
> <bill.slo...@ieee.org> wrote:
> >On Jun 3, 10:09=A0pm, Phil Hobbs
> ><pcdhSpamMeSensel...@electrooptical.net> wrote:
> >>BillSlomanwrote:
>
> >> > On Jun 3, 9:02 pm, Fred Abse <excretatau...@invalid.invalid> wrote:
> >> > > On Sun, 03 Jun 2012 05:11:52 -0700,BillSlomanwrote:
> >> > > > We've just measured a coupling of 0.98 in a gapped RM14 core - E=
PCOS
> >> > > > gapped it down from 6000uH/root turn for an ungapped pair to 630=
nH per
> >> > > > root turn by grinding back the centre pillar by 0.4mm,
>
> >> > > I think that should be "per turn squared".
>
> >> > Wrong. Inductance is proportional to the square of the number of
> >> > turns, as long as they are closely coupled.
>
> >> >http://en.wikipedia.org/wiki/Inductor
>
> >> If L =3D alpha * N**2, then alpha has units of henries per turn square=
d.
> >> (Of course a turn isn't really a unit, just as a radian and a steradia=
n
> >> aren't, but it sure isn't per square root turn.)
>
> >Applying dimensional analysis to a manufacturer's design fudge factor
> >is the sort of thing that physicists do.
>
> Engineers, too. My first engineering course at Tulane, first semister
> freshman year, was an introduction to units and dimensional analysis.
> It was taught by Dr Johnson, the Dean of the Engineering School, who
> thought it was important.
>
> Random noise increases as the square root of bandwidth, so we specify
> it as volts per root Hz.
>
> Inductance increases with turns squared, so we spec a core Al as
> henries per turn squared.
>
> See the difference?

It's 9:30am and my brain is working again, so yes - I do.

> >It's not a particularly useful activity. Reminding junior engineers at
> >every possible opportunity that inductance is proportional to the
> >square of the number of turns in a winding is an extremely useful
> >activity, and saves loads of time at design reviews.
>
> They were probably polite enough to laugh at you after you left the
> room.

Perhaps. But they'd got the point - attention-getting devices don't
have to be pedantically correct to work. Look at Howard Johnson on
high speed signal propagation.

--
Bill Sloman, Nijmegen
```
```On Sun, 03 Jun 2012 16:09:53 -0400, Phil Hobbs wrote:

> Bill Sloman wrote:
>>
>> On Jun 3, 9:02 pm, Fred Abse <excretatau...@invalid.invalid> wrote:
>> > On Sun, 03 Jun 2012 05:11:52 -0700,BillSlomanwrote:
>> > > We've just measured a coupling of 0.98 in a gapped RM14 core - EPCOS
>> > > gapped it down from 6000uH/root turn for an ungapped pair to 630nH
>> > > per root turn by grinding back the centre pillar by 0.4mm,
>> >
>> > I think that should be "per turn squared".
>>
>> Wrong. Inductance is proportional to the square of the number of turns,
>> as long as they are closely coupled.
>>
>> http://en.wikipedia.org/wiki/Inductor
>
> If L = alpha * N**2, then alpha has units of henries per turn squared. (Of
> course a turn isn't really a unit, just as a radian and a steradian
> aren't, but it sure isn't per square root turn.)
>

Precisely my point.

--
"For a successful technology, reality must take precedence
over public relations, for nature cannot be fooled."
(Richard Feynman)
```
```On Jun 3, 9:02=A0pm, Fred Abse <excretatau...@invalid.invalid> wrote:
> On Sun, 03 Jun 2012 05:11:52 -0700,BillSlomanwrote:
> > We've just measured a coupling of 0.98 in a gapped RM14 core - EPCOS
> > gapped it down from 6000uH/root turn for an ungapped pair to 630nH per
> > root turn by grinding back the centre pillar by 0.4mm,
>
> I think that should be "per turn squared".

Phil Hobbs and John Larkin both think that you are right, and so -
after mature consideration - so do I.

Unfortunately, it was one of those thinks that I thought I knew that
wasn't so.

Thanks for the correction, and my apologies for responding without
thinking hard enough.

--
Bill Sloman, Nijmegen
```