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'[EE] Calculating inductor saturation'
2010\07\09@123931 by

How would I calculate the saturation current of a inductor? I know the
formula probably needs to account for wire diameter, turns, turn
spacing and core permeability. Also, is there a formula for inductance
vs current so I could chart the inductance knee?

The reason I'm asking is because I'm working with a shorted RLC model,
but the model I'm using doesn't take into account the inductor
saturating.

Unfortunately, google and wikipedia haven't done me any good with this
problem, and I don't have any relevant text books (or know which ones
to look in).
On 09/07/2010 17:39, Adam Field wrote:
> How would I calculate the saturation current of a inductor? I know the
> formula probably needs to account for wire diameter, turns, turn
> spacing and core permeability. Also, is there a formula for inductance
> vs current so I could chart the inductance knee?
>
> The reason I'm asking is because I'm working with a shorted RLC model,
> but the model I'm using doesn't take into account the inductor
> saturating.
>
> Unfortunately, google and wikipedia haven't done me any good with this
> problem, and I don't have any relevant text books (or know which ones
> to look in).
It depends on the material
If you have RF or Audio on a DC bias current you can wind bifilar and
put equal DC down second wire to cancel the DC bias of your signal.
Then you are limited by Frequency and current.

Depending on the material, the higher the frequency, you can have more power

http://en.wikipedia.org/wiki/Inductance

http://en.wikipedia.org/wiki/Inductor

You can't know the saturation current for AC without knowing the core
type and frequency.

At 10:39 AM 7/9/2010, Adam Field wrote:
>How would I calculate the saturation current of a inductor? I know the
>formula probably needs to account for wire diameter, turns, turn
>spacing and core permeability. Also, is there a formula for inductance
>vs current so I could chart the inductance knee?

Can you make one and measure it?  Its pretty easy to do.

dwayne

--
Dwayne Reid   <dwaynerplanet.eon.net>
Trinity Electronics Systems Ltd    Edmonton, AB, CANADA
(780) 489-3199 voice          (780) 487-6397 fax
http://www.trinity-electronics.com
Custom Electronics Design and Manufacturing

> How would I calculate the saturation current of a inductor? I know the
> formula probably needs to account for wire diameter, turns, turn
> spacing and core permeability. Also, is there a formula for inductance
> vs current so I could chart the inductance knee?
>
> The reason I'm asking is because I'm working with a shorted RLC model,
> but the model I'm using doesn't take into account the inductor
> saturating.

Alas it can be considered a  simple problem with complex practice or a
complex problem :-).

Starting point:
Amp turns in coil provide core flux.
Looking at your above list, you can initially largely ignore wire
diameter and turns spacing. If you are working with a given
manufacturer's core profile and material then you can look up it's
amp-turn rating and expect to get a reasonably good idea. Reality in
the form of DC and AC currents, frequency effects in a given core
material, hysteresis etc will complicate things.
Reputable core makers will provide nomograms and formulae and/or
online calculators to make this all easy.

easier. Application, circuit, frequency, power level, DC component,
core material, amp turns, ... .

Have a look at http://www.micrometals.com/
Very good people to deal with, good products. wide range of materials,
good prices.
I'm just a very occasional satisfied customer.
Whether they have what you want depends on what you are doing.

In practice you can get a very good idea re saturation by looking at
current ramp when an eg square wave is applied to a core and power
level ramped up. Below saturation current will ramp relatively
linearly for constant applied voltage. As saturation is approached
current ramp will trend upwards from straight line and depending on
core etc can increase rapidly towards vertical above a certain level.
In a typical inverter circuit just looking at the current ramp will
give you an excellent idea if a core is being pushed beyond its
reasonable limits.

Note that temperature and losses can affect a core's long term
performance, depending on material. Micrometals goi into this in
detail in their literature.

Russell
> Knowing more about what you are doing would make question answering
> easier. Application, circuit, frequency, power level, DC component,
> core material, amp turns, ... .
>

This application is charging a capacitor, and discharging it
(practically shorted) through an array of series/parallel SCRs. The
test is designed to stress the end spray connection of film
capacitors.

I need inductance to limit di/dt so I don't destroy the SCRs. My
operation frequency and power level will be different depending on the
test I'm conducting (.1uF to 220uF). The frequency is usually in the
100kHz range, but only lasts a few cycles as the shorted RLC circuit
dampens.

Peak currents can be as high as 2100A. I have modeled the circuit with
an Excel spreadsheet and now with Mathcad, but I'm missing a key
formula, and that's inductor saturation.

I can use air core inductors, since (depending on who you talk to) can
never saturate. The only problem is that if I need 2uH of inductance
to slow di/dt an air core inductor is much larger and can have enough
series resistance to limit my peak current. In short, unworkable.

I would like to use a ferrite core inductor to keep the wire length
down (and the series resistance down) but they saturate severely at
current levels of 100-200A. Since my target peak amperage and charge
voltage will be moving targets, I would like a way to model a
saturated inductor.

I've thought of using SPICE, but I'm not sure of its inductor
saturation modeling, and I'd like a way to calculate the exact
inductance I need rather than a trial and error model.
> How would I calculate the saturation current of a inductor?

You don't.  You look it up in the inductor's datasheet.

Calculating saturation current is only done by little elves in a hollow tree
and requires a regular supply of dead fish.

Actually there are ways if you're not a elf, but it gets complicated.
Roughly you get the spec for the core material and find the magnetic flux
your particular core made from that material can take.  Then you determine
the loop current required to generate that flux, then divide that by the
number of turns to get the current thru the wire.

********************************************************************
Embed Inc, Littleton Massachusetts, http://www.embedinc.com/products
(978) 742-9014.  Gold level PIC consultants since 2000.
> You don't.  You look it up in the inductor's datasheet.
>
I know but with my setup, which I described a minute ago will
(practically) push any non air core inductor way past saturation.

> Calculating saturation current is only done by little elves in a hollow tree
> and requires a regular supply of dead fish.
>
> Actually there are ways if you're not a elf, but it gets complicated.
> Roughly you get the spec for the core material and find the magnetic flux
> your particular core made from that material can take.  Then you determine
> the loop current required to generate that flux, then divide that by the
> number of turns to get the current thru the wire.
>

So now that I can calculate the saturation point, what happens to
inductance? I know it doesn't drop to zero but from what I've measured
it drops off exponentially with rising current.

I know I'm off into elf zone with this, but I know it can be solved
with a mixture of work done by Ampere and Maxwell and perhaps others.
> So now that I can calculate the saturation point, what happens to
> inductance? I know it doesn't drop to zero...

Close, actually.  The knee is somewhat soft, but yes, that's what
"saturation" is.  The core can store no more magnetic energy.  It is full.
You now have a air core inductor for incremental currents above the
saturation threshold.

> I know I'm off into elf zone with this, but I know it can be solved
> with a mixture of work done by Ampere and Maxwell and perhaps others.

No, you're screwed.  You can't cheat physics.  You're going to need a really
big core no matter how you try to jiggle the number.

Another way to look at saturation is that the core material can only hold so
many joules per cubic meter.  Above that it transitions roughly to a air
core inductor.  Figure out how many joules our inductor needs to hold, then
look up some core material, then realize it's going to be big.

********************************************************************
Embed Inc, Littleton Massachusetts, http://www.embedinc.com/products
(978) 742-9014.  Gold level PIC consultants since 2000.
Hi - I have nothing to add to the discussion, but 2100amps peak.  Wow!
Real EE, not the wussy 30mA @ 3.3V digital yadda stuff normally seen on
PIClist and my workbench.  Let us know how it turns out...

Good luck!
J

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>> Knowing more about what you are doing would make question answering
>> easier. Application, circuit, frequency, power level, DC component,
>> core material, amp turns, ... .

> I need inductance to limit di/dt so I don't destroy the SCRs. My
> operation frequency and power level will be different depending on the
> test I'm conducting (.1uF to 220uF). The frequency is usually in the
> 100kHz range, but only lasts a few cycles as the shorted RLC circuit
> dampens.
>
> Peak currents can be as high as 2100A. I have modeled the circuit with
> an Excel spreadsheet and now with Mathcad, but I'm missing a key
> formula, and that's inductor saturation.
>
> I can use air core inductors, since (depending on who you talk to) can
> never saturate. The only problem is that if I need 2uH of inductance
> to slow di/dt an air core inductor is much larger and can have enough
> series resistance to limit my peak current. In short, unworkable.

If anything other than air is going to work then a powdered iron core
is probably a top contender.
The micrometals site has calculators / graphs etc that allow you to
determine if they can help.
BUT that's a very large current. It will be possible to build an air
core that meets your need - you just may not like what it looks like.
What maximum resistance is tolerable?
What is the full spec of what you want?
eg at least I max, L operating, minimum time between discharges, Rmax, ...

http://www.micrometals.com/software_index.html

Making some assumptions which may or may not suit - their E827-60 core
gives around 1 uH at 1000 A with a whole 2 turns, 0.0001 ohms
resistance :-), 31 C temperature rise at steady state at 100 kHz,
"Heavy wire", and 100+ W Cu loss steady state. And costs \$US117.46 (!)
for the core. Thats an 8" x 10" x 2.5" E core.

Attached too small jpg shows inductance with current - actually about
1.3 uH at 1000 A and down to about 0-.7 uH at 2000A.

ie Take this as a starting point - it seems they WILL have a core or
core stack that does what you want but you will need to talk to them
and they will probably design something for you.

BUT a suitable copper crowbar (probably a stranded crowbar) bent into
a few spiral turns is probably going to do what you want with no core.
Brain offers long ago formula. Brain says 'a' is diameter but MAY be

L = a^2n^/(9a+10b)

L uH
a = dia in inches
b= length in inches.
n = turns

Russell

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Micrometals RF design software may be useful.
Allows you to specify arbitrary core shapes and to make them of
unusual materials - wood etc.

> Peak currents can be as high as 2100A.
>
> 2uH of inductance

Note that this means the core needs to store 4.4J.  You can play all the
games you want with turns, wire thickness, core material, etc, but there is
no way to escape this basic physics.

********************************************************************
Embed Inc, Littleton Massachusetts, http://www.embedinc.com/products
(978) 742-9014.  Gold level PIC consultants since 2000.
On 10/07/2010 13:02, Olin Lathrop wrote:
>> Peak currents can be as high as 2100A.
>>
>> 2uH of inductance
> Note that this means the core needs to store 4.4J.  You can play all the
> games you want with turns, wire thickness, core material, etc, but there is
> no way to escape this basic physics.
Absolutely,
2uH isn't an impossible air core inductance. I have an HF manpack with
variable 1uH to 185uH or so air core inductor for aerial matching. It's
gold or brass braid over cord wound from a 1" metal spindle to 3" or 4"
plastic grooved drum. (possibly gold to stop corrosion in damp jungles).

At those kind of currents an air cored toroid shape. At higher frequency
silvered or varnished polished copper strip or tube works better than
solid wire. Don't use tinned wire or gold  plated. Both inferior to
lacquered polished copper or silvered copper for resistance, especially
sharp pulses/high frequency unless you WANT lower Q and higher losses.
>> Peak currents can be as high as 2100A.
>> 2uH of inductance

> Note that this means the core needs to store 4.4J.  You can play all the
> games you want with turns, wire thickness, core material, etc, but there
is
> no way to escape this basic physics.

I haven' seen anything that suggests an attempyt to evade "the Physics" -
but rather, a request for help in applying it.
The query seems to boil down to "is there a way that I can use a core
material that doesn't saturate, to increase the inductance for a given coil
resistance wrt an air wound coil so as to reduce the effective resistance?.

This seems to be a reasonable question, and the "first look" approaches that
I have suggested indicate that an eg Micrometals based powdered iron core
may well do the job  OK - and that umetal will quite likely design something
that meets the spec (as the core cost will be hundreds of dollars.

However/also, it seems to me that an air wound core will also be achievable
that works OK.
simplistic formula that I offered.

http://hamwaves.com/antennas/inductance.html

How good it is is uncertain, and what the target R is is unknown to me, but
it seems that 4 to 6 turns of eg 15mm silver plated copper tube wound in a
(tight ) 100 mm dia spiral with minimum inter turn clearances will produce
inductances of the order required. Resistances appropriateness need checking
but are probably bearable.
They give what seems to be AC resistance (ie skin effect modified
resistance) but I haven't even tried to check for reasonableness.

Plugging in a few figures I get the following.
Use courier or other fixed width font to view:

Dia = coil mean diamyter mm
t = conductor thickness (copper tube)
W - width or coil length mm
N  turns
Rac - resistance impedance at 100 kHz.  ????

N  Dia   t   W  LuH   Rac

4  100  10  50  1.5  .007
4  100  15  70  1.14 .005
4  200  15  70  3.53 .01
6  100  15  100 2    .008

Bifilar winding using eg silver plated 1/8" copper tubing will reduce AC
resistance due to skin effect reductions.

Values are such as to suggest that a handful of small gauge piping, some
silver plating (not expensive) and some playing, should yield an acceptable
result.

Russell McMahon
On 10/07/2010 13:50, RussellMc wrote:
>
> However/also, it seems to me that an air wound core will also be achievable
> that works OK.
> This page contains an apparently superb calculator that goes beyond the
> simplistic formula that I offered.
>
>                http://hamwaves.com/antennas/inductance.html
>
> How good it is is uncertain, and what the target R is is unknown to me, but
> it seems that 4 to 6 turns of eg 15mm silver plated copper tube wound in a
> (tight ) 100 mm dia spiral with minimum inter turn clearances will produce
> inductances of the order required. Resistances appropriateness need checking
> but are probably bearable.
> They give what seems to be AC resistance (ie skin effect modified
> resistance) but I haven't even tried to check for reasonableness.
Sounds like the correct ball park from my experience of high power HF
"Tank circuits".

>> Note that this means the core needs to store 4.4J.  You can play all the
>> games you want with turns, wire thickness, core material, etc, but there
> is
>> no way to escape this basic physics.

In my case, the inductor can fully saturate and still do its job. I
now realize that it's all about the core material. The coil only has
to keep the rate of current rise below a threshold. I was originally
looking for a way to model inductors way past their saturation point.

SCRs are available in many di/dt ratings. However, devices rated for
1000A/us are usually priced around \$500 each. Commodity SCRs that I
checked out had ratings of 100-200A/us (at 125C junction temp). I'm
trying to work out the best way to build this circuit. Expensive
silicon devices and forgo the di/dt hassles or cheap easily
replaceable SCRs with some not-so-easy inductor designing.

{Quote hidden}

I was hoping to have something below 5mOhms, or at least below
10mOhms. There are other areas I can give or take from to reduce the
effective series resistance. Lowering series resistance would free up
cheaper SCR choices.

A coil made like you described will probably work quite well, and it's
quite feasible to build. I'm still convinced I can do the job with a
smaller coil (if a balance of saturation vs inductance loss can be
found). However, to do that, looks like it will be all
experimentation.

The wikipedia has some good sections on magnetism which mention some
exotic materials like mumetal.
http://en.wikipedia.org/wiki/Permeability_(electromagnetism)

I found some good information from MIT too:
http://web.mit.edu/6.013_book/www/chapter9/9.4.html

Many thanks to the list and all the great minds that inhabit it.
Russell has helped me see an obvious solution that I missed, of a
really big coil.
On 10/07/2010 14:42, Adam Field wrote:
>
> The wikipedia has some good sections on magnetism which mention some
> exotic materials like mumetal.
>
I'd never have thought of mumetal as exotic as it's been used for
magnetic shielding since forever on CRTs, esp. in 'scopes.
Don't know when first used, but I remember an old Cossor 'scope with
octal valves (EF39s and such) that had it as screen on the CRT.
That's probably at least early 1950s.

Back then (or maybe 1930s) some loudspeakers used dc coils instead of
permanent magnets. Headphones only got small and light with
Samarium-Cobalt rare-earth type magnets.

The materials for shielding and magnets are not usually the sort of
materials for inductors which tend to use soft iron/silicon steel I
think for LF laminated cores or insulated iron dust (to stop eddy
current losses) cores and then various ferrite mixtures for various
frequencies and applications.

At really high current & less than 100uH (depending on space) you can't
beat silvered copper with air core. Or polished and polyurethane or
other suitable finish to prevent corrosion as cheap alternative. You can
buy pre-silvered solid copper wire and tube for RF applications. I've
experimented with silver plated 1mm wire sold for jewellery making for
VHF and UHF coils.

Also used is sometimes up to 20 or more enamelled copper wire in
parallel to achieve high flexibility and reduce skin resistance winding
1 or 2 turn centre tapped ferrite binocular or toroid ferrite cores for
25W to 400W 2MHz to 30MHz transmitter transistor or FET P.A. output
transformers. The older  valve P.A. tended to use solid silvered wire on
hollow ceramic tube former for essentially air cored inductor.

Hi Olin.

do you have a program to calculate inductors saturation?
If so where can I get it?

Peter

{Original Message removed}
On 11/07/2010 12:42, Peter Krengel wrote:
> Hi Olin.
>
> do you have a program to calculate inductors saturation?
> If so where can I get it?
>
> Peter
>
Olin wrote earlier:

{Quote hidden}

I agree

You don't.  You look it up in the inductor's datasheet.

Peter Krengel wrote:
> do you have a program to calculate inductors saturation?

No, I look in the datasheet for the inductor.

********************************************************************
Embed Inc, Littleton Massachusetts, http://www.embedinc.com/products
(978) 742-9014.  Gold level PIC consultants since 2000.
> do you have a program to calculate inductors
> saturation? If so where can I get it?
>
> Peter

EPCOS Design Tools
http://www.epcos.com/web/generator/Web/Sections/DesignTools/Overview/Page,locale=en.html

EPCOS Ferrite Magnetic Design Tool
www.epcos.com/web/generator/Web/Sections/DesignTools/Ferrites/Page,locale=en.html
I *hope* that this *third* attempt to post on this thread makes it.

As others have said calculating saturation is hard and inaccurate. It changes
with temperature, mchanical strain in the core due to mounting and other factors.

Bsat = Amperes * turns. Electronic circuits which measure saturation in real
time are very popular because of this, such as current mode dc/dc converters. A
very simple circuit which allows one to measure core saturation is a one or two
transistor voltage boost oscillator. The oscillator turns off exactly when the
core saturates so measuring the current will tell one exactly Bsat, given the
number of primary turns.

Modelling Bsat in LTspice is hard as there seems to be built in saturation
modelling but it does not work. Threads can be found where Helmut describes how
saturation can be modeled using atanh(). Atanh() models a soft saturation.

To model a hard saturation one can use a two inductor series model, with a small
inductor representing the air cored inductor and the large inductor the
remainder of the inductance with the unsaturated core. A current controlled
switch shorts the larger inductor when |Il| > Isat. Model the Rdc of the coil by
setting the Rdc of the air cored coil, and model saturation knee 'hardness' by
setting the Ron of the current controlled switch.

The atanh saturation model cannot be used with LTspice coupled coils
(transformers). The current controlled switch based one can be coupled (used as
a transformer model) using two Kxy L1 L2 0.95 Spice statements, one each to
couple the cored and the air cored inductors of the transformer (each winding is
represented as two coils in series as above).

-- Peter

Here's the setup in LTspice. Unfortunately my ancient version does not seem to
support signed calculations for the current via parameters, or I do not know how
to use that feature, so it uses two current sensing sources and two switches. An
advantage is that one can simulate all sorts of interesting situations, such as
a flux gate magnetometer measuring the Earth field by setting the saturation
currents for the two semiperiods to different values.

-- Peter

> Here's the setup in LTspice. Unfortunately my ancient version does not seem to
> support signed calculations for the current via parameters, or I do not know how
> to use that feature, so it uses two current sensing sources and two switches. An
> advantage is that one can simulate all sorts of interesting situations, such as
> a flux gate magnetometer measuring the Earth field by setting the saturation
> currents for the two semiperiods to different values.
>

That seams to work really well! I also found another reference that
can model nonlinear inductance in SPICE. In case you're interested:

http://www.beigebag.com/case_nonlinear_ind.htm
> Here's the setup in LTspice. Unfortunately my ancient version does not seem to
> support signed calculations for the current via parameters, or I do not know how
> to use that feature, so it uses two current sensing sources and two switches. An
> advantage is that one can simulate all sorts of interesting situations, such as
> a flux gate magnetometer measuring the Earth field by setting the saturation
> currents for the two semiperiods to different values.
>

That seams to work really well! I also found another reference that
can model nonlinear inductance in SPICE. In case you're interested:

http://www.beigebag.com/case_nonlinear_ind.htm
> That seams to work really well! I also found another reference that
> can model nonlinear inductance in SPICE. In case you're interested:
>
> http://www.beigebag.com/case_nonlinear_ind.htm

That's a fully parametric part, I'm not sure I like it more than the "hard" way
even if it simulates much faster probably. I posted the solution I gave on the
LTspice Yahoo mailing list, I hope that someone will take a look and maybe
improve it.

-- Peter

Adam, I posted my modest attempt in the LTspice mailing list and people
responded. One response is very elaborate (from analogieee.org):

http://tech.groups.yahoo.com/group/LTspice/message/38676

I still like the switch approach more but all the other options deserve careful
analysis.

-- Peter

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