Searching \ for '[EE] Calculating inductor saturation' in subject line. ()
Make payments with PayPal - it's fast, free and secure! Help us get a faster server
FAQ page: www.piclist.com/techref/index.htm?key=calculating+inductor
Search entire site for: 'Calculating inductor saturation'.

Exact match. Not showing close matches.
PICList Thread
'[EE] Calculating inductor saturation'
2010\07\09@123931 by Adam Field

flavicon
face
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).

2010\07\09@133725 by Michael Watterson

face picon face
 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.







2010\07\09@133847 by Dwayne Reid

flavicon
face
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   <spam_OUTdwaynerTakeThisOuTspamplanet.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

2010\07\09@134314 by RussellMc

face picon face
> 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.

Knowing more about what you are doing would make question answering
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

2010\07\09@180018 by Adam Field

flavicon
face
> 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.

2010\07\09@180108 by Olin Lathrop

face picon face
Adam Field wrote:
> 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.

2010\07\09@180859 by Adam Field

flavicon
face
> 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.

2010\07\09@184833 by Olin Lathrop

face picon face
Adam Field wrote:
> 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.

2010\07\09@221945 by Jesse Lackey

flavicon
face
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


Adam Field wrote:
{Quote hidden}

2010\07\09@222454 by RussellMc

face picon face
--000e0cd184fc84ea19048aff3982
Content-Type: text/plain; charset=ISO-8859-1

>> 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, ...

Micrometals download page here

    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
radius. Gargoyle knows.

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

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


Russell

--000e0cd184fc84ea19048aff3982
Content-Type: image/gif; name="L1000Ab300.gif"
Content-Disposition: attachment; filename="L1000Ab300.gif"
Content-Transfer-Encoding: base64
X-Attachment-Id: f_gbftr2c70
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--000e0cd184fc84ea19048aff3982
Content-Type: text/plain; charset="us-ascii"
MIME-Version: 1.0
Content-Transfer-Encoding: 7bit
Content-Disposition: inline

2010\07\09@224901 by RussellMc

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

                  www.micrometals.com/downloads/Toroid.zip

2010\07\10@080207 by Olin Lathrop

face picon face
> 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.

2010\07\10@082015 by Michael Watterson

face picon face
 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.

2010\07\10@085120 by RussellMc

face picon face
>> 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.

It's not obvious what your objections are to what's been asked.
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.
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.

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

2010\07\10@092556 by Michael Watterson

face picon face
 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".

2010\07\10@094253 by Adam Field

flavicon
face
>> 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.

2010\07\10@100919 by Michael Watterson

face picon face
 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.



2010\07\11@074206 by Peter Krengel

picon face
Hi Olin.

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

Thanks in advance
Peter



{Original Message removed}

2010\07\11@082355 by Michael Watterson

face picon face
 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?
>
> Thanks in advance
> Peter
>
Olin wrote earlier:

{Quote hidden}

I agree

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


2010\07\11@082738 by Olin Lathrop

face picon face
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.

2010\07\11@115328 by Marechiare

picon face
> do you have a program to calculate inductors
> saturation? If so where can I get it?
>
> Thanks in advance
> 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

2010\07\13@102800 by Peter

picon face
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


2010\07\13@114237 by Peter

picon face
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.

 http://omploader.org/vNHg0cg

-- Peter


2010\07\13@123332 by Adam Field

flavicon
face
> 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.
>
>  http://omploader.org/vNHg0cg

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

2010\07\13@123436 by Adam Field

flavicon
face
> 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.
>
>  http://omploader.org/vNHg0cg

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

2010\07\13@143035 by Peter

picon face
Adam Field <adam <at> badtech.org> writes:
> 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




2010\07\15@033356 by Peter

picon face
Adam, I posted my modest attempt in the LTspice mailing list and people
responded. One response is very elaborate (from .....analogKILLspamspam@spam@ieee.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

More... (looser matching)
- Last day of these posts
- In 2010 , 2011 only
- Today
- New search...