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Inductance Equations using SI Units

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chiron613

Jan 1, 1970
0
I've been planning to wind some coils. I want to get an idea of what
sort of inductance I'd get for a given winding, coil diameter and
length, and so on. These are all air-core, so I don't need to take
into account the effects of iron.

When I Google for information, I seem to get the same few formulas,
none of which are in SI units. I can find equations and formulas that
use inches, or that (apparently) were based on the CGS system; but
nothing that uses SI units.

Can anyone point me to a source of equations that stick with SI units?
Either a link or a reference to a book would be great - or even the
proper search terms to use with Google.
 
R

Rich Webb

Jan 1, 1970
0
Thanks, Ian. What I was looking for, though, were some equations or
formulas. I don't learn much from a calculator, and I don't really
have a good way to even know whether it's accurate. But I appreciate
your response.

This is also not the DIY equations that you're looking for but there's a
handy Windows calculator over at
<http://www.dl5swb.de/html/mini_ring_core_calculator.htm>

For the DIY question, the ARRL Handbook is a great resource but it's
very ... inchy. I can't reproduce all of the goodies, but for your basic
single layer air-core inductor, try
L = (d^2 * n^2) / (18 * d + 40 * l)
where L is in micro-henries, d is diameter of the winding circle (center
of wire to center of wire), l is inductor length, and n is the number of
turns, where length is >= 0.4 * d. And of course, it's all in inches.
Unit conversion left as an exercise, or something. ;-)
 
C

chiron613

Jan 1, 1970
0
On Wed, 06 Jun 2012 12:08:38 -0700


googling solenoid equation meters seems pretty good.

Rich, George, and John, thanks for the ideas. It looks like I'm going
to have to suck it up and do the conversions. I hesitate to do that,
because I often multiply when I should divide (or vice versa), and wind
up with something like furlongs per fortnight as units.
 
J

Jamie

Jan 1, 1970
0
chiron613 said:
On Wed, 06 Jun 2012 12:08:38 -0700


<snip>





Rich, George, and John, thanks for the ideas. It looks like I'm going
to have to suck it up and do the conversions. I hesitate to do that,
because I often multiply when I should divide (or vice versa), and wind
up with something like furlongs per fortnight as units.
I don't think many of us understand exactly what you're looking for? At
least I am a bit confused, if not for others here ;)

Doing induction calculations seems to be a black art it seems. For
years i've seen a variation of formula's to represent the value of a
coil once all the data is known.

For example..

In a long single coil, a formula of this type is used and there are
others, too.

u n^ A
L =---------
l

L = uH

u = permeability of air, some where around 1.26-05

A = cross section area of the coil in "m"^

l = Length of the coil in "m"

N = number of turns^

And now for the big HOWEVER>

If you were doing magnetic cores..
the math changes just a little.

0.012 n^ u A
L =-------------
Lc

In this case, the "u" permeability for air is 1.0

Note the constant 0.012? This was from a formula I got some where, it
was a note slide in one of my books that is so old it's turning yellow.

and "A" cross section area is now cm^ not "m"

and Lc is your magnetic size of the field, the physical length of it,
which can extend a bit depending on the form you're on.

I also have some math for inches.

Like I said, it's a black art. for the last few months I've been playing
around with a concept that involves using reluctance alterations to
monitor surface changes. This has forced me to dig out some older
references in my library.

It seems the internet is becoming a junk yard and is hard to find a
agreed method of doing certain things, like this for example.

Jamie
 
C

chiron613

Jan 1, 1970
0
On Wed, 06 Jun 2012 22:29:35 -0400

I don't think many of us understand exactly what you're looking for?
At least I am a bit confused, if not for others here ;)
OK, it's pretty simple. I can find all manner of equations, formulas,
calculators, etc., that calculate inductance but that use non-SI units
such as inches, feet, pounds (or whatever).

Of course I could just convert the various values into SI units, but...
it's a pain, and I tend to mix things up a bit and reverse the
calculations I should be doing (multiply when I should divide, etc.).

Doing induction calculations seems to be a black art it seems. For
years i've seen a variation of formula's to represent the value of a
coil once all the data is known.
Same here. To my understanding, the actual calculations (accurate
ones) require diffeq's. In order to simplify, accuracy is sacrificed
and they come up with various approximations that work under a certain
set of conditions (long solenoid; coil with thickness << than diameter;
single layer of turns, etc.).

Hmm... your math below came out kind of funny-looking in my reader. I
One equation looks like:

u n^ A
L=-----------
l

I assume the ^ should be indicating that n is squared?
For example..

In a long single coil, a formula of this type is used and there are
others, too.

u n^ A
L =---------
l

L = uH

u = permeability of air, some where around 1.26-05

A = cross section area of the coil in "m"^

l = Length of the coil in "m"

N = number of turns^

And now for the big HOWEVER>

If you were doing magnetic cores..

I don't know what you mean by magnetic cores. Do you mean using cores
that contain iron, that would affect the inductance?

the math changes just a little.

0.012 n^ u A
L =-------------
Lc

In this case, the "u" permeability for air is 1.0

Note the constant 0.012? This was from a formula I got some where, it
was a note slide in one of my books that is so old it's turning
yellow.

and "A" cross section area is now cm^ not "m"

and Lc is your magnetic size of the field, the physical length of it,
which can extend a bit depending on the form you're on.

I also have some math for inches.

Like I said, it's a black art. for the last few months I've been
playing around with a concept that involves using reluctance
alterations to monitor surface changes. This has forced me to dig out
some older references in my library.

It seems the internet is becoming a junk yard and is hard to find a
agreed method of doing certain things, like this for example.

You're right about that. Back in the olden days (when I was learning
this stuff) the problem was a lack of information. You had to either
have it in books at home, or go to the library or school for it.

Now there is an endless amount of information, but so much of it is
crap that you've got to sort through lots of chaff to find the wheat.
Way too much information, often unreliable, and too much to process in
a reasonable time.

Ah, well. Thanks for your ideas. Maybe I'll eventually figure this
out somehow. Or I *could* just wind the stupid coils and measure the
inductance, and try to figure out a relationship myself.
 
F

Fred Abse

Jan 1, 1970
0
Like I said, it's a black art. for the last few months I've been playing
around with a concept that involves using reluctance alterations to
monitor surface changes. This has forced me to dig out some older
references in my library.

At least SI units have got rid of a lot of pi ;-)

When I started it was CGS, then we had to change to MKS, then to
"Rationalized" MKS, then SI.
It seems the internet is becoming a junk yard and is hard to find a
agreed method of doing certain things, like this for example.

It has already become a junkyard, not helped by search engines that seem
to make up their own mind about what it is you're looking for, with
"advanced" searches that just plain don't work. A good proportion of the
"information" out there is seriously flawed, anyway. Give me a good old
fashioned textbook.
 
F

Fred Abse

Jan 1, 1970
0
Ah, well. Thanks for your ideas. Maybe I'll eventually figure this out
somehow. Or I *could* just wind the stupid coils and measure the
inductance, and try to figure out a relationship myself.

Look for the Ferrite Magnetic Design Tool from Epcos. It really works, for
their cores, obviously.
 
C

chiron613

Jan 1, 1970
0
Look for the Ferrite Magnetic Design Tool from Epcos. It really
works, for their cores, obviously.

Thanks, Fred. Actually, I was only going to use air-core coils, but
I'll file this away for future reference. If I can *find* it when I
need it, of course...
 
C

chiron613

Jan 1, 1970
0
For coils with no magnetic material, it's mostly freshman Physics.
(Didn't you keep your text book?) The N*flux(B) = L*i is like the

I kept all my books; but had a fire that took everything I had. Kind
of like an enforced spring cleaning. By that time I had about 2000
books, which made moving a *HUGE* pain. Suddenly, it became quite
easy, so I'm not complaining.
Q=C*V formula. It's some geometrical constant. It's sometimes useful
to also think about inducatnce in terms of energy. The energy in a
coil is 1/2L*i^2 and this is equal to the magnetic energy density
( B^2 /(2* mu(sub zero)) integrated over all space. Most of the time
a messy integral, but it helps sometimes when thinking about how the
inductance will change.
Thanks. That should be helpful... I'll need to review the math,
though, since I don't remember much of it. I've got more books now, so
this shouldn't be too difficult.

Thanks.
George H.
<snip>
 
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