Inductance Equations using SI Units

[chiron613]

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.

--
Hoare's Law of Large Problems:
Inside every large problem is a small problem struggling to get
out.

 

[Ian Field]

"chiron613" <chiron613@NOSPAM.gmail.com> wrote in message
news:20120606123653.18ef13fa@UL80JT...

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.

When I googled "inductance calculator + si units", I eventually navigated to
this:


http://www.technick.net/public/code/cp_dpage.php?aiocp_dp=util_inductance_circle

 

[chiron613]

On Wed, 6 Jun 2012 18:53:35 +0100
"Ian Field" <gangprobing.alien@ntlworld.com> wrote:

snip


When I googled "inductance calculator + si units", I eventually
navigated to this:


http://www.technick.net/public/code/cp_dpage.php?aiocp_dp=util_inductance_circle

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.

--
Cutler Webster's Law:
There are two sides to every argument, unless a person
is personally involved, in which case there is only one.

 

[John Larkin]

On Wed, 6 Jun 2012 12:36:53 -0500, chiron613
<chiron613@NOSPAM.gmail.com> wrote:

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.

googling solenoid equation meters seems pretty good.


--

John Larkin Highland Technology, Inc

jlarkin at highlandtechnology dot com
http://www.highlandtechnology.com

Precision electronic instrumentation
Picosecond-resolution Digital Delay and Pulse generators
Custom laser drivers and controllers
Photonics and fiberoptic TTL data links
VME thermocouple, LVDT, synchro acquisition and simulation

 

[Rich Webb]

On Wed, 6 Jun 2012 13:57:26 -0500, chiron613
<chiron613@NOSPAM.gmail.com> wrote:

On Wed, 6 Jun 2012 18:53:35 +0100
"Ian Field" <gangprobing.alien@ntlworld.com> wrote:


snip


When I googled "inductance calculator + si units", I eventually
navigated to this:


http://www.technick.net/public/code/cp_dpage.php?aiocp_dp=util_inductance_circle



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. ;-)

--
Rich Webb Norfolk, VA

 

[George Herold]

On Jun 6, 2:57 pm, chiron613 <chiron...@NOSPAM.gmail.com> wrote:

On Wed, 6 Jun 2012 18:53:35 +0100



"Ian Field" <gangprobing.al...@ntlworld.com> wrote:

snip

When I googled "inductance calculator + si units", I eventually
navigated to this:

http://www.technick.net/public/code/cp_dpage.php?aiocp_dp=util_induct....

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.

--
Cutler Webster's Law:
        There are two sides to every argument, unless a person
        is personally involved, in which case there is only one.

If it's a long solenoid then you can get a guesstimate from physics.

L*i = N*flux. (N= number of turns) For a long solenoid the B field
is roughly constant. B~ mu(sub zero)*i*N/L (where L is the coil
length) (MKS units)
So the flux is B*A (A is the area of the coil). Putting it all
together,

L = mu(sub zero) * N^2 * A/L

For a single loop there should be another (simple) solution, but the
integral will be a lot harder. (There's an equation in Terman that I
could quote.... It happens to be sitting on my desk.) A page down on
here looks like the same equation.

www.thompsonrd.com/induct2.pdf

George H.

 

[chiron613]

On Wed, 06 Jun 2012 12:08:38 -0700
John Larkin <jlarkin@highlandtechnology.com> wrote:


<snip>

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.

--
One of the most striking differences between a cat and a lie is that a
cat has only nine lives.
-- Mark Twain, "Pudd'nhead Wilson's Calendar"

 

[Jamie]

chiron613 wrote:

On Wed, 06 Jun 2012 12:08:38 -0700
John Larkin <jlarkin@highlandtechnology.com> wrote:


snip



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.

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

 

[Tim Wescott]

On Wed, 06 Jun 2012 15:25:15 -0400, Rich Webb wrote:

On Wed, 6 Jun 2012 13:57:26 -0500, chiron613
chiron613@NOSPAM.gmail.com> wrote:

On Wed, 6 Jun 2012 18:53:35 +0100
"Ian Field" <gangprobing.alien@ntlworld.com> wrote:


snip


When I googled "inductance calculator + si units", I eventually
navigated to this:


http://www.technick.net/public/code/cp_dpage.php?
aiocp_dp=util_inductance_circle



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. ;-)

Lessee. 18 / 25.4 = oh, this is too complicated.

--
My liberal friends think I'm a conservative kook.
My conservative friends think I'm a liberal kook.
Why am I not happy that they have found common ground?

Tim Wescott, Communications, Control, Circuits & Software
http://www.wescottdesign.com

 

[chiron613]

On Wed, 06 Jun 2012 22:29:35 -0400
Jamie <jamie_ka1lpa_not_valid_after_ka1lpa_@charter.net> wrote:

<snip>

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.

--
Happiness is good health and a bad memory.
-- Ingrid Bergman

 

[Fred Abse]

On Wed, 06 Jun 2012 22:29:35 -0400, Jamie wrote:

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.

--
"For a successful technology, reality must take precedence
over public relations, for nature cannot be fooled."
(Richard Feynman)

 

[Fred Abse]

On Thu, 07 Jun 2012 01:06:56 -0500, chiron613 wrote:

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.

--
"For a successful technology, reality must take precedence
over public relations, for nature cannot be fooled."
(Richard Feynman)

 

[George Herold]

On Jun 6, 10:29 pm, Jamie
<jamie_ka1lpa_not_valid_after_ka1l...@charter.net> wrote:

chiron613 wrote:
On Wed, 06 Jun 2012 12:08:38 -0700
John Larkin <jlar...@highlandtechnology.com> wrote:

snip

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.

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 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
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.

George H.

  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- Hide quoted text -

- Show quoted text -

 

[chiron613]

On Thu, 07 Jun 2012 06:07:05 -0700
Fred Abse <excretatauris@invalid.invalid> wrote:

On Thu, 07 Jun 2012 01:06:56 -0500, chiron613 wrote:

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.

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...

--
An Italian is COMBING his hair in suburban DES MOINES!

 

[chiron613]

On Thu, 7 Jun 2012 08:04:48 -0700 (PDT)
George Herold <gherold@teachspin.com> wrote:

On Jun 6, 10:29 pm, Jamie
jamie_ka1lpa_not_valid_after_ka1l...@charter.net> wrote:
chiron613 wrote:
On Wed, 06 Jun 2012 12:08:38 -0700
John Larkin <jlar...@highlandtechnology.com> wrote:

snip

  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 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

--
Kindness is a language which the deaf can hear and the blind can read.
-- Mark Twain

 

[Tim Wescott]

On Wed, 06 Jun 2012 15:25:15 -0400, Rich Webb wrote:

On Wed, 6 Jun 2012 13:57:26 -0500, chiron613
chiron613@NOSPAM.gmail.com> wrote:

On Wed, 6 Jun 2012 18:53:35 +0100
"Ian Field" <gangprobing.alien@ntlworld.com> wrote:


snip


When I googled "inductance calculator + si units", I eventually
navigated to this:


http://www.technick.net/public/code/cp_dpage.php?
aiocp_dp=util_inductance_circle



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. ;-)

This works if you put the "18" and "40" into units of inches/henry, then
convert to millimeters:

L = (d^2 * n^2) / ((475 mm/H)*d + (1016 mm/H)*l)

Or with meters:

L = (d^2 * n^2) / ((0.475 m/H)*d + (1.016 m/H)*l)

Or if you want to be demented about units:

L = (d^2 * n^2) / ((0.475 A^2/N)*d + (1.016 A^2/N)*l)

(Where, as any school child can figure out in a matter of seconds, one
amp squared per Newton is, of course, one meter per Henry)

--
My liberal friends think I'm a conservative kook.
My conservative friends think I'm a liberal kook.
Why am I not happy that they have found common ground?

Tim Wescott, Communications, Control, Circuits & Software
http://www.wescottdesign.com