Wikipedia: threat or menace?

[Uncle Steve]

So while reading up on air-core inductors I encountered three formulae
for calculating the inductance of cylindrical inductors.

>From an AARL publication:

http://www.arrl.org/files/file/Technology/tis/info/pdf/9708033.pdf
(and http://www.daycounter.com/Calculators/Air-Core-Inductor-Calculator.phtml)

d^2 * n^2 d = Diameter (in)
L = --------- n = Turns
18d + 40l l = length (in)

The coil I made last night was built on the basis of this function.
d = 1.15; l = 1.375; n = 24 which gives ~10uH


Then, Wikipedia:

http://en.wikipedia.org/wiki/Inductor
(and http://www.66pacific.com/calculators/coil_calc.aspx, which
references the AARL Handbook for Radio Communications)
(AND http://www.electronics-lab.com/blog/?p=2991)

d^2 * n^2
L = ---------
9d + 10l

With this function the calculation results in 31.6uH.


At http://www.eeweb.com/toolbox/coil-inductance/ is a calculator that
assumes the coils are adjacent. Fudging the wire diameter (1.375/24
= 0.573) results in 39.4uH. [The actual wire diameter is .03"].


Eventually I located this:
http://electronicsinfodesk.blogspot.ca/2011/12/how-to-make-air-core-inductor-urself.html

0.2 * a^2 * n^2 a = Diameter
L = --------------- b = Length
3a + 9b + 10c c = Wire diameter

Which for my inductor gives 9.45uH.



That's four (two, depending on how you count) different results from
several equations. Who's correct? It's all too common to read a
wikipedia article and assume it is more or less correct, but these
results are not encouraging for several reasons.

I don't know what a factor of 3 difference in inductance will mean to
a buck-converter circuit, but I suspect it is much more critical to
oscillators in RF circuits. I'm inclined to suspect the first formula
is correct since it closely matches the one directly above, but I have
no way of being sure about it.

In short, this sucks.


Regards,

Uncle Steve

--
There should be a special word in the English language to identify
people who create problems and then turn around and offer up their own
tailor-made bogus non-solutions designed to completely avoid the root
causes of the situation under consideration. 'Traitor' might be a
good choice, but lacks the requisite specificity. One of the problems
with contemporary English is it lacks many such words that would
otherwise categorically identify certain kinds of person, place, or
thing -- making it difficult or impossible to think analytically about
such objects. These shortcomings of the English lexicon are
representative of Orwellian linguistics at work in the real world.

[Jamie]

You need to look closer at the numbers,, some use CM and others use INCHES.

0.07(RN)^2
L = -----------
6R + 9l + 10b

d b
R = -- + --
2 2

N = number of Turns
d = core dia
b = coil buildup, inches
l = length, inches

That is a multlayer circuler air coil.

Long coil

u N^ A
L = -------
l

Short coil

u N^ A
L = -------
i + 0.45 d

L = H
u = permeability "4 * PI * 10^-7 " air
N = number of loops / turns
A = distance across the coil in m^2
l = length in m
d = dia in m

You need a chart for the u value..

I have more if interested :)

--
"I'd rather have a bottle in front of me than a frontal lobotomy"

"Daily Thought:

SOME PEOPLE ARE LIKE SLINKIES. NOT REALLY GOOD FOR ANYTHING BUT
THEY BRING A SMILE TO YOUR FACE WHEN PUSHED DOWN THE STAIRS.
http://webpages.charter.net/jamie_5"

[P E Schoen]

"Uncle Steve" wrote in message news:cd6e1b26ea...@gmail.com...

> So while reading up on air-core inductors I encountered three formulae for
> calculating the inductance of cylindrical inductors.

>> From an AARL publication:

> http://www.arrl.org/files/file/Technology/tis/info/pdf/9708033.pdf (and
> http://www.daycounter.com/Calculators/Air-Core-Inductor-Calculator.phtml)

> d^2 * n^2 d = Diameter (in)
> L = --------- n = Turns
> 18d + 40l l = length (in)

> The coil I made last night was built on the basis of this function.
> d = 1.15; l = 1.375; n = 24 which gives ~10uH


> Then, Wikipedia:

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

> d^2 * n^2
> L = ---------
> 9d + 10l

> With this function the calculation results in 31.6uH.

You got it wrong. It uses the radius (r) rather than diameter (d):

r^2 * n^2
L = ---------
9r + 10l

With that, I get 9.91 uH.

[snip]

I found a free calculator with which I got 10.94 uH.

http://www.lcbsystems.com/InduCalc.html

It also has a calculator for toroids, which includes various core materials.

> That's four (two, depending on how you count) different results from
> several equations. Who's correct? It's all too common to read a
> wikipedia article and assume it is more or less correct, but these results
> are not encouraging for several reasons.

> I don't know what a factor of 3 difference in inductance will mean to a
> buck-converter circuit, but I suspect it is much more critical to
> oscillators in RF circuits. I'm inclined to suspect the first formula is
> correct since it closely matches the one directly above, but I have no way
> of being sure about it.

> In short, this sucks.

These are rough estimate calculators. There are other factors such as the
size of the wire and the tightness of the coils. But the formulae agree
within about 10%, which is "close enough for government work". If you are
half serious about making your own inductors, you should get an LCR meter,
which can be had for $40 or so. It is a bit unusual to use an air core
inductor for a buck converter, and you can get a small ferrite core inductor
for $2 or so. You will probably need at least 50 kHz for a 3 amp switching
converter, which requires rather careful layout and wiring.

Paul

[Uncle Steve]

I verified the Wikipedia entry, and it explicitly states inches as the
units for the equation quoted above. Same with the first eqn from
ARRL. The calculator at www.eeweb.com allows you to pick your units,
which I did properly. So, no the problem described above is not with
the units. The AARL eqn specifies that it is valid for coils that are
0.4R or longer; the wikipedia entry only says it is for 'short
air-core cylindrical coil', and does not provide one for long coils.

Assuming 'u' quoted above is for air, A is the cross-sectional area
perpendicular to the coil axis, and that 'i' is actually 'l', I think
I get 38.8uH for my coil.

> I have more if interested :)

Presumably for different coil geometries? So far the values obtained
range from 10 - 60uH. All completely theoretical values, to boot.
What's happening here? I understand these equations are
approximations, but still, this is awesome.

[Uncle Steve]

On Sun, May 12, 2013 at 08:13:34PM -0400, P E Schoen wrote:
> "Uncle Steve" wrote in message news:cd6e1b26ea...@gmail.com...
>
> >So while reading up on air-core inductors I encountered three formulae for
> >calculating the inductance of cylindrical inductors.
>
> >>From an AARL publication:
>
> >http://www.arrl.org/files/file/Technology/tis/info/pdf/9708033.pdf (and
> >http://www.daycounter.com/Calculators/Air-Core-Inductor-Calculator.phtml)
>
> > d^2 * n^2 d = Diameter (in)
> >L = --------- n = Turns
> > 18d + 40l l = length (in)
>
> >The coil I made last night was built on the basis of this function.
> >d = 1.15; l = 1.375; n = 24 which gives ~10uH
>
>
> >Then, Wikipedia:
>
> >http://en.wikipedia.org/wiki/Inductor
>
> > d^2 * n^2
> >L = ---------
> > 9d + 10l
>
> >With this function the calculation results in 31.6uH.
>
> You got it wrong. It uses the radius (r) rather than diameter (d):
>
> r^2 * n^2
> L = ---------
> 9r + 10l

You're right; my bad. I don't do math often enough by a large amount,
but I should have noticed given the variance.

> With that, I get 9.91 uH.
>
> [snip]
>
> I found a free calculator with which I got 10.94 uH.
>
> http://www.lcbsystems.com/InduCalc.html
>
> It also has a calculator for toroids, which includes various core materials.

There's the Window's thing again. Not a big deal as my pencil and
notebook still works reasonably well when I'm careful.

> >That's four (two, depending on how you count) different results from
> >several equations. Who's correct? It's all too common to read a
> >wikipedia article and assume it is more or less correct, but these results
> >are not encouraging for several reasons.
>
> >I don't know what a factor of 3 difference in inductance will mean to a
> >buck-converter circuit, but I suspect it is much more critical to
> >oscillators in RF circuits. I'm inclined to suspect the first formula is
> >correct since it closely matches the one directly above, but I have no way
> >of being sure about it.
>
> >In short, this sucks.
>
> These are rough estimate calculators. There are other factors such as the
> size of the wire and the tightness of the coils. But the formulae agree
> within about 10%, which is "close enough for government work". If you are
> half serious about making your own inductors, you should get an LCR meter,
> which can be had for $40 or so. It is a bit unusual to use an air core
> inductor for a buck converter, and you can get a small ferrite core
> inductor for $2 or so. You will probably need at least 50 kHz for a 3 amp
> switching converter, which requires rather careful layout and wiring.

I didn't have to spend $6.00 and a couple hours to go shop for the
thing. Plus, making stuff by hand is soothing. Do you mind telling
me what that program said about the self-resonant frequency?

It is a little large... But the literature I've read says they don't
saturate when the current rises beyond the capacity of a ferrite core.
I suppose it doesn't matter so much for a low-capacity charger.

I'll have to read up on buck converters now to find out how they work.
As for layout, I suppose the main thing is keeping stray bits of metal
away from the ends where they might be heated or have currents
induced? I'll solder something up for this rather than use the
breadboard.

[Phil Hobbs]

The rules are summarized in NBS Publication C22 from about 1920. (My
copy is at the lab, or I'd post it.) The single-layer coil formula
L(uH) = a**2 * n**2 /(9*a + 10*b) with a, b in inches is good to about
1% if 'a' is the mean radius of the coil.

Cheers

Phil Hobbs

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

160 North State Road #203
Briarcliff Manor NY 10510 USA
+1 845 480 2058

hobbs at electrooptical dot net
http://electrooptical.net

[Uncle Steve]

Yeah, my bad. I just suck at math.

Tomorrow perhaps I will use a motor as a load and vary PWM frequency
and duty cycle to see what kind of output I get. Seems to me that a
buck converter should be really sensitive to load.

[P E Schoen]

"Uncle Steve" wrote in message news:211c681639...@gmail.com...

> I didn't have to spend $6.00 and a couple hours to go shop for the
> thing. Plus, making stuff by hand is soothing. Do you mind telling
> me what that program said about the self-resonant frequency?

About 62 MHz. Stray capacitance 0.59 pF. Wire length 91 inches. Max 16 AWG.

> It is a little large... But the literature I've read says they don't
> saturate when the current rises beyond the capacity of a ferrite core.
> I suppose it doesn't matter so much for a low-capacity charger.

> I'll have to read up on buck converters now to find out how they work.
> As for layout, I suppose the main thing is keeping stray bits of metal
> away from the ends where they might be heated or have currents
> induced? I'll solder something up for this rather than use the
> breadboard.

I found a pretty good overview of inductors and transformers here:
http://ludens.cl/Electron/Magnet.html
http://ludens.cl/Electron/trafos/trafos.html

Paul

[John Larkin]

A buck is not very load sensitive (ideally, not at all) as long as it's running
"continuous mode", which a synchronous converter always does, and a catch-diode
version does at higher load currents.

A synchronous buck is like a pair of gears. Its voltage ratio in one direction
is n (= duty cycle) and in the other it's 1/n. It works in both directions.


--

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

[John Fields]

On Sun, 12 May 2013 18:10:10 -0400, Uncle Steve <stev...@gmail.com>
wrote:

---
Why not just wind it and test it?

--
JF

[Tim Wescott]

The Wikipedia equation has substituted diameter for radius, into the
equation used in older copies of the ARRL handbook. If you observe that
d^2 = 4 * r^2, you can see that your first two equations are now
consistent.

A note sent to the Wikipedia editors would be helpful.

Note that all such equations are just approximations. In fact, they were
developed in the 1930's by Terman, by the simple expedient of winding up
a s**tload of coils and measuring their inductance. Precise numbers can
only be had either by a lot of very careful modeling using finite element
analysis, or some careful cut-and-try experimentation.

Note, too, that Terman's approximations are only good for a certain range
of aspect ratios of the coil (which range I can't remember, but I think
it encompasses a coil whose diameter:length ratio is 1:1). When you get
much outside of the given range, your approximation falls apart.

--
Tim Wescott
Control system and signal processing consulting
www.wescottdesign.com

[George Herold]

On May 13, 12:01 pm, Tim Wescott <t...@seemywebsite.please> wrote:
> On Sun, 12 May 2013 18:10:10 -0400, Uncle Steve wrote:
> > So while reading up on air-core inductors I encountered three formulae
> > for calculating the inductance of cylindrical inductors.
>
> >>From an AARL publication:
>
> >http://www.arrl.org/files/file/Technology/tis/info/pdf/9708033.pdf(and
> >http://www.daycounter.com/Calculators/Air-Core-Inductor-
> Calculator.phtml)
>
> >     d^2 * n^2    d = Diameter (in)
> > L = ---------    n = Turns
> >     18d + 40l    l = length (in)
>
> > The coil I made last night was built on the basis of this function.
> > d = 1.15; l = 1.375; n = 24   which gives ~10uH
>
> > Then, Wikipedia:
>
> >http://en.wikipedia.org/wiki/Inductor(and
> >http://www.66pacific.com/calculators/coil_calc.aspx, which references
> > the AARL Handbook for Radio Communications)

> > (ANDhttp://www.electronics-lab.com/blog/?p=2991)

>
> >     d^2 * n^2
> > L = ---------
> >     9d + 10l
>
> > With this function the calculation results in 31.6uH.
>

> > Athttp://www.eeweb.com/toolbox/coil-inductance/is a calculator that

I always go back to my freshman physics book. (Halliday and Resnick)
You can do the case of a thin coil (say a single turn) and also the
case of a very long coil.
(hmm I think for a single turn case, I'd have to assume that the B
field is constant across the area of the coil.. or solve for it
exaclty which would take me beyond freshman physics.)

Paging through Terman's book he claims the above formula is good to
~1%
for low frequencies and L > 0.8R (L = length, R = radius)

George H.
>
> --
> Tim Wescott
> Control system and signal processing consultingwww.wescottdesign.com- Hide quoted text -
>
> - Show quoted text -- Hide quoted text -
>
> - Show quoted text -

[John Fields]

On Mon, 13 May 2013 11:01:49 -0500, Tim Wescott
<t...@seemywebsite.please> wrote:


>The Wikipedia equation has substituted diameter for radius, into the
>equation used in older copies of the ARRL handbook. If you observe that
>d^2 = 4 * r^2, you can see that your first two equations are now
>consistent.

---
d^2 = 2 * r^2

--
JF

[Uncle Steve]

That is today's little project. I just wanted to read a bit about
inductors so I would be mostly clueless instead of completely
clueless.

[Tim Wescott]

Excuse me please? Diameter is now equal to root 2 times radius?

I think not!

d = 2 * r. d^2 = (2 * r)^2 = 2^2 * r^2 = 4 * r^2.

QED

(I'm not sure how quantum electrodynamics gets into mathematical proofs,
or, for that matter, how it's been there for centuries when QED was only
formulated in the mid 20th century. Feynmann's just awesome, I guess).

--
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

[Jim Thompson]

On Mon, 13 May 2013 11:47:18 -0500, John Fields

Duh <:-(

...Jim Thompson
--
| James E.Thompson | mens |
| Analog Innovations | et |
| Analog/Mixed-Signal ASIC's and Discrete Systems | manus |
| Phoenix, Arizona 85048 Skype: Contacts Only | |
| Voice:(480)460-2350 Fax: Available upon request | Brass Rat |
| E-mail Icon at http://www.analog-innovations.com | 1962 |

I love to cook with wine. Sometimes I even put it in the food.

[Uncle Steve]

So I can demonstrate my corroded math skills to two groups?

As much as I like to be flamed, there is a concept called 'too much of
a good thing' which might apply here.

> Note that all such equations are just approximations. In fact, they were
> developed in the 1930's by Terman, by the simple expedient of winding up
> a s**tload of coils and measuring their inductance. Precise numbers can
> only be had either by a lot of very careful modeling using finite element
> analysis, or some careful cut-and-try experimentation.

Brute force always works, but damn is it time-consuming.

> Note, too, that Terman's approximations are only good for a certain range
> of aspect ratios of the coil (which range I can't remember, but I think
> it encompasses a coil whose diameter:length ratio is 1:1). When you get
> much outside of the given range, your approximation falls apart.

I read it is valid for 10:1 to 2.5:1 diameter/length ratio and larger.

[Jasen Betts]

On 2013-05-13, Tim Wescott <t...@seemywebsite.please> wrote:
> On Sun, 12 May 2013 18:10:10 -0400, Uncle Steve wrote:

>> http://www.arrl.org/files/file/Technology/tis/info/pdf/9708033.pdf (and
>> http://www.daycounter.com/Calculators/Air-Core-Inductor-Calculator.phtml)

>> d^2 * n^2 d = Diameter (in)
>> L = --------- n = Turns
>> 18d + 40l l = length (in)

>> Then, Wikipedia:

>> d^2 * n^2
>> L = ---------
>> 9d + 10l
>>

wikipedia (lasted edited 9 may) actually says 'r' (radius) instead of 'd'

> The Wikipedia equation has substituted diameter for radius, into the
> equation used in older copies of the ARRL handbook. If you observe that
> d^2 = 4 * r^2, you can see that your first two equations are now
> consistent.

I could't find that on the "inductor" page (lasted edited 9 may)

> A note sent to the Wikipedia editors would be helpful.

Did you know that you can edit that page? :)


--
⚂⚃ 100% natural

--- news://freenews.netfront.net/ - complaints: ne...@netfront.net ---

[John Fields]

On Mon, 13 May 2013 13:02:28 -0500, Tim Wescott <t...@seemywebsite.com>

wrote:

>On Mon, 13 May 2013 11:47:18 -0500, John Fields wrote:
>
>> On Mon, 13 May 2013 11:01:49 -0500, Tim Wescott
>> <t...@seemywebsite.please> wrote:
>>
>>
>>>The Wikipedia equation has substituted diameter for radius, into the
>>>equation used in older copies of the ARRL handbook. If you observe that
>>>d^2 = 4 * r^2, you can see that your first two equations are now
>>>consistent.
>>
>> ---
>> d^2 = 2 * r^2
>
>Excuse me please? Diameter is now equal to root 2 times radius?
>
>I think not!
>
>d = 2 * r. d^2 = (2 * r)^2 = 2^2 * r^2 = 4 * r^2.
>
>QED

---
Well, my notation wasn't clear; it should have been: d^2 = (2r)^2.

I think the error is in your arithmetic, where you squared the
multiplier and the multiplicand (2 * r) when you should have squared
the product.

Considering that a circle with a diameter of 2" has a radius of 1",
then, if d = 2r and d^2 = (2 * r), d^2 = (2 * 1")^2 = 4.

If, however, for the same circle you say: d^2 = (4r)^2,
then d^2 = (4 * 1")^2, which is 16, so one of them must be wrong.

Which one, please?

--
JF

[John Fields]

On Mon, 13 May 2013 11:12:14 -0700, Jim Thompson
<To-Email-Use-Th...@On-My-Web-Site.com> wrote:

>On Mon, 13 May 2013 11:47:18 -0500, John Fields
><jfi...@austininstruments.com> wrote:
>
>>On Mon, 13 May 2013 11:01:49 -0500, Tim Wescott
>><t...@seemywebsite.please> wrote:
>>
>>
>>>The Wikipedia equation has substituted diameter for radius, into the
>>>equation used in older copies of the ARRL handbook. If you observe that
>>>d^2 = 4 * r^2, you can see that your first two equations are now
>>>consistent.
>>
>>---
>>d^2 = 2 * r^2
>
>Duh <:-(
>
...Jim Thompson

---
:-)

Small error in notation...

d^2 = (2 * r)^2 or,

d² = (2r)²

--
JF