Wikipedia: threat or menace?

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

From an AARL publication:

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(and
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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:

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(and
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which references the AARL Handbook for Radio Communications) (AND
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d^2 * n^2 L = --------- 9d + 10l

With this function the calculation results in 31.6uH.

At

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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:

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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

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Uncle Steve
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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 :)

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Reply to
Jamie

for

(and

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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.

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

results

a

is

way

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

Reply to
P E Schoen

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

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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.

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.

Regards,

Uncle Steve

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Uncle Steve

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

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

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.

Regards,

Uncle Steve

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Uncle Steve

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

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Phil Hobbs

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.

Regards,

Uncle Steve

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

I found a pretty good overview of inductors and transformers here:

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Paul

Reply to
P E Schoen

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.

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John Larkin

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Why not just wind it and test it?
Reply to
John Fields

Calculator.phtml)

inductor-urself.html

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.

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Tim Wescott

=
a
t

re

n
t

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.

e quoted text -

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George Herold

--
d^2 = 2 * r^2
Reply to
John Fields

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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.

Regards,

Uncle Steve

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Uncle Steve

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).

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Reply to
Tim Wescott

Duh

Reply to
Jim Thompson

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.

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

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

Regards,

Uncle Steve

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Uncle Steve

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

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

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

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Jasen Betts

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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 
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John Fields

...Jim Thompson

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Small error in notation... 
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