Brooks 1931 paper on inductance design

Excellent.

Thanks!

--Winston

No problem. You brought up the subject and I didn't mind seeing if I could find the seminal paper on the topic. I got lucky and figured I'd share the link.

I'm actually going through the steps required to better understand electromagnetic fields (gradients, divergence, curl, and operator calculus and Lagrangians, plus special theory of relativity as it relates to all this.) This feeds into self-inductance and energy in simplified cases, which many inductor forms come close enough as to be analyzable without going crazy in math. So it actually was a good time for me to look this up, too. So thanks back to you for that.

Jon

Clearly this stuff holds the same fascination for you as it does for me. It's just that you are operating at about 7 orders of magnitude greater 'informational resolution' than I am.

I appreciate the information.

Please say 'hi' to Algernon for me. :)

--Winston

Not likely. You are interested in this stuff so that probably means we aren't far apart.

The web link is interesting to read, but dry.

The concepts I mentioned above are quite easily read in Feynman's Physics Lectures, volume 2, chapters 2 and 3 for the most part. Actually, he (or his grad students) does a creditable job taking it slow and easy through the concept of scalar and vector fields and gradients and the rest.

I think most anyone would get it, especially if they had some calculus under their belt -- though that isn't strictly speaking entirely necessary to get at least some points across well.

Understanding scalar fields is nothing more than understanding elevation lines on a topographic map, really. Vector fields is no more than "seeing" the downhill/uphill directions on that same topographic map and where it is steeper and where it is less so. If you can handle that much in reading such maps, you've pretty much got most of what's needed in order to follow those chapters and segue into electromagnetic field theory.

It's not nearly as bad as it sounds, at first.

Then it is mostly learning to recognize a few useful tools and apply them.

Hehe.

Jon

In interest in the subjects, yes.

I skimmed it just now. I will have to read it carefully.

It's refreshing to see methodical, precise exposition, though I wish Google's document scanner had been more careful avoiding linearity errors on the edges of the pages. It's jarring. We like to make the obvious difficult, apparently.

Pity the word 'Electrotechnics' didn't catch the popular imagination. :)

I see that the nist.gov site does not admit ever hearing about H. B. Brooks.

The Physics Lectures were 'way over my head. I'm still waiting for the primer _Feynman for Dummies_.

I will look at _Six Easy Pieces_.

It couldn't be. :)

--Winston

Hi Jon, Did you have to download the whole 75 Meg to get the few pages you wanted or is there a trick I'm missing.

This is sort of fun. The question is not to get the maximum inductance from a given length of wire, but to get the longest time constant, L/R. (At least that's the way I read the beginning of the article.) Is that right?

George H.

Yeah. But luckily, I download at the rate of 10M byte per second, if the other site can go that fast and the network isn't overloaded, so I seem to recall it loaded in less than a minute. (My link is a near-commercial 80M bit fiber link.)

That's how I read it, as well. Or getting as much L for as little R as possible.

I haven't yet read the 1931 paper -- only very quickly skimmed it long enough to see the same goal you mention above. But the maximum time constant occurs at some curve peak, which means the derivative must be zero there. Which is why, I think, another comment I read (that the exact construction isn't as important because slight changes don't impact it much) makes sense, too.

Being ignorant, but just thinking this through, I start with:

d(L/R) = (R dL - L dR) / R^2 = 0

And arrive at:

L/R = dL/dR

There the rate of change in L versus the rate of change in R is equal to the existing time constant.

But maybe I need to think about this more and read the paper, too.

Jon

Hmm, I made a mistake. ("What, again?") If you are trying to maximize the time constant for a given wire length, tau=3D L/R, then this is the same as trying to maximize L, (because R is fixed by the wire length.)

And I thought that the maximum inductance for a given length of wire is achieved with one big loop. (But I've been trying to check this....I was looking for the inductance of a single loop of wire, but I couldn't find it quickly, ....)

OK how about this, (~ =3D proportional to) L ~ N*flux B, N =3D #turns.

Now B for a single turn ~ 1/R (R is radius of the coil.) and for N turns, B ~ N*1/R. But N ~ 1/R, so B ~ 1/R^2.

Then L ~ N*Area*B ~ 1/R * R^2 * 1/R^2. And it looks like L ~ 1/R. I'm going to have to check this with a piece of wire and an inductance bridge.

George H.

OK here are some numbers. I used 25 inches of magnet wire daimter =3D0.05" All tests done at 10kHz with SR720 LCR meter.

Num turn L (uH)

Plotting this vs 1/N does not look very much like a straight line. But at least inductance went up with more turns.

George H.

A 1986 paper was published in the Proceedings of the IEE that deals with the Brooks coil further.

I've posted it on alt.binaries.schematics.electronic.

Anybody who wants to accurately calculate inductances of various geometries should have this book:

Steve Moshier has created a small program that uses the very accurate formulas from the Bureau of Standards papers:

Another web site uses the same program:

(Information, cites)

Whoa, more cool resources! Thanks, Phantom!

--Winston

Sadly, I've no access to it anymore (Verizon dumped it.) Any chance you might consider sending it, directly?

Jon

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Excellent Thanks,

George

Is the email address in the header good to use? If not, post the one you want me to use.

Yes, it's fine. My address is open and correct.

Thanks, Jon

Watch your inbox, Jon.

--Winston