Inductor calculation?

I am trying to calculate the inductance of a multi-row, multi-layer air-core coil that has a square winding cross section, zero magnetic coupling to any other object.

Conceptually, it's a Brooks Coil, like you might use in a metal detector.

Of the internet and hard copy resources I've used, no two equations produce nearly the same results.

I've gotten everything from 219 mH on down to 2.2 pH.

One equation appeared to produce a result of *negative* 2.2nH! What is that, a capacitor? :)

Can you point me to an equation that correctly predicts the inductance of a Brooks Coil please?

--Winston

Reply to
Winston
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the first hit I got when I googled: "Brooks coil" was:

http://www.nessengr.com/techdata/brooks/brooks.html
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Reply to
John Fields

The inductance of an ideal coil is relatively easy to calculate.

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Make sure you know the difference between relative and absolute permeability as this could change the results drastically.

If your coil is not solenoid like then the results could be different.

Reply to
Jeff Johnson

Further searching produced results from three different equations that are within the same order of magnitude. This will do.

199 mH 153 mH 219 mH

Yup. Those yielded results that appear to be off a little. eq. 1 = 8.2 mH eq. 2 = 48.5 mH

I will do that now. I really like to have a good idea of what to expect before I hack together a prototype.

Now I suspect which watches were broken, I can toss them overboard. :)

Thanks!

--Winston

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Corporate executive forgets to commit a felony for 24 hours.
Film at 11.
Reply to
Winston

(...)

as this could change the results drastically.

Thanks, Jeff.

The hyperphysics site cite appears to provide 'single layer' results, so my input predicated on multiple layers produces an inductance that is somewhat higher than seems reasonable.

I now have results from three other equations that appear to match within reasonable tolerances.

Emergency over.

I appreciate your time.

--Winston

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Corporate executive forgets to commit a felony for 24 hours.
Film at 11.
Reply to
Winston

But like he said, make one, measure it, and that reinforces the calculation. Do it sloppily, or do just a partial wind, to get an idea of where it will go in the end product.

Michael

Reply to
Michael Black

Even the watch that isn't running is right twice a day. ;-)

CHeers! Rich

Reply to
Rich Grise

(...)

where it will go in the end product.

I see your point.

Thanks!

--Winston

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Corporate executive forgets to commit a felony for 24 hours.
Film at 11.
Reply to
Winston

My broken digital watch indicates 'no time'.

It is *always* accurate. :)

--Winston

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Corporate executive forgets to commit a felony for 24 hours.
Film at 11.
Reply to
Winston

I'd always thought of the Brooks coil as being that coil which maximizes inductance for a given length of wire. Which may be important for metal detectors... but I wouldn't know about that.

Which seems odd to me. The Brooks' criteria is that the cross section of the winding is square and the mean radius is about (3/2) of one side of that square.

The inductance value doesn't change a lot if the actual values are a little off, though. So it's not critical. I'd guess this is what you'd expect for any equation near a max or min, since at that point the slope should be close to zero. Since the Brooks coil is supposed to be a maximum... that fits.

It might be nice if you'd have stated the details. Are you paying enough attention to units or what they specify when reading about the formulas and applying them? I note that the two figures you give, above, have the exact same significant figures when taken to two places... 2.2. This is suggests that you are mixing up things like centimeters and meters. In any case, pH must be wrong.

Since the Brooks criteria set up a fixed relationship between the magnetic cross-section area and the winding, that (3/2) thing I mentioned above, the formulas I've seen simplify down to two ways of looking at it. You can either specify the side of the square of the coil winding's cross-section, which then specifies the mean radius, or else you can specify the mean radius and get the reverse.

If L is in micro-Henries and you specify the values of either the mean radius (r) or else the length of a full side of the coil (c) in centimeters, then:

L = 0.025491 * c * N^2 L = 0.016994 * r * N^2

That seems to be consistent from several sources I looked at, anyway. What did you find?

[The reason for figuring a Brooks coil as being wound square is that the square keeps the average distance between turns to a near-minimum (although, technically, while a circular cross section may be even better it is also harder to make.)]

Jon

Reply to
Jon Kirwan

where it will go in the end product.

If your general design fits the form factor for a Brooks arrangement, slight changes here and there should not matter much. This is a maximum inductance thing, which means the inductance vs dimensions curve is at zero slope at the peak. Which suggests that slight changes won't matter much.

That's relative change. Obviously, absolute value still remains to be something to check out.

Jon

Reply to
Jon Kirwan

:I am trying to calculate the inductance of a :multi-row, multi-layer air-core coil that :has a square winding cross section, zero :magnetic coupling to any other object. : :Conceptually, it's a Brooks Coil, like you :might use in a metal detector. : :Of the internet and hard copy resources I've :used, no two equations produce nearly the same :results. : :I've gotten everything from 219 mH :on down to 2.2 pH. : :One equation appeared to produce a result :of *negative* 2.2nH! What is that, a :capacitor? :) : : :Can you point me to an equation that correctly :predicts the inductance of a Brooks Coil :please? : : :--Winston

Reply to
Ross Herbert

(...)

Ah! That is the key. I didn't know that the mean radius was critical. When I set it to 1.5 x of one side, the arithmetic became internally consistent between the two approaches and the results are believable.

Clearly I needed a different equation that describes the inductance of a multi-row, multi-layer *non*-Brooks air core inductor. One that has a mean radius that is more like 4 x one side.

The three different equations I later stumbled across appear to fill that bill satisfactorily because they supplied very similar results.

Now I have the confidence necessary to wind some copper.

(...)

Easily done! My source for the Brooks equations failed to emphasize centimeters *or* the need to hold R = C x 1.5!

I agree. That result came from a stunningly Byzantine equation that had a couple random looking fudge - factors. Without a worked example, I was almost *bound* to get the wrong answer.

Excellent info.

Thanks for the education, Jon.

--Winston

Reply to
Winston

(...)

Yup.

I misunderstood the proper units and was unaware of all the criteria that defines the Brooks geometry.

I now have three equations that produce consistent, believable results for my non-Brooks inductor.

Thanks again.

--Winston

Reply to
Winston

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That program will help me confirm results from my other equations. A tiny nit is that I can't use it to determine inductance, given the physical constraints of the coil.

That sounds a little funny, but I can easily use an inductor of just about any reasonable value, I just needed to know what that value was likely to be.

It is a very useful program and I thank you.

--Winston

Reply to
Winston

I have used the above calculator to figure a 240uh Brooks inductor,

1" x 1" with 64 turns, is 265 uh. This requires a #8 wire making it difficult to make, but would require only 9 feet of wire. In comparison, I have a single layer 240uh coil that is 4-1/2" by 4-1/2" with 56 turns. The turns are spaced 1 wire width apart and uses #18 wire. This required 75 feet of wire. The important characteristic I'm trying to minimize is Q. The Brooks coil would have about 1/8 as much wire reducing resistance and ignoring (uh) other losses would increase Q. Might be interesting to wind this with 2700 strands of #46 litz wire. (.114" dia.) Equal to a #12 wire. Wonder what the bending radius is? With the close wire spacing capacitance would go up, however much less area (less wire) is in effect to make the capacitance so maybe it won't be a problem. Any comments? MikeK
Reply to
amdx

That should read, The important characteristic I'm trying to MAXIMIZE is Q. MikeK

Reply to
amdx

Many here will remember Reg Edwards, he developed many programs useful to hams and others. His programs are small, fast, and accurate. For your coil you want to use his program named Multilay, about 2/3 down the page.

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Reg's program came up with an answer of 99.56% of the inductance the Ness Engineering program listed somewhere in this thread.

This is the starting page for Reg's programs.

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There are over 100 programs the page. Reg is a silent key now, Thank you, Reg. MikeK

Reply to
amdx

Whew! I was about to say, if you want _low_ Q, don't use Litz wire!

Cheers! Rich

Reply to
Rich Grise

(...)

A useful tool.

Thanks!

--Winston

--
Corporate executive forgets to commit a felony for 24 hours.
Film at 11.
Reply to
Winston

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