calculate inductance DD-Coil and square coil

[Gwil]

One of my experiments



This is a roughly 'D' shaped coil with 80 turns (centre tapped) of 30swg wire, outside diameter 0.344 mm. To find the area it enclosed I drew the internal shape on graph paper - as this was an experiment I tried to get it as accurate as I could, which meant I ended up counting square millimetres. The area was 153.1 square centimetres.

For a circle, Area = pi*radius squared
Therefore radius = sq root (Area/pi)
From this the radius of a circle whose area is 153.1 sq cm is 6.98 cm or 69.8 mm.

Putting this radius into Qiaozhi's Inductance Calculator along with the no. of turns and the wire diameter gives a result of 2.31 mH. The measured inductance was 2.29 mH.
That's close enough for me - I'm convinced the 'Area' approach is correct, and should work for any shape coil as there's nothing special about this one.

What is interesting is that the ITMD method described in post #2 also gives, for this coil at least, a surprisingly good calculated result (2.37 mH). This method is mathematically equivalent to finding a circle with the same area as an ellipse, and it is true that a lot of 'D' coils do roughly resemble ellipses with both ends skewed over to one side. More evidence that the 'Area' approach is right, I reckon.

Summing up: For the best accuracy, measure the area enclosed by the coil. For what may be good enough accuracy use the ITMD method, but this will depend on the coil shape.

[Skippy]

Gwil's coil is pretty close to circular, and I feel that all of these alternative methods will give viable results for such a coil shape. It would be the more extreme ellipses that would show up the strengths and weaknesses of the different strategies. Eg. a 2.5:1 ellipse, where the area is more markedly reduced.

I'll have a think about the maths later, maybe post any thoughts.

[green]

Calculated inductance based on area for four shapes. Kept circumference the same. 20 turns, .4mm diameter wire, Qiaozhi's coil formula. Don't know if using circumference or area to calculate radius for the formula is more correct. Using area predicts a greater change than Skippy or I got in our tests using circumference(compared change in shape against a round coil). Wrapping a string or piece of wire around the coil form to get circumference, calculating radius and using Skippy's calculation reply #14 would be easier than measuring the area.

[Skippy]

I read up on the maths of ellipses, and learnt something new in the process. Surprisingly, there is no precise formula for the circumference/perimeter of an ellipse, only good approximations. The formula I vaguely remembered,
Perimeter = pi * sqrt(2 * (a^2 + b^2))
is only a simple approximation, there's two other better ones, which I used in my calculations.

I assumed a circular coil of radius 1 (metre), and then calculated the dimensions of various ellipses when the same coil is re-shaped. So the circumference remains unchanged. For each elliptic shape, I calculated the area, expressed as a percentage of the circle's area. I then worked out an equivalent circular coil radius, based on this elliptic area.
These figures are shown on the attached jpg.

So, as an example, the ( 2.5 : 1 ) elliptic coil:

If you used the "circumference method", you'd end up with a radius the same as the original circle, obviously. This would give you a real coil with a slightly low inductance, something like 6%. You would compensate for this intuitively, for example using Green's photo of his re-shaped test coils as a guide.

If you worked out your equivalent circle size based on elliptic area, you would have R of 86.3% of the original circle, ie. 14% down. This looks to be over-compensating, compared to experimental data indicating about 6% lower inductance.

If you used the "mean of the two diameters" method, you would end up using an equiv. R = (1.365 + 0.546)/2 = 0.955, ie. 4.5% lower than the original circle. This is actually pretty close to the experimental data.

As a summary, I think:
*The "circumference method" works regardless of whether the coil is an ellipse or a squashed D shape, but it does require some empirical guesswork to compensate for the off-round shape.
*The "mean-of-two-diameters" works well for true ellipses, but for flat-sided shapes it requires a bit of 'fine-tuning', which I'm not sure about.
* The "area method" gets progressively worse as the elliptic shape gets more severe. For near-round shapes it's not too bad, but there are simpler ways of achieving the same result, in these cases.

Here's a link to some ellipse maths:
http://mathworld.wolfram.com/Ellipse.html

And attached are my calculations:

[Dave J.]

The advantage of the circumference (actually perimeter) method is that it doesn't care what the shape is (within reasonable limitations) and is based on fundamental physics (inductance of free space). In other words it gets you "almost there" from first principles using elementary school math. After you've actually wound the coil and measured it, guess what-- your prediction will be off! so you change the number of turns in proportion to the square root of how much you missed it by. The second pass usually gets you within the resolution of a finite number of turns. ......No matter what method you use, that second try is almost always necessary anyhow. Sometimes a third. So you may as well keep it simple and use the "circumference" method.

The worst part about going to college is that the professors make everything look so difficult, no wonder that it's hard to find a recent EE grad who can change a light bulb. Back in the olden days we used to learn this stuff as kids, mostly from ham radio and ex-military publications written by people who either made stuff work before they wrote, or had to teach grunts working knowledge in a hurry. If you went to college, it was mostly to use your GI Bill, broaden your knowledge, and get your ticket punched. And your continuing education was via work experience, trade magazines (those paper things), and semiconductor data books written by manufacturers who wanted you to use their products. Alas, the golden days of electronics are over-- the resources that converged to make it happen have pretty much disappeared.

[stefan-s]

Thanks for sharing all

[homefire]

[QUOTE=Dave J.;235249]The advantage of the circumference (actually perimeter) method is that it doesn't care what the shape is (within reasonable limitations) and is based on fundamental physics (inductance of free space). In other words it gets you "almost there" from first principles using elementary school math. After you've actually wound the coil and measured it, guess what-- your prediction will be off! so you change the number of turns in proportion to the square root of how much you missed it by. The second pass usually gets you within the resolution of a finite number of turns. ......No matter what method you use, that second try is almost always necessary anyhow. Sometimes a third. So you may as well keep it simple and use the "circumference" method.

LOL, "" had to teach grunts working knowledge in a hurry. "" Brain Got Fried with what they tried to cram in me in the USAF . 740 hours of Electronics, all in 8 hour day increments. Months on end. I,m sure my ears were smoking when they got done.

[Dave J.]

Well, HF, you became a guru posting on Geotech, so evidently some of what the USAF taught you actually stuck. And I'd say not a coincidence: before they stuck you in electronics, they did aptitude testing. If you had no aptitude for such things, you wouldn't have been in the class.

Many years ago at the old Fisher we hired a new out of school EE. No experience, but straight A student. She literally didn't know what a soldering iron was, we had to teach her how to solder. Fortunately on the job she was also a good student.

Then there was the guy we hired about the same time, EE degree and something like 2 years experience. He was shocked that I did designs with a pencil and piece of paper, no Spice simulation or anything like that. He was sure that my designs must be crap. So I told him "well, let's design a simple bandpass filter. Sallen & Key, 1 kHz, Q=1, sound good to you?" He agreed. So I told him "You knock yourself out on your computer. I'll do it entirely in my head, and 5 minutes from now I'll write the solution on a piece of paper and hand it to you in an envelope. When you've got your answer, open the envelope."

About an hour later, he had what he believed to be a solution. The capacitors were in the hundreds of farads. I told him he won't be able to fit that on perfboard because the capacitors are the size of a house. He was operating in pure fantasyland and didn't even know it. After a few more hours screwing around he decided that my solution was correct.

[Qiaozhi]

When I was at university studying Physics and Electronics, I found that most of my fellow students were really good at passing exams, but next to hopeless in any practical work. Maybe it's just that I had the advantage of having worked in industry before going to University. Also, I find it amazing that some engineers say that they're digital engineers, and don't understand analog, and vice-versa, or they can design a circuit but have no idea about PCB layout, or can build hardware but not write software. To me it's all part of the world of electronics. My philosophy is essentially: "How hard can it be?".

Sometimes it's a lot easier than you imagined, and sometimes it was a lot harder. Whichever it is, you always learn something.

[Dave J.]

My favorite simplification is to explain "bandgap", emitter resistance, current, voltage, and temperature coefficients of all three as a simple family of straight-line "curves" that converge at zero Kelvin on the Y axis and 1.2 volts on the X axis. Everything is right there on that one very simple graph. Once you've seen the graph and drawn it yourself, from then on out you never need to go screwing around with a bunch of fancy equations. You don't even need to keep a copy of the graph, because once you've drawn it yourself you'll never forget how you did it and can re-create it from scratch in about 3 minutes. .......I'd wager that of newly minted EE grads one in 100 could solve any of that mathematically in less than a day. Because it was presented in class as hifalutin physics math that mere mortals weren't likely to ever understand anyhow. So of course the students blew it off, and the semiconductor junction remained forever a mystery to them. The profs never had to actually design something and make it work, so they didn't know the subject matter was actually teachable.

I do most of my AC circuit design using the stone age ARRL reactance chart. To which I have added 300 Kelvin thermal noise on the resistance axis, and copied and pasted the 1% resistor value series. When the other guys come to my office asking about a circuit, I usually say "just a minute while I reboot my computer" and drag out a dog-eared xerox copy of the ARRL chart. The guy in the group who's rapidly becoming a first class analog engineer in his own right, the light bulb finally went on and he printed out a fresh one for his own use off the Internet.

Another simplification easy to commit to memory: both capacitive 1 uF and inductive 1 uH reactance equal 1 ohm at 159 kHz. For any other frequency or L or C value it's just a matter of shifting decimal points.

[Gwil]

This is a very interesting thread but a bit heavy on theorizing and speculation. Nothing wrong with theorizing and speculation but with more experimental results we might end up with calculation methods that work for practical purposes, without trial and error being needed. Any volunteers?

[Qiaozhi]

This is a very interesting thread but a bit heavy on theorizing and speculation. Nothing wrong with theorizing and speculation but with more experimental results we might end up with calculation methods that work for practical purposes, without trial and error being needed. Any volunteers?

Coil calculators are designed to get into the "ballpark", and will never provide an exact result. This is because the parameters are not rigidly controllable (at least when building this stuff by hand) as the inductance can vary somewhat depending on how accurately the actual coil matches the parameters you put into the calculator. It's a simple case of rubbish-in rubbish-out.

For example, if you wind your coil around a circle of nails or screws, then the diameter may not be exactly what you defined. One of the main factors is also how tight you bind the bundle. Plus you need to consider the accuracy of your inductance measurement equipment. The Coil Calculator in this forum will usually get you to within +/- one winding, as long as you get the coil radius correct in the first place. At least the result using Brook's equation is better than Wheeler's (which is intended for solenoids, and not multi-layered air cored coils).

[Gwil]

Agreed. That's why I said "for practical purposes". There's no point in struggling to get an exact result for a coil if the tuning capacitor across it has a tolerance of +/- 5%, or even +/-10%. I'm just hoping that a few percent may be attainable.

[Dave J.]

Measure the length of wire in one turn, in meters. Multiply that number by 1.27 times 10 exp-7 Henries per meter. That's a good estimate of the inductance of one turn. Now multiply that number by the square of the number of turns. That's your estimate of inductance.

Wind the coil, measure the inductance, and then correct the number of turns if necessary. You don't need all those other formulas. None of them are going to account for the poorly characterized and poorly controlled factors in coil winding.

This is for coils where the winding cross-section is small relative to the dimensions of the coil itself, the kind of coils normally used in metal detectors. It won't work for solenoids or pancake spiral coils.



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[homefire]

Yep,, Calculations are only good for estimating how much wire to buy ! LOL In the end you do what needs to be done .