calculate inductance DD-Coil and square coil

[stefan-s]

Hallo,

I was wondering if it is possibel to calculate the inductance of a DD-coil and square coil. So for the DD-coil how much the inductance of both coils ar (tx-rx) this will hel allot in building different coils.

Best regards
Stefan

[Qiaozhi]

Hallo,

I was wondering if it is possibel to calculate the inductance of a DD-coil and square coil. So for the DD-coil how much the inductance of both coils ar (tx-rx) this will hel allot in building different coils.

Best regards
Stefan

This problem is mentioned on page 210 of "Inside the METAL DETECTOR".
"The coil calculator is intended for circular coils only, but it is often asked if it can be used to find the number of turns required for either a D-shaped or elliptical coil. A reasonable estimate can be found by taking the long and short diameters, adding them together, dividing by 4, and using this figure for the inner radius."

I'm not sure what can be done about the square coil, but you could try taking the horizontal and diagonal diameters and using those in the same way.

[Gwil]

I've done some experiments on different shaped coils, and found that as I suspected it's the area enclosed by the coil that matters. Find that area, then calculate the size of a circle with the same area. Put its radius into Qiaozhi's famous inductance calculator and there you are (checked with a digital LCR meter). II I can dig out my test results I'll post an example.

[stefan-s]

That would be nice Gwil

[Skippy]

There's plenty of relevant information contained in this thread:
http://www.geotech1.com/forums/showt...oil-Calculator

[homefire]

I'm thinking if you just figure the Area 1m + 1m / Pi (3.14) would get you in the ball park. Any one Tried that ?

[Skippy]

Regarding this from George 'Q':
"...... about the square coil, .. you could try taking the horizontal and diagonal diameters and using those in the same way."

I assume this should read "horizontal and vertical diameters....", or, seeing as it's a square, simply use the horizontal figure twice in the calculation.

I've just had a play with the maths for the square coil:

Consider a 1m x 1m coil:
a circular coil fitting inside the square has radius, R = 0.500
a circular coil outside of the square has R = 0.707

So the appropriate 'circular equivalent' will be between these limits, my instinct says closer to the R = 0.500 model.

The mean of the above two figures is R = 0.604, I think this is likely to be the upper limit for equivalent R.

If you consider the 'equivalent area' method, you have (pi * R^2) = 1; hence R = 0.564

If you use the equivalent circumference method (which I found good for elliptic/off-round shapes), you have:
(2 * pi * R) = 4; this gives R = 0.637, which in this case is too high, those pointy corners with the currents flowing nowhere-near the correct direction throw things askew.

My thoughts would be to use an equivalent somewhere between R = 0.54 and R = 0.58 in your calculations, and add an extra isolated turn or two to allow fine-tuning (see the thread I linked to above).

How pointy your coils corners are may affect your results, too.

[Qiaozhi]

Regarding this from George 'Q':
"...... about the square coil, .. you could try taking the horizontal and diagonal diameters and using those in the same way."

I assume this should read "horizontal and vertical diameters....", or, seeing as it's a square, simply use the horizontal figure twice in the calculation.

No ... that was meant to be as stated.
If you use the horizontal diameter twice on a square coil, you will just end up with a round coil of the same diameter as the horizontal. That's why I suggesting using the diagonal to compensate for the corners. Obviously this will only be an approximation.

[Skippy]

OK, George, I see your logic, and the maths would give an equivalent circle radius, R = 0.5 * (0.5 + 0.707) = 0.604. (see my post for comparisons). It just seemed a little extreme, with the diagonal being 41% greater than the width, however it works better for rectangular coils. If you had a 2:1 ratio rectangle, for making a square-ish DD coil, the diagonal wouldn't be that much larger than the greater of the widths (12% greater).

[kt315]

crosslinked to http://www.geotech1.com/forums/showt...55-Square-Coil

[green]

Made a 10inch diameter single layer vertical coil that I could bend to different shapes awhile back. Took some pictures with different shapes and measured inductance.The round coil had a little higher inductance, the others close. 95% of the round diameter inductance would come close for the others. Don't know if bundle wound coils would be similar. Could try to bend to other shapes if anyone is interested.

[6666]

This sort of plays tricks on your mind as to what should the inductance do if you bend the coil out of shape, guess what the inductance did when I bent a folded 8 coil.

[Nandor]

Green thanks for sharing it, very informative.

[Skippy]

Some years ago, I did a similar experiment to Green, with a smaller bundle-wound coil. I had similar results, a rectangular 2:1 aspect ratio coil was about 6% lower inductance than the circle.
In one of the other previous threads on this topic, I reported this, and as a result, recommended using the circumference of an off-round coil as the basis for a circular mathematical model, just allow for 3 - 6% drop depending on the severity of the shape.

[Dave J.]

Skippy's got it right. If you backtrack to the physics of why a conductor has inductance, it almost doesn't care what the area enclosed by the current loop is. It's mostly the length traveled along that loop. For that matter, you can get a crude approximation by using the physical constant for the inductance of free space, 1.27 x 10 exp -7 Henries/meter.

For more precise formulas, Google is your friend. https://en.wikipedia.org/wiki/Inductance https://en.wikibooks.org/wiki/Electronics/Inductors