calculate inductance DD-Coil and square coil

[Skippy]

Quote Gwil:"This is .. a bit heavy on theorizing and speculation.... with more experimental results we might end up with calculation methods that work for practical purposes, without trial and error being needed."

Agreed, for our amateur one-off builds, we don't want to do any trial-and-error, unwanted iterations, or have to make lots of adjustments/bodges etc to get something that works. It all wastes time, costs money, may give poor results, etc. So predictable and repeatable guidelines, good mathematical modelling, attention to detail, understanding what's important and what's less so, all contribute to a successful build.

[Skippy]

Quote Q:"the inductance can vary somewhat depending on how accurately the actual coil matches the parameters you put into the calculator"

This is true, and another factor that could cause a discrepancy is the difference between our coils and the coil that Brooks formula models. His coil is square (or rectangular) in cross-section, and his windings are arranged in a square grid. Our coils will nearly always be circular in cross-section, and the round wires will tend to align in a hexagonal-close-packed fashion, (like honeycomb). Both these factors should increase mutual coupling between windings, and increase the inductance. However, our coils are normally scramble-wound, which upsets the hexagonal arrangement a fair bit, and I don't think the circular vs square shape is that significant, so it seems to work quite well in practice. ( It would be interesting to compare a square-section neatly machine-wound coil with a hand-built one and with maths theory).

[Gwil]

A couple of thoughts -

1) In this context the inductance of free space is 4*pi*10 exp-7 , about 1.25664*10 exp-6 Henries per metre

2) I've wound some centre tapped coils and my experience was that adding the second half of the windings didn't increase the inductance by a factor of four, but about 3.8. This suggests that for our kind of coils inductance is proportional to number of turns raised to the power 1.92 or thereabouts. I suspect that this is due to the coil getting fatter as turns are added. Can anyone else confirm this?

[Dave J.]

The square factor is for 100% mutual coupling between turns. As the cross-section of the winding gets fatter in relation to the "diameter", the individual turns are not sharing the same magnetic field so the square factor is less than a factor of two.

Some of the coil formulas take this into account, but what they don't take into account is the fact that the coil as actually wound, does not conform to the assumptions underlying the coil formula. Therefore the customary approach is to wind a coil of the shape in question with the number of turns based on intelligent guesswork, measure the inductance, and then try again using a square law correction factor.

Another thing that's often done is to put more turns on the coil than you think you'll need, and then remove turns until you achieve the desired inductance.

[green]

The square factor is for 100% mutual coupling between turns. As the cross-section of the winding gets fatter in relation to the "diameter", the individual turns are not sharing the same magnetic field so the square factor is less than a factor of two.

Some of the coil formulas take this into account, but what they don't take into account is the fact that the coil as actually wound, does not conform to the assumptions underlying the coil formula. Therefore the customary approach is to wind a coil of the shape in question with the number of turns based on intelligent guesswork, measure the inductance, and then try again using a square law correction factor.

Another thing that's often done is to put more turns on the coil than you think you'll need, and then remove turns until you achieve the desired inductance.

Any thought on how many more turns to start with using your formula? Maybe 10,15 or 20% more turns than calculated for the desired inductance.

[Dave J.]

Just based on experience. Fat windings, throw on more turns. And of course you can always resort to the "coil formulas".

[homefire]

With Enamel Wire I just wind what I think is close , strip enough enamel to measure. If Short dab some nail polish on that spot and keep winging. I know, Not right but it works for me.

[Koala]

Even round coils come out slightly different to the calculations. Whether the error is in the winding or the measuring who knows. I now either add or subtract windings till the frequency is as expected on a VLF. Seems to work well.

[bbsailor]

Just based on experience. Fat windings, throw on more turns. And of course you can always resort to the "coil formulas".

This is a good rule of thumb. Here is how I do it.

1. Wind a test coil the same diameter and near the calculated amount of turns.
2. Measure the inductance of this coil which is usually less than calculated, especially if you are using thicker insulation wire.
3. Calculate how many more turns it will take to reach the desired inductance by doing this. If your 20 turn coil measures as 300 uH then how much more will it be if I add two turns? 22 turns is 10 percent higher. Just square the 10 percent extra or 1.1 squared and get 1.21.
The 22 turn coil will now be close to 1.21 times 300uH or about 363 uH.

This is technique should get you very close to your desired inductance since the initial reading takes into account the wire insulation thickness on your first measurement and the added turns, when measured, will be very close to the calculated result using this technique.

I hope this helps?

Joseph J. Rogowski

[Dave J.]

When dealing with a new coil size or geometry, I either do it that way, or throw on an extra (say) 10% number of turns and then peel off the extras until the desired inductance is achieved.

Most of the time when I'm winding a new coil, it's using a mandrel we already have and I can base my estimate on the coils we're already pulling off that mandrel. Most hobbyists however don't have that convenience.

[6666]

A couple of thoughts -

1) In this context the inductance of free space is 4*pi*10 exp-7 , about 1.25664*10 exp-6 Henries per metre

2) I've wound some centre tapped coils and my experience was that adding the second half of the windings didn't increase the inductance by a factor of four, but about 3.8. This suggests that for our kind of coils inductance is proportional to number of turns raised to the power 1.92 or thereabouts. I suspect that this is due to the coil getting fatter as turns are added. Can anyone else confirm this?

I have done this experiment a couple of times the results are interesting
go to Q's coil calculator
choose any coil size and wire size
then start at 4 turns and note inductance
continue adding 1 turn up to 25 turns noting inductance each time
and note the changes in inductance if you double the turns
for example a 8" coil with .4mm wire
10 turns is 67 uH
but 20 turns is 249 uH
I have seen a discussion on another forum where they were fighting over do you centre tap the turns or inductance.