Inductance calculation

[steveB]

In Electrician's link, it is very very interesting that in examples 52 and beyond a little they obtained inductance values from the formulas in units of length: centimeters <har har>. For example, L=654pi centimeters instead of L=654pi nanohenries
Funny too as this error seems to carry over several other examples. Glad we had such people working on papers like this way back then

I haven't had a chance to look through the document in detail, but it looks like a great reference to have handy.

About this, we should caution the OP to be careful about units. There are so many different electromagnetic systems of units. Typically, we use SI in engineering now, but many references use Gaussian, or other units. I assume here they are using the modified Gaussian system where inductance has units of length.

Well the formula you presented was for a cylindrical coil not a flat coil, so naturally i assumed you wanted a coil like that.

When I saw that formula, I felt it was very similar to the typical formula for a single loop, not a solenoid. Then it appears the N^2 was added as an attempt to consider multiple turns. However, I agree with you and The Electrician that there is an issue that the loops can not occupy the same space, so I don't think the formula can be very good for multiple turns. If the dimension of the coil are such that the wire diameter is considered, then loops that are offset from the "ideal" loop will have a big effect on the answer, I would think.

 

[BobW]

For multilayer coils, you may find this of some use:
**broken link removed**
A couple of simple BASIC program functions are provided to handle a couple of different cross sectional geometries, and they could be modified for other geometries. These functions can be dropped into an Open Office spreadsheet (in the macro editor) and then called up like any standard spreadsheet function.

 

[rakibulraju]

Why don't you post a picture of your coil so we can see what it really looks like? Also, tell us more about its construction. What gauge wire did you use? How many turns are there? What are the dimensions of the coil?

sir here i s my coil picture.please suggest me a formula.

 

[Nigel Goodwin]

Measure it!!.

 

[MrAl]

I haven't had a chance to look through the document in detail, but it looks like a great reference to have handy.

About this, we should caution the OP to be careful about units. There are so many different electromagnetic systems of units. Typically, we use SI in engineering now, but many references use Gaussian, or other units. I assume here they are using the modified Gaussian system where inductance has units of length.



When I saw that formula, I felt it was very similar to the typical formula for a single loop, not a solenoid. Then it appears the N^2 was added as an attempt to consider multiple turns. However, I agree with you and The Electrician that there is an issue that the loops can not occupy the same space, so I don't think the formula can be very good for multiple turns. If the dimension of the coil are such that the wire diameter is considered, then loops that are offset from the "ideal" loop will have a big effect on the answer, I would think.

Hello there Steve and rak,

Steve:
Thanks for pointing that out. They are working in the cgs system. So we can read all the results instead of say 320 cm we can read 320 nH. But also interesting is the pi factor that often accompanies their results like 654pi cm, which i think may translate to 654 nH. I'll have to look at this in more detail i guess. I really do appreciated your pointing these things out

The formula with N^2 is an accepted form even though the wire has diameter, but there is a constraint regarding the ratio of the wire diameter to the coil diameter (or radii). I dont remember what it is offhand, but the wire diameter is usually considered to fit loosely into the equation anyway where it doesnt have a super significant effect, except of course in extreme cases.

rak:
Yeah, for that coil there is no way to calculate the inductance without knowing the exact three dimensional path of every wire in that loop pictured and it's diameter assuming constant diameter. Since the wires are randomly wound that's what is required. If they were not randomly wound however (no crisscrossed wires) but uniformly wound into layers even if the layers are shallow, then we have book formulas we can throw at it and come up with an approximation.
Until the coil assumes a known shape like that however, you would do best to follow Nigel's advice to measure the coil. If you intend to use it in a circuit, then you should insert it into the circuit and adjust based on some other circuit response such as a peak or dip...that's the traditional way of doing it anyway because once it is in the circuit things again change even if you've calculated the exact inductance somehow and it really was the right inductance at the same frequency and all other things considered about the detached coil worked out to perfection.