Mutual Inductance: Formula & Coaxial Loop Model

[Mica]

Hi everyone,

I'am trying to find the formulas of the mutual inductance of an one single layer coil (the cross section is rectangular i.e. the wire is rectangular or a round loop with rectangular cross section)on cylindrical winding form. Does anyone know how to calculate this mutual inductance? Can I approximate the mutual inductance with the coaxial loops model?

Thanks,

Mica

 

[turin]

M₂₁ = N₂Φ₂₁/I₁

 

[Mica]

Hi,

Thanks for yours response.
I would like to have a form like this :

M12 = m (a1a2)1/2 2/k [(1-k2/2) K(k) – E(k)],
k= (4 a1a2 / ((a1 + a2) + h2))
and K(k), E(k)] are elliptic integrals

This is for coaxial loops .

Is it possible to obtain like this form?

Regards,
Mica

 

[Mica]

Hi,

The correct formulas is :

M12 = (a1a2)1/2 2/k [(1-k2/2) K(k) – E(k)],
k= (4 a1a2 / ((a1 + a2) + h2))
and K(k), E(k)] are elliptic integrals

and another question : how can you subscript or postscript the lettres?

Thanks,

Mica

 

[turin]

I appologize. I didn't expect you to be so far along in math. In that case, please try to describe your general situation again. Is the cross-section of the wire itself important to you, or only the shape of the loop (cross-section of coil)? Are the loops coplanar? What are a1 and a2?

For future reference, if you want to find out how to do the scipts, or any special characters that you see in someone else's post, then you can click on the "quote" button to see how they did it.

 

[Mica]

Hi,

You are a polite person, you don’t need to apologize, you are helping me.

I have a coil (single layer ) which wound around a cylindrical conductor. I explain.
If I have such system, I can find the total inductance by breaking down into three parts.

1)Find the self-inductance (which is the inductance of each loop)
2)Find the mutual inductance (which is between loops i.e. loop1 with loop2, loop1 with loop3, vice versa, etc.)
3)Find the mutual inductance between the coil and the conductor ( assume the coil can be a cylindrical conductor if the loops are close)

So, the total inductance is the sum of the three statements above. The second and third statement can be approximate by use filaments (see p.1 attachment Use filament example).

I have the same system but the only change is the wire is round with a cross section rectangular . I can call it “ single layer coil with round wire but the cross section is rectangular which wound on a cylindrical conductor”. I found the self conductance for this system. (see attachment p.1 Disk coil example) But for the mutual inductance I didn’t find it. Any ideas will be appreciate. I will send the two attachment separately because of their size.

You can find the whole document on this website : http://

Cheers,

Mica

 

[Mica]

p1 attachment

 

[Mica]

p2 attachment

Thanks again,

Mica

 

[turin]

I'll have to look at this stuff for a while.

 

[Mica]

Is O.K. when you have time,you can give me some ideas.

Thanks,

Mica