Discussion Forum

Hi,

first normB is wrong.

For a more detailed answer what to do we will need more info. Is it 2D or 3D? I assume 3D because
there is a Bz.

The coils are closed lines, right? Then you chose a surface (yes "a" because there can be many) and integrate the dot product of B and the surface normal. If the surface happens to be normal to the z-axis, it is an integral over Bz.

However, this may be numerically not a good choice. If you look into vector calculus you find that
the flux is equal to the line integral of the vector potential over the closed line. This is better because
B is a (numerical) derivative and A is the plain degree of freedom.

If your coil is a volume region then this becomes more difficult but you can follow the same idea.

Regards

Jens

Appreciate Jens,

1) yes it is 3-D model
2) The coils are planar and spiral. We use PCB tracks as coils.
3) To compute the surface integral of flux (for the secondary), I compute this integral for each surface (assumed for each turn) separately and then add them to find the total flux passed through all turns in secondary (that is generated by primary).

- Are you suggesting to use the line integral of the vector potential over the closed line instead of B?
- Why normB is wrong?

By the way, I tried to attach the mph file but it was too large. Is there any specific trick to make it smaller?

Regards,
Babak

To shrink the model you can remove the solution and the mesh (in the Edit-menu). Also you can
compact the history (File-menu)

normB is wrong because it neglects direction If you have an in-plane field nomrB might be
non-zero but the flux is zero.

Yes the integral I am thinking of is flux=int(A.dl). Make sure that the tangential vectors follow
the direction of the current flow.

I don't see yet how a spiral, planar and closed line is possible without intersection.

Jens

Thank you Jens,
I attach the model to have the better understanding of my model.
For Magnetic vector potential: flux=int(A.dl) A is the magnetic vector potential normal to the current flow, but in my model, the secondary coil is open and there is no current flow, therefore the only thing that I should be sure about that is: the magnetic vector direction is in the same direction with coil conductor: Then, because coil is square and in the X-Y plane, I should have two integral in X and two integral in Y direction, Right?
Regards,
Babak

The files helps. The wires are not lines but volume domains and it is not strictly planar. So
much of I wrote yesterday is not applicable. One trick that you can do for the primary coil is
to integrate
(mef.Jx*Ax+mef.Jy*Ay+mef.Jz*Az)/10[A]
over the coil volume. The current vector over the current gives the direction of the coil.

For the secondary coil you can define the directions in the variable definition an do a similar
integration.

Regards

Jens

> For the secondary coil you can define the directions in the variable definition an do a similar
> integration.

I've just seen that it not so easy, you may need to cut the domains such that each straight
part is a domain by itself.

Jens

thanks Jens,
you are saying to integral (mef.Jx*Ax+mef.Jy*Ay+mef.Jz*Az)/10[A] over primary?
I just need to calculate induced voltage in the secondary and if I compute the above integral in the secondary and divide by 10 [A], which is the primary current, it gives the mutual inductance, am I right?
we can neglect the tiny deviation from strict planar, and approximately we can consider the above analysis correct, do you agree?