# Discussion Forum

## DC resistance of a coil

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Johan Gustafsson

December 4, 2009 10:34am UTC

DC resistance of a coil

Hi,

I would like to calculate the DC resistance of a coil. I'm using an axisymmetric model. The coil has a few hundred turns in reality but I'm modelling it as a homogenous single coil. I know that the cross-section fill factor is approximately 55%. Because the different turns have different radius (the turns are stacked on top of each other) I can't excite the coil using constant voltage (Vloop), instead I must use a constant current density. I thought that I could integrate the E-field in the coil to obtain the average voltage drop and multiply this with the number of turns to get the voltage. And calculate the resistance from ohm's law, but I am not able to calculate the voltage this way. Is this a feasible approach, or am I missing something? (There is also a permanent magnet, magnetized in the z-direction included in the model)

Thanks,
Johan

Johan Gustafsson

December 19, 2009 6:50pm UTC in response to Johan Gustafsson

Re: DC resistance of a coil

Hi,

I realized that there is an easier way. I calculated the DC resistance from the following formula:

Resistance_DC = length * (resistivity/fill factor) / cross-section area

where the fill factor is the amount of copper in the cross section of the coil domain and the length is calculated as the coils volume divided by its cross-section area. This method gave an reasonable value of the resistance.

//Johan

Ivar Kjelberg

December 19, 2009 10:24pm UTC in response to Johan Gustafsson

Re: DC resistance of a coil

Hi

I agree, if you are in AC/DC static and not interested in higher frequency effects nor in theral effects.

Basically for axis-symmetry, the length of a loop is L=2*pi*r, the current cross section area is a simple integration coupling variable over the subdomain of "1" (implicit int(int(1,dr),dz)), while the volume is an integration couling variable over the subdomain of "2*pi*r (implicit int(int(2*pi*r,dr),dz)). So as you say the average loop length is Volume/Area or simply L_ave= 2*pi*(r_min+r_max)/2.

Now if you try a 2D axi "emqa" (azimuthal current) analysis in static mode you can either apply a loop voltage and get the total current by integrating the results over the coil section, and you should check by hand that you get U=R*I, with I=int(int(Jphi_emqa,r),z) = boundary integration over coil section area of "Jphi_emqa", and R[Ohm]=Lave[m]/(AreaCoil[m^2])/(sigma[s/m]), with sigma the conductivity = 1/(resisitivty[Ohm*m])

or you apply a curret density Je_phy, and get the loop voltage drop through the total energy (power) of the magnetic field (provided you are integration on a large enough area to catch most of the field in the coil and in the air), see the ACDCmodellib doc "Inductance in a Coil" example, or via the resisitve heating over the volume which is Q=U*I=R*I^2

If you apply your good engineer value 55% fill factor for a N multiple winding coil and you get your
N*Area_wire=Area_coil*Fill_Factor.

This gets slightly more complex if you want to consider thermal effects in the coil and or skin effects, but this menas also transient or harmonic analysis, then the coil windings should be modelled in more detail

Pls carefully check when you select/deselect the 2*pi*r multiplier = "Compute volume integral" in the postprocessing subdomain integral window

good luck
Ivar

Johan Gustafsson

February 1, 2010 2:57pm UTC in response to Ivar Kjelberg

Re: DC resistance of a coil

Hi Ivar,

I would like to thank you for your clarifications on DC resistance calculations a while ago...

When it comes to harmonic analysis of multiple winding coils I would like to suggest reading David Meekerâ€™s paper "Continuum Representation of Wound Coils via an Equivalent Foil Approach" (www.femm.info/examples/prox/notes.pdf) where the coil is represented as a single domain using complex conductivity and permeability. I have not set this kind of model up in COMSOL yet, so I am not sure about how well is works, but it sounds interesting.

//Johan

Ivar Kjelberg

February 2, 2010 10:58am UTC in response to Johan Gustafsson

Re: DC resistance of a coil

Hi Johan
that looks promishing, will have a detailed look
Thanks again
Ivar

Matthias Richwin

August 23, 2010 10:23am UTC in response to Johan Gustafsson

Re: DC resistance of a coil

Hi Johan,

now again a while ago: Have you implemented such a model? I am currently facing the same problem, and have to implement it in V4.0a.

Did you achieve you any results that you could share? That would be highly appreciated.

Update to make it clearer:

I'd model the coil windings anyhow as geometry. But I am concerned about the inner structure of the windings - we are going to use litz wires, and I'd have to cope with the remaining skin and proximity effects in the single turns.

Best regards
Matthias

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