For FDTD simulation is it valid to simulate skin depth in a wire by adjusting conductivty?

[Aspire-Design-Ltd]

Hi.

I wondered what peoples thoughts were on adjusting the conductivity of a wire to simulate skin depth.

If you have a copper wire say 1.2mm diameter at 2.4GHz the skin depth is 1.3um.

Area of active current = skin depth x circumference = $2 \pi r \delta$
Area of wire being simulated = $\pi r^2$

Adjust conductivity by $\frac{2\delta}{r}$ to compensate for the majority of current flowing in the skin depth of the wire. This should make the resistance of the wire greater by the effect of the skin depth but is this assumption going to invalidate the FDTD simulation.

Any thoughts anybody?
MPC

[SengerM]

As far as I understand, the skin effect should naturally arise in an FDTD simulation. You only need to worry about having a dense enough mesh so that you don't miss it, i.e. the mesh should be fine enough close to the surface of the wire.

[VolkerMuehlhaus]

If you are only interested in the accuracy around a particular frequency such as 2.4GHz. Is it reasonable just a use the conductivity adjustment due to the skin depth in a wire?

@Aspire-Design-Ltd
Skin effect also leads to an imaginary part of surface impedance that is equal to the real part, so besides more resistance your inductance would also change by some amount due to skin effect.

I think we need some more background about you intended use of the model, otherwise it is difficult to see what side effects your workaround will create.

[Aspire-Design-Ltd]

I was not suggesting changing the wire diameter, only the conductance of the material to adjust for the additional resistance due to skin effect. The wire diameter does not change.

My goal is to improve the accuracy of the simulated impedance of a normal mode helix antenna and far field antenna pattern. Skin effect causes the current to flow close to the surface of the wire and so increases resistance. By adjusting the material conductivity should compensate for the increased resistance.

Would the imaginary part of the impedance change much by the fact that the current flows on the surface and not within the entire wire?
Am I wrong to think that charge Q moving on surface of a conductor would have the same effect as charge moving evenly through the conductor. This is for small diameter wire compared to wavelength of interest.

[VolkerMuehlhaus]

Sorry for my misinterpretation, I already realized that and removed that part of my comment.

For the antenna, I don't think that the imaginary part of Zs will have much effect on antenna response. I will try to run both cases, i.e. lossy metal with proper skin effect model and your modified-conductivity model, in a commercial FDTD that supports both. Comparing results, we can hopefully see if your approximation is good enough!

[VolkerMuehlhaus]

I will try to run both cases, i.e. lossy metal with proper skin effect model and your modified-conductivity model, in a commercial FDTD that supports both.

@Aspire-Design-Ltd

Here are commercial FDTD solver results comparing (1) proper skin depth model and (2) your workaround solution.
I did a quick & dirty design of a 5 turn helix for 2.5 Ghz that uses 2.4mm Aluminium wire.

In the workaround solution (2), the Alumium conductivity is reduced by factor 2δ/r = 1/363 and metal loss model is set to bulk loss, similar to openEMS material with conductivity.

Return loss, black curve is your workaround, red curve is proper skin effect model

The parameter where you would see loss is antenna efficiency: pretty much identical at 95%.

So your workaround seems to be valid, but for such an antenna the loss in the antenna is very low anyway.
That said, we might check if FDTD is a good choice for this type of antennas. The staircasing effect from FDTD mesh means you need many mesh cells to model the curvature of the wire. In my model I used 6.4M FDTD cells for almost 70k timesteps, this will take a while to simulate in openEMS.

[Aspire-Design-Ltd]

Thank you.