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Do you use skin depth to determine the minimum thickness of your conductor? In other words, if I calculate skin depth to be 200 microns at the lowest frequency, should my wire, at a minimum, be 200 microns thick?

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    \$\begingroup\$ It can be thicker or thinner depending on what you're after. The simplest reason to not go thicker is a bunch of copper that isn't doing anything. Thinner can give beneficial effects for higher frequencies. I'm not clear on the specifics but at least one effect is similar to why magnetic core laminations are made thin: to reduce eddies. That's a different effect than the skin effect though. \$\endgroup\$
    – DKNguyen
    Jan 27 at 6:24
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    \$\begingroup\$ Read Wiki's article on Litz wire. There are pros and cons no matter what you do. No bright lines. \$\endgroup\$ Jan 27 at 7:13

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The skin effect calculation is not giving you the minimum thickness needed for a conductor. It is basically telling you that if your conductor is thicker than this (actually 2x the value), that the inner cross section of the conductor is becoming inefficient. This is due to the internal cross section seeing a higher AC resistance (impedance) due to the magnetic affects of the AC current. So increasing your conductor beyond a certain thickness will not give the expected improvement in current carrying capacity.

For this reason a wide flat PCB trace can actually have a better AC current carrying characteristic (lower impedance) than a solid round wire of a similar cross section area.

Using a conductor thinner than 2x the skin effect value can still have a lower current carrying capacity but that condition will not be due to the skin effect.

The direct link to the WikiP page for "Skin Effect" can be found here.

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... if I calculate skin depth to be 200 microns at the lowest frequency, should my wire, at a minimum, be 200 microns thick?

No one can say "should" or "shouldn't". The practical world doesn't work like that.

As stated in Nedd's answer, if your wire diameter is less than or equal to twice the calculated skin depth (because the skin depth can be thought of as the thickness of the outer ring of a circle), the conductor will be used more effectively.

However...

It's not always possible to follow that in practice. For example, if you are designing a transformer, you may want to design the "acceptable" one considering the cooling, size, cost, availability, etc, which means that you don't have to select the lowest (i.e. twice the skin depth or less) wire diameter. Not only the skin depth should be considered, but also the AC resistance and losses as well as other practical conditions such as cooling, size, etc. so this is a bit of a compromise.

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AC current doesn't get distributed uniformly in conductors, the current density decreases in deeper from the surface. The current density vs depth from the surface and vs frequency is well explained numerous sources.

Skin effect increases the resistance of a wire as the frequency grows because the current gets more packed near the surface. But there's some current still left in the middle of the wire, too.

Skin depth:

Lets assume we have a normal round wire which has cross section radius = R. Let the frequency be so high that the skin depth S is smaller than R. In that case the resistance of the wire is as high as the DC resistance of a hollow pipe which has outer radius = R and inner radius = R-S.

In circuits low enough resistance of the wires is a must. How low - thet depends entirely on the application. The skin depth can in microwaves be only some micrometers. That makes round wires often useless in microwaves, but for example at 100 MHz few centimeter long round wires can well work acceptably, because the skin depth is about 0,2 millimeters. The wires must be max. few centimeters long mostly to prevent them to work as antennas or resonant circuits, the resistance caused by the skin effect is secondary.

Often the wires are thinner than the skin depth. The resistance of a round wire wire can well be low enough also in cases where the wire thickness is as low as 10% of the skin depth. Proof: at 50 Hz the skin depth of copper is 10 millimeters. I bet you have in your home numerous power cables which have only 1 mm or less thick wires and they work well without getting hot or causing too much voltage drop.

As said, the total resistance is decisive. The consequences of the skin effect depend radically on the application. Even at 50 Hz in high current power distribution systems the skin effect persuades engineers to use wide flat wires instead of round ones to make the resistance low enough. Wide flat cross-section profile has much less the not so useful far-from-the surface metal.

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In a lot of RF and microwave applications, the skin depth is so shallow that the current effectively flows only along the surface of the conductor, and so the conductor is way thicker/bigger than it needs to be.

Here's an example. At 1 GHz, the skin depth in copper is 2 microns. The thickness of 0.5 oz copper on a PCB is ~15 microns. So even at 1 GHz, the current flows almost entirely on the surface.

Now bump that frequency up to 10 GHz. the skin depth is now 0.2 microns. At this point, the surface roughness of the copper trace can start having effects such as increasing the path length of a signal, and so increasing the losses.

Bump that frequency up to 30 GHz or 40 GHz, and those effects become even more pronounced.

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