# How does the Skin Effect at RF frequencies affect wire ampacity?

Through simulation we can find the current going through an inductor that is part of a filter network and this 1-sheet paper points out that ampacity diminishes with higher frequency because of the Skin Effect.

When sizing inductor wire for use at RF frequencies, how can you find the effective ampacity of a given wire guage (or cross-sectional area) at a particular frequency and a target temperature rise?

We plan to wind our own inductors for a UHF/VHF diplexer for a satcom project. The target design is to support 100W transmission through the diplexer near 146MHz and 437MHz.

At some point, ampacity becomes irrelevant. Two reasons:

1. You can't measure currents. You can only measure power.

Sure, you can set up a current probe that drops a minimum amount of voltage, but that voltage will always vary with frequency, and in particular, at very high frequencies, that voltage drop becomes considerable with respect to the surrounding circuit. The circuit might not have any points that can be probed, either: for example, how do you hook a current transformer or Rogowski coil around a PCB microstrip trace? Even if you made a transition structure to elevate the trace far enough above the substrate to get a probe in there (while maintaining $$\Z_0\$$), the impedance changes when you introduce the probe (effectively leakage inductance, or capacitance to its casing/windings).

Instead, we measure power, and direction. Whereas a voltage probe (like a large-value resistor or capacitor divider) or current probe (like a CT) would introduce reflection and mismatch (as above), we use directional couplers to measure incident and reflected power, at the minor expense of insertion loss (which is less important), while $$\Z_0\$$ is preserved (which is very important). We use attenuators to measure total output power, or amplifiers to supply it.

2. Even if you can measure currents, it need not be the most meaningful design parameter going into an inductor. When you have wires nearby (as in a multi-turn winding), they induce eddy currents into each other -- proximity effect. This reduces the ampacity further, and not in a straightforward manner (we use estimates or simulations to prove this out, when we do).

More likely, you'll design for a certain target Q factor, based on applied power, permissible dissipation, and other requirements (the filter requires a certain maximum system Q, i.e. the Q of the component's reactance with respect to the other components around it, or ultimately $$\Z_0\$$ of the overall system; component Q must be much greater than system Q). This isn't trivial either, as component dissipation varies with size, and you don't know right away how big a component is going to be, to achieve some Q; typically iteration and experience will be involved here. At high frequencies, these inductors are small, so it's not like it's a big deal to make a bunch and test them.

There are techniques to restore ampacity, but they only work at lower frequencies -- litz cable is suitable up to a few MHz or so. Beyond that, round solid or tube is used, or perhaps strip. This is acceptable because, while skin effect causes the cross section to fall as $$\\sim \frac{1}{\sqrt{f}}\$$, inductive reactance rises as $$\\sim f\$$, so Q factor goes up as $$\\sim \sqrt{f}\$$ overall. A Q factor of 300 is not hard to achieve with solid wire in the 10-1000MHz range.

At the highest frequencies, ampacity loses all meaning as currents no longer flow along wire, but in loops on faces -- such as in waveguides. For these, the resistivity of the plating and the design parameters (inner dimensions, aspect ratio, corner radius, etc.) dictate the power handling. Power handling may also be limited by dielectric breakdown (an air-filled waveguide will typically arc over, long before the walls melt, I think?). Even at lower frequencies, we can employ resonator structures (e.g. helical resonator) to achieve quite high Q factors with only mildly-inductive-looking geometry.

It's not obvious what frequency band you're looking to target, but unless it's for IF stage filtering (which will be at signal level: ampacity is again irrelevant because currents are small), it will be much more than 30MHz (below which satellites are unreachable due to ionospheric absorption/reflection), so solid wire inductors seem the likely case.

(Also here again, ampacity doesn't seem useful unless you're transmitting; the received power even in very nearby antennas is minuscule.)

• FYI, updated OP with power and frequency details. You are correct, transmission is the consideration here, receive power wouldn't matter. Commented Nov 29, 2022 at 1:20