Skin Effect in Ham Radio: Why RF Runs on the Surface
A copper wire that has a resistance of a few milliohms for direct current behaves differently when it carries a signal on 14 MHz. The current no longer uses the whole cross section of the wire. It crowds into a thin layer at the surface, and the centre of the conductor does very little. This is the skin effect, and it is one of the reasons why the resistance of an antenna wire, a coil or a piece of coax is higher on the air than on the bench multimeter. For a station builder the effect has practical consequences: how thick a wire should be, why hollow tubing is as good as a solid rod, why silver plating is used on the inside of a cavity and why a tightly wound coil can lose more power than a large and simple one. This guide explains the idea with real numbers and then turns them into rules that you can apply at the workbench.
What Happens Inside the Conductor
When an alternating current flows in a wire, it produces a changing magnetic field, and the field induces small circulating currents, called eddy currents, inside the metal. The eddy currents oppose the main current near the centre of the wire and add to it near the surface. The net result is that the current density is highest at the outer surface and falls off exponentially towards the middle. The distance at which the density has dropped to about 37 percent of its surface value is called the skin depth. The Wikipedia article on the skin effect gives the formula, and it shows that the depth depends on the resistivity and the permeability of the metal and on the square root of the frequency.
The consequence is simple. If the wire is much thicker than the skin depth, the metal beneath the surface layer carries almost nothing, and the useful cross section is a thin ring. The resistance of that ring is higher than the resistance of the full wire, and it rises with the square root of the frequency. At direct current the whole wire is used. At 100 kHz the skin depth in copper is about 0.2 mm, and by the VHF bands it is a few micrometres.
Skin Depth on the Amateur Bands
For copper the skin depth in micrometres is close to 66 divided by the square root of the frequency in megahertz. The table applies this rule, and the same rule for aluminium with a constant of about 83. The values are rounded, because the exact figure depends on the purity and the temperature of the metal.
| Band | Frequency | Copper skin depth | Aluminium skin depth |
|---|---|---|---|
| 80 meters | 3.5 MHz | 35 micrometres | 44 micrometres |
| 40 meters | 7 MHz | 25 micrometres | 31 micrometres |
| 20 meters | 14 MHz | 18 micrometres | 22 micrometres |
| 10 meters | 28 MHz | 12.5 micrometres | 16 micrometres |
| 2 meters | 144 MHz | 5.5 micrometres | 7 micrometres |
| 70 centimetres | 432 MHz | 3.2 micrometres | 4 micrometres |
A human hair is about 70 micrometres thick, so on 20 meters the current in a copper conductor lives in a layer that is thinner than a quarter of a hair. This is the reason why the wall thickness of a tube makes no difference to the performance of an antenna element: a wall of 1 mm is already fifty times the skin depth, and the inside of the tube carries no current at all.
What It Means for Antenna Wire
The RF resistance of a round wire can be estimated by treating the current as flowing in a ring with the thickness of one skin depth. For a copper wire of 2 mm diameter at 14 MHz the resistance is about 0.16 ohm per metre. A 10 metre dipole therefore has a loss resistance of a couple of ohms in the wire, compared with a radiation resistance of about 70 ohms, and the efficiency of the wire itself is above 95 percent. The conclusion is encouraging: for a full-size wire antenna the skin effect is not the problem, and the choice of wire is dominated by strength, weight and weather resistance. Our guide to HF antenna wire compares the common types, and the skin effect explains why copperweld, a steel core with a copper skin, works so well for a dipole: the RF current flows in the copper layer, and the steel provides the strength.
The picture changes for antennas that are short in terms of wavelength. The radiation resistance of a shortened antenna can fall to a few ohms, and the same fraction of an ohm in the wire is now a large share of the total. This is the situation described in our article on antenna efficiency, and it is the reason why builders of small loops use copper tube of a large diameter and keep the joints short and clean.
Why Coils Suffer More Than Straight Wire
A coil has an additional problem that is called the proximity effect. The current in one turn is influenced by the magnetic field of its neighbours, and it is pushed to the sides of the wire that face away from each other. The effective area of the conductor is reduced even further, and the loss of a close-wound coil can be several times larger than that of the same wire stretched in a line. The remedy is known from the construction of high-Q coils: use a thick wire, space the turns by about the diameter of the wire, choose a large coil diameter in proportion to its length and do not place the coil close to metal. This is the reason why the loading coils of good shortened antennas look so large and open. Our article on the loading coil and the capacity hat shows how much the loss resistance matters when an antenna is made short.
The same principle affects the transmitting coils inside a tuner, the tank circuit in an amplifier and the inductors in a low-pass filter. In the high-power parts the builders use silver-plated copper tube or flat strap, because the surface carries the current and the surface is where the resistance is decided.
Plating, Corrosion and Surface Quality
If the current flows within a few micrometres of the surface, the condition of the surface counts more than the quality of the metal below it. Silver has the lowest resistivity of all metals, and a plating of a few micrometres is thicker than the skin depth on all the amateur bands above 7 MHz. For that reason, silver-plated conductors are used in cavities, filters, relays and connectors for the VHF, UHF and microwave bands. The disadvantage is that silver tarnishes, but the black silver sulphide is a fairly good conductor and the effect on the resistance is small. A greater risk is the corrosion of the contact points between different metals, where oxide of aluminium or green copper salts form a barrier of high resistance.
On the contrary, a rough or dirty surface lengthens the path of the current. A stranded wire that has been out in the weather for several years can have corroded strands, and each strand surface is a separate conductor with a few contact points. In a rope of fine wires the current uses the outside of each strand, and the effective resistance can be higher than that of a solid wire of the same total area. This is the reason why feedpoints and connectors deserve more attention than they usually get; the guide to weatherproof coax connectors describes how to keep the water out.
Litz Wire: When It Helps and When It Does Not
Litz wire is made of many thin insulated strands that are twisted or woven so that each strand takes a turn at the centre and at the surface of the bundle. If the diameter of each strand is smaller than the skin depth, the whole copper cross section is used, and the loss falls. The method is excellent for coils at low frequencies, such as the loops of an AM broadcast receiver or the inductors in a power supply operating at several tens of kilohertz. On the HF amateur bands the skin depth is already so small that the strands would have to be extremely thin, and the insulation and the contact between strands bring their own problems. For that reason you will not see Litz wire in a 20 meter loading coil; the builders of HF coils prefer a thick solid wire or a tube with spacing between the turns.
Skin Effect in Coaxial Cable
A coaxial cable has two surfaces where the skin effect acts, the outside of the centre conductor and the inside of the braid. The loss in the conductors rises with the square root of the frequency, and it accounts for most of the attenuation of a cable at HF, while the loss in the dielectric becomes important at the higher VHF and UHF bands. This is the reason why thicker cables have a lower loss: the centre conductor has a larger circumference, and so the same current flows through a larger surface. The comparison in our article on coaxial cable types reflects this, and the better cables have a solid copper centre and a double screen. A copper-plated steel or aluminium centre conductor is acceptable on the low bands where it is only a part of the loss, but the cheapest cables with a thin copper layer and a poor braid can be noticeably worse on VHF.
Practical Rules for the Workshop
- Do not worry about the wire in a full-size antenna. A wire of 1.5 to 2.5 mm is perfectly good on all HF bands; spend the effort on the support and the feedpoint.
- Make small antennas from thick conductors. Tube of 15 to 22 mm, or wide copper strap, lowers the resistance of a loop or a short radiator.
- Space the turns of a coil. A gap of about one wire diameter between the turns reduces the proximity effect.
- Keep surfaces clean. Clean and tighten joints, use an antioxidant paste on aluminium and seal the connectors.
- Use hollow conductors freely. A tube has the same RF resistance as a rod of the same diameter and weighs much less.
- Save plating for the right place. Silver plating pays off in high-power contacts and VHF to microwave hardware, not in a long wire antenna.
The Bottom Line
The skin effect pushes RF current into a thin surface layer whose depth falls with the square root of the frequency, from about 35 micrometres in copper on 80 meters to a few micrometres on the VHF bands. As a result the resistance of a conductor is higher at radio frequencies than at direct current, tubes work as well as rods, and a coil is lossier than the same wire in a straight line. For a full-size antenna the effect is small, but for short antennas, loops, loading coils, filters and cables it decides how much power is lost. Choose thick conductors, space the turns, keep every contact clean and use plating where it makes a measurable difference.
Frequently Asked Questions
What is skin depth?
It is the depth below the surface of a conductor at which the current density has fallen to about 37 percent of its surface value. In copper it is about 18 micrometres at 14 MHz.
Does the skin effect make hollow tubing worse than solid rod?
No. The current flows within a few micrometres of the outer surface, so a tube with a wall of even a fraction of a millimetre has the same RF resistance as a solid rod of the same outside diameter.
Is silver plating worth it on an HF antenna wire?
Usually not. A full-size wire has a loss resistance that is a small part of the radiation resistance, so the improvement is hardly measurable. Plating matters more for contacts, cavities and VHF to microwave parts.
Why are the loading coils on good shortened antennas so large?
A larger diameter and spaced turns reduce the proximity effect and the length of wire needed, which lowers the coil resistance and the power lost as heat.
Can I use Litz wire for HF coils?
It rarely helps above a few megahertz, because the strands would need to be thinner than the skin depth, and the extra insulation and contacts add problems. Thick solid wire or tube is the normal choice on HF.
Does the skin effect cause the loss in coax cable?
It causes much of it at HF. The conductor loss rises with the square root of the frequency, and thicker cables lose less because the current flows over a larger surface.