# Skin depth calculator

This calculator calculates the skin depth in a uniform round conducting material.

SkinDepth=(2*resistivity/(2*pi*frequency*permeability))^0.5

Rrf/Rdc uses (Knight 2013).

 F (MHz) Resistivity (µΩm) Conductivity (MS/m) Relative permeability µ Round conductor diameter (mm) Skin Depth δ (µm) Rrf/Rdc

# Resistivity and permeability

Resistivity of a material is the resistance from face to opposite face of a 1m cube of a material. Resistivity varies with different metals, a few common conductors are listed below.

Permeability is the ratio of flux density to magnetising force, self inductance is proportional to permeability.

 Conductor Resistivity (µΩ-m) Relative Permeability (µr) Conductivity (MS/m) Copper 0.0168 59.52 1 Silver 0.0159 62.89 1 Aluminium 0.0282 35.46 1 Aluminium 7xxx annealed 0.045 22.22 1 ZA ZAL 0.059 17 1 Zinc 0.059 16.95 1 Brass 0.064 15.63 1 Nickel 0.064 15.63 1240 Iron 0.100 10.00 200 Tin 0.109 9.17 1 Solder (63/37 Eutectic) 0.145 6.90 1 Mild steel 0.20 5.00 800 Lead 0.22 4.55 1 Stainless steel 316 0.75 1.33 1 Stainless steel 17-7 PH 0.82 1.22 120

A note about stainless steels. Pure austenitic steels do not exhibit ferro magnetism, relative permeability is unity. Many stainless steels are austenitic, but the process of hardening them, or the hardening as a result of working them (eg drawing wire) can create martensite, and they may exhbit µr significant greater than unity. Be suspicious of hardened stainless steel, check it with a magnet. If it is attracted to the magnet, it may have high µr and as a result may have quite high RF resistance. Stainless 316 tends to not develop ferromagnetism with work, 304 a little, and in the table above, 17-7PH has quite high µr in the hardened state (you wouldn't use it in the annealed state).

For a simple uniform round conductor with diameter much greater than skin depth, Rrf/Rdc is approximately diameter/(4*δ).

# Examples

## Example 1

A very popular form of commercial ladder line is that using #18 wire, comprised of 19 strands of #31 30% IACS conductivity copper clad steel. The copper cladding on such a conductor is about 14µm in thickness.

What is the lowest frequency at which RF resistance will be equivalent to a copper conductor?

For copper like performance, we need the cladding to be at least three times the skin depth, so we need to find the frequency where skin depth is equal to 14/3=4.67µm.

Calculating skin depth in copper at 1MHz, we get 65.23µm. Since the skin depth is inversely proportional to square root of frequency, the frequency where skin depth is the target 4.67µm will be (65.23/4.67)^2*1=195MHz.

At frequencies where the skin depth is less than about one third of the copper cladding thickness, the effective RF resistance is determined almost solely by the copper cladding (Terman, 1955, 21). For conductors with 14µm copper cladding, the effective RF resistance above about 200MHz is almost identical to copper, fine for their original purpose, VHF TV feed line.

## Example 2

The question is whether a certain antenna for 3.5MHz is made from #12 (2mm) Alumoweld (Aluminium clad steel) single strand, and the question is whether the RF resistance near equivalent to Aluminium.

The RF resistance will be near equivalent to the cladding material (Aluminium) if the cladding thickness is at least three times skin depth at the frequency of interest.

The wire specifications state that the Aluminium cladding is 10% of the radius, so for a 2mm diameter wire, the cladding is 0.1mm or 100µm in thickness.

From the table, the resistivity of Aluminium is 0.0282µΩm and relative permeability is 1.

Entering that data into the calculator, the skin depth is 45µm, and the cladding needs to be 3*45=135µm for Aluminium like performance. In this case, it is less than that and resistance will be higher than an equivalent solid Aluminium conductor.

Interesting to note that for this wire, above 6.5MHz (where there is at least three skin depths of cladding), although the resistivity of Aluminium is 67% higher than Copper, the effective RF resistance of a round conductor is the square root of 1.67 times or 30% higher than that of a Copper conductor of the same size. This is due to the fact that the current flows to a greater depth in the higher resistivity material, offsetting some of the effect of the higher resistivity. Alternatively, the Aluminium conductor has similar RF resistance to a copper conductor of three quarters of the diameter.