Library / Electrical / ELE-29
Electrical
Skin depth
Depth to which an alternating current or radio wave penetrates a conductor before dropping to 37 % of its surface value.
- Ref
- ELE-29
- Rev
- v1
- Field
- Electrical
- Result
- δ [µm]
f is the frequency in MHz, μᵣ the relative permeability (1 for copper, aluminium and most non-magnetic metals) and σ the conductivity in MS/m (about 58 for copper). δ is the depth at which the field and current density have dropped to 1/e (37 %) of the surface value; the answer is in micrometres.
Depth to which an alternating current or radio wave penetrates a conductor before dropping to 37 % of its surface value. Higher frequencies stay nearer the surface.
Calculator
- Thickness giving about 99 % screening, 5δ330.4 µm
- Skin depth at 100 times the frequency6.609 µm
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- Copper at 1 MHz has a skin depth of 66 µm, but at 50 Hz it is 9.3 mm. A thin foil screens radio waves well but a thick bar is needed for mains frequencies.
- Current crowds into the outer layer, so a thick wire at high frequency has a higher resistance than at DC. This is why RF conductors are hollow or silver-plated and why coil resistance grows with frequency.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (µm) | Local step | Change in result |
|---|---|---|---|---|---|---|
| f Frequency | 0.001 to 100,000 MHz | 0.209 | 2,090 | 2,090 | +10% | −4.65 % |
| σ Conductivity | 0.1 to 100 MS/m | 50.33 | 1,592 | 1,541 | +10% | −4.65 % |
| μr Relative permeability | 1 to 1,000 | 2.09 | 66.09 | 64 | +10% | −4.65 % |
Sweep of Frequency
| Frequency (MHz) | Skin depth (µm) |
|---|---|
| 0.001 | 2,090 |
| 0.01 | 660.9 |
| 0.1 | 209 |
| 1 | 66.09 |
| 10 | 20.9 |
| 100 | 6.609 |
| 1,000 | 2.09 |
| 10,000 | 0.6609 |
| 100,000 | 0.209 |
Sweep one variable
Variables and how each one contributes
Skin depth
What the equation gives you. Everything else feeds it.
Frequency
The frequency of the current or wave, in MHz. Inverse square root: 100 times the frequency makes the depth 10 times smaller.
Relative permeability
Relative permeability of the conductor. Inverse square root: a magnetic steel with μᵣ of 100 has a skin depth 10 times smaller than copper at the same frequency.
Conductivity
Electrical conductivity of the metal, in MS/m. Inverse square root: a better conductor has a thinner skin. Aluminium (37 MS/m) is about 25 % thicker than copper.
Worked example with the values above
- Convert units: f = 1 MHz = 1,000,000 Hz, σ = 58 MS/m = 5.8×107 S/m.
- Product π f μᵣ μ₀ σ = 2.29×108; square root 15,130.
- δ = 1 / 15,130 = 66.09 µm.
Assumptions and limits
- A good conductor, where conduction current far exceeds displacement current.
- A flat surface and a conductor much thicker than δ, with linear μ and σ.
Common mistakes
- Thinking the field is zero beyond δ. It has only fallen to 37 %, and about 5δ is needed for a deep cut.
- Entering f in Hz when the box is in MHz.
Statistics and uncertainty
δ ∝ (f μᵣ σ)−½, so the relative errors are halved: 10 % uncertainty in conductivity (typical of an alloy) gives about 5 % in δ. Surface roughness and plating change the real loss more than the formula suggests.
Where it is used
- Choosing the thickness of screening, gaskets or enclosure plating.
- Estimating AC resistance of conductors at radio frequency.
Maths you need
- Exponential decay: e⁻¹ = 37 %
- Square roots: inverse square root scaling