What is Skin Depth?

Skin depth (δ) is the distance into a conductor where an electromagnetic (EM) wave's amplitude reduces to 1/e (≈37%) of its surface value due to absorption. It describes how deeply RF and EM energy can penetrate conductive materials.

At higher frequencies, skin depth decreases dramatically, confining current to the conductor's surface layer. This effect is crucial in design of shielding, coaxial cables, waveguides, antennas, and high-frequency circuits where current flows primarily on conductor surfaces.

Skin Depth Formula

\delta = \frac{1}{\sqrt{\pi f \mu \sigma}}

Skin depth in meters, where f = frequency (Hz), μ = permeability (H/m), σ = conductivity (S/m).

\mu = \mu_0 \mu_r = 4\pi \times 10^{-7} \times \mu_r

Permeability from free-space permeability μ₀ and relative permeability μᵣ.

\rho = \frac{1}{\sigma}

Resistivity (ρ) is the reciprocal of conductivity (σ).

Key Relationships

Skin depth has several important dependencies:

Inverse frequency: Higher frequency → smaller skin depth (exponentially).
Inverse conductivity: Better conductors → smaller skin depth.
Permeability: Higher μᵣ → smaller skin depth (magnetic materials confine EM waves more).
Doubling frequency: Skin depth reduces by factor of √2 ≈ 1.41.

Material Conductivities

Reference conductivity values (S/m) at room temperature for common materials:

Copper: 5.96 × 10⁷ S/m (excellent conductor)
Aluminum: 3.77 × 10⁷ S/m (good conductor)
Seawater: ~5 S/m (moderate conductor)
Soil: 0.01–1 S/m (varies widely)
Dry rock: 10⁻⁶–10⁻³ S/m (insulating)

How to Use the Skin Depth Calculator

Enter frequency: Choose units Hz, kHz, MHz, or GHz.
Input conductivity: Enter material conductivity in S/m (e.g., copper = 5.96e7).
Set relative permeability: Most conductors μᵣ ≈ 1; iron/nickel μᵣ >> 1.
Click Calculate: Get skin depth and resistivity.
Review results: Interpret penetration depth and material properties.

Practical Applications

Skin depth is essential in:

EMI/RFI Shielding: Determining required shield thickness for frequency attenuation.
Coaxial & Waveguides: Understanding current distribution and losses.
Antenna Design: Surface current behavior on conductors.
Geophysics: EM wave penetration in soil/rock for exploration.
Plating & Surface Treatment: Predicting electrical behavior of thin coatings.
High-Frequency PCB Design: Transmission line impedance and losses.

Practical Example

Scenario: 1 MHz signal in copper (σ = 5.96×10⁷ S/m, μᵣ = 1).

δ = 1 / √(π × 10⁶ × 4π×10⁻⁷ × 5.96×10⁷)
δ ≈ 1 / √(223.3) ≈ 67 μm
At 1 MHz, EM energy penetrates ~67 micrometers into copper.
At 10 MHz (10× frequency), δ ≈ 21 μm (reduces by √10 ≈ 3.16).

This explains why thick copper shielding is unnecessary at high frequencies; thin foil suffices.

Why does skin depth decrease at higher frequencies?

Higher frequencies induce stronger eddy currents in the conductor surface, which create opposing magnetic fields that confine energy to a thin surface layer.

What does "1/e" mean in skin depth?

The field amplitude at depth δ is reduced to 1/e ≈ 0.368 (about 37%) of the surface value. Beyond δ, the field continues to decay exponentially.

How thick should shielding be?

At least 3–5 skin depths for ~99% attenuation. Use this calculator to find required thickness for your frequency and material.

Does material type matter (copper vs aluminum)?

Yes. Conductivity (σ) directly affects skin depth. Better conductors have smaller skin depth, improving shielding effectiveness.

What is relative permeability (μᵣ)?

It compares material permeability to free space. Most metals μᵣ ≈ 1; iron/nickel μᵣ much greater than 1, reducing skin depth significantly.

Skin Depth Calculator – Electromagnetic Wave Penetration

Skin Depth Calculator

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