Skin Depth
δ = 1 / √(πfμσ)
Quick answer
This calculator solves δ = 1 / √(πfμσ) for δ. With Frequency 10 MHz, Permeability (H/m) 0.001 H/m, Conductivity (S/m) 1 × 10⁶ S/m, the result is 5.64 × 10⁻⁶ m.
Calculator
Formula
Description
At high frequencies, alternating current concentrates near the surface of a conductor due to eddy currents generated by the changing magnetic field. The skin depth is the distance from the surface at which the current density drops to 1/e (about 37%) of its surface value. Beyond about 3-5 skin depths, virtually no current flows. This effect increases the effective resistance of conductors at high frequencies because less of the cross-sectional area is utilized. Skin effect is a major design consideration for RF circuits, power transmission at 50/60Hz, and high-speed digital signal traces.
Variables
- δ — Skin depth (m)
- f — Frequency (Hz)
- μ — Permeability of the conductor (H/m)
- σ — Conductivity of the conductor (S/m)
Practical Notes
For copper at room temperature (σ = 5.8×10⁷ S/m, μ = μ₀): skin depth at 60 Hz is 8.5mm, at 1 MHz is 66μm, at 1 GHz is 2.1μm. This is why RF PCB traces only need to be a few skin depths thick. Litz wire (bundles of thin insulated strands) is used at kHz-MHz frequencies to mitigate skin effect losses in inductors and transformers.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| f | Frequency | MHz | Hz, kHz, MHz, GHz |
| mu | Permeability (H/m) | H/m | H/m |
| sigma | Conductivity (S/m) | S/m | S/m |
Step by step
- 1. What you know: Frequency 10 MHz, Permeability (H/m) 0.001 H/m, Conductivity (S/m) 1 × 10⁶ S/m
- 2. The relation: δ = 1 / √(πfμσ)
- 3. Substitute: f = 10 MHz, mu = 0.001 H/m, sigma = 1 × 10⁶ S/m
- 4. Result: δ = 5.64 × 10⁻⁶ m
Worked examples
Minimum range
Given: Frequency 100 kHz, Permeability (H/m) 1 × 10⁻⁷ H/m, Conductivity (S/m) 1000 S/m
Result: δ = 0.1784 m
Low range
Given: Frequency 1 MHz, Permeability (H/m) 1 × 10⁻⁶ H/m, Conductivity (S/m) 10000 S/m
Result: δ = 0.005642 m
Typical
Given: Frequency 10 MHz, Permeability (H/m) 0.001 H/m, Conductivity (S/m) 1 × 10⁶ S/m
Result: δ = 5.64 × 10⁻⁶ m
High range
Given: Frequency 100 MHz, Permeability (H/m) 1 H/m, Conductivity (S/m) 5.8 × 10⁷ S/m
Result: δ = 7.41 × 10⁻⁹ m
Maximum range
Given: Frequency 1 GHz, Permeability (H/m) 10 H/m, Conductivity (S/m) 5.8 × 10⁸ S/m
Result: δ = 2.34 × 10⁻¹⁰ m
How δ changes with Frequency
| Frequency (input) | δ (result) |
|---|---|
| 1 MHz | 1.78 × 10⁻⁵ m |
| 2.5 MHz | 1.13 × 10⁻⁵ m |
| 5 MHz | 7.98 × 10⁻⁶ m |
| 7.5 MHz | 6.51 × 10⁻⁶ m |
| 10 MHz | 5.64 × 10⁻⁶ m |
| 15 MHz | 4.61 × 10⁻⁶ m |
| 20 MHz | 3.99 × 10⁻⁶ m |
| 40 MHz | 2.82 × 10⁻⁶ m |
| 70 MHz | 2.13 × 10⁻⁶ m |
| 100 MHz | 1.78 × 10⁻⁶ m |
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<p><a href="https://vbatpower.com/formulas/skin-depth/">Skin Depth</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Skin Depth?
Use δ = 1 / √(πfμσ). With Frequency 10 MHz, Permeability (H/m) 0.001 H/m, Conductivity (S/m) 1 × 10⁶ S/m, δ works out to 5.64 × 10⁻⁶ m.
What is the formula for Skin Depth?
The formula is δ = 1 / √(πfμσ). At high frequencies, alternating current concentrates near the surface of a conductor due to eddy currents generated by the changing magnetic field.
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