Skin Effect AC Resistance
Rac = Rdc × (1 + (d/(2δ))²)
Quick answer
This calculator solves Rac = Rdc × (1 + (d/(2δ))²) for Rac. With DC Resistance 50 mΩ, Wire Diameter 10 mm, Skin Depth 22 mm, the result is 52.58 mΩ.
Calculator
Formula
Description
At high frequencies, the skin effect forces current to flow near the surface of a conductor, effectively reducing the useful cross-sectional area and increasing resistance. This simplified formula estimates the AC resistance increase as a function of the wire diameter relative to the skin depth. When the wire diameter is much less than the skin depth (d << δ), Rac ≈ Rdc and skin effect is negligible. When d >> δ, the AC resistance increases significantly. This effect is particularly important for power transmission at 50/60 Hz with large conductors and for RF applications.
Variables
- Rac — AC resistance at the operating frequency (Ω)
- Rdc — DC resistance of the conductor (Ω)
- d — Wire diameter (m)
- δ — Skin depth at the operating frequency (m)
Practical Notes
For copper at room temperature: skin depth at 60 Hz = 8.5 mm, at 1 kHz = 2.1 mm, at 1 MHz = 66 µm, at 1 GHz = 2.1 µm. Litz wire (multiple thin insulated strands) mitigates skin effect at kHz to low MHz frequencies. At microwave frequencies, only a thin surface layer carries current, so surface roughness and plating quality affect resistance significantly.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| Rdc | DC Resistance | mΩ | mΩ, Ω, kΩ, MΩ |
| d | Wire Diameter | mm | mm |
| delta | Skin Depth | mm | mm |
Step by step
- 1. What you know: DC Resistance 50 mΩ, Wire Diameter 10 mm, Skin Depth 22 mm
- 2. The relation: Rac = Rdc × (1 + (d/(2δ))²)
- 3. Substitute: Rdc = 50 mΩ, d = 10 mm, delta = 22 mm
- 4. Result: Rac = 52.58 mΩ
Worked examples
Minimum range
Given: DC Resistance 0.1 mΩ, Wire Diameter 0.1 mm, Skin Depth 0.22 mm
Result: Rac = 0.1052 mΩ
Low range
Given: DC Resistance 1 mΩ, Wire Diameter 1 mm, Skin Depth 2.2 mm
Result: Rac = 1.052 mΩ
Typical
Given: DC Resistance 50 mΩ, Wire Diameter 10 mm, Skin Depth 22 mm
Result: Rac = 52.58 mΩ
High range
Given: DC Resistance 0.5 Ω, Wire Diameter 100 mm, Skin Depth 220 mm
Result: Rac = 0.5258 Ω
Maximum range
Given: DC Resistance 5 Ω, Wire Diameter 1000 mm, Skin Depth 2200 mm
Result: Rac = 5.258 Ω
How Rac changes with DC Resistance
| DC Resistance (input) | Rac (result) |
|---|---|
| 5 mΩ | 5.258 mΩ |
| 12.5 mΩ | 13.15 mΩ |
| 25 mΩ | 26.29 mΩ |
| 37.5 mΩ | 39.44 mΩ |
| 50 mΩ | 52.58 mΩ |
| 75 mΩ | 78.87 mΩ |
| 100 mΩ | 105.2 mΩ |
| 0.2 Ω | 0.2103 Ω |
| 0.35 Ω | 0.3681 Ω |
| 0.5 Ω | 0.5258 Ω |
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<p><a href="https://vbatpower.com/formulas/skin-effect-ac-resistance/">Skin Effect AC Resistance</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Skin Effect AC Resistance?
Use Rac = Rdc × (1 + (d/(2δ))²). With DC Resistance 50 mΩ, Wire Diameter 10 mm, Skin Depth 22 mm, Rac works out to 52.58 mΩ.
How do you calculate resistance skin effect?
Rearrange for Rac: with DC Resistance 1 mΩ, Wire Diameter 1 mm, Skin Depth 2.2 mm, Rac is 1.052 mΩ.
What is the formula for Skin Effect AC Resistance?
The formula is Rac = Rdc × (1 + (d/(2δ))²). At high frequencies, the skin effect forces current to flow near the surface of a conductor, effectively reducing the useful cross-sectional area and increasing resistance.
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