Free RF Skin Depth & AC Resistance Calculator
Calculate high-frequency skin depth (δ), AC-to-DC resistance ratio (Rac/Rdc), and optimal Litz wire gauge for RF coils and SMPS magnetics.
📡 Conductor & Frequency Parameters
📊 Skin Depth & High-Frequency Loss
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How the Skin Effect Multiplies High-Frequency Resistance
When direct current (DC) flows through a wire, current density is distributed evenly across the conductor's entire cross-sectional area. However, when alternating current (AC) flows, changing magnetic fields induce circular eddy currents inside the wire that oppose current flow in the center and reinforce it near the outer surface.
1. The Classical Skin Depth Equation
The skin depth ($delta$) is defined as the depth beneath the conductor surface where current density drops to $1/e$ (approx 36.8%) of its surface value:
For copper ($
ho = 1.724 imes 10^{-8} Omegacdot ext{m}$, $mu_r = 1.0$), this simplifies to the famous rule:
δ (mm) ≈ 66.1 / √f_Hz
- At 60 Hz (mains): $delta = 8.5 ext{ mm}$ (0.33 inches) — skin effect is negligible in household wire.
- At 100 kHz (SMPS): $delta = 209 mu ext{m}$ (8.2 mils).
- At 10 MHz (HF Radio): $delta = 20.9 mu ext{m}$ (0.82 mils).
- At 2.4 GHz (WiFi): $delta = 1.35 mu ext{m}$ (53 micro-inches!).
2. Why Litz Wire Defeats Skin Effect
Litz wire (from German Litzendraht, woven wire) bundles hundreds of individually insulated, ultra-fine copper strands woven in a specific transposition pattern so each strand occupies every position from the center to the outside equally. By keeping each strand's diameter smaller than $2 imes$ the skin depth ($le 2delta$), current remains evenly distributed throughout the entire bundle cross-section.
Frequently Asked Questions
Why are RF tank coils made of hollow copper tubing instead of solid wire?
At 14 MHz or 28 MHz, current only travels in the outermost 15 to 20 microns of copper. The center 98% of a solid wire carries zero current but adds massive thermal weight and cost. Using hollow copper refrigeration tubing provides maximum surface area with minimal weight and allows liquid cooling.
Does silver plating copper wire really improve RF performance?
Yes! Because pure silver has roughly 8% lower electrical resistivity than copper, and high-frequency current travels exclusively in the outermost microns, plating a thin 5 to 10 micron layer of silver onto copper wire significantly boosts Q-factor and reduces I2R ohmic heat in RF power amplifiers.
What is the proximity effect and how does it relate to skin effect?
The skin effect describes current crowding caused by a conductor's own internal magnetic field. The proximity effect describes current crowding caused by the magnetic fields of adjacent conductors (such as tightly packed transformer winding layers), which can inflate AC resistance by 5x to 10x beyond the skin effect alone.
Can Litz wire be used at microwave frequencies (e.g. 1 GHz)?
No. Above 2 to 3 MHz, capacitive coupling between adjacent insulated strands creates displacement currents that bypass the insulation, causing the bundle to behave as a single solid conductor and negating the Litz effect.