Advanced Skin Depth, AC Resistance & Inductance Calculator

Skin Depth & Effect Analyzer

Advanced Electromagnetic Analysis

Calculate AC Resistance ($R_{ac}$), Internal Inductance ($L_{int}$), Skin Depth ($\delta$), and Power Density heatmaps. Features Levasseur precision approximations, temperature correction, and high-precision material properties for Power (50/60Hz) and RF (MHz/GHz) applications.

LOAD SCENARIO:

Cu Busbar (50Hz)

RF Coax (100MHz)

PCB Trace (1GHz)

1. Material & Environment

Conductor Material

Operating Temperature ($T$) (°C)

System Frequency ($f$)

2. Conductor Geometry & Load

Shape

Diameter ($D$) (mm)

Length ($L$) (meters)

Load Current ($I_{rms}$) (Amps)

Analysis Report

Method: Levasseur (High-Precision)
Date:

Electrical Performance

Skin Depth ($\delta$)	0.00 mm
DC Resistance ($R_{dc}$)	0.00 mΩ
AC Resistance ($R_{ac}$)	0.00 mΩ
AC/DC Ratio ($K_s$)	1.00
Internal Inductance ($L_{int}$)	0.00 nH/m
Effective Area Usage	100 %
Voltage Drop ($V_{drop}$)	0.00 V
Power Loss Total ($P_{loss}$)	0.00 Watts
Surface Power Density	0.00 W/cm²

Resistivity corrected to 75°C: 0 $\Omega \cdot m$.

Current Density Heatmap

Density Decay Profile

Step-by-Step Calculation

1. Skin Depth Calculation ($\delta$)
The effective depth of current penetration based on material resistivity ($\rho$) and frequency ($f$).

2. AC Resistance Ratio ($K_s = R_{ac}/R_{dc}$)
Using Levasseur's approximation for high precision across frequency ranges.

3. Internal Inductance ($L_{int}$)
Internal magnetic flux contribution, which decreases as skin effect pushes current to the surface.

Technical Reference Manual

Introduction

When Alternating Current (AC) flows through a conductor, a time-varying magnetic field induces eddy currents that oppose the main flow at the center and reinforce it at the surface. This "crowding" effect is the Skin Effect.

Concept

Skin Depth ($\delta$)

Defined as the depth where current density falls to $1/e$ (approx 37%) of surface density. At 5$\delta$, current is effectively zero.

$$ \delta = \sqrt{\frac{\rho}{\pi f \mu}} $$

Physics

AC vs DC Resistance

DC uses the full cross-section. AC uses a thin shell. The ratio $K_s = R_{ac}/R_{dc}$ increases with frequency. This calculator uses Levasseur's approximation for <0.5% error across the spectrum.

Analysis

Internal Inductance

At DC, $L_{int} = \mu/8\pi$ H/m. As frequency rises and current hugs the surface, the internal magnetic flux linkage drops to zero. Critical for signal integrity in PCBs.

Signal Integrity

Power Applications

For 50/60Hz busbars (>2000A), skin effect is significant. Engineers use hollow tubes or laminated bars to maximize surface area vs weight.

Power

RF Applications

At GHz, skin depth is microns. Conductors are often silver-plated to lower resistance at the surface where 99% of current flows. Core material conductivity matters less.

RF / Microwave