Skin Effect / Skin Depth Calculator

Inspectable records

Ledger state

The current ledger marks this instrument verified clean within the source-bound verification corpus.

Area

Electrical & Electronics Engineering — Circuits, Power Systems, Electronics Lab

Tranche

tranche-7

Evidence ID

t7-092

Ledger rows

1

No ledger note is attached.

Review findings

The two core formulas are standard under SI-unit and high-frequency assumptions. The instrument should be labelled as a high-frequency isolated-round-wire skin-effect approximation, not as a general AC-resistance calculator. The copper resistivity value 1.68×10^-8 Ω·m at 20 °C is used in three vectors, and the aluminium value 2.82×10^-8 Ω·m at 20 °C is used in one; these are widely tabulated textbook entries. NEEDS_REVIEW is required because the input contract does not specify temperature, magnetic-property convention, validity checking for d≫δ, or the fallback method for thin conductors.

Formula and scope findings

• The skin-depth formula δ=sqrt(ρ/(π f μ)) is standard and equivalent to sqrt(2ρ/(ωμ)), provided f is in hertz, ρ is in ohm-metres, and μ is absolute permeability in henries per metre.
• The round-wire approximation Rac/Rdc ≈ d/(4δ) is only a high-frequency asymptote. It requires d/δ to be much greater than 1; it is not valid for thin conductors or at low frequency, where the ratio approaches 1 rather than 0.
• The claimed effective AC resistance increase is underspecified: the result is only an internal skin-effect resistance ratio for an isolated round conductor, excluding proximity effect, external magnetic fields, strand construction, and other geometry effects.
• Material resistivity must be temperature-qualified, and permeability may be frequency- and field-dependent. A material name alone is insufficient for a generally correct result.

Unit assumptions

• Frequency f is in hertz.
• Resistivity ρ is in ohm-metres.
• Wire diameter d is in metres; millimetre inputs must be converted before calculation.
• Permeability μ is absolute permeability in henries per metre, calculated as μ=μrμ0.
• For copper and aluminium in these examples, μr=1 is assumed because they are treated as nonmagnetic conductors.
• The tabulated resistivities are assumed to apply at 20 °C.

Boundary hardening

BREAK_CLAIMED · SELF_FLAGGED

The instrument can fail or mislead at zero or negative frequency, and it lacks a defined full Bessel-function calculation for the thin/intermediate-conductor branch. Unit and diameter-versus-radius ambiguity can also change the reported resistance ratio substantially.

Errata and corrections

No applied erratum is attached to this unique-name record.

Inspectable example

4 review vectors are recorded. One source-bound sample is shown below.

{
  "inputs": {
    "material": "copper",
    "resistivity_ohm_m": 1.68e-8,
    "relative_permeability": 1,
    "frequency_hz": 1000000,
    "wire_diameter_m": 0.01
  },
  "expected_outputs": {
    "skin_depth_m": 0.00006523,
    "skin_depth_um": 65.23,
    "rac_rdc_ratio": 38.33
  },
  "reference_data": {
    "copper_resistivity_ohm_m_20C": 1.68e-8,
    "copper_resistivity_source_convention": "widely tabulated standard value; CRC/IEC textbook value at 20 °C",
    "mu0_H_per_m": 0.0000012566370614,
    "mu0_source_convention": "widely tabulated standard value, μ0=4π×10^-7 H/m",
    "copper_relative_permeability": 1,
    "relative_permeability_source_convention": "widely tabulated standard value for nonmagnetic copper"
  },
  "working": "μ=μrμ0=1×1.2566370614×10^-6=1.2566370614×10^-6 H/m. δ=sqrt(ρ/(πfμ))=sqrt(1.68×10^-8/(π×1.00×10^6×1.2566370614×10^-6))=sqrt(4.2555×10^-9)=6.523×10^-5 m=65.23 μm. d/(4δ)=0.010/(4×6.523×10^-5)=0.010/2.6092×10^-4=38.33. Here d/δ≈153.3, so the high-frequency approximation is appropriate."
}

Related workflows

No source-defined multi-instrument workflow membership is recorded.

Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

• VERIFIED_LEDGER.json · VERIFIED_CLEAN
• evidence-tranche7/tranche7-results.json
• BOUNDARY_HAZARD_CATALOG.json