Source: https://guthlabs.ai/docs/instruments/skin-effect-skin-depth-calculator/mechanism/
instrument mechanism / verified-clean
# Skin Effect / Skin Depth Calculator mechanism
The inspectable method record for Skin Effect / Skin Depth Calculator, kept separate from implementation and qualification.
Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**
## Model scope
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.
- 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.
## Units and conventions
- 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.
## Inspectable vector
One of 4 source-bound review vectors:
````
{
"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."
}
````
## Failure boundary
**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.
## Other records
[01**Overview**]()[03**Implementation**]()[04**Qualification**]()
## Sources and evidence
These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.
- `VERIFIED_LEDGER.json`
- `evidence-tranche7/tranche7-results.json`
- `BOUNDARY_HAZARD_CATALOG.json`