Source: https://guthlabs.ai/docs/instruments/mutual-inductance-coupled-coil-calculator/mechanism/

instrument mechanism / verified-clean

# Mutual Inductance / Coupled Coil Calculator mechanism

The inspectable method record for Mutual Inductance / Coupled Coil Calculator, kept separate from implementation and qualification.

Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**

## Model scope

The formulas M = k*sqrt(L1*L2), Ltotal(aiding) = L1 + L2 + 2M, and Ltotal(opposing) = L1 + L2 - 2M are standard under the stated unit and polarity assumptions. Review is required because the input-unit policy, k sign/range, physical constraints, and honest user-facing limitations are not specified.

- The algebraic formulas are standard, but the sign convention for k is unspecified. If k is a nonnegative coupling magnitude, M is normally reported as a magnitude and the aiding/opposing choice supplies the sign. If k may be signed, the interaction between the sign of M and the aiding/opposing mode must be defined explicitly.

- The specification does not state that L1 and L2 must be positive finite self-inductances, or that the coupling coefficient must satisfy 0 <= k <= 1 for passive coupled coils.

## Units and conventions

- L1 and L2 must use the same inductance unit before multiplication or addition; M and Ltotal use that same unit.

- k is dimensionless.

- sqrt(L1*L2) has the same inductance unit as L1 and L2 because both inductances use the same unit.

- The test vector with mixed H and mH explicitly converts all values to henries before calculation.

- Aiding and opposing refer to the relative winding-polarity/current-reference convention, not merely a numerical label.

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "L1": 0.004,
    "L1_unit": "H",
    "L2": 0.009,
    "L2_unit": "H",
    "k": 0.5,
    "connection": "series aiding"
  },
  "expected_outputs": {
    "M": 0.003,
    "M_unit": "H",
    "Ltotal": 0.019,
    "Ltotal_unit": "H"
  },
  "working": "M = k*sqrt(L1*L2) = 0.5*sqrt(0.004*0.009) = 0.5*sqrt(0.000036) = 0.5*0.006 = 0.003 H. Ltotal(aiding) = L1 + L2 + 2M = 0.004 + 0.009 + 2(0.003) = 0.004 + 0.009 + 0.006 = 0.019 H."
}
````

## Failure boundary

**BREAK_CLAIMED** · SELF_FLAGGED

The specification leaves the handling of negative inductances, signed coupling coefficients, and invalid square-root arguments unspecified. It can also produce different results if the sign of k and the aiding/opposing switch are both used to encode winding orientation.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/mutual-inductance-coupled-coil-calculator/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/mutual-inductance-coupled-coil-calculator/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/mutual-inductance-coupled-coil-calculator/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-tranche5/tranche5-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`