# Coupled inductors cause divergence or invalid-matrix errors

Check the complete inductance matrix for passivity. Keeping each coupling factor between -1 and 1 is necessary but does not guarantee a valid multi-inductor model.

## Compatibility

2.9.0 release target; review-build/source evidence

Published guidance with release-applicability limits. Confirm package applicability before following this guide.

## Check the model

1. Verify that every referenced inductor exists and its inductance is finite and nonnegative.
2. Check each signed k value and the orientation convention. The mutual inductance is Mij = kij × sqrt(Li × Lj).
3. Check the whole connected group's symmetric inductance matrix for positive semidefiniteness. The magnetic energy must be nonnegative for every current vector.
4. Check duplicate pair declarations: the maintained reference says their mutual inductances add.

## Interpret the current diagnostic

The maintained source documents validation of each connected coupled group, including source locations. Consistent perfect coupling can be valid; changing every k away from 1 is not a general physical correction.

Changing a load resistance or reducing the timestep can obscure an invalid circuit mode without making its inductance matrix passive. Fix the physical model first, then check timestep convergence.

## Sources and verification details

Recorded inputs/builds only. Complete walkthrough and final-package acceptance remain separate.

- VAL-009: Installed JoSIM-Pro 2.9.0 Windows. CLI passive control and non-passive three-coil rejection Tests validation behaviour, not solver accuracy across coupled models.


- support:SUP-013: Generalised editorial finding; outcome qualification retained
- josim-pro:docs/manual_source/sections/syntax.tex: Mutual inductive coupling
- validation:windows-cli-20261102: VAL-009; scope and limits recorded
- owner:technical-review-20261102: JoSIM-Pro 2.9 chosen as the public starting path; release availability must be checked before publication

- The owner accepted the modelling explanation on 2 November 2026. Applicable release/platform and unrecorded walkthrough checks remain pending.

## Related guides

- [JoSIM®-Pro reports that the matrix has no solution](/knowledge-base/josim-singular-circuit)
- [Check temperature, noise bandwidth and sample time in JoSIM®-Pro](/knowledge-base/josim-noise-settings)