Lemonergy · Studio block

Coupled inductors

Symmetric positive-definite inductance matrix; no saturation, hysteresis or winding losses

Implementation ID: mutual-inductor
Reviewed: 2026-10-27

Behavior

Conserving component solved simultaneously with the connected network. Symmetric positive-definite inductance matrix; no saturation, hysteresis or winding losses

Interface

Original Lemonergy interface view. Lines identify ports; they are not a completed simulation circuit.

Ports and observed outputs
Name	Direction	Unit	Meaning
`p`	terminal	V; A	electrical conserving connection; voltage across and current through the connected branch.
`n`	terminal	V; A	electrical conserving connection; voltage across and current through the connected branch.
`s`	terminal	V; A	electrical conserving connection; voltage across and current through the connected branch.
`t`	terminal	V; A	electrical conserving connection; voltage across and current through the connected branch.
`voltageSecondary`	output	V	Recorded voltage on the secondary port measurement from the conserving simulation.
`currentSecondary`	output	A	Recorded current on the secondary port measurement from the conserving simulation.
`current`	output	A	Recorded current measurement from the conserving simulation.

Parameters

Defaults are initial model values. Select values for your own model and operating conditions.

Configuration fields
Parameter	Unit	Default	Meaning and limits
Primary self-inductance `primaryInductanceH`	H	1	Self-inductance of the primary winding. Minimum 1e-09; Maximum 1000000000
Secondary self-inductance `secondaryInductanceH`	H	1	Self-inductance of the secondary winding. Minimum 1e-09; Maximum 1000000000
Magnetic coupling coefficient `coupling`	fraction	0.5	Signed mutual coupling; its magnitude must remain below one. Minimum -0.999999; Maximum 0.999999
Initial primary current `initialPrimaryCurrentA`	A	0	Current entering the primary winding at initialization. Minimum -1000000; Maximum 1000000
Initial secondary current `initialSecondaryCurrentA`	A	0	Current entering the secondary winding at initialization. Minimum -1000000; Maximum 1000000

Equations and rules

Vp = Lp dIp/dt + M dIs/dt
Vs = M dIp/dt + Ls dIs/dt
M = k sqrt(Lp Ls)

Worked example

Coupled inductors worked example

Editable first-party network. supply: voltageV=1; short: voltageV=0. Checks below were verified in the native execution engine.

Open Studio example after release →

Numerical checks for the bundled synthetic example
Output	Time (s)	Expected value	Unit	Absolute tolerance
voltageSecondary `target/voltageSecondary`	1	`0`	V	1e-10
currentSecondary `target/currentSecondary`	1	`-0.666666667`	A	6.666666666666666e-07
current `target/current`	1	`1.33333333`	A	1.3333333333333328e-06

Use in a workflow

Coupled inductors worked example

Symmetric positive-definite inductance matrix; no saturation, hysteresis or winding losses

Coupled inductors: Conserving component solved simultaneously with the connected network. Symmetric positive-definite inductance matrix; no saturation, hysteresis or winding losses
- Use the block reference for settings and connections.
- Implementation tested locally; public release pending.

Open Studio example after release

Connected concepts

Limits and interpretation

Symmetric positive-definite inductance matrix; no saturation, hysteresis or winding losses
Demonstration parameters are not calibrated hardware data. Singular or incompatible ideal constraints and unsupported state ranges stop the run.

Scientific and mathematical references

These sources explain the scientific and mathematical background. The behavior, interface and limits above define the Lemonergy implementation; a citation does not imply every model option in the source is implemented.

Mutual Inductance
OpenStax, Rice University
Technical reference · Underlying physical law or reduced-model basis; Lemonergy implementation choices and limits are documented separately.

Implementation sources

This reference follows the public interface and locally verified numerical checks for an upcoming release.

Contract: Lemonergy Studio public contract · Verification record: verification-2026-10-27

docs/glossary/native-block-verification.json

This implementation and its workflow uses (JSON) · Knowledge graph (JSON-LD)