Transformer (coupled)

Two coupled inductors with mutual inductance M.

  • electrical
  • Modelica Standard Library
  • 4 ports
  • 3 parameters
BlockTransformer (coupled)KindmutualInductorLibraryElectrical

Description

Two magnetically coupled inductors: a transformer described by its self and mutual inductances. Use it when leakage and magnetizing inductance matter.

Example

Transformers and a saturating inductor A coupled-inductor and an ideal transformer on a 10 V sine, and an inductor that saturates as its current rises.

10 V 50 HzCoupled inductorsLoad 10 kΩv coupledGroundGround (coupled)10 V 50 Hz (ideal)Ideal transformerLoad 100 Ωv idealGround (ideal)Ground (ideal out)1 A/sCurrent sourceSaturating inductorv LGround (saturating)
In Gradara, select a Transformer (coupled) block and press F1, then choose Open example. It opens as a new model in My models, ready to run.

Also in this example:Voltage sensorGroundRampResistorSaturating inductorIdeal transformerAC voltageControlled current

Ports

Conserving terminals 4

  • 1+p1electrical

    Primary positive pin. Current into p1 is the primary current i1.

  • 1−n1electrical

    Primary negative pin.

  • 2+p2electrical

    Secondary positive pin. Current into p2 is the secondary current i2.

  • 2−n2electrical

    Secondary negative pin.

Parameters

  • Primary inductanceL11 H

    ≥ 0

    Primary self-inductance, in henries.

  • Secondary inductanceL21 H

    ≥ 0

    Secondary self-inductance, in henries.

  • Mutual inductanceM0.9 H

    ≥ 0

    Mutual inductance, in henries. For a physical coupling keep M ≤ √(L1 · L2); the coupling factor is M / √(L1 · L2).

Equations

Modelica
v1 = p1.v − n1.v, i1 = p1.i, p1.i + n1.i = 0
v2 = p2.v − n2.v, i2 = p2.i, p2.i + n2.i = 0
v1 = L1 · di1/dt + M · di2/dt
v2 = M · di1/dt + L2 · di2/dt

Implementation

Modelica Standard Library 4.1.0Modelica.Electrical.Analog.Basic.Transformer
MSL documentation

Assumptions and limitations

  • Linear: no saturation, core losses, or winding resistance. Add Resistors in series for copper loss.
  • The values are not checked: M > √(L1 · L2) is accepted but not physical.

Tips

  • The dotted ends are p1 and p2: with M > 0, a rising current into p1 makes p2 positive with respect to n2.
  • Each side needs its own path to Ground if the two circuits are otherwise separate.

See also

Select a block in Gradara and press F1 to open its page offline.