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Transformer models

Multi-winding transformer with signed turns for ratio and polarity Compare its models in the same order shown in the component inspector.

Symbol

Transformer symbol11
Default symbol for a new Transformer component.

Model choice belongs to each placed Transformer component. Changing one component does not change other instances or the default for future placements.

1

Ideal

Turns ratio only, with no magnetizing, leakage, or winding loss.

Default
Qualified analyses
  • AC sweep
  • Transient

Model definition

The Ideal model enforces the signed turns ratio between each winding and the first primary winding. A negative turns value reverses that winding's dot polarity.

It transfers voltage, current, and impedance without magnetizing current, leakage flux, copper loss, core loss, or saturation.

Equations

ni=NiN1,vi=niv1n_i=\frac{N_i}{N_1},\qquad v_i=n_i v_1
Each winding voltage is referred to the first primary winding. The sign of nᵢ sets dot polarity.
i1+∑i=2mniii=0i_1+\sum_{i=2}^{m}n_i i_i=0
The dependent current sources enforce instantaneous power conservation across all windings.
is=−ipn,Zin=Zsn2i_s=-\frac{i_p}{n},\qquad Z_{\mathrm{in}}=\frac{Z_s}{n^2}
For two windings, current and reflected impedance reduce to the familiar ideal-transformer relationships.

Parameters

This model has no editable model parameters.

Limits

  • No-load current is zero.
  • Leakage inductance, winding resistance, core loss, and saturation are omitted.
  • Only AC sweep and Transient analyses are qualified.
2

Linear

Adds magnetizing inductance, finite coupling/leakage, and winding resistance. No saturation.

Qualified analyses
  • AC sweep
  • Transient

Model definition

The Linear model represents each winding with an inductor and series resistance, then couples the inductors with the selected coupling coefficient.

Magnetizing inductance is primary-referred. OhmSpice scales every other winding inductance by the square of its signed turns ratio.

Equations

ni=NiN1,Li=ni2Lmn_i=\frac{N_i}{N_1},\qquad L_i=n_i^2L_m
Magnetizing inductance Lₘ is referred to the first primary. Every winding inductance scales with turns squared.
Mij=kLiLj,0<k<1M_{ij}=k\sqrt{L_iL_j},\qquad 0<k<1
Every winding pair uses the same coupling coefficient. Turn signs determine the mutual-voltage polarity.
vi=Rwii+Lidiidt+∑j≠isijMijdijdtv_i=R_w i_i+L_i\frac{\mathrm di_i}{\mathrm dt}+\sum_{j\ne i}s_{ij}M_{ij}\frac{\mathrm di_j}{\mathrm dt}
Each winding is a series resistance and coupled inductor. sᵢⱼ is +1 or −1 from the two winding polarities.
Lsc,1=Lm(1−k2),Xm=2πfLmL_{\mathrm{sc},1}=L_m(1-k^2),\qquad X_m=2\pi fL_m
For a two-winding transformer, the short-circuit primary inductance represents leakage while Xₘ sets no-load current.

Parameters

ParameterDefaultAccepted values
Magnetizing inductancePrimary-referred magnetizing inductance.10 mHGreater than 0
CouplingCoupling coefficient between windings (0 to 1, exclusive).0.999Greater than 0 and less than 1
Winding resistanceSeries resistance applied to each winding.100 mΩAt least 0

Limits

  • The core remains linear, with no saturation, hysteresis, or frequency-dependent core loss.
  • The same winding-resistance value applies to every winding.
  • Coupling must remain below 1 because exact unity coupling is singular in this formulation.
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