Coupling Factor

The coupling factor (or coupling coefficient) is a measure of how effectively two inductors or coils transfer energy between each other through their magnetic fields. It quantifies the strength of magnetic interaction, with values ranging from 0 (no coupling) to 1 (perfect coupling), and is a key parameter in the analysis and design of transformers, coupled inductors, and other magnetically linked circuits.

Series-aiding Series-opposing Method

According to international standard IEC 61007:2020, Clause 4.4.7, the coupling factor between windings is dependent on the following factors between the two inductors:

where,

  • Lsa is the inductance in aiding series
  • Lso is the inductance in the opposing series
  • L10 is the inductance of the primary winding with the secondary open-circuit
  • L20 is the inductance of the secondary winding with the primary open-circuit

Lsa (Aiding Series Inductance)

Here, current flows in the same direction through both windings (terminals connected in aiding series). Magnetic fields reinforce each other, maximizing total inductance, this quantifies mutual inductance under additive flux conditions.

Lsa is measured by passing current in the same direction through both windings, resulting in maximum inductance due to the reinforcing magnetic fields.
Set up for Aiding Series Inductance

Lso (Opposite Series Inductance)

Current flows in opposite directions through the windings (terminals connected in opposing series). Magnetic fields partially cancel, minimizing total inductance, this quantifies mutual inductance under subtractive flux conditions.

Lso is obtained by running current in opposite directions through the windings, leading to minimum inductance as the magnetic fields partially cancel.
Set up for Opposite Series Inductance showing terminal allotment

L10 (Primary Open-Circuit Inductance)

Current flows through the primary winding while the secondary is open-circuited. Measures primary self-inductance.

L10 is the self-inductance of the primary winding measured with the secondary open-circuited, capturing the effect of induced voltage in the secondary.
Set up for Primary Open Circuit showing the Primary and Secondary allocation to coil

L20 (Secondary Open-Circuit Inductance)

Current flows through the secondary winding while the primary is open-circuited. Measures secondary self-inductance.

L20 is the self-inductance of the secondary winding with the primary open-circuited, reflecting the induced voltage in the primary.
Set up for Secondary Open Circuit showing the Primary and Secondary allocation to coil
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