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Multi turn winding inductance

The inductance of multi turn winding can be calculated with DC magnetic module of QuickField. We may consider a multi turn winding as several single turns connected in series. Let's start with the single-turn winding:

single turn inductance

Inductance of the single turn winding can be obtained from the equation:

L = ψ / i, where ψ - is a flux across the winding.

To calculate the magnetic flux in QuickField you should use the integral calculator:

single turn magnetic flux linkage

Multi-turn winding, considered as a series of single-turn windings, may be shown as:

multi turn winding inductance

Magnetic flux linked with each turn is Φ = n·ψ. The single turn inductance is:

L1 = Φ / i

Multi turn winding inductance (series connection):

Ln = n·L1 = n · Φ / i = n · n·ψ / i = n2 ·ψ / i = n2 · L

Multi turn winding inductance (parallel connection):

Ln = Φ / I = n·ψ / n·i = ψ / i = L

The inductance of multi turn winding (with n turns connected in series) can be obtained by following algorithm:

  1. Replace multi turn winding by single turn with total current I = n·i.
  2. Calculate magnetic flux Φ.
  3. Calculate inductance of the single turn L = Φ / I.
  4. Multiply inductance by the n2.

Download one turn loop simulation problem files.