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Multi turn winding inductance

# 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:

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:

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

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

*L*_{1} = *Φ* / *i*

**Multi turn winding inductance (series connection):**

*L*_{n} = *n*·*L*_{1} = *n · Φ* / *i* = *n* · *n·ψ* / *i* = *n*^{2} ·*ψ* / *i* = *n*^{2} · L

**Multi turn winding inductance (parallel connection):**

*L*_{n} = *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:

- Replace multi turn winding by single turn with total current
*I* = *n*·*i*.
- Calculate magnetic flux
*Φ*.
- Calculate inductance of the single turn
*L* = *Φ* / *I*.
- Multiply inductance by the
*n*^{2}.

Download one turn loop simulation problem files.