6.1.1 Theoretical reminder

Current transformers have similar compositions to "conventional" transformers. A magnetic circuit (generally made of an iron alloy) in the shape of a torroid is surrounded by n ₁ turns on the primary and n2 turns on the secondary (see Figure 6-1).

Figure 6-1: n ₁ > 1 wound primary type current transformer

The primary can be reduced to a simple conductor passing through the torroid ( n ₁ = 1) (see Figure 6-2).

Figure 6-2: n ₁ = 1 ring type current transformer

Let I _p be the current flowing through the n ₁ primary turns and I _s be the current flowing through the n ₂ secondary turns.

According to Ampere's theorem, the sum of ampere-turns is equal to the circulation of the magnetic field vector :

: vectorial element tangent to the circle generated by the torroid (see Figure 6-1)

The magnetic circuit channels the magnetic field, which is thus tangential to the circle created by the torroid, thus is parallel to (see Figure 6-1).

Hence:

where:

• ? ₀ : magnetic vacuum permeability

• ? _r : relative permeability of the magnetic circuit (for iron ? _r ?