Sommaire général

Bobines d'induction en régime sinusoïdal

III. Influences entre plusieurs bobines

3. Inductance mutuelle (Mutuelle)

a. Définition

Influence de la bobine `cc B_1` sur la bobine `cc B_2`

Dans le dispositif ci-contre, la bobine `cc B_1` est parcourue par un courant `i_1(t)` non nul, l’intensité dans la bobine `cc B_2` est nulle.

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B1B2i1(t)v1(t)B1B2i2(t) = 0v2(t)e2(t)e1(t)Φ(t)

Le flux `Phi_12(t)` dépend de `i_1(t)` mais aussi des caractéristiques géométriques du circuit.

Cette dépendance est représentée par un coefficient `M_12`, appelé « coefficient de mutuelle induction » ou « inductance mutuelle » ou « mutuelle », tel que  `Phi_12(t) = M_12 .i_1(t)`. Il traduit l’influence de la bobine `cc B_1` sur la bobine `cc B_2`.

Influence de la bobine `cc B_2` sur la bobine `cc B_1`

Dans le dispositif précédent, l’intensité dans la bobine `cc B_1` est nulle, la bobine `cc B_2` est parcourue par un courant d’intensité `i_2(t)` non nulle.

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B1B2i1(t) = 0v1(t)B1B2i2(t)v2(t)e2(t)e1(t)Φ(t)

Par analogie avec ce qui précède, on introduit la mutuelle `M_21` telle que : `Phi_21(t) = M_21 . i_2(t)`. Cette mutuelle `M_21` traduit l’influence de la bobine `cc B_2` sur la bobine `cc B_1`.

L’influence de la bobine `cc B_1` sur la bobine `cc B_2` étant identique à celle de la bobine `cc B_2` sur la bobine `cc B_1`, les coefficients de mutuelle sont identiques : `M_12 = M_21 = M`. On peut donc écrire `Phi_12(t) = M .i_1(t)` et `Phi_21(t) = M .i_2(t)`

Coefficient de couplage

On appelle coefficient de couplage entre les deux bobines la grandeur : `k = M/sqrt{L_1 . L_2}`

En pratique, pour `k` proche de 1, le couplage est dit serré ; pour `k` proche de 0, il est dit lâche.

Remarque : la notion de mutuelle peut être étendue à un nombre quelconque de circuits électriques.