Analysis of coupled circuits

ANALYSIS OF COUPLED CIRCUITS

Consider the coupled circuits.

Each circuit contains a voltage source. As both currents i, and i2 enter the coils through the dotted ends, M is taken as positive. By applying KVL, the two loop equations may be written as below:

In the sinusoidal steady state the above equations become,

(R₁ + jωL₁) I₁ + jωMI₂ = E₁ … (21)

joM I₁ + (R₂ + jωL₂) = E₂ … (22)

In the matrix form, the last two equations may be written as,

The equations (21) & (22) may be written as

[R₁ + jω (L₁ – M + M) I₁ ] E₁ … (24)

and jωMI₁ + (R₂ – jω (L₂ – M + M) ] I₂ … (25)

The coupled circuit of fig. 5.20 may be now re-drawn as in fig. 5.28. It is called conductively coupled equivalent circuit of the mutually coupled circuit. It is so called because of the common conducting element M.