Magnetic coupling

In electronics, magnetic coupling is the physical phenomenon whereby the passage of an electric current that varies over time through a coil produces a potential difference between the ends of the other coils in the circuit. When this phenomenon occurs in an undesired way, it is called crosstalk.

This phenomenon is explained by combining Ampère's and Faraday's laws. From the first, we know that any electric current that varies in time creates a proportional magnetic field, also variable in time. The second tells us that any time-varying magnetic flux that crosses a surface closed by a circuit induces a potential difference in this circuit.

Analysis of circuits with coupled coils

Symbol of a coil with a terminal marked with a point.

For the analysis of circuits with coupled coils, a terminal of each of the coils is usually fixed —generally marking it with a dot—, so that, if the current in all the coils is entering or leaving that terminal, the voltages induced in each coil by magnetic coupling with the others will be in the same direction as the voltage of the coil itself, so they will be added to it. Conversely, if the current is incoming through the marked terminal in one of the coils and outgoing in another, the induced voltage between the two will oppose the voltage of each coil.

Coefficients of Mutual Induction

The value of the voltage induced in a coil is proportional to the coil current that induces it and to the so-called mutual induction coefficient, represented by the letter M, which is given by the expression:

${displaystyle M=Kcdot {sqrt {L_{1}cdot L_{2}}}}}}}$

Where K is the coupling coefficient that varies between 0 (no coupling) and 1 (perfect coupling) and L₁ and L₂ the inductances of the two coils.

Therefore, the total voltage in a coil L₁ through which a current I₁ passes magnetically coupled with another coil L₂ > through which a current I₂ passes would be given by the expression:

${displaystyle V_{1}=V_{L1}pm V_{M}=I_{1}cdot jomega L_{1}pm I_{2}cdot jomega M}$

The sign depends on the position of the reference terminal of each coil with respect to the currents that pass through them.