Magnetic Coupling and Mutual Inductance

Flashcards covering key definitions, mathematical formulas, and connection configurations for mutual inductance and magnetically coupled circuits.

Magnetic Coupling

The condition where a portion of the magnetic flux excited by current in a primary circuit is simultaneously linked with a secondary circuit.

Dynamic Definition of Mutual Inductance

The definition expressing mutual inductance through induced voltage and time-varying current: $u_2 = M \times \frac{\Delta i}{\Delta t}$, giving $M = \frac{u_2}{\frac{\Delta i}{\Delta t}}$.

Static Definition of Mutual Inductance

The definition expressing mutual inductance as the ratio of linked magnetic flux in the second circuit to the current in the first circuit: $M = \frac{\Psi_{12}}{I_1} = \frac{\Phi_{12} \times N_2}{I_1}$.

Self-Inductance ($L$)

The property of a coil defined by the linked flux per unit current: $L = \frac{\Psi}{I} = \frac{\Phi \times N}{I} = \frac{N^2}{R_m} = N^2 \times \Lambda$.

Coupling Factor ($k$)

A dimensionless coefficient with values between $0$ and $1$ ($k \le 1$) that defines the degree of magnetic coupling between two coils: $M = k \times \sqrt{L_1 \times L_2}$.

Permeance-Based Mutual Inductance ($M$)

The mutual inductance determined by the turns of both coils and magnetic permeance: $M = N_1 \times N_2 \times \Lambda$, where permeance is $\Lambda = \frac{\mu \times S}{d}$.

Series Uncoupled Inductance

The equivalent inductance of two coils connected in series that do not magnetically affect each other: $L = L_1 + L_2$.

Series Aiding (Concordant) Inductance

The total inductance of two series-connected coils whose magnetic fluxes reinforce each other: $L = L_1 + L_2 + 2 \times M$.

Series Opposing (Discordant) Inductance

The total inductance of two series-connected coils whose magnetic fluxes oppose each other: $L = L_1 + L_2 - 2 \times M$.

Parallel Uncoupled Inductance

The total equivalent inductance of two coils connected in parallel that do not magnetically interact: $\frac{1}{L} = \frac{1}{L_1} + \frac{1}{L_2}$, which simplifies to $L = \frac{L_1 \times L_2}{L_1 + L_2}$.