Magnetic Coupling Coefficient Calculator

Formula

The formula for calculating the magnetic coupling coefficient is:

$k = \frac{M}{\sqrt{L_1 \cdot L_2}}$

Where:

$k$ is the magnetic coupling coefficient
$M$ is the mutual inductance
$L_1$ is the primary inductance
$L_2$ is the secondary inductance

What is a Magnetic Coupling Coefficient?

The magnetic coupling coefficient, often denoted as $k$ , is a dimensionless parameter that quantifies the degree of magnetic coupling between two inductors. It ranges from 0 to 1, where 0 indicates no coupling and 1 indicates perfect coupling. This coefficient is crucial in transformer design and other applications involving inductive coupling, as it affects the efficiency and performance of the system. The value of $k$ depends on factors such as the distance between the inductors, their orientation, and the magnetic permeability of the medium between them.

Example Calculation

Let's assume the following values:

Mutual Inductance (M) = 0.5 Henrys
Primary Inductance (L₁) = 2 Henrys
Secondary Inductance (L₂) = 3 Henrys

Using the formula to calculate the magnetic coupling coefficient:

$k = \frac{0.5}{\sqrt{2 \cdot 3}} = \frac{0.5}{\sqrt{6}} \approx 0.2041$

The magnetic coupling coefficient is approximately 0.2041.