I recently made a coupled inductor on an EE core and wanted to calculate the coupling coefficient at different airgaps. The windings were each on their own outer leg and the airgap was inserted in all three legs and the coupling coefficient was calculated by following equation:
$$ k = \frac{M}{\sqrt{L_1\cdot L_2}}$$
Where \$k\$ is the coupling coefficient, \$M\$ is the mutual inductance and \$L\$ is the inductance of each winding.
I measured the required above parameters for different airgaps (0mm to 2mm with 0.2mm increment) and noticed that the coupling coefficient was constant at around 0.33 for all airgaps, why is this? Before doing the measurement I expected to see better coupling coefficient at lower airgaps and lower coupling coefficient at higher airgaps.