Calculating coupling between 2 variometer coils

Mutual inductance calculator (Variometer)

Reminders about mutual inductance.

We know that two coils with inductances \(L_1\) and \(L_2\) placed in series are equivalent to a single coil with inductance \(L\) = \(L_1\) + \(L_2\). This rule is only applicable if the components are sufficiently far from each other (or if their axes are perpendicular) so that they do not interact.
When the interaction is no longer negligible, we introduce a coupling coefficient \(K\). This depends on the respective geometries of the coils and their relative positions. A (complex and approximate calculation) tool for \(k\) is proposed on this site for two classic cases in vintage radio:

• the coils are coaxial, with distinct diameters
• the coils are coaxial, with identical diameters or collinear

In practice, vintage radio manufacturers sought or adjusted coupling coefficients experimentally. Moreover, beyond 2 coils, the physical modeling is more complex. I developed these tools for my SPICE simulations. Indeed, this famous software manages the interaction between 2 coils based on the coupling coefficient \(K\).