Two chokes on one core

With the charging and blocking chokes coupled, what inductance does the loop see, and what does the blocking choke present?

M = \pm k \sqrt{L₁ \cdot L₂} \qquad L = L₁ + L₂ + 2 \cdot M \qquad B = L₂ + M

Method

1. Find the mutual inductance: the coupling coefficient times the geometric mean of the two inductances, M = k√(L₁L₂). For independent chokes k is taken as zero whatever was entered.
2. Give it a sign. Fields aiding, M is positive; fields opposing, negative. The sign is the whole difference between the two windings, so it is carried in M rather than written into two separate formulae.
3. The loop inductance is L₁ + L₂ + 2M: each choke's own inductance, plus the flux each induces in the other, counted once for each direction.
4. The blocking inductance is L₂ + M: what the return choke looks like to the current leaving the cell, given that the same current is flowing in the charging choke and inducing a voltage in this one.

Assumptions

• The same current flows in both chokes, which is true of a series loop and is what makes L₁ + L₂ + 2M the right sum. During the gate-off period, with the cell holding charge and the drive open, the currents differ and neither formula applies exactly.
• The coupling coefficient is a single number. On a real core it depends on frequency and on how hard the core is driven, and it falls as the core approaches saturation.
• Fields opposing with k near 1 cancels most of the inductance — L tends to (√L₁ − √L₂)² — and the loop stops being a resonant circuit. The calculation reports the number and says so, rather than refusing.
• Which sense Meyer wound his chokes in is a question for the drawings and the people who built from them, not for this arithmetic. The claim taken from the patents is only that the two chokes share a core.