I'm studying FCML converters, especially the 4-level / 3-cell topology. It's clear that when the flying capacitors become imbalanced (e.g., one undervolted), the switching node voltages deviate from their expected levels.

I’ve read that the output inductor plays a key role in naturally restoring capacitor balance, acting somewhat like an integral controller. However, I'm struggling to intuitively understand how the inductor's current slope becomes a self-correcting mechanism.

My current understanding:

• Capacitor imbalance leads to incorrect switching node voltages.
• This creates a voltage across the inductor.
• The inductor responds with a current slope.
• That current redistributes charge between capacitors during different phases.

But I’m not clear on why this current flow ends up correcting the imbalance over time — or what ensures that the charge moves in the “right” direction to fix it.

Could anyone explain this concept in simple terms, or point me to visual/numerical resources that demonstrate this?

Thanks in advance!