Wind a second coil on the same ring and you have a transformer. The first side and the second side never touch — no copper joins them — yet a message crosses, carried only by the flux they share. Paper I said a toroid passes edges, not levels. Now watch those edges leap the gap, and a PWM message arrive on a side that's electrically a world away.
A transformer is just Paper I's core with a second winding added. Drive a changing current in the primary; it makes a changing flux in the shared ring; that changing flux induces a voltage in the secondary — Faraday again, vₛ = Nₛ·dΦ/dt. The ratio of turns sets the ratio of voltages: more secondary turns, more secondary volts (and proportionally less current — power is conserved, not created).
The quiet miracle is what isn't there: no electrical connection between the two sides. The only thing they share is flux in iron. That's galvanic isolation — the secondary can float at a thousand volts above the primary and the signal still crosses, because the signal was never a current in a wire; it was a change in a field. And because it rides on change, a steady primary current induces nothing across the gap.
Here is the whole point of the series, working end to end. You want to send a value — a duty cycle — from one side to a side it can't touch. You can't just push the PWM across: the transformer refuses the DC, so the secondary comes out AC-coupled — the same edges, but the levels shifted to swing about zero (precisely the volt-second balance from Paper I; the average across the core must be zero). The duty cycle looks lost.
It isn't. The duty cycle was never stored in a level — it lives in the timing of the edges, and the edges crossed perfectly. So the far side reconstructs: a comparator catches each edge and rebuilds a clean full-height pulse — high on the rising edge, low on the falling — recreating the original PWM, duty intact. A low-pass filter then averages it back to the value. The message made it across a gap with no wire, riding entirely on change.
The DC could not cross — but the DC was never the message. The message was the edges, and the edges always cross. That is why a toroid speaks PWM.
This isn't a toy demonstration of a principle — it's the working guts of equipment you use constantly. Every one of these sends information through a tiny toroid (or a transformer very like one), across an isolation barrier, on the edges:
In each, the rule from Paper I holds without exception: a steady level would die in the core, so the data is sent as edges and rebuilt on the far side. The toroid is the wall and the messenger at once.
One instrument left to close the series: the common-mode choke — the toroid wound so it ignores the noise both wires share and passes only the difference that carries the message. Selective listening, magnetic edition.