Steady-period switched state models; zero-current diode blocking included. Coupled inductors in the ideal-coupling limit: bridge excitation current is neglected; flyback magnetizing current is explicitly simulated. No leakage or saturation. Half bridge integrates split-capacitor charge with a variable midpoint and solves a periodic boundary; startup and midpoint stability are not yet simulated. The center-tapped secondary uses one housing with separate paddle sectors and particles for the winding currents. Restored gears illustrate coupling ratio; the paddle sectors and flyback storage links represent the additional freedom needed for circulating current and energy storage, not a fully derived gearbox. Bridge timing follows the course: alternating pulses of length DT, complete magnetic period 2T. Optional losses are lumped conduction resistance and diode drop, not transistor switching transients. Flyback shows a separate magnetizing inertia wheel with input/output power links that engage during their conducting intervals. The dashed links are a power-flow explanation, not a fully derived mechanical gearbox. A rigid transformer gear alone cannot store its energy. Pressure is 100 Pa/V; shading interpolates between port pressures. Water geometry is schematic, not a CFD solution. All plots use the physical state, independently of visual amplification.