Mathematical Modeling, High-Voltage Resonant Optimization, and Digital Twin Simulation of a Unipolar Voltage Intensifier Circuit (VIC) for Energy-Efficient Water Electrolysis

This paper presents a rigorous mathematical model, system topology optimization, and QSpice digital twin simulation of a Unipolar High-Voltage Resonant Voltage Intensifier Circuit (VIC) designed for high-efficiency capacitive water electrolysis. Conventional Faraday water electrolysis suffers from severe Ohmic thermal losses (I²R) caused by high continuous current conduction across low-impedance conductive electrolytes. The Voltage Intensifier Circuit circumvents electrolyte conduction by applying an intense, unipolar electrostatic field across a high-impedance pure water dielectric cell (C_cell = 1 nF, R_water = 1 MΩ). The proposed system employs a 12V DC input, dual-frequency pulse modulation (8,667 Hz carrier gated at 100 Hz burst, 50% duty cycle), a step-up transformer (L1 = 50 µH, L2 = 150 mH), and magnetically aiding bifilar resonant chokes (L3 = 47 mH, L4 = 47 mH, k = -0.99) with total secondary inductance L_sec_total = 337.06 mH. Analytical energy equilibrium calculus and shape factor integration (K_shape = 0.50) mathematically predict an exact peak cell voltage of 4,359.5V (4.4 kV) and net cell power of 9.50W under an average battery power draw of 9.94W, yielding a remarkable system electrical efficiency of 95.56%. Furthermore, Quality Factor (Q-factor) sensitivity analysis demonstrates that water dielectric purity governs over 90% of total system Q (Q_total = 49.5), validating Stanley Meyer's hypothesis of capacitive water molecule polarization under high electrostatic voltage magnification.