Fig. 2: Fundamental principles of phase-shift engineered TENGs.

a Simulated coupling current waveforms of TENGs with different phase numbers (2, 3, 4, 6 phases) under the optimal phase-shift condition (optimal phase-shift = 1/2n, where n = number of phases); the coupling current becomes more stable as the phase number increases. b Quantitative relationship between phase number and crest factor (CF, defined as the ratio of peak current to equivalent current): CF decreases significantly with increasing phase number, dropping to 1.01 for 6 phases (approaching ideal constant current, CF = 1). c Simulated coupling current waveforms of triangular pulse signals with different phase numbers under optimal phase-shift. d Relationship between phase number and CF for triangular waveforms: CF approaches 1.00 as phase number increases, and reaches 1.00 when the phase number is a multiple of 2. e Schematic of current and voltage superposition for a conventional pulse-voltage TENG (PV-TENG, 6 units without phase-shift), showing typical discontinuous pulse outputs. f Schematic of current and voltage superposition for a phase-shift engineered constant-voltage TENG (CV-TENG, 6 units with optimal phase-shifts): rectified unidirectional pulses of each unit fill the gaps between individual signals, resulting in continuous, smooth constant current (CC) and constant voltage (CV) outputs with minimized fluctuations. Reproduced with permission from ref. ⁵⁴, copyright (Royal Society of Chemistry, 2022).