This paper presents an energy-harvesting system consisting of amorphous-silicon (a-Si) solar cells and thin-film-transistor (TFT) power circuits on plastic. Along with patterned planar inductors, the TFTs realize an LC-oscillator that provides power inversion of the DC solar-module output, enabling a low-cost sheet for inductively-coupled wireless charging of devices. Despite the low performance of the TFTs (ft=1.3MHz at a voltage of 15V), the oscillator can operate above 2MHz by incorporating the device parasitics into the resonant tank. This enables increased quality factor for the planar inductors, improving the power-transfer efficiency and the power delivered. With 3cm-radius single- and double-layer inductors, the system achieves 22.6% and 31% power-transfer efficiency (approaching the analytically-predicted bound), while the power delivered is 20mW and 22mW.