One major challenge to the usability of IoT devices is limited onboard battery lifetime. Integrating an energy harvester to scavenge the energy from ambient sources is a viable green option. In recent 5 years, Triboelectric Nanogenerators (TENG) have gained attention for harvesting ambient vibration energy from sources ranging from ocean waves to human body motion due to their flexibility in the choice of materials and fabrication processes. However, due to the high nonlinearly varying impedance (typically in mega ohms) of TENG, standard full wave rectifier based AC to DC conversion for energy extraction is unable to provide a matching impedance needed for optimized energy transfer. In the presented work, Synchronous Charge Extraction (SCE), Parallel and Series synchronized switch harvesting on inductor (P-SSHI and S-SSHI) energy extraction circuits are mathematically modeled, analyzed, simulated, and compared with the standard full wave rectifier (FWR) circuit for the first time to the best of our knowledge. While the above-mentioned extraction schemes have been studied for piezoelectric transducers, the models (and gains) are different in the case of triboelectric transducers. For TENG with an area, 12 x 8 cm2, surface charge density 8 μC=m2, and subjected to vibration with 3 mm amplitude and 1 Hz frequency, energy gains of 2.8, 14.5, 385 over FWR were realized for P-SSHI, S-SSHI and SCE for a 5V battery load respectively. The above findings were also confirmed by SPICE-based circuit simulation.