Harvesting the highest power from tiny electrostatic transducers with CMOS circuits

Although energy in vibrations is often vast, the electrostatic force with which tiny variable capacitors draw power from motion is miniscule, so output power is low. Thankfully, extracting energy at higher voltages generates more power because the electrical damping force that impedes motion to draw power is stronger. Clamping the transducer to a battery is convenient in this respect, but limiting because battery voltages are low. Using a capacitor to clamp the transducer to a higher voltage is better, but only to the extent that capacitance keeps that voltage from reaching the breakdown level of the switches. In fact, when neglecting parasitic power losses in the switches and the controller, a grounded clamping capacitor can yield up to 100% of the theoretical maximum power, and up to 87% with 2.5 nF, 15-V switches, and a 3.3-V battery from a 30-250-pF transducer at 27.6 Hz. Under similar conditions, this paper also shows that battery-clamped and asynchronous and stacked capacitor-clamped systems generate 4%, 17%, and 53%.