A Recursive <i>N</i>-Path Switched-Capacitor Rectifier for Piezoelectric Energy Harvesting

This article presents a recursive N-path switched-capacitor (SC) rectifier that improves the amount of power extracted from a piezoelectric transducer (PT) over prior SC PT interface circuits while using the same passive volume size. The proposed rectifier increases the number of generated steps per capacitor exponentially over that of previous SC harvesters by moving the capacitor array after the employed full-bridge rectifier (FBR) and connecting the array capacitors together in series in all possible permutations. With a larger number of steps, the proposed rectifier achieves a smaller PT internal capacitance switching loss and a higher harvesting efficiency than that of prior SC rectifiers using the same passive volume size. The proposed SC rectifier also emulates conjugate matching by generating a staircase approximation of the maximum power point voltage waveform across a PT in response to its current, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${i} {_{P}}$ </tex-math></inline-formula>, which minimizes the harmonic losses in the internal transducer shunt resistance. The rectifier capacitors successively accumulate the charge supplied by <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$i_{P}$ </tex-math></inline-formula>, and therefore, their voltages naturally settle at the average of the input part that they see each cycle. Measurements of a 0.18-<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu $ </tex-math></inline-formula>m prototype demonstrate the merits of the proposed rectifier where up to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$13.9{\times }$ </tex-math></inline-formula> power extraction improvement is achieved over an active FBR.