Impedance Modeling of Switched-Inductor Bias-Flip Piezoelectric Energy Harvesting Circuits

This paper evaluates the equivalent input impedance, Z<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">in</inf>, that a parallel synchronized switch harvesting on inductor (P-SSHI) rectifier presents to the internal current, i<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</inf>, of a piezoelectric transducer. Unlike prior impedance modeling work, the charge balance principle is used in this paper to break down Z<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">in</inf> under a P-SSHI circuit into three shunt components that are independent of each other and solely determined by the internal capacitance, C<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</inf>, and resistance, R<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</inf>, of a piezoelectric transducer, as well as the rectifier’s dc load resistance, R<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</inf>, respectively. By isolating the part of Z<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">in</inf> that relies on C<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</inf>, the proposed modeling can quantify the enhancement that a P-SSHI interface circuit provides to the equivalent impedance of C<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</inf>, and hence, the improvement to the piezoelectric transducer output power. This approach facilitates performance comparison between a P-SSHI and other piezoelectric interface circuits in terms of the improvement an interface provides to the equivalent impedance of the transducer’s internal capacitance, C<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</inf>, independent of the transducer’s internal current, i<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</inf>, which typically varies with the amount of power extracted in transducers of high electromechanical coupling. Another advantage of breaking down Z<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">in</inf> into three independent shunt components is that the optimal dc load resistance, ${R_L}^{\ast}$, that maximizes the output power of a P-SSHI interface circuit can be directly found from Z<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">in</inf>. The developed models are verified using circuit simulations.