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Supplementary explanation for the chosen electrical connection
It is no doubt that connecting the PZT elements in series can increase sensitivity of the
measurement, and in the energy-harvesting literature multiple elements are almost always connected in
parallel in order to reduce the optimal load resistance to a lower value and increase current.
But, when a circuit is attached to the harvester to efficiently save or manage the harvested energy,
the power consumptions of circuit elements can’t be ignored. A traditional matching circuit (Fig. I) for
piezoelectric-material-based energy harvesters consists of equivalent electrical components of
piezoelectric-materials, transform, rectifier diode and storing capacitor. Because the PZT elements
connected in parallel increases circuit current (I1 or I2 in Fig. I ), the power consumptions of circuit
elements (especially, the rectifier diode) also get greater.
Fig. I. Traditional matching circuit for piezoelectric-material-based energy harvesting
More specifically, we consider about the effect of electrical connection (for multiple PZT
elements) on the power consumption (PD) of the rectifier diode. Now, we make an assumption that all
the PZT elements (the number of PZT elements is n, n>1) have same size and performance, and each
PZT element has output voltage of Vos, current of Ios, and power of Pos (=Vos·Ios) under an optimal load
resistance of Ros. Thus, when PZT elements are electrically connected in parallel, total output voltage
Vo=Vos, total current Io= nIos, and total power of Po=nPos under an optimal load resistance of Ro(=Ros/n);
when PZT elements are electrically connected in series, total output voltage Vo=nVos, total current Io=Ios,
and total power of Po=nPos under an optimal load resistance of Ro(=nRos). Besides, the power
consumption (PD) of the rectifier diode is PD=I2VD, where VD is the forward voltage drop (the typical
value is 0.3 V). The ratio (η) of useless power to total output power is η=PD/Po. For simplicity, the turns
ratio of transform is set as 1:1, so the primary current (I1) equals the second current (I2). According to
impendence matching, I2=I1=nIos, PD=nIosVD and η=PD/Po=nIosVD/nIosVos=VD/Vos as PZT elements
connected in parallel; I2=Ios, PD=IosVD and η=PD/Po=VD/nVos as PZT elements connected in series.
Consequently, the power consumption PD of the rectifier diode and the ratio η of useless power to total
output power as PZT elements connected in parallel are both n times greater than those as PZT plates
connected in series. As n increases, η for the connection way of “in series” decreases and it gets more
advantageous to connect PZT elements in series instead of parallel.
Furthermore, when the output voltage of the harvester is low, such as Vos=0.6 V, the ratio of
useless power to total output power can be η=VD/Vos=0.3/0.6=50% as connecting PZT elements in
parallel, which leads to a huge waste of harvested energy. Hence, to significantly improve the circuitry
efficiency, we can connect PZT elements (such as n=100) in series and thus η decreases markedly (to
approximately η=nVD/Vos=0.5%).
As a result, in energy harvesting it is more advantageous to connect PZT elements in series instead
of parallel, especially when the output voltage of the harvester is low.