*2.2. Power Comversion Efficiency*

Figure 3 is used to estimate the power conversion efficiency (PCE). When the voltage drop at a rectifier is sufficiently low in comparison with the amplitude of the voltage source (VA) and the DC output (VDD), an average output power can be estimated by (1) in a steady state. The maximum available power PAV, which is defined by the output power when the load resistance is as large as the output impedance of the transducer |ZS|, is given by (2). Then, PCE is calculated by (3). Figure 4 shows η vs. VDD at V<sup>A</sup> = 10 V, 30 V, 60 V, and 100 V. When VDD is controlled to be 1 V, η decreases as V<sup>A</sup> (>10 V) increases, which is the weakest point for the proposed circuit. Lower VA, or, in other words, lower output impedance, is preferred for an electrostatic energy transducer. η η η η

$$\overline{\mathbf{P\_{\rm OUT}}} = \frac{2\mathbf{V\_{\rm OUT}}^2}{\pi|\mathbf{Z\_{\rm S}}|} \left\{ \sqrt{\left(\frac{\mathbf{V\_{m}}}{\mathbf{V\_{\rm OUT}}}\right)^2 - 1} - \cos^{-1}\left(\frac{\mathbf{V\_{\rm OUT}}}{\mathbf{V\_{m}}}\right) \right\} \tag{1}$$

$$\begin{array}{cccc}\hline\hline\text{---} & \text{---} & \text{---} & \text{---} & \text{---} \\ & & \text{~} & \text{~} & \text{~} & \text{~} \\ & & & \text{~} & & \text{~} \\ & & & \text{~} & & & \text{~} \\ & & & & \text{~} & & \end{array} \tag{2}$$

$$
\eta = \frac{\overline{\mathcal{P}\_{\text{OUT}}}}{\overline{\mathcal{P}\_{\text{AV}}}} \tag{3}
$$

η ൌ

P തതതതതത

**Figure 3.** Circuit model for estimating the power conversion efficiency. (**a**) Circuit model; (**b**) voltage waveform.

**VDD [V]** η **Figure 4.** PCE η vs. VDD at V<sup>A</sup> = 10 V, 30 V, 60 V, and 100 V.

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