Efficiency of harvesting energy from colored noise by linear oscillators

We investigate the performance of a linear electromechanical oscillator as an energy harvester of finite-bandwidth random vibrations. We derive exact analytical expressions for the net electrical power and the efficiency of the conversion of the power supplied by the noise into electrical power for arbitrary colored noise. We apply our results to the important case of exponentially correlated noise and discuss the tuning of parameters to achieve good performance of the device.

Figure 1

Schematic of the conversion mechanism of the external random power to the net electrical power. The power transferred is shown for each step.

Figure 2

Comparison of the results obtained from (5.2), (5.3), (5.4), and (5.5) (solid curves) with simulations (symbols). $a=b=\omega =k_c=k_v=V_0=1$; $\mathcal{C}={\tau }_p=2$. Inset: Comparison of the result obtained from (4.3) with numerical simulations.

Figure 3

Maximum net electrical power, $P^{*}$, efficiency at the maximum power, ${\eta }^{*}$, and characteristic frequency of the noise at the maximum power, ${\lambda }^{*}$, as a function of ${\tau }_p$, $k_c$, $k_v$, and $\omega$. In each panel we vary the corresponding parameter and set all other parameters equal to 1. For all plots we have taken $\mathcal{C}=1$.