## 4 Simulation and Experimental Results
Figure 10: Power gain \(\eta_{P}\) of the double coil harvester with respect to the single coil harvester, as a function of the frequency displacement from the resonance frequency \(\Delta f\). Figure 11: **(a)** Alternative form of the equivalent circuit of a double coil electromagnetic harvester. **(b)** Experimental implementation of the electromagnetic harvesters by using electronic components. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Test Case** & & **n. 1** & **n. 2** & **n. 3** & **n. 4** \\ \hline \multirow{3}{*}{Test conditions} & \(\Delta f\) & \(-10\%\) & \(-20\%\) & \(-20\%\) & \(-30\%\) \\ \cline{2-5}  & \(f_{VIB}\) & \(0.9\)-\(f_{\text{RES}}\) & \(0.8\)-\(f_{\text{RES}}\) & \(0.8\)-\(f_{\text{RES}}\) & \(0.7\)-\(f_{\text{RES}}\) \\ \cline{2-5}  & \(A_{VIB}\) & \(1\) g & \(1\) g & \(2\) g & \(2\) g \\ \hline \multirow{3}{*}{Single coil harvester} & \(R_{LOAD\_OPT}\) & \(388\)\(\Omega\) & \(388\)\(\Omega\) & \(388\)\(\Omega\) & \(388\)\(\Omega\) \\ \cline{2-5}  & \(C_{LOAD\_OPT}\) & \(1\)\(\mu\) & \(1\)\(\mu\) & \(1\)\(\mu\) & \(1\)\(\mu\) \\ \cline{2-5}  & \(P_{OPT}\) & **2.36 mW** & **0.56 mW** & **2.19 mW** & **0.84 mW** \\ \hline \multirow{3}{*}{Double coil harvester} & \(R_{LOAD\_1\_OPT}\) & \(558\)\(\Omega\) & \(558\)\(\Omega\) & \(558\)\(\Omega\) & \(558\)\(\Omega\) \\ \cline{2-5}  & \(C_{LOAD\_1\_OPT}\) & \(558\)\(\Omega\) & \(558\)\(\Omega\) & \(558\)\(\Omega\) & \(558\)\(\Omega\) \\ \cline{2-5}  & \(C_{LOAD\_2\_OPT}\) & \(1\)\(\mu\) & \(1\)\(\mu\) & \(1\)\(\mu\) & \(1\)\(\mu\) \\ \cline{2-5}  & \(P_{OPT\_2}\) & \(3.14\) mW & \(1.19\) mW & \(5.03\) mW & \(3.33\) mW \\ \cline{2-5}  & \(P_{OPT\_D}=P_{OPT\_1}+P_{OPT\_2}\) & **5.3 mW** & **1.72 mW** & **7.22 mW** & **4.12 mW** \\ \hline Power Gain & Experiments & 224\% & 307\% & 330\% & 490\% \\ \cline{2-5} \(\eta=P_{OPT\_D}/P_{OPT}\) & Simulations & 244\% & 342\% & 342\% & 515\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Experimental tests on the electrical circuits of single coil and double coil harvesters. Figure 12: Oscilloscope screenshots obtained in the optimal conditions for the first test case. Test for the single coil circuit in Figure 8: (**a**), input voltage \(v_{OC}(t)\) (yellow line) and instantaneous load power \(p_{OPT}(t)\) (blue line); (**b**) load voltage \(v_{LOAD}(t)\) (yellow line) and load current \(i_{LOAD}(t)\) (blue line). Test for the double coil circuit in Figure 11a: (**c**) input voltage \(v_{OC}(t)\) (yellow line), additional voltage \(\delta y(t)\) (red line), instantaneous power on the first load \(p_{OPT\_1}(t)\) (blue line), and instantaneous power on the second load \(p_{OPT\_2}(t)\) (green line); (**d**) first load voltage \(v_{LOAD\_1}(t)\) (yellow line), first load current \(i_{LOAD\_1}(t)\) (blue line), second load voltage \(v_{LOAD\_2}(t)\) (red line), and second load current \(i_{LOAD\_2}(t)\) (green line). Moreover, for each of the four test cases, for the double coil harvester the values of the first load resistance \(R_{LOAD\_1}\), the first load capacitance \(C_{LOAD\_1}\), the second load resistance \(R_{LOAD\_2}\), and the second load capacitance \(C_{LOAD\_2}\) were varied to determine the optimal values that ensure the maximum power extraction, \(P_{OPT\_D}=\max(P_{LOAD\_1}+P_{LOAD\_2})\). For the first test case, oscilloscope screenshots of the voltages, currents and power measured in the optimal condition of the double coil harvester are reported in Figure 12c,d. For all the four test cases, the trends of the measured average load power of the double coil circuit are reported in Figure 14 as a function of the load resistances and load capacitances. The optimal values of the load resistances and capacitances for each test case are summarized in Table 2, together with the maximum average extracted powers. Starting from the maximum average powers extracted from the single coil harvester and from the double coil harvester in each test case, it is possible to calculate the power gain \(\eta_{P}=P_{OPT\_D}/P_{OPT}\), i.e., the performance improvement for the double coil harvester.