## 4 Simulation and Experimental Results  
Simulations and experimental tests were performed to show that the double coil electromagnetic harvester is able to deliver an amount of energy significantly greater than that provided by a standard single coil electromagnetic harvester. Firstly, numerical simulations of the circuit of the single coil harvester shown in Figure 2 and of the circuit of the double coil harvester shown in Figure 5 were performed. The parameters used for the single coil harvester are those obtained by the experimental characterization of the commercial harvester reported in the previous section. The parameters used for the double coil harvester are the same as for the single coil harvester with the  
Figure 9: Comparison of measurements performed on the considered commercial harvester and on its equivalent circuit. (**a**) Oscilloscope screenshot of the gain and phase of the transfer function \(G_{CIRCUIT}\) of the equivalent circuit. (**b**) Transfer functions \(G_{CIRCUIT}\) measured on the commercial harvester and on the implemented equivalent circuit. addition of \(R_{c2}=R_{c1}=R_{c}\), \(L_{c2}=L_{c1}=L_{c}\) and \(\theta_{2}=\theta_{1}=\theta\). For each value of the vibration frequency, the load of the single coil harvester was varied to determine the optimal load that allows the maximum power extraction \(P_{OPT}=\max(P_{LOAD})\). Also, the values of the loads of the double coil harvester were varied to determine the optimal loads that allow the maximization of the total extracted power \(P_{OPT\_D}=\max(P_{LOAD1}+P_{LOAD2})=P_{OPT1}+P_{OPT2}\). Then, the performance improvement of the double coil harvester was calculated as the power gain \(\eta_{P}(\Delta f)\) in (12). The power gain obtained by numerical simulations and reported in Figure 10 shows that an increase of the extracted power is obtained by using the double coil harvester for any vibration frequency. Moreover, this increase is particularly significant for frequencies lower and far from the resonance frequency. Experimental tests were performed on the electrical circuit of a single coil harvester reported in Figure 8 and on the electrical circuit of a double coil harvester reported in Figure 11a. These circuits were implemented by using electronic components mounted on a solderless breadboard as shown in Figure 11b. It should be emphasized that the experimental tests were performed on the equivalent circuits of the harvesters and not on the harvesters themselves because a double coil harvester has never been built up. Therefore, before constructing a double coil harvester, it seems useful to preliminarily investigate its potential. Tests were performed for four case studies, which differ for the vibration frequency (\(f_{VIB}=0.9\)\(f_{RES}\), \(f_{VIB}=0.8\)\(f_{RES}\), \(f_{VIB}=0.7\)\(f_{RES}\)) and for the acceleration amplitude (\(A_{VIB}=1\) g, \(A_{VIB}=2\) g), as detailed in Table 2.  
For each of the four test cases, for the single coil harvester the values of the load resistance \(R_{LOAD}\) and of the load capacitance \(C_{LOAD}\) were varied to determine the optimal values, \(R_{LOAD\_OPT}\) and \(C_{LOAD\_OPT}\), that ensure the maximum average power extraction, \(P_{OPT}\). It is worth noting that only ohmic-capacitive loads were considered since, at the working frequency \(f_{VIB}\) (lower than \(f_{RES}\)), in all the considered test cases the equivalent harvester impedance was always ohmic-inductive. The phase relationships of the voltages, currents and power, measured in the first test case in the optimal condition, and reported in Figure 12a,b, confirm the ohmic-capacitive nature of the optimal load. For all the four test cases, the trends of the measured average load power of the single coil circuit are reported in Figure 13 as a function of the load resistance \(R_{LOAD}\) and of the load capacitance \(C_{LOAD}\). The optimal values of \(R_{LOAD}\) and \(C_{LOAD}\) for each test case are summarized in Table 2, together with the maximum extracted power \(P_{OPT}\).