## 3 Commercial Harvester Characterization  
A commercial single coil electromagnetic energy harvester was characterized to obtain the parameters of its equivalent circuit, which will be used in the next Section to perform simulations and experimental tests. The photo and the block diagram of the experimental setup employed for the harvester characterization are shown in Figure 6a,b, respectively. In particular, the electromagnetic harvester model-D by ReVibe, the photo of which is shown in Figure 6c and the technical parameters reported in Figure 6d, is mounted on the shaker Sentek VT-500. The driving current of the shaker is generated by the LA-800 Power Amplifier and the driving signal of the power amplifier is provided by the controller Spider-81 by Crystal Instruments that implements the closed loop vibration control by measuring the acceleration of the vibration generated by the shaker. To test the open circuit behavior of the considered electromagnetic harvester, a sinusoidal vibration having a constant acceleration equal to \(A_{VIB}=1\) g and a varying frequency was applied to the harvester with open output terminals. The measured amplitude of the open-circuit voltage \(v_{\text{OC}}(t)\) is reported in Figure 7a. Moreover, to test the behavior of the harvester feeding different resistive loads, a sinusoidal vibration with a constant acceleration equal to \(A_{VIB}=1\) g and a varying frequency was applied to the harvester with the output terminals connected to different load resistors, i.e., \(R_{LOAD}=1200\)\(\Omega\), \(R_{LOAD}=1000\)\(\Omega\) and \(R_{LOAD}=820\)\(\Omega\). The measured voltage amplitudes and the measured average powers delivered to the loads are reported in Figure 7b,c, respectively, and are in line with data declared by the harvester manufacturer [8]. The above measurements allowed us to deduce that the mechanical resonance frequency, i.e., the frequency at which the open-circuit voltage reaches the maximum amplitude value, is equal to \(f_{RES}=98.5\) Hz. Moreover, they allowed us to determine the amplitude of the open-circuit voltage at the resonance frequency, \(V_{OC\_MAX}(1\) g\()=19.9\) V, the open-circuit 3-dB  
Figure 6: (**a**) Characterization setup for the electromagnetic energy harvester model-D by ReVibe. (**b**) Block diagram of the characterization setup. (**c**) Photo of the harvester. (**d**) Technical parameters of the harvester as reported in the datasheet. bandwidth, \(B_{3 dB}=2.6\) Hz and the optimal load resistance, \(R_{LOAD\_MAX}=1000\)\(\Omega\), which is the resistance that allows the maximum average power extraction at the resonance frequency. The resistance and the inductance of the coil of the considered electromagnetic harvester were measured by using the LCR Meter U1733C by Keysight Technologies. It resulted as \(R_{C}=300\)\(\Omega\) and \(L_{C}=135\) mH. By exploiting the above measurements, the parameters of the equivalent circuit of the single coil electromagnetic harvester model-D by ReVibe were deduced. In detail, from the analytical expression of the optimal load resistance obtained by the maximum power transfer theorem,  
\[R_{LOAD\_MAX}=\sqrt{\left(R_{m}+R_{c}\right)^{2}+\left(2\pi f_{\text{RES}}\cdot L _{c}\right)^{2}} \tag{13}\]  
Figure 7: Measurements carried out on the commercial harvester model-D by ReVibe. (**a**) Open-circuit voltage amplitude; (**b**) output voltage amplitude for different loads; (**c**) extracted average power for different loads. it was possible to calculate \(R_{m}=700\)\(\Omega\). From the expression of the maximum open-circuit voltage amplitude at the resonance frequency under 1 g acceleration,  
\[V_{OC\_MAX}=k\cdot A_{VIB}\cdot R_{m} \tag{14}\]  
it was deduced that \(k=28\) mA/g. From the open-circuit 3 dB bandwidth,  
\[B_{3 dB}=\frac{1}{R_{m}\cdot C_{m}} \tag{15}\]  
the capacitance value \(C_{m}=87.5\)\(\mu\)F was obtained. Finally, from the expression of the resonance frequency \(f_{RES}\)  
\[f_{RES}=\frac{1}{2\cdot\pi\cdot\sqrt{L_{m}\cdot C_{m}}} \tag{16}\]  
it was calculated that \(L_{m}=29.9\) mH.