## 4 Measurements, Simulations and Discussion
The relative error \(\mathrm{E_{rel}^{RMS}}\) has been computed as follows:  
\[\mathrm{E_{rel}^{RMS}}=\frac{\left|\mathrm{V_{out,\,meas}^{RMS}-\mathrm{V_{out, \,sim}^{RMS}}}\right|}{\mathrm{V_{out,\,meas}^{RMS}}}\times 100 \tag{2}\]  
where \(\mathrm{V_{out,\,meas}^{RMS}}\) and \(\mathrm{V_{out,\,sim}^{RMS}}\) are the measured and simulated RMS output voltage, respectively. The relative error peaks are limited to 5.25% at \(\mathrm{f_{in}}\) = 20 Hz, 3% at \(\mathrm{f_{in}}\) = 50 Hz and 5.35% at \(\mathrm{f_{in}}\) = 80 Hz. Moreover, the total average relative errors are 2.98%, 1.26% and 1.36% at 20, 50 and 80 Hz, respectively. Furthermore, the relative error peaks are located in working regions where the AC-DC converter should not work as a voltage booster. Then, the goodness of simulations results compared with experimental data show the possibility to use LTspice circuital model for further comparing simulations of this technique with respect to a standard switching technique, reported in the Appendix A. One of the main figures of merit in the design of an electronic interface is the conversion efficiency. The efficiency (\(\eta\)) has been computed as:  
\[\eta=\frac{\mathrm{P_{out}}}{\mathrm{P_{in}}}\times 100 \tag{3}\]  
where \(\mathrm{P_{in}}\) and \(\mathrm{P_{out}}\) are the measured RMS input and output power of the boost converter. The discrepancy between \(\mathrm{P_{in}}\) and \(\mathrm{P_{out}}\) is represented by the Power losses (\(\mathrm{P_{loss}}\)), which is  
Figure 10: Mapping of the relative errors between measured RMS output voltages and simulated data with respect to Duty Cycle (D) and Time Delay (\(\mathrm{T_{D}}\)) at different frequencies (\(\mathrm{f_{in}}\)) of the input voltage. The insets show the top view of each surface, while the red dots point out the maximums. Figure 9: Mapping of the RMS output voltages with respect to the Duty Cycle (D) and Time Delay (\(\mathrm{T_{D}}\)), at different frequencies (\(\mathrm{f_{in}}\)) of the input voltage. The insets show the top view of each surface, while the red dots point out the maximums. mally due to the switching, conduction and passive devices losses [40]. Figure 11 shows the efficiencies of the considered AC-DC boost, with respect to Time Delay and Duty Cycle, at three different input voltage frequencies. As expected, it is observable that the efficiency increases within the f\({}_{\text{in}}\) because of the related increase in switching frequency. Furthermore, it seems that the efficiency peak is located in low D and medium T\({}_{\text{D}}\) value regions at 20 Hz, while it moves towards higher D and lower T\({}_{\text{D}}\) by increasing the input frequency. Another important figure of merit to take into account in the design of an AC-DC converter is the Ripple Factor (RF). Indeed, in order to reduce the size of converters, it is necessary to use small inductors and capacitors, with a corresponding increase in ripple value. An estimation of the signal shape is the Form Factor (FF), which is defined as [45]:  
\[\text{FF}=\frac{\text{V}_{\text{out}}^{\text{RMS}}}{\text{V}_{\text{out}}^{ \text{AVG}}} \tag{4}\]  
where V\({}_{\text{out}}^{\text{RMS}}\) and V\({}_{\text{out}}^{\text{AVG}}\) are the RMS and average output voltage computed in a certain time interval, respectively. A measure of the ripple content of the output is then the Ripple Factor, defined as [45]:  
\[\text{RF}=\sqrt{(\text{FF})^{2}-1} \tag{5}\]  
Figure 12 shows the Ripple Factor of the considered AC-DC boost, with respect to Time Delay and Duty Cycle, at three different input voltage frequencies. It can be seen that the RF is very low (about 3% at 20 Hz), and it decreases around zero by increasing the input frequency, without a clear dependency with respect to D and T\({}_{\text{D}}\). The lower the RF is, the lower the discrepancy between RMS and average output voltages. Consequently, the designed boost converter seems to have a low harmonic content in the output voltage, which is a desiderable property.