# A Transformer-Less Buck-Boost Grid-Tied Inverter with Low Leakage-Current and High Voltage-Gain
## 5 Experimental Results  
To prove the correctness of the previous analysis, a prototype is built and measured according to the schematic illustrated in Figure 3 and the specifications shown in Table 2.  
For avoiding the duty ratio being too large, its maximum value is set to 0.45. Since the maximum duty ratio occurs at the peak output voltage of 312 V and the minimum input voltage of 100 V, the turn ratio \(N\) can be calculated from Equation (7) as around 1.6. In the design example, the turn ratio \(N\) of 1.5 is chosen. \begin{table}
\begin{tabular}{c c} \hline \hline \multicolumn{1}{c}{**Specifications**} \\ \hline Input voltage, \(V_{in}\) & 100–200 V \\ Voltage of mains, \(v_{s}\) & 220 Vrms \\ Frequency of mains, \(f_{ac}\) & 60 Hz \\ Frequency of switching, \(f_{s}\) & 20 kHz \\ Rated power, \(P_{o}\) & 500 W \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Electrical specifications of the laboratory prototype. Figure 9: The power loss comparison curves of the proposed inverter and the traditional two-stage system: (**a**) conduction loss of all inductors; (**b**) conduction loss of all switches; (**c**) switching loss of all switches; (**d**) conduction loss of all diodes. By combining Equations (9) and (11), the BCM inductance \(L_{B}\) is able to be obtained as in Equation (36):  
\[L_{B}=\frac{R\times d_{Bo}(1-d_{Bo})^{2}}{2(1+N)(1+Nd_{Bo})\times f_{S}} \tag{36}\]  
By selecting the inductor current to be BCM at the peak of sinusoidal voltage and 50% rated power, the BCM inductance \(L_{B}\) is able to be obtained from Equation (36) as 155 \(\mu\)H. In the implementation example, 200 \(\mu\)H is chosen for the inductance of \(L_{I}\) and \(L_{2}\). Table 3 shows the selected component parameters according to the analysis and design addressed before. The investigated transformer-less buck-boost grid-tied inverter is controlled by SPWM. Figure 10 illustrates the experimental waveforms of the output voltage \(v_{o}\) and the driving signals of the switches \(S_{BuI}\), \(S_{Bol}\), and \(S_{1}\). When the inverter operates in the step-down mode, the switch \(S_{BuI}\) is switched at high frequency, and the switches \(S_{Bol}\) remain off. Conversely, when the inverter operates in the step-up mode, the switch \(S_{Bol}\) performs high-frequency switching. The switch \(S_{1}\) continuously conducts during the positive half-cycle to provide an energy transmission path. During the negative half-cycle, the switch \(S_{2}\) replace the switch \(S_{1}\) to conduct continuously, and the switch \(S_{1}\) remains off. Under the condition of 100 V input voltage and 500 W load, Figure 11 illustrates the experimental waveforms of the input voltage \(V_{in}\), the output voltage \(v_{o}\), and the output current \(i_{o}\). It can be seen that \(v_{o}\) and \(i_{o}\) are low-distortion and close to an ideal sinusoidal wave. These results verify that the proposed buck-boost grid-tied inverter can achieve the function of DC to AC conversion. Figure 12 illustrates the experimental waveforms of the output voltage \(v_{o}\), and the inductor currents \(i_{L1}\), \(i_{L3}\). As shown in Figure 12a, the step-down mode is performed when the instantaneous voltage of \(v_{o}\) is below 100 V; on the contrary, the step-up mode is performed. The inductor currents \(i_{L1}\), \(i_{L3}\) are in CCM to reduce current peaks and ripple. Figure 12b shows zoom-in waveforms on the peak of output voltage. It can be seen that the inductor \(L_{1}\) is charging alone and discharging in series with the \begin{table}
\begin{tabular}{c c} \hline \hline \multicolumn{2}{c}{**Component Parameters**} \\ \hline Input capacitor, \(C_{dc}\) & 3300 \(\mu\)F \\ MOSFETs & 47N60C3 \\ Power diodes & C3D10060A \\ Turn ratio, \(N\) & 1.5 \\ Inductors, \(L_{1}\), \(L_{2}\) & 200 \(\mu\)H \\ Inductors, \(L_{3}\), \(L_{4}\) & 450 \(\mu\)H \\ Capacitor of filter, \(C_{f}\) & 5 \(\mu\)F \\ Inductor of output, \(L_{s}\) & 1 mH \\ Capacitor of output, \(C_{s}\) & 5 \(\mu\)F \\ \hline \hline \end{tabular}
\end{table}