## 2 Modified Boost Converter (MBC)
### Comparison of the Conventional Cascaded and Proposed Converters  
The main purpose of this section was a comparison between the inductor currents and capacitor voltage ripples for a classical cascade and our proposed converters. Table 1 summarizes these equations. In this table, \(V_{C1}\) and \(V_{C0}\) are the steady state voltages of the \(C_{1}\) and \(C_{2}\) capacitors; \(D_{1}\) and \(D_{2}\) are the duty cycles of PWM signals for \(S_{1}\) and \(S_{2}\) power MOSFETs of the conventional cascaded boost converter; \(D\) is the duty cycle for the proposed converter's switch, respectively; \(T_{S}\) is the switching frequency; and \(\Delta i_{LX}\) and \(\Delta i_{LY}\) are the current ripples for the inductors \(L_{X}\) and \(L_{Y}\), respectively. Additionally, \(I_{0}\) is the output current and \(V_{in}\) is the input voltage of the structures. By considering the same duty cycle for all switches, the current ripples for inductors were the same for both configurations, while the proposed converter uses only one power switch and has a simpler structure and needs to simple with a one controller topology to guarantee a fixed output voltage at the output of the converter. Part of simulations is presented in Section 3, and can show the first inductor currents, output diode currents, power switch currents, and the average values of these converters. All results can easily confirm the equations presented in Table 1.  
Table 2 illustrates all of the component conduction and switching losses for both conventional, cascaded, and proposed power boost converters comprehensively. This table was written according to [22]. In this table, the \(P_{con}\) and \(P_{sw}\) are the conductive and switching losses, respectively. For example, \(P_{con,D1}\) is the conductive losses of the power diode \(D_{1}\) and \(P_{sw,D2}\) is the switching losses for the diode \(D_{2}\). \(P_{LX}\) and \(P_{LY}\) are the conductive losses on inductors. Additionally, \(V_{f}\) is the forward voltage on diodes; \(f_{S}\) is the frequency switching value; and \(Q_{rr1}\), \(Q_{rr2}\), and \(Q_{rr3}\) are the electrical charges of the \(D_{1}\), \(D_{2}\), and \(D_{0}\) diode forward capacitors. \(T_{ON}\) and \(T_{OFF}\) are presenting the transition times for the power switches for the ON and OFF states, respectively. The dissipated energy for the turn ON and OFF \begin{table}
\begin{tabular}{c c} \hline \hline \multicolumn{2}{c}{**Classical Cascaded Converter**} \\ \hline
**First Block** & **Second Block** \\ \hline \(\Delta i_{LX}=\frac{V_{in}}{L_{X}}D_{1}T_{s}\) & \(\Delta i_{LY}=\frac{V_{C0}-V_{C1}}{L_{Y}}(1-D_{2})T_{s}\) \\ \(\Delta V_{C1}=\frac{I_{LY}}{C_{1}}D_{1}T_{s}\) & \(\Delta V_{C0}=I_{o}D_{2}T_{s}\) \\ \hline \multicolumn{2}{c}{**Proposed Converter**} \\ \hline \(\Delta i_{LX}=\frac{V_{in}}{L_{X}}DT_{s}\) & \(\Delta i_{LY}=\frac{(V_{C0}-V_{C1})-V_{in}}{L_{Y}}(1-D)T_{s}\) \\ \(\Delta V_{C1}=\frac{I_{LY}}{C_{1}}DT_{s}\) & \(\Delta V_{C0}=I_{o}DT_{s}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Capacitor voltage and inductor current ripples for both converters. momentary times are presented by \(W_{ON}\) and \(W_{OFF}\). \(D^{\prime}\) presents the time that the power switch is in OFF mode. The main advantage of the proposed converter is that it has only one power switch. Therefore, there are no conductive and switching losses for the second power switch. In addition, it should be considered that it has three power diodes compared with a conventional cascaded converter and the projected converter will have these losses for the third diode. This presents a preferable condition compared with conventional cascaded structures. ### Comparison of the Conventional Cascaded and Proposed Converters  
By considering the ideal conditions for all inductors, capacitors, power diodes, and power switches, the voltage gain of the proposed converter can be obtained. Based on the charging and discharging states of inductors, mathematical evaluation for the voltage gain will appear in two different modes.