## 2 Modified Boost Converter (MBC)
### Comparison of the Conventional Cascaded and Proposed Converters
\begin{table}
\begin{tabular}{c c} \hline \hline
**Conventional Cascade Converter** & **Proposed Converter** \\ \hline \(I_{\text{LX}}=\frac{1}{(1-d_{1})\times(1-d_{2})}\times\frac{V_{0}}{R}\) & \(I_{\text{LX}}=\frac{1}{(1-d)^{2}}\times\frac{V_{0}}{R}\) \\ \hline \(I_{\text{LX}}=\frac{1}{(1-d_{2})}\times\frac{V_{0}}{R}\) & \(I_{\text{L2}}=\frac{1}{(1-d)}\cdot\frac{V_{0}}{R}\) \\ \hline \(P_{\text{LX}}=R_{\text{LX}}\Big{(}\frac{d_{1}^{2}}{\text{LX}}+\frac{\Delta_{1 }^{2}}{12}\Big{)}\) & \(P_{\text{LX}}=R_{\text{LX}}\Big{(}\frac{d_{1}^{2}}{\text{LX}}+\frac{\Delta_{1 }^{2}}{12}\Big{)}\) \\ \hline \(P_{\text{LY}}=R_{\text{LY}}\Big{(}\frac{d_{1}^{2}}{\text{LY}}+\frac{\Delta_{1 }^{2}}{12}\Big{)}\) & \(P_{\text{LY}}=R_{\text{LY}}\Big{(}\frac{d_{1}^{2}}{\text{LY}}+\frac{\Delta_{1 }^{2}}{12}\Big{)}\) \\ \hline \(P_{\text{conD1}}=V_{f1}I_{\text{LX}}D_{1}^{\prime}+R_{\text{onD1}}D_{1}^{ \prime}\Big{(}\Big{(}I_{\text{LX}}^{2}+\frac{\Delta_{1}^{2}}{12}\Big{)}\) & \(P_{\text{conD1}}=\\ V_{f1}(I_{\text{LX}}+I_{\text{LY}})D_{1}^{\prime}+R_{\text{onD1}}D_{1}^{ \prime}\Big{(}\Big{(}I_{\text{LX}}+I_{\text{LY}})^{2}+\frac{\Delta_{1}^{2}}{12 }\Big{)}\) \\ \hline \(P_{\text{conD2}}=V_{f2}I_{\text{L2}}D_{2}^{\prime}+R_{\text{onD2}}D_{2}^{ \prime}\Big{(}I_{\text{L2}}^{2}+\frac{\Delta_{1}^{2}}{12}\Big{)}\) & \(P_{\text{conD2}}=\\ V_{f2}(I_{\text{L1}}+I_{\text{L2}})D_{2}^{\prime}+R_{\text{onD2}}D_{2}^{ \prime}\Big{(}\Big{(}I_{\text{L1}}+I_{\text{L2}})^{2}+\frac{\Delta_{1}^{2}}{12 }\Big{)}\) \\ \hline \(P_{\text{conD0}}=0\) & \(P_{\text{$\gamma$3}}(I_{\text{LX}}+I_{\text{LY}})D_{2}^{\prime}+R_{\text{onD3}}D_{2}^{ \prime}\Big{(}\Big{(}I_{\text{LX}}+I_{\text{LY}})^{2}+\frac{\Delta_{1}^{2}}{12 }\Big{)}\) \\ \hline \(P_{\text{conM1}}=R_{\text{$\delta$M$M1}}D_{1}\Big{(}\Big{(}\frac{2}{\text{LX}} +\frac{\Delta_{1}^{2}}{12}\Big{)}\) & \(P_{\text{$\text{conM2}}=R_{\text{$\delta$M$M2}}D\Big{(}\Big{(}I_{\text{LX}}^{2} +\frac{\Delta_{1}^{2}}{12}\Big{)}\) \\ \hline \(P_{\text{$\text{swD1}}$}=V_{\text{C1}}Q_{\text{rrr1}}f_{s}\) & \(P_{\text{$\text{swD1}}$}=V_{\text{c1}}Q_{\text{rr1}}f_{s}\) \\ \hline \(P_{\text{$\text{swD2}}$}=V_{\text{c2}}Q_{\text{rr2}}f_{s}\) & \(P_{\text{$\text{swD2}}\[V_{in}D+(V_{in}-V_{\text{C1}})(1-D)=0\Rightarrow V_{\text{C1}}=\frac{V_{in}}{ 1-D} \tag{28}\]0\text{swD0}}\[V_{in}D+(V_{in}-V_{\text{C1}})(1-D)=0\Rightarrow V_{\text{C1}}=\frac{V_{in}}{ 1-D} \tag{28}\]1\text{swD0}}$}=V_{\text{c3}}Q_{\text{rr3}}  
State 2: Voltage across inductor \(L_{Y}\) when the power switch is in ON and OFF modes:  
The voltage drops can be calculated as Equation (29):  
\[V_{in}D+(V_{in}-V_{\text{C1}})(1-D)=0\Rightarrow V_{\text{C1}}=\frac{V_{in}}{ 1-D} \tag{28}\]2  
By replacing Equation (28) into Equation (29), the voltage gain of the proposed structure can be calculated:  
\[V_{in}D+(V_{in}-V_{\text{C1}})(1-D)=0\Rightarrow V_{\text{C1}}=\frac{V_{in}}{ 1-D} \tag{28}\]3  
Therefore, the voltage gain of the proposed structure can be obtained by Equation (32):  
\[V_{in}D+(V_{in}-V_{\text{C1}})(1-D)=0\Rightarrow V_{\text{C1}}=\frac{V_{in}}{ 1-D} \tag{28}\]4  
Through a simple calculation, the relation between the input and output current values can be calculated as:  
\[V_{in}D+(V_{in}-V_{\text{C1}})(1-D)=0\Rightarrow V_{\text{C1}}=\frac{V_{in}}{ 1-D} \tag{28}\]5  
For the proposed converter, we can find the values of the inductor currents from the below equations:  
\[V_{in}D+(V_{in}-V_{\text{C1}})(1-D)=0\Rightarrow V_{\text{C1}}=\frac{V_{in}}{ 1-D} \tag{28}\]6  
\[V_{in}D+(V_{in}-V_{\text{C1}})(1-D)=0\Rightarrow V_{\text{C1}}=\frac{V_{in}}{ 1-D} \tag{28}\]7  
So, the oscillation of the current for these inductors can be presented by:  
\[V_{in}D+(V_{in}-V_{\text{C1}})(1-D)=0\Rightarrow V_{\text{C1}}=\frac{V_{in}}{ 1-D} \tag{28}\]8  
\[V_{in}D+(V_{in}-V_{\text{C1}})(1-D)=0\Rightarrow V_{\text{C1}}=\frac{V_{in}}{ 1-D} \tag{28}\]9  
Additionally, the voltage fluctuation for the output capacitor can be presented by Equation (37):  
$\gamma$0  
For the simulation and experimental analysis, considered one percent for these oscillations, the values of the inductors and capacitors can be calculated.