Mode
3,\(\left(1-D\right)T_{s}\leq t\leq(1-D)T_{s}+\frac{T_{s}}{2}\):
In this mode, the switches \(G_{2}\) and \(G_{3}\) are on, while\(G_{1}\) and \(G_{4}\) are off. The following equations are resulted in
this mode.
\(V_{L1}=V_{\text{in}}-V_{c2}\) (10)
\(V_{L2}=V_{L3}=V_{\text{in}}\) (11)
\(V_{L4}=V_{\text{in}}-V_{c4}\) (12)
Therefore inductors \(L_{2}\) and \(L_{3}\) are charged with the rate of\(\ \frac{V_{\text{in}}}{L_{2}}\) and\(\frac{V_{\text{in}}}{L_{3}}\),
respectively. Also the voltages of inductors \(L_{1}\) and \(L_{4}\) are
reduced with the rate of \(\frac{(V_{\text{in}}-V_{c2})}{L_{1}}\)and\(\ \frac{(V_{\text{in}}-V_{c4})}{L_{4}}\). This mode is shown in
Fig. 5.
Mode
4\(,\ \frac{T_{s}}{2}+\left(1-D\right)T_{s}\leq t\leq T_{s}\):
In this mode, the switches \(G_{2}\) and \(G_{4}\) are on, while\(G_{1}\) and \(G_{3}\) are off. The following equations are resulted in
this mode.
\(V_{L1}=V_{L2}=V_{\text{in}}-V_{c2}\) (13)
\(V_{L3}=V_{L4}=V_{\text{in}}\) (14)
Therefore inductors \(L_{3}\) and \(L_{4}\) are charged with the rate of\(\frac{V_{\text{in}}}{L_{3}}\) and\(\ \frac{V_{\text{in}}}{L_{4}}\),
respectively. Also the voltages of inductors \(L_{1}\) and \(L_{2}\) are
reduced with the rate of \(\frac{(V_{\text{in}}-V_{c2})}{L_{1}}\)and\(\frac{(V_{\text{in}}-V_{c2})}{L_{2}}\). This mode is shown in
Fig. 6.