# Single-Switch Non-Isolated Resonant DC-DC Converter for Single-Input Dual-Output Applications
## 3 Model and Experimental Prototype  
In order to verify the analysis of the SIDO ZVS-QR SEPIC-Cuk combined converter, simulation and experimental results were carried out using a simulation model and an experimental prototype for low-power but scalable for higher-power values. Therefore, the circuit in Figure 3 has been implemented and developed as shown in Figure 6. The objective is to provide results that will allow the validation of the newly developed configuration. In a similar way as in the design of single-input single-output converters, in the ZVS-QR SEPIC-Cuk combination converter, some basic rules must be considered. The values of the inductances \(L_{1}\), \(L_{2}\) and \(L_{3}\) must be chosen in such a way that they can limit the ripple in the input current (\(\Delta i_{L1}\)) and the output currents (\(\Delta i_{L2}\) and \(\Delta i_{L3}\)). In this sense, the following inequalities must be satisfied:  
\[ \begin{array}{l}\Delta i_{L_{1}}=\frac{V_{g}}{L_{1}}\left(T_{s}-t_{off} \right)<<I_{g}\\ \Delta i_{L_{2}}=\frac{V_{g}^{+}}{L_{1}}t_{off}<<I_{o_{1}}\\ \Delta i_{L_{3}}=\frac{V_{g}^{-}}{L_{3}}t_{off}<<I_{o_{2}}\end{array}  \tag{10}\]  
Similarly, for the selection of the output filtering capacitors, the maximum acceptable ripple of the converter output voltage must be considered. In this sense, the voltage ripples in \(C^{+}{}_{o}\) and \(C^{-}{}_{o}\) are given by:  
\[ \begin{array}{l}\frac{\Delta v_{g}^{+}}{V_{g}^{-}}=\frac{\left(T_{s}-t_{off} \right)}{R_{s}^{+}\cdot C_{g}^{+}},\text{for SEPIC side}\\ \frac{\Delta v_{g}^{-}}{V_{g}}=\frac{t_{off}}{8\cdot L_{3}\cdot C_{g}\cdot f_{ g}},\text{for Cuk side}\end{array}  \tag{11}\]  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Switch \(Q\)** & \(D_{1}\) & \(D_{2}\) \\ \hline Peak Voltage on Semiconductors & \(\frac{V_{g}}{m}\left(1+\frac{(1-m)\cdot Z_{s}}{R_{s}\cdot m}\right)\) & \(\frac{V_{g}}{m}\) & \(\frac{V_{g}}{m}\) \\ \hline Average Current across the Semiconductors & \(\frac{V_{g}\cdot(1-m)^{2}}{R_{s}\cdot m^{2}}\) & \(\frac{V_{g}\cdot(1-m)}{R_{s}^{+}\cdot m}\) & \(\frac{V_{g}\cdot(1-m)}{R_{s}\cdot m}\) \\ \hline  & \(V_{C1}\) & \(V_{C2}\) & \\ \hline Average Voltage across the Link Capacitors & \(V_{g}\) & \(\frac{V_{g}}{m}\) & \\ \hline  & \(I_{L1,AVG}\) & \(I_{L2,AVG}\) & \(I_{L3,AVG}\) \\ \hline Average Current across the Filter Inductors & \(\frac{V_{g}\cdot(1-m)^{2}}{R_{s}\cdot m^{2}}\) & \(\frac{V_{g}\cdot(1-m)}{R_{s}\cdot m}\) & \(\frac{V_{g}\cdot(1-m)}{R_{s}\cdot m}\) \\ \hline  & **Average** & \multicolumn{2}{c}{**Peak**} \\ \hline Voltage across the Resonant Capacitor (\(C_{R}\)) & \(V_{g}\) & \(\frac{V_{g}}{m}\left(1+\frac{(1-m)\cdot Z_{s}}{R_{s}\cdot m}\right)\) \\ \hline  & **Average** & \multicolumn{2}{c}{**Peak**} \\ \hline Current across the Resonant Inductor (\(L_{R}\)) & \(\frac{V_{g}\cdot(1-m)^{2}}{R_{s}\cdot m^{2}}\) & \(\frac{V_{g}\cdot(1-m)}{R_{s}\cdot m^{2}}\) \\ \hline  & \(With:\)\(\frac{1}{R_{s}^{2}}=\frac{1}{R_{Lo  
In addition, the selection of the link capacitors is based on the assumption that the voltage in those capacitors must be constant. Their values must be chosen so that the resonant frequency, formed by inductor filters and link capacitors, is much lower than the switching frequency. So, for Cuk and SEPIC, the resonance frequency is given by:  
\[ \begin{array}{l}\omega_{r_{1}}^{2}=\frac{1}{C_{1}\left(L_{1}+L_{2}\right)} \textit{for SEPIC side}\\ \omega_{r_{2}}^{2}=\frac{1}{C_{2}\left(L_{1}+L_{3}\right)}\textit{for Cuk side}\\ \textit{furthermore}:\\ \par C_{1}>\frac{\left(T_{t}-t_{off}\right)^{2}}{2\cdot T_{s}\cdot R_{s}^{2} }\textit{ and }C_{2}>\frac{\left(T_{s}-t_{off}\right)^{2}}{2\cdot T_{s}\cdot R_{s}^{2}} \end{array}  \tag{12}\]  
In this regard, the voltage ripple in \(C_{1}\) and \(C_{2}\) is given by:  
\[ \begin{array}{l}\frac{\Delta v_{e}^{+}}{V_{e}^{-}}=\frac{\left(T_{s}-t_{off} \right)}{R_{s}^{+}-C_{s}^{+}}\textit{,for SEPIC side}\\ \frac{\Delta v_{e}^{-}}{V_{e}^{-}}=\frac{t_{off}}{8\cdot L_{2}\cdot C_{s}^{-} \cdot f_{s}}\textit{,for Cuk side}\end{array}