## 4 Sensitivity Analysis  
### Push-Pull Converter Design: Case Studies  
To determine the best trade-off between complexity and practical viability of the model in terms of topology, power and operating frequency, a sensitivity analysis is required to determine the influence of each non-ideality on its dynamic response. Thus, based on Equations (2)-(29), two topologies of push-pull converters, boost and buck, have been designed for four power ranges under study (cases), and three ranges of typical operating frequencies used in the scientific literature and in commercial converters. This determines a total of 24 different converter cases to be studied. Specifically, for the design of the buck topology, typical voltage values based on single-phase power supplies of 300 VDC input and a converter output of 30 VDC have been considered. In contrast, for the case of the boost topology, practical cases of integration of low-voltage renewable energy sources at 30 VDC input and a converter output of 300 VDC have been considered. Finally, due to the small number of applications, extreme low-power applications (<1 W) and operating frequencies above 500 kHz have not been considered in this study. The four cases under study are as follows:  
**Case 1**: Very low power (1 W-10 W) and operating frequencies of 100 kHz, 300 kHz and 500 kHz. **Case 2**: Low power (10 W-100 W) and operating frequencies of 50 kHz, 75 kHz and 150 kHz. **Case 3**: Medium power (100 W-1 kW) and operating frequencies of 50 kHz, 75 kHz and 150 kHz. **Case 4**: High power (1 W-10 kW) and operating frequencies of 25 kHz, 50 kHz and 75 kHz. For the sizing of each converter for each topology and case, the design power has been considered as the upper power limit of the case under study, as well as the lowest operating frequency of the established range, being the most restrictive conditions. Likewise, a conservative maximum duty cycle of 0.45 has been considered to avoid short circuits due to operating at duty cycles close to 0.5. For the design of the different converters according to the established cases and considerations, a market study was carried out based on commercial power electronic devices from widely known manufacturers. From this preliminary study, a first selection of suitable devices was obtained, considering different models but with a similar performance and parameters. Finally, the components were selected considering that their nominal parameters would fit the parameters calculated for each topology, buck and boost, and for each power range under study. Once the components were selected, their main parameters were obtained from the nominal values given in their datasheets in the case of the power switching devices and the output low-pass filter components and from Equations (7)-(20) for the power transformer. Tables 1-4 show the main parameters of the converters designed from the selected components for both topologies and cases. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{**Buck Topology**} & \multicolumn{2}{c}{**Boost Topology**} \\ \hline
**Element** & **Model and Rated Values** & **Parameters** & **Model and Rated Values** & **Parameters** \\ \hline Output low-pass filter & \begin{tabular}{c} MAE211651338E3, VISHA\({}^{\text{\textregistered}}\) \\ (Malvern, PA, USA) \\ 50 VDC \\ \end{tabular}  & \begin{tabular}{c} C\({}_{F}:3.3\) uF \\ \(R_{C_{F}}:3.1\) O \\ \(R_{C_{F}}:3.1\) O \\ \(L_{F}:150\) O \\ \(L_{F}:150\) O \\ \(L_{F}:150\) O \\ \(L_{F}:520\) O \\ \end{tabular}  & \begin{tabular}{c} B32911A3333M000, TDK\({}^{\text{\textregistered}}\) \\ (Hutchinson, MN, USA) \\ 50 VDC \\ \end{tabular}  & \begin{tabular}{c} C\({}_{F}:30\) nF \\ \(R_{C_{F}}:1\) O \\ \(L_{F}:150\) O \\ \(L_{F}:52\) O \\ \end{tabular}  \\ Output low-pass filter & \ \begin{tabular}{c} SRR1005-151K, Bourns\({}^{\text{\textregistered}}\) \\ (Riverside, CA, USA) \\ \end{tabular}