## 4 Sensitivity Analysis
### Discussion
This results in a lower induced voltage on the transformer secondary. \(L_{S}\) similarly affects the current dynamics of the transformer secondary circuit. A high value increases the opposite induced voltage at its terminals, which reduces the slope of the secondary current and its final value. This causes variations in the dynamic response and a reduction in the steady-state value of the converter output voltage. Based on the above, the effect that each non-ideality has on the converter response depends on the value of the self-inductance coefficient of \(L_{P}\) and \(L_{S}\) (highly dependent on the winding method and other factors), the operating frequency and the operating current in both the primary and secondary circuits of the transformer (see errors for \(L_{P}\) and \(L_{S}\) in Figures 4 and 5). Therefore, it is complex to make a statement about the influence of these parameters on a certain topology under certain operating conditions. A general solution is to always consider these non-idealities in the design of the converter model. Finally, although the values of the leakage capacitances of the transformer windings (\(C_{P_{x}}\) and \(C_{S_{x}}\)) depend on the method of winding the conductors, the number of layers, the insulation thickness, the use of shielding, etc., the values obtained are usually much lower than those of the output capacitances of switching devices and the output filter capacitance (see Tables 1-4). Therefore, their effect on the converter dynamics for the switching frequencies under study can be considered negligible (see errors for \(C_{P_{x}}\) and \(C_{S_{x}}\) in Figures 4 and 5). Considering the results of the above analysis, the non-idealities of the transformer core (\(L_{M}\) and \(R_{Nu}\)),and the winding resistances (\(R_{LP}\) and \(R_{LS}\)) and leakage capacitances (\(C_{P_{x}}\) and \(C_{S_{x}}\)) can be eliminated from the equivalent simplified model for all cases under study (see Figures 4 and 5). This simplification cannot be applied to the primary and secondary winding leakage inductances (\(L_{P}\) and \(L_{S}\)), whose influence depends on the converter topology, operating power and switching frequency (see Figures 4 and 5). Considering power switching devices and, first, power transistors (Mosfets), the effect of non-idealities, \(R_{DS}\) and \(C_{OSS_{x}}\) will be analysed. As explained above, \(R_{DS}\) affects both the dynamic and steady-state behaviour of the converter. The dynamics of the transformer primary variables are determined by the resistors \(R_{DS}\) and \(R_{LP}\), which determine the dynamics of the core magnetisation process and the energisation of the transformer primary winding leakage inductances. This follows from the analysis of the RLC circuit generated in the transformer primary by \(R_{DS}\), \(R_{LP}\), \(L_{P}\) and \(C_{OSS_{x}}\) (see Figure 2). In view of the above, it is the ratio between \(R_{DS}\) and \(R_{LP}\) which determines their effect on the dynamic behaviour of the converter. An example of this can be seen in the dynamic response for the buck topology cases (Figure 4), where \(R_{DS}\), several orders higher than \(R_{LP}\) (see Tables 1-4), imposes the dynamics of the magnetising current flow and has a more noticeable effect on the dynamic behaviour of the converter (see the errors for \(R_{DS}\) in Figures 4 and 5 and Tables 5 and 6).