In the present work, the analysis and simulation of the DC-DC Flyback converter is carried out, which is used in most lithium-ion battery chargers in the country. The main objective of this paper is the implementation of an example of a flyback converter using a state space model for continuous conduction mode (CCM) and discontinuous conduction mode (DCM) not reported in the literature review. To accomplish this objective, the values of the power elements were calculated and the steady-state behavior of the converter was analyzed. Furthermore, the state space model was applied to the converter and the validation process was through bode waveforms. The results demonstrate the correct operation of the converter for all simulated contingencies using the state space model for this type of power converter.