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This study presents an accurate and fast method for large-signal discrete-time simulation of current controlled DC/DC buck converter in continuous conduction mode. It employs modal decomposition of the state transition matrix for each topology, resulting in an exact and computationally efficient set of decoupled discrete-time state equations. This enables one to obtain an accurate solution for duty ratios iteratively, by equating the switching conditions of the state variables with state equations, which are non-linear in duty ratio. In the absence of a compensating ramp, an efficient way to compute duty ratios explicitly, without iteration, is also suggested. Subsequently, state variables are propagated through the ON and OFF periods, using the state equations exactly but without the need to compute a matrix exponential. This way numerical integration at multiple intermediate points between two switching instants of interest is avoided, which makes the simulation considerably faster, leading to significantly reduced storage requirement compared to common simulation methods, such as using SPICE. It is shown under different parametric conditions that the proposed method has superior accuracy over several approximate simulation methods proposed in the literature. The method can be generalised for other converter topologies, operational modes and control configurations with appropriate changes.