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This work presents a resonant fault current limiter (FCL) controlled by power semiconductor devices. Initially the operation of two ideal resonant circuit topologies as fault current limiter are discussed. The analysis of these circuits is used to derive an alternative topology to the fault current limiter based on the connection of a series and a parallel resonant circuit. Digital models are implemented in the SimPowerSystem/Matlab simulation package to investigate the performance of the proposed FCL to protect transmission and distribution electric networks against short circuit currents. Transfer functions of the linear limiter models are used to identify the effect of each element of the FCL over its stability and its transient response. The developed analysis will be used to derive modifications in the FCL topology in such a way to improve their dynamic response.