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In this letter, we present a detailed circuit model for single-photon avalanche diodes. The model can be implemented in many computer aided design circuit simulation environments and provides a representation of the detector's behavior in the above-breakdown (Geiger-mode) operation. The model implements the self-sustaining and self-quenching processes and correctly characterizes the reverse current-voltage curve. We show very good matching with experimental measurements obtained with both passive and active quenching circuits, and both single-photon and photon burst excitations.