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In this paper we deal with the synchronization of the Colpitts oscillator. The synchronization problem for chaotic systems is treated as an observation problem, some results based on a differential algebraic approach are used in order to determine observability with the measurements from the system. The strategy consists of proposing a slave system (observer) which tends to follow asymptotically the Colpitts oscillator, refereed as master system. The methodology was tested in a real-time implementation by means of a reduced order observer.