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This paper considers a mutually pulse-coupled system of chaotic circuits. Each circuit has a switch to short its capacitor, and the mutually pulse-coupling is realized by impulsive and simultaneous switching of the capacitors, depending on the states of both circuits. The coupled system exhibits synchronization of chaos and breakdown. The error expanding ratio between the units can be described by a simple theoretical formula. It enables us to classify the phenomena and to evaluate the dependence of the error expanding on the initial state. Fundamental bifurcation diagrams are given for the unit circuit and the coupled system. Some of the phenomena are confirmed by laboratory experiments.