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We present a pulse-coupled network of integrate-and-fire circuits that have refractoriness. The network can be implemented by a simple electrical circuit, and various periodic synchronization phenomena are observed in the laboratory. The phenomena are characterized by a ratio of phase locking. Using a return map having a trapping window, the ratio can be analyzed in a parameter subspace rigorously. We clarify effects of the refractoriness on pulse coding ability of the network.