An analytic method is developed for studying the electrodynamic properties of Josephson junctions biased with a sequence of delta-function pulses. Such investigations are of interest in connection with developing, on the basis of the Josephson effect, analog-to-digital converters and synthesizers producing signals of a preset form with a fundamental precision. Analytic expressions are obtained that determine phase lock conditions, the mean voltage across the junction, and the boundaries of Shapiro's steps. The results obtained are presented in a graphical form for the cases of unipolar and bipolar bias of a junction. The results are discussed and compared with those known from previous investigations.
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