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A circuit model is presented for Josephson junctions (JJs) that solves the nonlinear long-junction equation, driven by a nonuniform current distribution. This extended resistively shunted junction (ERSJ) model consists of a parallel array of ideal resistively shunted JJs coupled by inductors. The junction array is connected to an array of current sources that simulate the time- and space-dependent current distribution in a stripline. The rf-current dependent complex impedance of a long JJ calculated using this model agrees with measured data on a YBCO grain-boundary JJ and provides an explanation of the measured steps in the resistance resulting from the creation, annihilation, and motion of Josephson vortices under the influence of rf currents. This model contributes to a better understanding of the power-handling characteristics of high-Tc microwave devices, in which the power losses are believed to result from JJ effects associated with imperfections in the films. The model also predicts second-harmonic generation with a highly nonlinear and nonmonotonic power dependence. Details of the dynamics of Josephson vortices are presented and discussed.