SPECIFIC PROBLEMS OF NUMERICAL ANALYSIS OF THE JOSEPHSON JUNCTION CIRCUITS.

The authors describe solutions of two specific problems of numerical simulation of the Josephson junction circuits. The first problem is the modeling of circuits comprising many Josephson tunnel junctions within the framework of the microscopic (Werthamer) theory, resulting in nonlinear integrodifferential relation between the junction current and voltage. The second problem is the optimum averaging of variables, which is necessary to filter out the Josephson and other high-frequency oscillations. The authors have solved this problem using ideas from the theory of digital time-dependent filters. Algorithms based on these methods are incorporated into a CAD program named COMPASS, which is extensively used for analysis of various analog and digital devices based on the Josephson effect.