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In this article, a compact unconditionally stable two-dimensional (2-D) stochastic weighted Laguerre polynomial finite-difference time-domain (S-WLP-FDTD) method for geometric uncertainty in superconducting transmission lines is proposed. It calculates both the Maxwell equations and the London equations and uses a weighted Laguerre polynomial (WLP) scheme to eliminate the stability constraint. The mean and the standard deviation of electromagnetic fields, voltages, and currents are calculated. Compared with the Monte Carlo method and 2-D S-FDTD method, the proposed method has the same accuracy but much higher efficiency. The runtime of the proposed S-WLP-FDTD method is only 2.4% of that of the S-FDTD method. Thus, the proposed method is suitable for predicting the influence of geometric uncertainty on superconducting transmission lines. [ABSTRACT FROM AUTHOR]

In this article, a stochastic finite-difference time-domain (S-FDTD) method is proposed for analyzing the influence of physical size uncertainty on the time-domain response of superconducting transmission lines. The formulations of the proposed method are, in detail, derived with the two-fluid model and London equation. A typical superconducting microstrip line is simulated to verify the effectiveness of the proposed algorithm. Compared with the Monte Carlo simulation, the proposed method has the same accuracy but much higher efficiency. The computation time of the proposed S-FDTD method is only about 3% of that of the Monte Carlo simulation. Therefore, the proposed method shows a promising prospect on predicting the variability in transmission line's performance caused by variation in superconducting manufacturing. [ABSTRACT FROM AUTHOR]

With the development of rapid single-flux-quantum (RSFQ) circuits, signal integrity issues of interconnects, such as signal distortion and crosstalk, become critical. Josephson junctions, as driver and receiver of interconnects, also affect signal integrity. Hence, it is significant to coanalyze time-domain responses of multicoupled passive transmission lines (PTLs) and Josephson junctions in RSFQ circuits. In this article, an accurate numerical method based on finite-difference time-domain (FDTD) is proposed to coanalyze multicoupled PTLs and Josephson junctions. The FDTD method is used to solve the telegraph equations of PTLs, and an iteration algorithm based on the contractive mapping theorem is proposed to solve the nonlinear equations generated by the Josephson junctions. In addition, the existence and uniqueness conditions of the nonlinear equations are also provided. The numerical and simulation results show that the proposed coanalysis method has the same accuracy as but higher efficiency than WRspice. [ABSTRACT FROM AUTHOR]