Quasi Static Modeling of Weak Nonlinearity in Superconducting Transmission Lines with Sub-Wavelength Non-Uniformity

Superconducting passive microwave devices unlike routine normal conductor ones, due to dependence of superfluid density (ns) to current distribution, have a nonlinear behavior called Nonlinear Meissner Effect (NME). In this paper, a nonlinear distributed circuit model for HTS transmission lines with sub-wavelength longitudinal non-uniformity in the case of weak nonlinearity is proposed. This model is based on the quasi-TEM approximation of sub-wavelength non-uniform transmission lines (SW-NUTLs) that proposes closed form formulas for effective characteristic impedance and complex propagation constant of SW-NUTLs. Any NUTLs can be modeled with the mentioned method through dividing it into adequately small subsections to fulfill sub-wavelength condition. Regarding these propagation parameters relations, some effective equations for RLGC parameters are inferred. Because of dependence of the penetration depth and the real part of conductivity on ns, the proposed effective resistance and inductance depend on current distribution that in case of weak nonlinearity, follow a square-law form. As such the nonlinear microwave effects such as Intermodulation distortion (IMD) and harmonic generation can be calculated with harmonic balance (HB) Analysis. This semi-analytical approach shows great accuracy in different test cases.