Modeling the Nonlinearity of Superconducting Strip Transmission Lines

This paper reports the use of the Ginzburg-Landau (GL) theory to predict the nonlinear behavior in a superconducting stripline resonator as a function of input current. A method for calculating the nonlinear inductance and the fractional change in the resonant frequency (Delta f/f) of a stripline resonator is presented. By solving the GL equations inside the superconducting strip, the spatial variation of the number density of superconducting electrons n(s)((r) over bar), and hence, the spatial variation of the magnetic penetration depth lambda((r) over bar) are obtained for different values of input current. First, an infinite parallel plate transmission line is considered where the one-dimensional GL equations are solved. The two-dimensional case of a stripline is then considered. Nonlinear inductances are calculated as functions of input current for different superconducting striplines. Comparisons of the calculated Delta f/f with measurements for YBa2Cu3O7-x stripline resonators show excellent agreement.