Modeling the nonlinearity of superconducting strip transmission lines

The use of the Ginzburg-Landau (GL) theory to predict the nonlinear behavior in a superconducting stripline resonator as a function of input current is reported. 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 and, hence, the spatial variation of the magnetic penetration depth 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 YBa/sub 2/Cu/sub 3/O/sub 7-x/ stripline resonators show excellent agreement.<
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