Geometry dependence of nonlinear effects in high temperature superconducting transmission lines at microwave frequencies

We investigate the nature of low-power nonlinear effects in high-temperature superconducting microwave devices by measuring third harmonic generation at 76 K in coplanar waveguide transmission lines of different geometries fabricated from YBa2Cu3O7-delta thin films. The measured power in the third-harmonic signal changes systematically with film thickness, center conductor linewidth, and line length. We analyze these results using a simple model for a transmission line with a nonlinear inductance arising from a current-dependent superconducting penetration depth. This analysis describes quantitatively the observed differences in harmonic generation for transmission lines of different dimensions, and yields a single geometry-independent parameter (the nonlinear scaling current density J(0)) to quantify the observed nonlinear behavior. For the thin film samples studied here J(0)=3.0x10(7) A/cm(2) at 76 K for all geometries investigated. These results provide the means to establish a lower limit for the expected nonlinear response of superconducting components of arbitrary geometry at microwave frequencies. (C) 1999 American Institute of Physics. [S0021-8979(99)05614-5].