Wideband Nonlinear Response of High-Temperature Superconducting Thin Films From Transmission-Line Measurements

We report on a technique for extracting an accurate value of the nonlinear inductance in superconducting transmission lines. This novel technique assesses the frequency dependence of the transmission line's nonlinear response. A wideband nonlinear measurement system was used to simultaneously measure the third-order spurious signals at 2f
₁
- f
_2,
2f
₂
- f
₁
+ f
₂
, 2f
₂
+ f
₁
, 3f
₁
, and 3f
₂
frequencies. Measurements for different values of the fundamental frequencies f
₁
and f
₂
allow us to study the spurious signal generation from 1 to 21 GHz. We demonstrate this technique by measuring several superconducting YBa
₂
Cu
₃
O
_7-x
coplanar waveguide transmission line geometries patterned in a single chip at 80 K. The results show a linear frequency dependence of the nonlinear response, indicating a dominant contribution of the nonlinear inductance over the nonlinear resistance omegaDeltaL(i) Gt DeltaR(i). The experimentally obtained nonlinear inductances are then used to determine device-independent measures of the linearity of the thin-film material in order to provide the foundation for modeling the nonlinear response of specific devices.