Inductances and attenuation constant for a thin-film superconducting coplanar waveguide resonator

Abstract

The geometric, kinetic, and total inductances and the attenuation constant are theoretically analyzed for a thin-film superconducting coplanar waveguide (CPW) resonator consisting of a currentcarrying central conductor, adjacent slots, and ground planes that return the current. The analysis focuses on films of thickness d obeying d < 2λ (λ is the London penetration depth), for which the material properties are characterized by the two-dimensional screening length Λ = 2λ 2 /d. Introducing a cut-off procedure that guarantees that the magnitudes of the currents in the central conductor and the ground planes are equal, new and simpler results are obtained for the kinetic inductance and the attenuation constant for small Λ. Exact results for arbitrary Λ are presented for the geometric, kinetic, and total inductances in the limit of tiny slot widths, and approximate results are presented for arbitrary slot widths.

Temperature and power characteristics of quarter-wavelength superconducting coplanar waveguide resonator

“…The coupling between the resonator and the external transmission line adopts the capacitance coupling of an interdigital structure [14,15]. And the coupling capacitance between the CPW cavity and the external transmission line affects the loaded quality factor of the resonator and the resonant frequency of the whole resonator.…”

Probing dynamics of micro-magnets with multi-mode superconducting resonator

“…A simple criteria for applicability imply conditions where the internal Q-factor of the resonator (Q i ) remains below the designed coupling Qfactor. At H ¼ 0, the internal Q-factor can be estimated as Q i $ 1/a r L, where a r is Clem's microwave quasi-particle attenuation in superconducting coplanar transmission line 66 associated with Mattis-Bardeen quasi-particle conductivity, 67,68 and L ¼ 80 mm is the length of resonator. Figure 8 shows the log Q i ðf ; TÞ colormap calculated using geometrical parameters of the fabricated resonator and the following realistic physical properties of Nb film: superconducting critical temperature T c ¼ 9. , and normal state conductivity r n ¼ 1.5 Â 10 7 (X m) À1 .…”

50 Ohm Transmission Lines with Extreme Wavelength Compression Based on Superconducting Nanowires on High-Permittivity Substrates

“…This analytical model uses the established conformal mapping approach for CPW transmission lines made from conventional materials 30,31 combined with a model based on BCS theory developed by Clem for the kinetic inductance per unit length of a superconducting CPW. 32 First the capacitance per unit length C of the CPW geometry is calculated using a Schwarz-Christoffel conformal mapping. This process has been described previously 30,31 and the details are in the Supplementary Material.…”

“…A procedure for calculating L K for all center conductor widths was developed by Clem. 32 In this approach, L K is found from…”