Physics – Condensed Matter – Superconductivity
Scientific paper
2011-08-15
Physics
Condensed Matter
Superconductivity
19 pages, 8 figures, updated after JAP review
Scientific paper
We examine the transmission through nonideal microwave resonant circuits. The general analytical resonance line shape is derived for both inductive and capacitive coupling with mismatched input and output transmission impedances, and it is found that for certain non-ideal conditions the line shape is asymmetric. We describe an analysis method for extracting an accurate internal quality factor ($Q_i$), the Diameter Correction Method (DCM), and compare it to the conventional method used for milli-Kelvin resonator measurements, the $\phi$ Rotation Method ($\phi$RM). We analytically find that the $\phi$RM deterministically overestimates $Q_i$ when the asymmetry of the resonance line shape is high, and that this error is eliminated with the DCM. A consistent discrepancy between the two methods is observed when they are used to analyze both simulations from a numerical linear solver and data from asymmetric coplanar superconducting thin-film resonators.
Khalil Shahid M.
Osborn Kevin D.
Stoutimore Micah J. A.
Wellstood Frederick C.
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