Role of superconductivity in superconducting transmission line resonator

In order to understand the role of superconductivity in superconducting transmission line resonator, we derive the mode equations using the macroscopic wavefunction of the Cooper pairs. We make an appropriate scaling to obtain the dimensionless form of equations and establish the validity of good conductor approximation under most circumstances. Quantization of superconducting transmission line resonator is realized by the black-box principle. We also briefly discuss that the deviation from good conductor behavior would result in the observable effects, such as the considerable decrease of phase velocity and the soliton.