Network modeling of non-ideal superconducting resonator circuits

We originally develop a network analysis method to study the non-ideal superconducting resonator circuits. We model the resonator device by a 3-block serial network, consisting of input feedline, resonator-coupler and output feedline. We show that the resonance curve will be modified if non-negligible discontinuity (reflection) exists at input or output side of the resonator. The extracted resonance parameters (such as coupling quality factor Q(c)) from only fitting the transmission deviate from their true values as originally defined in matched impedance conditions, and the deviation depends on a single parameter which includes all the non-ideal effects from the circuits. We prove that the internal quality factor Q(i) can be accurately extracted from the modified transmission curve by using a very simple graphical method. Our methods and results are quantitatively verified by both simulations and experiments on superconducting microstrip resonators. Comparing to the usual circuit analysis, our network analysis method is more intuitive and easier to understand. It can serve as a general tool to study the non-ideal superconducting resonator circuits.