New Method for Determining the Quality Factor and Resonance Frequency of Superconducting Micro-Resonators from Sonnet Simulations

Abstract

Lithographed superconducting microwave resonators (micro-resonators) are useful in a number of important applications, including microwave kinetic inductance detectors (Day et al., Nature 425:817, 2003), as memory elements in quantum information circuits, and as readouts of qubits and nanomechanical resonators. One of the major tasks in designing these devices is to find the resonance frequency (f$_{r}$) and quality factor (Q) for these microwave circuits using EM simulation software such as Sonnet. The traditional method iteratively runs simulations over successively smaller frequency ranges. In this way the simulated transmission S$_{21}$ data is zoomed in on to yield a well-sampled resonance curve of a circuit. Designing microwave resonators in this manner is often time consuming since it requires many simulation runs. In this work, we show a new—and much faster—method for determining f$_r$ and Q by adding an internal (virtual) port in the Sonnet model and examining the input impedance through the added port. Accurate f$_r$ and Q values can be retrieved from a single simulation with a wide frequency sweep. This method works on many types of resonance circuits and dramatically reduces the simulation time.