Quality factor of a transmission line coupled coplanar waveguide resonator

TL;DR

This paper analytically investigates the coupling characteristics of a coplanar waveguide resonator with a feedline, providing formulas for impedance and coupling that aid in designing quantum and microwave devices.

Contribution

It introduces an analytical approach using conformal mapping to derive mode impedances and coupling coefficients for asymmetric multi-conductor transmission lines.

Findings

Derived expressions for characteristic mode impedances.

Calculated external quality factor and frequency shift.

Results applicable to quantum and microwave device design.

Abstract

We investigate analytically the coupling of a coplanar waveguide resonator to a coplanar waveguide feedline. Using a conformal mapping technique we obtain an expression for the characteristic mode impedances and coupling coefficients of an asymmetric multi-conductor transmission line. Leading order terms for the external quality factor and frequency shift are calculated. The obtained analytical results are relevant for designing circuit-QED quantum systems and frequency division multiplexing of superconducting bolometers, detectors and similar microwave-range multi-pixel devices.