Coupled‐Mode Theory and Numerical Analysis of High‐Q Reconfigurable Split‐Ring Resonators (SRRs) for Graphene/rGO Conductivity‐Based Microwave Sensing

Abstract This paper presents a theoretical and numerical study of a reconfigurable high‐quality ( Q) split‐ring resonator (SRR)‐based microwave sensor for detecting the conductivity of 2D carbon materials, specifically single‐layer graphene (SLG) and reduced graphene oxide (rGO). The proposed sensor, integrated into a coplanar waveguide (CPW) circuit, enables tunable resonance through angular rotation of the SRR. Among the resonant modes, the deep resonance of the SRR configuration is analytically investigated using a coupled‐mode theory (CMT) model. The specific SRR configuration achieves a high Q ‐factor (≈191), with excellent agreement between simulation and CMT model (R 2 ≥ 0.95). The sensing performance of high‐ Q SRRs loaded with SLG and rGO is evaluated across a wide conductivity range from 1 × 10 2 to 5 × 10 7 S m −1 . The simulated results clearly resolve rGO and SLG films within their respective conductivity ranges 1–5 × 10 3 S m −1 and 1–5 × 10 5 S m −1 with both resonant frequency and amplitude strongly dependent on conductivity. As a result, these findings demonstrate the feasibility of the proposed high‐ Q SRR device as a compact, sensitive, and miniaturized platform for microwave characterization of ultrathin films, providing a robust foundation for future experimental implementation.