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By introducing the frequency tuning sensitivity, an analytical model based on equivalent LC circuit is developed for the relative frequency tuning range of THz semiconductor split-ring resonator (SRR). And the model reveals that the relative tuning range is determined by the ratio of the kinetic inductance to the geometric inductance (RKG). The results show that under the same carrier density variation, a larger RKG results in a larger relative tuning range. Based on this model, a stacked SRR-dimer structure with larger RKG compared to the single SRR due to the inductive coupling is proposed, which improves the relative tuning range effectively. And the results obtained by the simple analytical model agree well with the numerical FDTD results. The presented analytical model is robust and can be used to analyze the relative frequency tuning of other tunable THz devices.
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