An analytical model for a square split ring resonator (S-SRR) having a single split-gap is considered here to reliably estimate the fundamental resonance frequency of the ring. An S-SRR is assumed to be equivalent to a series-resonant LC loop. The approximate formulas for equivalent self-inductance and total capacitance of the ring are derived separately. The total capacitance of the ring is expressed as a sum of a gap capacitance and a surface capacitance (which is associated with charges on the SRR walls). Both the capacitances are influenced by not only the medium in split-gap but also the dielectric constant of substrate. These are taken care of by including appropriate weight factors in the expressions for the capacitances. Again, using the software CST Microwave Studio, the resonance frequencies are calculated for several values of split-gap and SRR side length. Then the results of simulation are compared with the results obtained from our formula. It is found that simulation results agree quite well with the analytical results. Also, the analytical result for resonance frequency of SRR shows good agreement with a previously published experimental result. This model can be used for studies of the resonant properties of split rings in the microwave and terahertz regions.

中文翻译：

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验证方形开口环谐振器谐振频率的理论方法

这里考虑了具有单个裂隙的方形裂环谐振器 (S-SRR) 的分析模型，以可靠地估计环的基本谐振频率。假设 S-SRR 等效于串联谐振 LC 环路。分别推导出环等效自感和总电容的近似公式。环的总电容表示为间隙电容和表面电容（与 SRR 壁上的电荷相关）的总和。两者的电容不仅受裂隙介质的影响，还受基板介电常数的影响。这些是通过在电容表达式中包含适当的权重因子来解决的。再次使用 CST Microwave Studio 软件，共振频率是针对裂隙和 SRR 边长的几个值计算的。然后将仿真结果与我们的公式得到的结果进行比较。发现模拟结果与分析结果非常吻合。此外，SRR 共振频率的分析结果与先前公布的实验结果非常吻合。该模型可用于研究微波和太赫兹区域中裂环的谐振特性。