A Metamaterial Inspired Single Split Ring Resonator for Sensing Applications - A Practical Design Approach
Metamaterial inspired unit cells are those spiral structured artificial magnetic media designs commonly used in sensing applications. Split ring resonators (SRR) consists of two concentric rings either in circular or in square shape with a gap and can be simplified into an Inductor-Capacitor (LC) resonant tank. The resonance frequency of such unit cells depends on the value of L and C and can be represented by the following equation.
For the split ring resonator, the gaps or splits support realizing higher resonance frequencies without increase in the size of the ring thereby making the SRR a good candidate for realizing miniaturized RF structures. One of the classic advantages of SRR is that they have low radiative losses and are used to make left-handed media with a negative refractive index. When a time-varying magnetic field is applied on the ring, current loops are generated and the capacitance in the gap allows completion of such loops leading to the resonance behavior forming an LC tank or resonator.
The total inductance and capacitance of the loop is dependent on the different structural dimensions of the loop. For a single split ring structure, the following analytical expression can be used to compute the resonance frequency of the structure.
The equivalent inductance of the ring can be calculated using eq (3)
where,
The total capacitance can be calculated using eq (4).
where,
where,
For example, let 
The resonance frequency computed using the above equations is ~ 3 MHz.
For simulating such a ring resonator, there are multiple techniques available in Feko. In this example, a periodic boundary condition approach with a plane wave excitation is used as shown in Fig 1.
Fig 1. Simulation set up for a single split ring resonator using PBC.
The resonance frequency of the structure in Fig 1 was found to be 4.4 MHz as shown in Fig 2. The result agrees well with the theoretical value and the small discrepancy between them can be attributed to the approximate assumptions chosen for calculating the surface capacitance.
Fig 2. Simulated transmission coefficient for the single split ring resonator.
One of the biggest advantages of this design is that it can be easily used for creating reconfigurable RF structures by adding a non-linear element such as a varactor diode in the gap of the ring resonator, enabling easy tuning of the resonance frequency.