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Interest in the electromagnetic properties of loop structures has surged with the recent appearance of split-ring resonator meta-materials (SRRs) and nano-antennas. Understanding the resonances, anti-resonances, and harmonics of these loops is key to understanding their response to a wide range of excitation wavelengths. We present the classical analytical solution for the input impedance of a loop structure with circumference on the order of the wavelength, and we show how to identify these resonances from the function. We transform the classical solution into a new RLC formulation and show that each natural mode of the loop can be represented as a series resonant circuit, such that the full response function can be resolved by placing all of these circuits in parallel. We show how this formulation applies to SRRs.

The analytical basis for the resonances and anti-resonances of loop antennas and meta-material ring resonators