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

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.