Reducing the electrical size of magnetic metamaterial resonators by geometrical modifications: a comparative study for single-sided and double-sided multiple SRR, spiral and U-spiral resonators

In this study, this paper presented the simulation results that both increasing N and doubling the resonator structure provide additional capacitive effects and hence reduces the resonance frequency and electrical size, f₀ and u, noticeably. For example, increasing N from 2 to 6 for the MSRR, SR, USR, DMSRR, DSR, and DUSR structures caused their u and f₀ values changed to the %75, %38, %52, %76, %27, and %31 of their initial values, respectively. Besides, doubling a six-turn MSRR, a six-turn SR, and a six-turn USR reduced their u and f₀ values to 76%, 52%, and 35% of their initial values, respectively, where it is important to note that all these structures have the same unit cell size. Among all structures investigated in this work, the electrically largest resonator is the two-turn MSRR with u=lambda₀/12 and f₀=2.24 GHz while the electrically smallest one is the six-turn DUSR with u=lambda₀/133 and f₀= 0.20 GHz. In other words, the double-sided U-type spiral resonator (DUSR) with N=6 turns has an electrical size which is only 9 percent of the electrical size of the multi Split Ring Resonator (MSRR) with N=2 turns, although both structures have the same physical cell size of l=8 mm.