Design and Analysis of Vertical Split Ring Resonator and Its Application to Unbalanced–Balanced Filter

We present a design method and analysis for a vertical split ring resonator (SRR). Furthermore, we propose an unbalanced-balanced filter using vertical SRRs. First, we explain vertical SRR with a stepped impedance resonator (SIR) using virtual ground. The resonance frequency is theoretically derived based on asymmetric coupled transmission lines. The resonance frequencies of vertical SRRs, calculated by our derived equation, are in good agreement with those of 3-D simulations and measurements. Next, this resonator is applied to an unbalanced-balanced filter based on low-temperature co-fired ceramic (LTCC). The attenuation poles of this filter are controlled by coupling between high-impedance lines similar to a two-pole filter with a SIR. The dimensions of the measured filter implemented with LTCC are 2.0 ?? 1.2 ?? 0.60 mm. The insertion loss is 2.80 dB in a 2.4-GHz band. Good agreement between measured and computed results is obtained.