Resonance Frequency and Bandwidth of the Negative/Positive nth Mode of a Composite Right-/Left-Handed Transmission Line

In this study, the analytic expression for the positive/negative nth-mode resonance frequency of an N unit cell composite right-/lefthanded (CRLH) transmission line is derived. To explain the resonance mechanism of the nth mode, especially for the negative mode, the current distribution of the N unit cell CRLH transmission line is investigated with a circuit simulation. Results show that both positive and negative nth resonance modes have n times current variations, but their phase difference is 180 degrees as expected. Moreover, the positive nth resonance occurs at a high frequency, whereas the negative nth resonance transpires at a low frequency, thus indicating that the negative resonance mode can be utilized for a small resonator. The correlation between the slope of the dispersion curve and the bandwidth is also observed. In sum, the balanced condition of the CRLH transmission line provides a broader bandwidth than the unbalanced condition.