General condition to achieve negative group delay transmission in coupled resonator structure

The general condition to achieve negative group delay (NGD) transmission in electromagnetic coupled resonators is investigated. Different from previous studies, this work focuses on deriving the relationship between the NGD and the energy storage capability of the resonator, which is usually denoted by the quality (Q) factor. In this derivation, the Q factor is divided into two parts, including the external (Qe) and internal quality (Qi) factors. By analyzing the equivalent circuit of the coupled resonator, the relationship between group delay and Q factor is extracted, as the group delay is related to ratio of Qe and Qi. Furthermore, the group delay is with a sudden change from positive to negative as Qe is beyond the catastrophe point. Finally, frequency and time domain experimental validation is provided to prove the efficiency of derived condition.