Analytical Design of Compact Dual-Band Filters Using Dual Composite Right-/Left-Handed Resonators

A new kind of compact dual-mode dual-composite right-/left-handed resonators is proposed. Dual-band bandpass filters (BPFs) are consequently designed with over 88% size reduction. To assist the filter design, an analytical design method is further presented, with which one filter can be designed flexibly according to the desired frequencies and bandwidths (BWs). To alleviate the design difficulties, a synthesis design technique and a feedback-based optimization process are both employed. In addition, the independent control of frequencies, BWs, and coupling coefficients are also realized, which provide large freedom for designing BPFs. To ensure the feasibility of the design method, the valid ranges of center frequency and BW ratios are first determined. Furthermore, four compact BPFs are designed with a large/small center frequency ratio (3.11/1.6) and a large/small BW ratio (2.52/0.52). Good agreement between the measurements and simulations are observed, indicating the validity of the proposed design method.