Self-coupled dual-mode ring resonator with turning transmission zeros in microwave bandpass filter for planar metamaterial: analysis and design

An H-shape dual-mode closed resonator with self-coupled segments is reported. The self-coupling between ring segments renders an equivalent mode perturbation effect as the normal ways of adding stub, cutting notch, or varying line impedance to the ring resonator. The mode perturbation and transmission-zero generation from the self-coupling effect and step-impedance were analyzed using the even–odd mode theory. By regulating the impedance ratio and coupling coefficients of self-coupled sections, the self-coupled ring resonator can produce either the capacitive or inductive perturbation. The input and output positions affect the number and locations of transmission zero. The positions of input and output ports are properly selected. In the capacitive perturbation case, when the two transmission zeros are located on both sides of the passband, and bring about a pseudo-elliptic bandpass response. The analysis of finding optimized taping positions of input and output ports is proposed. Comparing to the regular uniform ring resonator, the H-shaped self-coupled ring resonator has shorter ring length, is easily to be folded and does not destroy the dual-mode characteristics. The feature of compact size is favorable in the design of a bandpass filter. A 2.45-GHz bandpass filter based on the H-shaped self-coupled ring resonator was performed to verify the proposed theory. A schematic bandpass filter was implemented with a compact size which is only 20% of the conventional dual-mode bandpass filter.