Microwave bandstop filters with minimum through-line length

The theory of bandstop filters with minimum through-line length is developed in this paper. In contrast to conventional similar-resonator bandstop filters that employ odd multiples of 90-degree impedance inverters between resonators, the proposed design technique enables filters with through-line length restricted to only that which is required to obtain a desired coupling coefficient magnitude between a resonator and the through-line. Both even- and odd-order designs are shown to verify the concept. A 4^th-order microstrip prototype with 45 degrees of through-line length per resonator was fabricated, measured, and compared to two conventional designs. It has half the through-line length of conventional designs.