A Tri-band Bandpass Filter Realized Using Tri-mode T-shape Branches

In this paper, we present a tri-band filter design using tri-mode T-shaped branches connected by λ/4 transmission lines. By analyzing the input admittance of a T-shape branch with commensurate electrical lengths, three resonant modes with two transmission zeros between are found and design formulas are derived. The filter can be regarded as a combination of three bandpass filters with only one set of coupling elements. To realize different bandwidths for each, the admittance slope of each resonating mode is set as required. A genetic algorithm is used in solving related equations to obtain the impedance of each line in a T-shape branch, followed by a final optimization. A three-pole tri-band filter having passbands of 0.6– 0.9, 1.35–1.65 and 2.1–2.4 GHz, is designed, fabricated and measured with low passband insertion losses of < 0.7 dB and high rejection of > 60 dB between the passband regions. As a generalization, necessary to achieve a tri-band filter with arbitrary passbands, a non-commensurate version of the T-shape branch is introduced. An example filter design Corresponding author: Y. Liu ([email protected]). † Also with State Key Laboratory of Millimeter Waves, Southeast University, Nanjing 210096, China. 426 Liu, Dou, and Zhao is given with the passbands asymmetrically located at 0.7–1, 1.65– 1.95, and 2.2–2.3 GHz. This technique is able to achieve good design flexibility with respect to bandwidth ratios. This is validated by studying the maximum impedance variations of a T-shape branch when the bandwidth ratios vary.