Bandpass Filters with Increased to 3N+1 Number of Attenuation Poles

Abstract

N-order bandpass filter (BPF) with parallel resonators and cross and mixed couplings can have (N + 1) transmission zeros (TZ) located on the complex plane s = σ + jω. TZs at real frequencies (jω axis) are also called attenuation poles (AP). The authors propose an alternative possibility of AP forming in filters using resonators with special properties, which significantly increases the AP number from (N + 1) to (3N + 1). Increasing the AP number with fewer resonators allows us to increase the selectivity and rejection level and reduce BPF insertion losses. The special properties of resonators are that their input admittance Y has one or two poles (ω_p1, ω_p2) located next to the resonance frequency ω₀. This leads to the appearance of AP in a BPF. We propose and analyze three resonators with special properties. They are formed by a cascade connection of a quarter-wave resonator and lumped L and C. The input of the resonators is located on the side of the lumped elements. It was found that the Q-factors of lumped elements do not affect the filter losses in the passband. The reduction of Q_L and Q_C leads only to the decrease of the AP “depth.” For the first time, 7 APs were implemented in the experimental second-order microstrip BPF.