Comprehensive Analysis of Varactor-Series-Loading Scheme in λ/4 Resonator and Its Applications in BPF With Wide Tuning Range

This article presents a comprehensive tuning mechanism analysis of a varactor-series-loading scheme in a quarter-wavelength ( $\lambda $ /4) resonator. The theoretical analysis and mathematical derivation of this tuning mechanism are thoroughly investigated across various characteristic parameters of the resonator to explore the optimization of the fundamental frequency ( $f_{1}$ ), third harmonic ( $f_{3}$ ), and their tuning ranges (TRs) for the resonator. The position of current null point (CNP) of the $f_{3}$ on the resonator is, furthermore, examined in detail. The finding is significant in that loading a varactor at the CNP not only extends the TR of the $f_{1}$ without compromising it to achieve a fixed $f_{3}$ but also has no impact on the voltage null point (VNP) of $f_{3}$ . Based on this, a novel harmonic dual-null-points loading and exciting scheme is introduced. The varactor series loaded at the CNP effectively extends the TR of the $f_{1}$ while simultaneously fixing the $f_{3}$ throughout the entire TR. The feedline exciting at the unaffectable VNP consistently suppresses the $f_{3}$ and ensures a wide upper stopband. Subsequently, tunable bandpass filters (BPFs) with wide frequency TR, constant absolute bandwidth (ABW) or fractional bandwidth (FBW), and wide upper stopbands are designed, assembled, and measured. Good agreement between the simulation and the measurement results demonstrates the correctness and applicability of the analysis conducted in this study. The solid theoretical and practical foundation can serve as guidance for future tunable BPF designs.