Overall Study of Frequency-Agile Mechanism of Varactor-Loaded <italic>λ</italic>/4 Resonator for Designing Tunable Filter With Stable Wide Stopband

Abstract

This paper presents an overall investigation of the frequency-tuning mechanism of the varactor-loaded λ /4 stepped impedance resonator (SIR). The relationships between the tuning ranges of the resonant frequencies (fundamental frequency $(f_{1})$ and harmonics) and the basic parameters of the varactor-loaded SIR are theoretically analyzed and given in detail. It can be found that the loading location of the varactor and the SIR parameters (characteristic impedances and length ratio of the two sections) have significant effect on the frequency-tuning range. Benefiting from the discriminating responses of $f_{1}$ and $f_{3}$ (third harmonic) to the loading location of the varactor, $f_{1}$ can be well tuned as the varactor's capacitance changes while $f_{3}$ is fixed, when the varactor is loaded at the voltage-null point of $f_{3}$ on the λ /4 SIR. Thus, a stable wide stopband can be achieved due to the fixed $f_{3}$ , which acts as the lowest spurious in the design of tunable filter. For demonstration, a second-order tunable filter with stable wide stopband and constant fractional bandwidth is implemented and measured. In the tuning process of the passband operating at $f_{1}$ , the lowest spurious resulting from $f_{3}$ is immobile, which is always more than ${\text{4}}f_{1}$ . The simulated and measured results with good agreement are presented to verify the theoretical predictions.