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 <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> ) 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 <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> and f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> (third harmonic) to the loading location of the varactor, f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> can be well tuned as the varactor's capacitance changes while f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> is fixed, when the varactor is loaded at the voltage-null point of f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> on the λ/4 SIR. Thus, a stable wide stopband can be achieved due to the fixed f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> , 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 <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> , the lowest spurious resulting from f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> is immobile, which is always more than 4f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> . The simulated and measured results with good agreement are presented to verify the theoretical predictions.