Design of Wideband Bandpass Filters Based on Three Types of Coupled Stub-Loaded Resonators

In this article, a novel wideband quasi-elliptic bandpass filter (BPF) is presented. The proposed structure comprised of two critical parts: the upper part circuit consisting of two cascaded quarter-wavelength coupled line (CL) structures and two shunted quarter-wavelength short-circuited stubs; the lower part circuit consisting of three types of coupled stub-loaded resonators, that is, coupled stub-loaded half-wavelength resonator (CSHR), coupled stub-loaded T-shaped resonator (CSTR), and coupled stub-loaded <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Pi $</tex-math> </inline-formula>-shaped resonator (CS<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Pi$</tex-math> </inline-formula>R). A general closed-form synthesis theory is then proposed to realize the quasi-elliptic bandpass filtering response, and the general quasi-elliptic function is given as <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$F$</tex-math> </inline-formula> <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${}_{\text {formula}} =$</tex-math> </inline-formula> cos(<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2\phi + \xi + 2\gamma _{1}$</tex-math> </inline-formula>) for CSHR and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${F} _{\text {formula}} =$</tex-math> </inline-formula> cos(<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2\phi + \xi + 2\gamma _{1} + 2\gamma _{2}$</tex-math> </inline-formula>) for CSTR and CS<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Pi $</tex-math> </inline-formula>R. Distributed parameters are directly used to design wideband bandpass performance without any approximation and optimization procedure. Furthermore, the proposed synthesis theory could not only get equal-ripple performance in the passband but also newly realize equal-ripple response in the stopband. Finally, three prototype circuits were fabricated and measured, respectively. The simulation results are in good agreement with the measured results.