A Synthesis Theory of Wideband Quasi-Elliptic Bandstop Filter With Back-to-Back Open-Ended Spanner Structure

In this article, a quasi-elliptic wideband bandstop filter (BSF) is presented with the proposed synthesis theory. In order to analyze the novel mechanism of creating extra two reflection zeros (RZs) in back-to-back open-ended spanner structure, both without coupling structure (BSF I) and with coupling structure (BSF II) are analyzed and discussed in detail where BSF I consists of two open stubs, two cascaded transmission lines (TLs), and a stepped-impedance open stub, which is shunted in the center of the filter; by dividing the stepped-impedance open stub into two coupled line (CL) sections, BSF I becomes BSF II, which includes a back-to-back open-ended spanner structure. The proposed synthesis theory proves that BSFs I and II belong to the same theoretical quasi-elliptic response transfer function. Considering the urgent needs of design specifications for BSF, the proposed synthesis theory could directly design and control the stopband with equal-ripple performance, such as the fractional bandwidth of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$S_{21}$ </tex-math></inline-formula> (FBW<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$^{S_{21}}$ </tex-math></inline-formula>) and stopband rejection of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$S_{21}$ </tex-math></inline-formula> (SR). After design theory, flowchart and design charts are summarized and discussed, and six design examples are also selected for theoretical verification. Furthermore, by inserting <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2N$ </tex-math></inline-formula> TLs in the center of the proposed filter, extra <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2N$ </tex-math></inline-formula> RZs can be generated accordingly. Because of limited pages, only two selected examples are listed for demonstration. Finally, two fabricated circuits for BSFs I and II are fabricated at 1 GHz for experimental demonstration. Excellent agreement between the simulated and measured results is achieved so as to successfully prove the proposed synthesis theory.