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 S21 (FBWS21 ) and stopband rejection of S21 (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 2N TLs in the center of the proposed filter, extra 2N 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.