# A Reconfigurable Single-/Dual-Bandstop Filter with Controllable Equal-Ripple Performance
## 4 Discussion  
In this paper, a novel synthesis approach for compact reconfigurable BSF is proposed. The switch between two filtering states (S-BSF and D-BSF) is realized by switching the ON/OFF state of PIN diodes. The proposed reconfigurable BSF is composed of five types of characteristic impedances, providing five design parameters. Based on the proposed synthesis approach, independent control over the RL and SR of the S-BSF, and the RLs for the two different passbands of the D-BSF is realized, which consumes four restricted conditions. In addition, another restricted condition needs to be met to eliminate the unexpected resonance. Consequently, unique solutions for the characteristic impedances that simultaneously satisfy the specific RL and SR of S-BSF and the specific RLs of D-BSF can be obtained. To validate the proposed synthesis approach, a prototype reconfigurable BSF with a miniaturized size was fabricated and measured. The measured results met well with the simulation results, which verified the correction of the proposed theory. In our future works, we will focus on designing a modified topology to further implement the arbitrary control of the BW and more efficiently employ the limited spectrum resources. Conceptualization, Y.G., X.W., S.X., W.S., and C.-P.C. ; methodology, Y.G. and X.W. ; software, Y.G. ; validation, Y.G. and X.W. ; formal analysis, Y.G. and X.W. ; investigation, Y.G. and X.W. ; resources, X.W. ; data curation, Y.G. ; writing--original draft preparation, Y.G., X.W., C.-P., and S.X. ; writing--review and editing, Y.G., S.X., X.W., and C.-P.C. ; visualization, Y.G., X.W., W.S., and T.X. ; supervision, X.W. ; project administration, X.W. ; funding acquisition, X.W. All authors have read and agreed to the published version of the manuscript. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Key Performance** & **Circuit Simulation** & **EM Simulation** & **Measured** \\ \hline \(RL_{S}\) (dB) & 25.000 & 27.18 & 23.100 \\ \hline \(SR_{S}\) (dB) & 20.000 & 17.53 & 17.500 \\ \hline \(RL_{D1}\) (dB) & 10.000 & 10.37 & 10.000 \\ \hline \(RL_{D2}\) (dB) & 15.000 & 13.06 & 16.400 \\ \hline \(SR_{D}\) (dB) & 34.300 & 33.31 & 33.200 \\ \hline \(BW\)\(\otimes RL_{S}\) (GHz) & 0.258 & 0.237 & 0.275 \\ \hline \(BW\)\(\otimes SR_{S}\) (GHz) & 1.478 & 1.572 & 1.594 \\ \hline \(BW\)\(\otimes RL_{D1}\) (GHz) & 0.489 & 0.480 & 0.480 \\ \hline \(BW\)\(\otimes RL_{D2}\) (GHz) & 0.346 & 0.370 & 0.317 \\ \hline \(BW\)\(\otimes SR_{D}\) (GHz) & 0.237 & 0.254 & 0.265 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: The key performance of the circuit simulation, EM simulation, and measured results of S-parameters for the miniaturized reconfigurable BSF. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Ref.** &
\begin{tabular}{c} **Reconfigurable** \\ **Performance** \\ \end{tabular} & **Response** & **Number of Diodes** & **Synthesis Design of Equal-Ripples** \\ \hline
[20] & No & BSF & - & No synthesis design approach of PB * \\ \hline
[21] & No & BSF & - & No synthesis design approach \\ \hline
[14] & Yes & BPF/DBPF */BSF & 6 & No synthesis design approach \\ \hline
[22] & Yes & NBPF */WBPF */BSF & 6 & No synthesis design approach \\ \hline
[23] & Yes & DBPF/DBSF * & 7 & No synthesis design approach \\ \hline This work & Yes & SBSF */DBSF & 2 &
\begin{tabular}{c} Synthesis equal-ripple design of PB \\ and SB * \\ \end{tabular} \\ \hline \hline \end{tabular}  
* NBSF: Narrow BSF; WBSF: Wide BSF; DBPF: Dual BPF; DBSF: Dual BSF; SBSF: Single BSF; PB: Passband; SB: Stopband.  
\end{table} 
Table 8: Comparison between the proposed reconfigurable BSF and recent studies. **Funding:** This work was supported by the National Natural Science Foundation of China (Grant No. 62271229), the Project of Jilin Province Development and Reform Commission (Grant No. 2022C047-6), the Project of Science and Technology Development Program of Changchun City (Grant No. 21 ZY23), and Grand-in-Aid for Scientific Research from the Ministry of Education, Culture, Sports, Science and Technology (Grant No. 23K03963), Japan.