# A Reconfigurable Single-/Dual-Bandstop Filter with Controllable Equal-Ripple Performance
## 1 Introduction  
Microwave passive filters have been widely used in wireless communication systems to eliminate noise and interference signals. With the swift development of radio frequency (RF) microwave technology, RF components are expected to achieve multiple functionalities while exhibiting a limited circuit size. Consequently, reconfigurable filters [1; 2; 3] have become a research hotspot, which can be, respectively, designed by positive intrinsic negative (PIN) diodes [2; 4; 5], micro-electro-mechanical system (MEMS) switches [6; 7; 8], and iron electrical devices [9; 10; 11], etc. Recently, PIN-based reconfigurable filters have been favored by researchers because of their strong reconfigurability, low cost, and easy integration. For instance, a novel reconfigurable bandpass-bandstop filter is presented based on varactor-loaded closed-ring resonators [12]. Moreover, a switchable microstrip bandpass filter (BPF) is designed based on two switchable delay lines [13]. This switchable BPF can switch between the Chebyshev response and the quasi-elliptic-function response. However, the circuit analyses of the abovementioned reconfigurable filters have not been conducted, and their performance indexes cannot be controlled specifically. In [2], a compact reconfigurable with a wide tuning range is presented, which can be switched between bandstop filter (BSF) and BPF and achieves a wide tuning range of frequency. Based on the parallel-coupled lines, a multifunctional switchable filter is proposedin [14]. This multifunctional switchable filter can switch between three different filtering states: BPF, dual-BPF (D-BPF), and BSF. In [15], an electronically reconfigurable stub topology-based BSF is presented, and the response of the BSF filter can be switched from single to dual-band. A bandpass filter with four switchable configurations is proposed based on two parallel-connected dual-band bandpass filters [16]. Recently, a novel multifunctional frequency-selective surface-based switchable absorber/reflector was demonstrated [17]. In the absence of ground and air spacers, it works as a spatial BPF and BSF, respectively. In these studies, the reconfigurable filters have been simply analyzed. However, there is still a lack of analysis to achieve arbitrary control of the performance index, which is essential to the application of the filter. To fulfill the arbitrary control of the circuit performance, ref. [18] presents a switchable BPF for broadband, dual-band, and tri-band operations, and the relationship between bandwidths (BWs) and return losses (RLs) is analyzed by the proposed algorithm. Moreover, in our previous work, a reconfigurable BSF based on ring structure is proposed and exhibits two filtering states: single-BSF (S-BSF) and dual-BSF (D-BSF) [19]. The control of RL and stopband rejection (SR) is realized initially. However, the controlling mechanism is not detailed and verified. However, the detailed analysis of the proposed reconfigurable BSF is not given and the design theory for equal-ripple is not clear. Based on [19], a synthesis approach to the reconfigurable BSF is newly introduced in this paper. By switching the ON/OFF state of the PIN diodes, the proposed reconfigurable BSF can be switched between S-BSF and D-BSF. Regarding the number of design parameters, the proposed reconfigurable BSF consists of five types of transmission lines with different characteristic impedances, providing five design parameters. Based on the proposed synthesis approach, the RL and SR of the S-BSF and the RLs for the two different passbands of the D-BSF can be independently controlled, which consumes four design conditions. Moreover, to eliminate the unexpected resonance appearing in the S-parameter response, another design condition needs to be satisfied. Therefore, based on the above-restricted conditions, unique solutions for the characteristic impedances satisfying specific RLs and SRs can be obtained. For verification, a prototype reconfigurable BSF is simulated, fabricated, and measured.