A wideband bandstop filter with two independently controllable equal‐ripple levels

In this letter, a novel wideband bandstop filter with controllable equalripple response is newly presented. The proposed topology consists of two cascaded transmission lines and three open-circuited stubs, where, one two-section OS is shunted between two transmission lines, two three-section OSs are shunted at two output ports, respectively. By using the proposed design approach, both passband and stopband provide controllable equal-ripple responses independently, where there are five transmission zeros and six reflection zeros in a single period of frequency domain. For demonstration, an experimental BSF centered at 2 GHz with 20-dB FBW 129.5% and 30-dB stopband rejection is designed and fabricated. The simulations and measurements agree with the design theory very well.

✉ Email: smalld729@hotmail.com In this letter, a novel wideband bandstop filter with controllable equalripple response is newly presented. The proposed topology consists of two cascaded transmission lines and three open-circuited stubs, where, one two-section OS is shunted between two transmission lines, two three-section OSs are shunted at two output ports, respectively. By using the proposed design approach, both passband and stopband provide controllable equal-ripple responses independently, where there are five transmission zeros and six reflection zeros in a single period of frequency domain. For demonstration, an experimental BSF centered at 2 GHz with 20-dB FBW 129.5% and 30-dB stopband rejection is designed and fabricated. The simulations and measurements agree with the design theory very well.
Introduction: Bandstop filters (BSFs) are one of the essential components in RF/microwave to filter out unwanted signals, which can be used in various applications [1,2]. The coupled line (CL) structure BSF can not only reduce circuit size of BSFs, but also create extra transmission zeros (TZs) [3,4]. Because of the limited coupling strengths of CLs, such structures are not suitable to realize equal-ripple for both S 11 and S 21 with different bandwidths ranges. By using two transmission line (TL) paths with different electrical lengths, transversal signalinterference technique is the other approach to create extra TZs [5,6] with wideband bandstop response, but the circuit size is large. Furthermore, extra TZs can be also provided by inserting extra capacitors or TLs at the end of λ/4 open-circuited stubs (OSs) [7,8]. However, there is no approach to adjust equal-ripple levels and bandwidth independently [9][10][11]. To sum up, to the best of the authors' knowledge, the following two key problems have not been solved in wideband BSF design: (1) Except elliptic function [11], there is no general approach to realize equalripple for both passband and stopband at the same time. (2) The return loss (RL) of S 11 and stopband rejection (SR) of S 21 cannot be controlled independently in the desired bandwidth. By using the proposed design approach, a wideband BSF is newly presented in this letter. The following performances can be realized: (1) Five TZs and six reflection zeros (RZs) can be realized. (2) S 11 in the passband and S 21 in the stopband are both controllable equal-ripples. (3) The bandwidth of passband, RL and SR can be designed independently.
Analysis and design: The proposed wideband BSF is shown in Figure 1. The topology consists of two cascaded λ/4 TLs and three OSs, where, one two-section λ/4 OS is shunted between two λ/4 TLs and two threesection λ/4 OSs are shunted at two output ports, respectively. Z 1 ; Z s11 , Fig. 1 The proposed wideband BSF From Figure 1, the ABCD matrices of the single TL, three-section OS and two-section OS can be listed as [ respectively. Then, the total ABCD matrix of proposed wideband BSF can be expressed as and S 11 and S 21 can be derived as following equations: Finally, the filtering function F circuit can be summarized as where h up 2i , h down 2i are polynomial functions which are also determined by all the normalized characteristic impedances of the proposed wideband BSF.
When RL = 20 dB and SR = 30 dB are determined, both θ c S11 and θ c S21 can be designed in a large range.  Figure 2.
In order to improve AR, which can be defined as  Experiments: In the experiment, Example II is selected for fabrication on ROGERS RT/duroid ® 5880 substrate. The layout circuit is shown in Figure 5. The circuit simulation, EM simulation (Sonnet) and measurements are shown in Figure 6. The simulated and measured results are matched very well. Measured SR is 28.6 dB, RL is 18.3 dB, FBW is 129.5%, insert loss is less than 0.43 dB of the lower passband and less than 1.1 dB of the upper passband, and the AR is 226.7 dB/GHz. Comparing with several previous works [9]- [11] in Table 1, the performance of proposed topology is better. It is worth mentioning that the proposed circuit is 50% compact than that in [11] with the same number of TZs and RZs.
Conclusion: A wideband BSF with 5 TZs and 6 RZs is newly presented in this letter. Equal-ripple levels and bandwidths for both passband and stopband can be controlled independently, and AR can be improved dramatically. Comparing with the former BSF topologies, the proposed work provides better AR, more TZs and RZs, wider bandwidth, and controllable equal-ripples for both passband and stopband. The simulated and measured results show good agreements.