Design of Notched-Wideband Bandpass Filters With Reconfigurable Bandwidth Based on Terminated Cross-Shaped Resonators

In this paper, a series of novel reconfigurable-bandwidth notched-wideband bandpass filters (NWB BPFs) with controllable notch bands are proposed. The proposed filters start from a passive filtering structure, which is formed by a terminated cross-shaped resonator (TCSR) with a pair of parallel-coupled lines and two open-ended stubs. Theoretical analysis finds that the filter bandwidth can be independently controlled by the TCSR, while the center frequencies and bandwidth of notch bands are mainly controlled by the rest parts. According to this, a BPF with controllable notch bands can be designed. To achieve the reconfigurable-bandwidth NWB BPFs with controllable notch band, whose bandwidth and center frequency can be maintained unchanged under different work states, two PIN diodes and a varactor are employed. By controlling the work states of PIN diodes, three bandwidth states can be achieved with fixed center frequency. By controlling the applied voltage on the varactor, other NWB BPF with independently tunable lower passband edge can be realized. For verification, three prototypes are designed and measured. The measured results agree well with the theoretical analysis and simulated ones, verifying a simple and effective design approach of reconfigurable-bandwidth NWB BPFs.

The associate editor coordinating the review of this manuscript and approving it for publication was Abhishek K. Jha .
In the high data-rate and multi-standard remote-sensing and telecommunication systems, notched-wideband (NWB) BPFs with good filtering responses are urgently needed to eliminate the unexpected in-band interference. Recently, such filters have been designed by different techniques, which can be classified into four main categories: 1) the introduction of additional notch resonators [13] - [15]; 2) asymmetrical coupled fed lines [16], [17]; 3) embedded open stubs [18], [19]; 4) intrinsic zeros of multi-mode resonators (MMRs) [20], [21]. Although all the above filters can own excellent filtering responses and desired notch band simultaneously, they still cannot satisfy the demands of modern multi-standard transceivers, which need NWB BPFs owning different reconfigurabilities to reduce the design complexity and system size.
The reconfigurable NWB BPFs have been studied over ten years [22] - [29]. Previous works are mainly focused on the reconfigurable notch band(s) and fixed bandwidth [22] - [27]. For the NWB BPFs with reconfigurable bandwidth, little effort has been devoted, except for some ones in [28], [29], which suffer from many drawbacks including non-electrically reconfigurable, uncontrollable notch bandwidth, and varied center frequencies and bandwidth of notch bands under different work states. Due to the lack of study on the reconfigurable-bandwidth NWB BPFs, the development of telecommunication will be largely restricted. To tackle this, it is very significant to explore different topologies for the design of NWB BPFs with a new reconfigurable-bandwidth property in designing multistandard advanced transceivers for the practical applications of high-performance circuits and systems.
In this paper, a class of new reconfigurable-bandwidth NWB BPFs with controllable notch band are presented. The proposed design starts from a passive fundamental topology, which is composed of a terminated cross-shaped resonator (TCSR) with some added parts, including two open-ended stubs and a pair of parallel-coupled lines (PCLs). After theoretical analysis, it is found that the filter bandwidth is determined by the characteristic impedances of TCSR, and the notch bandwidth is mainly controlled by the ones of the added parts. Furthermore, the center frequencies of notch bands are totally controlled by the electrical length of openended stubs. As such, a NWB BPF with controllable notch bands can be designed. In addition, some reconfigurablebandwidth NWB BPFs with controllable notch band, whose bandwidth and center frequency are fixed under different work states, can be realized by inserting two PIN diodes and a varactor into TCSR. By controlling the work states of PIN diodes, the lower and upper passband edges can be shifted in same absolute ranges. By controlling the applied voltage on the varactor, the lower passband edge can be independently reconfigurable in continuous manners. Thus, two kinds of reconfigurable NWB BPFs with fixed center frequency and bandwidth of the controllable notch band can be designed, including one with fixed center frequency, and the other one with fixed upper passband edge. To validate this, three prototypes are fabricated and measured. To the best knowledge of authors, such reconfigurable-bandwidth BPFs with controllable notch band, whose center frequency and bandwidth are fixed under different work states, have never been reported before. This paper is organized as follows. Besides the introduction in Section I, the discussion of the fundamental topology with an emphasis on the transmission poles and zeros is presented with the design of a basic NWB BPF. In Section III, the design of reconfigurable-bandwidth NWB BPFs in discrete and continue manners are presented with the simulated and measured results. Finally, a conclusion is summarized in Section IV.

II. BASIC THEORY AND NWB BPF
In Fig. 1, the fundamental topology for the design of a NWB BPF with controllable notch bands is plotted. The fundamental topology is constructed by a TCSR with a pair of PCLs and two open-ended stubs. For the TCSR, its electrical length is θ = π/2 at the center frequency f 0 , while characteristic impedances are Z 2 , Z 3 , and Z 3 , respectively. Thus, the input impedance of the TCSR can be written as where holds. To incorporate the TCSR for a BPF with controllable notch bands, extra poles and zeros should be introduced. Hence, a pair of PCLs with two open-ended stubs are added. For the PCLs, its electrical length is θ = π/2 at the center frequency f 0 and characteristic impedances are Z oe , Z oo , respectively. For the open-ended stubs, its electrical length is θ 1 and θ 2 , and characteristic impedance is Z 1 .

A. TRANSMISSION POLES AND ZEROS
When θ 1 = θ 2 = θ, the fundamental topology is symmetrical. Under this condition, its transmission poles (TPs) can be determined by even-odd-mode analysis method. The odd-and even-mode equivalent circuits are shown in Fig. 2 (a) and (b), respectively. For the odd-mode input admittance Y ino in Fig. 2(a), it can be expressed as where When Y ino is zero, the odd-mode resonant frequencies can be determined. As such, a pair of odd-mode TPs can be VOLUME 8, 2020 For the even-mode input admittance Y ine in Fig. 2(b), it can be expressed as When Y ine is infinite, the even-mode resonant frequencies can be derived. After some algebraic operations, three evenmode TPs can be obtained and expressed as For the transmission zeros (TZs), they can be used to achieve notch bands, wide stopbands, and sharp selectivity. Its TZs are determined by rigorous odd-even-mode analysis method and S-parameter theory together. The transmission coefficient can be expressed [30] as where Y 0 is the normalized admittance. Under the condition that S 21 = 0, five TZs can be derived and written as According to the above theoretical analysis, it is obvious that the fundamental topology owns five TPs and five TZs when the electrical length is uniform. All the TPs/TZs are symmetrical to the center frequency f 0 , and the relationship of Considering that the effect of f ep2 on filter performance is eliminated by f z3 when the electrical length is uniform, the fundamental topology is suitable to design BPFs with a notch band at the center frequency, whose calculated frequency responses are shown in Fig. 3. For the TZs of f z1 and f z5 , they are used to ensure the wide stopband; for the TZs of f z2 and f z4 , they are used to sharp the skirt selectivity; for the TZ of f z3 , it is used to implement the notch band.
For the TPs of f ep1 , f op1 , f op2 , and f ep3 , they can be used to ensure the broad and flatness passband. Besides, the filter bandwidth is determined by the TPs of f ep1 , f ep3 and TZs of f z2 , f z4 together, while the notch bandwidth is controlled by the TPs of f op1 and f op2 . To better understand the design mechanism of the fundamental topo-logy, the relationships among the parameters of Z 1 , Z 2 , Z 3 , Z oe , Z oo and TPs/TZs of The TPs and TZs under investigation respect to different Z 1 , Z 2 , Z 3 , Z oe are shown in Fig. 4. Apparently, the locations of f op1 and f op2 are mainly controlled by Z 1 and Z oe , while the locations of f ep1 , f ep3 , f z2 , f z4 are independently determined by Z 2 and Z 3 . With the increase of Z 1 and decrease of Z oe , the TPs of f op1 and f op2 will move closer to each other. With the increase of Z 2 and decrease of Z 3 , the TPs of f ep1 and f ep3 will move apart, and the same phenomenon is happened to the TZs of f z2 and f z4 too. Reflected to the filter responses, the filter bandwidth can be independently determined by Z 2 and Z 3 , and the notch bandwidth is independently controlled by Z 1 37418 VOLUME 8, 2020 and Z oe . Hence, the filter with wide bandwidth should choose the parameters of Z 2 with large value and Z 3 with small value, while the one with narrow notch bandwidth should choose the parameters of Z 1 with large value and Z oe with small value. After slightly adjusting the values of Z 1 , Z 2 , Z 3 , Z oe and Z oo together, the filter with desired responses can be realized.
To vividly demonstrate that the notch bandwidth can be independently controlled, two BPFs with narrow and wide notch bandwidths are illustrated in Fig. 5. Obviously, the notch bandwidth will be changed from narrow to wide by only controlling the parameters of Z 1 , Z oo , and Z oe , while the filter bandwidth is maintained unaltered. As such, the notch bandwidth can be independently controlled by Z 1 , Z oo , and Z oe together.

B. CONTROLLABLE CENTER FREQUENCIES OF NOTCH BANDS
From Part A, we can know that the notch bandwidth can be independently controlled by the parameters of Z 1 , Z oo , and Z oe . To further prevent the wireless communication systems from in-band interfering conveniently and effectively, the center frequencies of notch bands also should be controllable. In this part, the center frequencies of notch bands will be discussed by varying the electrical length of two openended stubs.
To vividly demonstrate this, we assume that θ = θ 1 − θ = θ − θ 2 at first. Then, the improved topology of Filter I for theoretical analysis is plotted in Fig. 6. When the value of Z 1 is very large, the TPs and TZs under study respect to different θ are shown in Fig. 7. Seen from Fig. 7, the TZ of f z3 is divided into two ones of f z3_L and f z3_U when θ is not equal to zero. With the increase of θ, the distance between f z3_L and f z3_U will become larger, while the TPs of f op1 and f op2 move apart. For the rest TPs and TZs, they are fixed. Furthermore, the locations of f z3_L and f z3_U can be determined as Considering the filter responses, the proposed topology will own two notch bands when the electrical length θ 1 and VOLUME 8, 2020  θ 2 is not equal. With the increase of θ 1 , the notch band of f z3_L will move downwards independently, while the notch band of f z3_U and filter bandwidth are unaltered, as plotted in Fig. 8(a). With the decrease of θ 2 , the notch band of f z3_U will move upwards independently, while the notch band of f z3_U and filter bandwidth are kept fixed, as shown in Fig. 8(b). Thus, the center frequencies of the notch bands can be independently controlled with the help of the electrical length θ 1 and θ 2 . It is noteworthy that: when the electrical length of θ 1 and θ 2 is too large or small, the notch bands will not be existed in the passband.

C. DESIGN PROCEDURE
On the basis of the above theoretical analysis, a simple and effective design procedure for Filter I can be summarized as: 1) Input the specifications of Filter I, such as, center frequency, filter bandwidth, selectivity, notch bands (including center frequencies and bandwidth).

4)
Slightly adjust the parameters of Z 1 , Z 2 , Z 3 , Z oe , Z oo , θ 1 and θ 2 to obtain the desired performances. Based on this design procedure, the final parameters of a NWB BPF with 3-dB fractional bandwidth (3-dB FBW) of 82.7% and a narrow notch band at center frequency can be determined as: Z 1 = 1700 , Z 2 = 65 , Z 3 = 65 , Z oe = 162 , Z oo = 58 , and θ 1 = θ 2 = θ = 90 • . The corresponding calculated frequency responses are plotted in Fig. 3. As the employed substrate in this paper is Rogers RO4003C with thickness of 0.813 mm and dielectric constant of 3.38, the layout and final dimensions can be determined with the aid of commercial software. The layout is plotted in Fig. 9. As predicted, the notch bandwidth can be independently controlled by the parameters of w 1 , w F , s 1 , and s F , which are corresponding to the characteristic impedances of Z 1 , 37420 VOLUME 8, 2020  Z oo , and Z oe . When the parameters of w 1 and w F are fixed, the notch bandwidth can be varied from narrow to wide by only controlling the parameters of s 1 and s F , while the filter bandwidth is fixed, as shown in Fig. 10. Hence, the notch bandwidth can be independently controlled.
For the number and center frequencies of the notch bands, they are determined by the physical length of l L l_V , l H l_V , l L l_H and l R l_H together, which are corresponding to the electrical length of θ 1 and θ 2 . As predicted, only one notch band is existed in the passband when l L l_V = l R l_V and l L l_H = l R l_H . In addition, the center frequency of notch band will become smaller with the increase of l L l_V (l R l_V ) and l H l_V (l R l_H ), as shown in Fig. 11. Under the condition that l L l_V = l R l_V while l L l_H = l R 1_H ,there are two notch bands existed in the passband. Through increasing l R l_V while maintaining l L l_V , the lower notch band will move downwards while the other one is unaltered, as shown in Fig. 12(a). Meanwhile, there are also two notch bands existed in the passband when l L l_V = l R l_V while l L l_H = l R l_H . As l L l_H decreases while l R l_H keep unaltered, the upper notch bands will move upwards and the rest one is fixed, which is shown in Fig. 12 (b). According to the above analysis, it is apparent that the center frequencies of notch bands can be independently controlled.

D. SIMULATED AND MEASURED RESULTS
For the designed NWB BPF with a notch band at 3.0 GHz, its measured results are compared with the simulated ones in Fig. 13 (a). Apparently, the measured frequency responses agree well with the simulated ones. The measured passband range is from 1.74 to 4.19 GHz with center frequency VOLUME 8, 2020 of 2.97 GHz when the impedance matching is better than 10.0 dB, and the minimum insertion loss is 0.55 dB in the passband. Therefore, the corresponding FBW is 82.6%. Four TPs are observed at 1.86, 2.46, 3.38, and 3.98 GHz respectively, ensuring the wide passband and excellent flatness. Two TZs for wide stopbands are located at 0 and 6.38 GHz. Over 20-dB attenuation in the lower and upper stopbands is realized from DC to 1.51 GHz and 4.45 to 7.50 GHz, indicating a high isolation level. The attenuation slop in the lower and upper transition bands is 217 and 64 dB/GHz, with two TZs for sharp selectivity located at 1.44 and 4.64 GHz. A notch band with isolation loss more than 25 dB is found at 3.01 GHz. The in-band variation of the measured group delay is smaller than 0.27 ns, showing a good passband linearity. In Fig. 13 (b), the photograph is illustrated.

III. RECONFIGURABLE-BANDWIDTH NWB BPFs
To effectively protect the telecommunication systems from in-band interfering, the bandwidth and center frequencies of the controllable notch bands should be kept fixed when the reconfigurable-bandwidth WB BPFs work in different states. From Section II, it is apparent that the filter bandwidth can be independently controlled by the parameters of TCSR, while the center frequencies and bandwidths of the notch bands are independently controlled by the parameters of the rest parts. Thus, the desired reconfigurable-bandwidth NWB BPFs with controllable notch bands, whose center frequencies and bandwidths can be maintained fixed under different work states, can be designed by inserting some tuning elements into the TCSR. To simplify the analysis, only the condition that θ 1 = θ 2 = θ is considered in this paper. One thing should be noted: when θ 1 = θ 2 , the proposed reconfigurable BPFs will own two controllable notch bands, whose center frequencies and bandwidth also can be maintained unaltered under different work states.
A. FILTER II From Fig. 4(c), it is obvious that Z 3 controls the filter bandwidth, and no effect on the center frequency and notch band. Considering that all the TPs and TZs are symmetrical to f 0 , a reconfigurable-bandwidth BPF with fixed notch band and center frequency in each work state can be designed by altering the value of Z 3 . To realize this goal, two PIN diodes are inserted, as shown in Fig. 14. By controlling the work states of PIN diodes, the value of Z 3 will be changed. For arbitrary Z 3 and Z 3 , the value of Z 3 can be concluded in Table 1, and the relationship is held as As such, the filter bandwidth will be increased when the work states of PIN diodes are altered from Case A to C.
To validate this, a reconfigurable NWB BPF with three bandwidth states is designed on a substrate called Rogers RO4003C with dielectric constant of 3.38 and thickness of 0.813 mm. The circuit parameters should be determined on the basis of the following design procedure at first: 1) Find out the specifications of Filter II with the widest bandwidth, including center frequency, filter bandwidth, selectivity, and notch bandwidth. 2) According to the design procedure of Filter I, determine the parameters of Z 1 , Z 2 , Z 3 , Z oe , Z oo .   3) Based on the specifications of Filter II with the rest two filter bandwidths, determine the parameter of Z 3 . 4) Slightly adjust the parameters of Z 1 , Z 2 , Z 3 , Z 3 , Z oe and Z oo to obtain the desired performances.
Based on the design procedure mentioned above, the circuit parameters can be generalized as: Z 1 = 1700 , Z 2 = 65 , Z 3 = 143.1 , Z 3 = 220 , Z oe = 162 , Z oo = 58 , and θ 1 = θ 2 = θ = 90 • . As such, the value of Z 3 is 220, 87.6, and 54 for Case A to C, respectively. The filter layout is shown in Fig. 15. Two PIN diodes called MADP-000907-14020 are used as the tuning elements, whose dimensions are 0.2 mm×0.2 mm×0.5 mm. They can be modelled by a lumped-element capacitor of 0.025 pF for isolation and 5.2 for connection. In addition, two DC sources are used to control the work states of the inserted PIN diodes, three lumped resistors with large value are used as the protective element and radio frequency (RF) choke. For the simulated and measured results of Case A (minimum bandwidth), Case B (medium bandwidth), and Case C (maximum bandwidth), they are illustrated in Fig. 16 and summarized in Table 2. Apparently, the measured results agree well with the simulated ones. With the help of the  suitable DC bias and tuning elements, the absolute bandwidth (ABW) can be reconfigurable from 1.22 to 2.46 GHz, while the center frequency and notch band are maintained about 2.94 and 3.01 GHz, respectively. Hence, the FBW is varied from 41.6% to 83.4% with 41.8% tuning range. In the passband, the measured average insertion loss is about 1.9 dB, and the measured return loss is better than 10.0 dB. The in-band variation of measured group delay is smaller than 0.87 ns. Besides, 20-dB insertion loss is observed in notch band. In Fig. 17, the photograph of Filter II is shown. VOLUME 8, 2020

B. FILTER III
The equivalent circuit of Filter III is plotted in Fig. 18. The independently tunable lower passband edge is achieved by inserting a varactor into lower stub of TCSR. By varying the supplied voltage of DC source, the capacitance C V will be altered. For a NWB BPF based on the proposed topology, C V has much greater effect on the lower passband edge than the upper one while no effect on the notch band. Hence, the desired reconfigurable-bandwidth NWB BPFs with fixed upper passband edge and notch band in each work state can be achieved by using the proposed topology.
To verify this, a NWB BPF based on the proposed topology is implemented on a substrate called Rogers RO4003C. At first, the circuit parameters should be determined based on the following design procedure: 1) Input the specifications of Filter III with the widest bandwidth, including center frequency, selectivity, filter bandwidth, and notch bandwidth.  2) Based on the design procedure of Filter I, determine the parameters of Z 1 , Z 2 , Z 3 , Z 3 , Z oe , Z oo . 3) According to the requirements of Filter III with narrowest bandwidth, determine the value of C V . 4) Slightly adjust the parameters of Z 1 , Z 2 , Z 3 , Z 3 , Z oe , Z oo , and C V to obtain the desired performances.
According to the design procedure mentioned above, the final circuit of Filter III can be summarized as: Z 1 = 1700 , Z 2 = 65 , Z 3 = 84 , Z oe = 162 , Z oo = 58 , θ = 90 • , C V = 18.22 pF (wide bandwidth), and C V = 2.38 pF (narrow bandwidth). With the help of commercial software, the lay-out can be determined, as plotted in Fig. 19.  In this design, a varactor called SMV1235 is used as the tuning elements, whose typical capacitance is varied from 2.38 to 18.22 pF, while series resistance and inductance are 0.60 and 0.45 nH respectively. Besides, the varactor dimension is 0.5 mm×0.6 mm×1.0 mm. Two lumped resistors with large value are used as the protective elements and RF choke. For the final dimensions, they can be generalized as follows (unit: mm): l F = 16.2, w F = 0.3, s F = 0.1, l 1 = 16.3, w 1 = 0.3, s 1 = 0.3, l 2 = 16.6, w 2 = 1.4, l 3 = 16.9, w 3 = 0.1, l 3_V = 3.1, l 3_H = 13.9, w 3 = 0.1. The overall circuit size is 43.0 mm× 33.0 mm (0.62 λ g × 0.48 λ g , where the λ g is the guided wavelength in the used substrate at center frequency).
In Fig. 20, the relationships among C V , TZs for notch band and sharp selectivity, and upper/lower passband edges are plotted. It is apparent that the lower passband edge will move upwards with the decrease of C V , while the upper one and notch band with TZ for sharp selectivity near the upper passband edge are kept unaltered. Besides, the TZ for sharp selectivity near lower passband edge also moves upwards with the decrease of C V . This phenomenon can ensure the good selectivity for each work states near the lower pass-band edge. Therefore, the desired reconfigurablebandwidth NWB BPFs can be designed by using this design topology.
In Fig. 21, the measured S-parameters are compared with the simulated ones. When the supplied voltage is 0 V, the proposed filter owns a maximum bandwidth of 2.08 GHz from 1.86 to 3.94 GHz. When supplied voltage is 20 V, the proposed filter owns a minimum bandwidth of 1.62 GHz from 2.33 to 3.95 GHz. If the center frequency is assumed as 2.95 GHz, the FBW can be varied from 54.9% to 70.5%. Therefore, the FBW tuning range is 15.6%. Besides, the measured insertion loss is better than 1.6 dB, and the return loss is better than 10 dB. The in-band variation of measured group delay is smaller than 0.91 ns. Furthermore, a notch band with 20-dB insertion loss is found at about 3.02 GHz. Besides, the TZ for sharp selectivity near the lower pass-band edge is elevated from 1.44 to 1.91 GHz when the DC voltage changes from 0 to 20 V. In Fig. 22, the photograph of Filter III is shown.
To highlight the advantages of the proposed NWB BPFs, the comparisons with some previous works are listed in Table 3. As the third reported works about reconfigurablebandwidth NWB BPFs, the center frequency and bandwidth of the notch band not only can be independently controlled, but also kept unaltered under different work states. Besides, they also own wider tuning ranges. Hence, they not only can be used to reduce the design complexity and system size, but also prevent the high data-rata telecommunication transceivers from in-band interference more effectively and conveniently. Furthermore, NWB BPFs with independently reconfigurable notch bands and bandwidth can be designed by inserting some varactors into the open-ended stubs of the topologies for the design of Filter II and III.

IV. CONCLUSION
A series of novel topologies for the design of reconfigurablebandwidth NWB BPFs with controllable notch bands, whose center frequencies and bandwidths are fixed under different VOLUME 8, 2020 work states, are proposed in this paper. Theoretical analysis finds that the center frequencies and bandwidth of the notch bands not only can be independently controlled, but also kept unaltered under different bandwidth states. Three prototypes are designed and fabricated. All the filters have successfully demonstrated wide bandwidth and tuning ranges, excellent passband flatness, high isolation level, and sharp selectivity. It is anticipated that this simple methodology can be broadly used in multi-standard microwave communication systems TAO YUAN (Member, IEEE) received the bachelor's and master's degrees from Xidian University, China, and the Ph.D. degree from the National University of Singapore, Singapore. He is currently a Professor with the College of Information Engineering, Shenzhen University, Shenzhen, China. His current research interests include developing novel RF modules and antennas for mobile terminal and 5G applications. VOLUME 8, 2020