Reconﬁgurable Single- / Dual-Wideband Bandpass Filters Based on a Novel Topology

: Based on a new topology, a series of single- / dual-wideband bandpass ﬁlters (SWB / DWB BPFs) with reconﬁgurable masses of properties are presented. The proposed design starts from a dual-wideband passive ﬁltering structure, which owns ﬁve transmission zeros in the stopbands and three transmission poles in each passband. Then, three capacitors are employed as the tuning elements. By controlling these three capacitors, DWB BPFs with di ﬀ erent reconﬁgurable properties, including three independently tunable passband edges, tunable center frequency of lower passband with ﬁxed absolute bandwidth, tunable bandwidth of lower passband with ﬁxed center frequency, and switchable lower passband, can be realized. In addition, SWB BPF with tunable bandwidth also can be achieved by varying the inserted capacitors. For veriﬁcation, a prototype with di ﬀ erent capacitors is designed and fabricated. As the measured and simulated results agree well with each other, a simple design approach of reconﬁgurable SWB / DWB BPFs can be veriﬁed.


Introduction
In the high-data telecommunication systems, single-/dual-wideband bandpass filters (SWB/DWB BPFs) with compact size and good responses play an important role, and various approaches have been proposed for such filters [1][2][3][4][5]. For example, SWB BPF without reflection can be designed by using multilayered substrate [2]. Meanwhile, DWB BPF with a controllable stopband has been designed based on terminated multi-mode resonator [4]. Although all the desired responses can be achieved in the above filters, they still could not satisfy the requirements of modern multi-service wireless systems, which need filters with different reconfigurable properties to reduce the design complexity, cost, and size.
Early developments in reconfigurable BPFs mainly focused on center-frequency tuning [6][7][8][9][10]. For example, the center frequency of a four-pole SWB BPF can be varied from 1.05 GHz to 1.40 GHz while its corresponding absolute bandwidth is fixed about 134.5 MHz [8]. However, little effort has been devoted to DWB ones with fixed absolute bandwidths. Later, research on the switchable passbands

Operation Principle and Design
As shown in Figure 1, the novel topology is composed of a passive filtering structure with three capacitors. The passive filtering structure starts from a terminated T-shaped resonator with open terminations, whose characteristic impedances and electrical length are Z 3 , Z 2 , Z 3 , and θ = π/2 at the operating frequency f 0 , respectively. Thus, its input impedance can be written as Based on (1), it is apparent that the T-shaped resonator owns a pole f T p1 and two zeros of f T z1 , f T z2 . For arbitrary Z 2 and Z 3 , the relationship of f T z1 < f T p1 = f 0 < f T z2 exists. To incorporate it for a dual-band BPF with good filtering responses, extra poles and zeros should be introduced, while the intrinsic pole of f T p1 must be eliminated. Therefore, a pair of PCLs and three shunt open-ended stubs are added. The parameters of Z oe , Z oo , and θ present the characteristic impedances and electrical length of PCLs, while Z 1 , Z 4 , Z 1 , and θ L , θ, θ R denote those of the added stubs, where θ L = θ 1 + θ 2 , and θ R = θ 1 + θ 3 .
1 T p f must be eliminated. Therefore, a pair of PCLs and three shunt open-ended stubs are added. The parameters of Zoe, Zoo, and θ present the characteristic impedances and electrical length of PCLs, while Z1, Z4, Z1, and θL, θ, θR denote those of the added stubs, where θL = θ1 + θ2, and θR = θ1 + θ3.

Transmission Poles and Zeros
To simplify the theoretical analysis, we assume θL = θR = θ at first. Under this condition, the passive filtering structure is symmetrical. Hence, its TPs can be determined by using even-odd-mode analysis method. Figure 2 depicts the odd-and even-mode equivalent circuits. After analyzing the odd-mode equivalent circuit in Figure 2a, its input admittance can be written as Under the condition that Yino is zero, two odd-mode resonant frequencies can be determined as Under the condition that Y ino is zero, two odd-mode resonant frequencies can be determined as Electronics 2020, 9, 2149 4 of 14 For the even-mode equivalent circuit in Figure 2b, its input admittance can be expressed as where When Y ine is zero, two pairs of even-mode resonant frequencies can be obtained as where To achieve sharp skirt selectivity and ensure high isolation levels, TZs are essential. For this topology, its TZs can be determined by using even-odd-mode analysis method and S-parameters theory together. The transmission coefficient S 21 can be written as After some algebraic operations, three TZs can be obtained and written as It is apparent that the passive filtering structure owns six TPs and three TZs when θ L = θ R = θ, and all the TPs and TZs are symmetrical to f 0 . In addition, the relationships of f z1 < f ep1 < f op1 < f ep2 < f z2 = f 0 < f ep3 < f op2 < f ep4 < f z3 always hold for arbitrary Z 1 , Z oe , Z oo , Z 2 , Z 3 , and Z 4 . Hence, the proposed topology is suitable to design triple-mode DWB BPFs. Furthermore, the filter bandwidths are mainly controlled by the locations of f ep1,2,3,4 , while the skirt selectivity near the first and fourth passband edges are mainly determined by those of f z1 and f z2 . To better understand this, TPs/TZs with respect to different characteristic impedances of Z 1 , Z 2 , Z 3 , Z 4 , Z oo , and Z oe , are shown in Figure 3.
Obviously, the locations of f ep1 and f ep4 are sensitive to Z 2 and Z 3 , while the locations of f ep2 and f ep3 are mainly determined by Z oo and Z oe . Reflected to filter responses, the first and fourth passband edges will move closer to each other as Z 2 decreases or Z 3 increases, and the second and third ones will move apart as Z oo decreases or Z oe increases. Hence, a filter with a wide bandwidth should own large Z 2 and small Z 3 , while a filter with a large center frequency ratio need choose small Z oo and large Z oe . For the rest of the parameters, they are used to ensure good matching in each passband and sharp skirt near the first and fourth passband edges.
Electronics 2020, 9, x FOR PEER REVIEW  5 of 14 filter with a large center frequency ratio need choose small Zoo and large Zoe. For the rest of the parameters, they are used to ensure good matching in each passband and sharp skirt near the first and fourth passband edges. Due to the lack of TZs near the second and third passband edges, the corresponding selectivity is poor under the condition that θL = θR = θ. To deal with this, the electrical length of θL and θR should be studied. To better demonstrate these, a revised topology for the theoretical analysis is shown in Figure 4. First of all, Δθ = 1.11(θ − θL) = θR − θ. When Δθ is zero, there is only one TZ between Due to the lack of TZs near the second and third passband edges, the corresponding selectivity is poor under the condition that θ L = θ R = θ. To deal with this, the electrical length of θ L and θ R should be studied. To better demonstrate these, a revised topology for the theoretical analysis is shown in Figure 4. First of all, ∆θ = 1.11(θ − θ L ) = θ R − θ. When ∆θ is zero, there is only one TZ between passbands, as analyzed above. As ∆θ increases, another two TZs of f I1 and f I2 are introduced and move apart gradually. Meanwhile, TPs of f ep2,3 and f op1,2 move apart slightly. For the rest of the TPs/TZs, they are maintained unaltered, as shown in Figure 5. Hence, the skirt selectivity of the passive filtering structure near the second and third passband edges can be improved by generating TZs of f I1 and f I2 through suitably choosing θ L and θ R . Furthermore, the relationships among f I1 , f I2 , θ L , and θ R can be approximately obtained as Electronics 2020, 9, x FOR PEER REVIEW 6 of 14 apart gradually. Meanwhile, TPs of fep2,3 and fop1,2 move apart slightly. For the rest of the TPs/TZs, they are maintained unaltered, as shown in Figure 5. Hence, the skirt selectivity of the passive filtering structure near the second and third passband edges can be improved by generating TZs of fI1 and fI2 through suitably choosing θL and θR. Furthermore, the relationships among fI1, fI2, θL, and θR can be approximately obtained as One thing should be noted: whatever the electrical lengths of θL and θR are, the relationships of fz1 < fep1 < fop1 < fep2 < fI1 < fz2 = f0 < fI2 < fep3 < fop2 < fep4 < fz3 always exist. Hence, the second and third passband edges can be independently controlled by varying θL and θR, as the ones in [4,23].

Reconfigurable Properties
To realize the desired reconfigurable properties, some tuning elements should be inserted into the passive filtering structure. At first, a lumped capacitor CF is employed as one of the tuning elements, which is located at the middle of the lower stub of T-shaped resonator with open Electronics 2020, 9, x FOR PEER REVIEW 6 of 14 apart gradually. Meanwhile, TPs of fep2,3 and fop1,2 move apart slightly. For the rest of the TPs/TZs, they are maintained unaltered, as shown in Figure 5. Hence, the skirt selectivity of the passive filtering structure near the second and third passband edges can be improved by generating TZs of fI1 and fI2 through suitably choosing θL and θR. Furthermore, the relationships among fI1, fI2, θL, and θR can be approximately obtained as One thing should be noted: whatever the electrical lengths of θL and θR are, the relationships of fz1 < fep1 < fop1 < fep2 < fI1 < fz2 = f0 < fI2 < fep3 < fop2 < fep4 < fz3 always exist. Hence, the second and third passband edges can be independently controlled by varying θL and θR, as the ones in [4,23].

Reconfigurable Properties
To realize the desired reconfigurable properties, some tuning elements should be inserted into the passive filtering structure. At first, a lumped capacitor CF is employed as one of the tuning elements, which is located at the middle of the lower stub of T-shaped resonator with open One thing should be noted: whatever the electrical lengths of θ L and θ R are, the relationships Hence, the second and third passband edges can be independently controlled by varying θ L and θ R , as the ones in [4,23].

Reconfigurable Properties
To realize the desired reconfigurable properties, some tuning elements should be inserted into the passive filtering structure. At first, a lumped capacitor C F is employed as one of the tuning elements, Electronics 2020, 9, 2149 7 of 14 which is located at the middle of the lower stub of T-shaped resonator with open terminations. Under this condition, the input impedance of T-shaped resonator with capacitor C F can be expressed as where If the inserted capacitor C F is large enough, the input impedance of T-shaped resonator with capacitor can be simplified to the one without capacitor. Under this condition, the effect of the inserted capacitor on the filter responses is insignificant. With the decrease in C F , however, the conditions are changed, and the effect of the inserted capacitor C F on f ep1 is much larger than the ones on f ep2 , f ep3 , f ep4 . Reflected to the filter responses, the first passband edge can be independently tunable by altering C F , while the other three are fixed, as illustrated in Figure 6a, where the 3-dB passband edges with TZs for sharp selectivity are depicted with respect to different C F .
As mentioned in Part A, the second and third passband edges can be independently controlled by varying θ L and θ R . Hence, the other two capacitors of C S and C T are then inserted into the open-ended stubs with Z 1 for independent tunabilities of these two passband edges. In Figure 6b,c, 3-dB passband edges with TZs for sharp selectivity with respect to different capacitors of C S and C T are depicted. Apparently, these two passbands also can be independently tunable by controlling the capacitors of C S and C T , respectively.
If the inserted capacitor CF is large enough, the input impedance of T-shaped resonator with capacitor can be simplified to the one without capacitor. Under this condition, the effect of the inserted capacitor on the filter responses is insignificant. With the decrease in CF, however, the conditions are changed, and the effect of the inserted capacitor CF on fep1 is much larger than the ones on fep2, fep3, fep4. Reflected to the filter responses, the first passband edge can be independently tunable by altering CF, while the other three are fixed, as illustrated in Figure 6a, where the 3-dB passband edges with TZs for sharp selectivity are depicted with respect to different CF.
As mentioned in Part A, the second and third passband edges can be independently controlled by varying θL and θR. Hence, the other two capacitors of CS and CT are then inserted into the openended stubs with Z1 for independent tunabilities of these two passband edges. In Figure 6b,c, 3-dB passband edges with TZs for sharp selectivity with respect to different capacitors of CS and CT are depicted. Apparently, these two passbands also can be independently tunable by controlling the capacitors of CS and CT, respectively. According to the theoretical analysis mentioned above, the first and second passband edges can be independently tunable. Thus, the reconfigurable properties, i.e., independently tunable center frequency of lower passband with fixed absolute bandwidth, and independently tunable bandwidth of lower passband with fixed center frequency, can be directly realized by suitably selecting the capacitors of CF and CS. Furthermore, it is interesting that the lower passband will disappear when According to the theoretical analysis mentioned above, the first and second passband edges can be independently tunable. Thus, the reconfigurable properties, i.e., independently tunable center frequency of lower passband with fixed absolute bandwidth, and independently tunable bandwidth of lower passband with fixed center frequency, can be directly realized by suitably selecting the capacitors of C F and C S . Furthermore, it is interesting that the lower passband will disappear when C F is small and C S is large enough. Hence, the switchable lower passband also can be achieved. As the third passband edge is independently controlled by the capacitor of C T , a SWB BPF with tunable bandwidth can be designed too. For verification, a prototype with different capacitors is designed and measured, which will be presented in detail in Section 3.

Design Examples
Based on the theory in Section 2, a simple and effective design procedure for the desired prototype can be concluded as: (1) On the basis of DWB BPF with the widest bandwidth, initially determine the design para-meters of the passive filtering structure, i.e., Z 1 , Z 2 , Z 3 , Z 4 , Z oo , Z oe , θ 1 , θ 2 , and θ 3 . (2) Based on the different locations of first and third passband edges, determine C F and C T .
(3) Based on the various locations of second passband edge, determine C S and θ 3 . (4) After slightly optimizing, obtain the final parameters.
On the basis of the above procedure, the design parameters of a reconfigurable DWB BPF with widest fractional bandwidths (FBWs) of 25.7%, 17.5%, and center frequencies (CFs) of 2.82 GHz and 4.12 GHz can be concluded as: 4 pF, and f 0 =3.47 GHz. Then, the reconfigurable properties can be achieved by only changing the inserted capacitors. As the fabricated filter is implemented on Rogers RO4003B with dielectric constant of 3.38 mm and thickness of 0.813 mm, its dimensions and layout can be determined with the aid of commercial software, as shown in Figure 7. In this layout, a design skill is used: to enlarge the equivalent value of Z 1 and enhance the coupling strength of PCLs, some parts of the open-ended stubs with Z 1 are parallel to PCLs. bandwidth can be designed too. For verification, a prototype with different capacitors is designed and measured, which will be presented in detail in Section 3.

Design Examples
Based on the theory in Section 2, a simple and effective design procedure for the desired prototype can be concluded as: (1) On the basis of DWB BPF with the widest bandwidth, initially determine the design para-meters of the passive filtering structure, i.e., Z1, Z2, Z3, Z4, Zoo, Zoe, θ1, θ2, and θ3.  The filtering responses under different cases are measured by a Keysight N5224A network analyzer. For Case A with CF = CT = 100 pF, and CS = 2.4 pF, the corresponding measured results are plotted with the simulated ones in Figure 8. Apparently, they agree well with each other, except for some slight discrepancies, which are caused by the fabrication and measured tolerances. Under the condition that the matching is better than 10.0 dB, the measured FBWs are 26.6%, 17.8% with CFs of 2.82 GHz and 4.10 GHz for the first and second passbands, respectively. In addition, over 20-dB insertion loss can be found in the stopband between two passbands from 3.33 GHz to 3.63 GHz, indicating high isolation level. Five TPs for good flatness in the passbands are found at 2.52 GHz, 2.90 GHz, 3.12 GHz, 3.80 GHz, and 4.30 GHz, respectively, while five TZs for sharp skirt and high isolation levels are located at 2.12 GHz, 3.34 GHz, 3.46 GHz, 3.59 GHz, and 4.88 GHz. In addition, the group delay within two passbands is no more than 1.78 ns. The overall size of the fabricated filter is 36.0 × 25.0 mm. The filtering responses under different cases are measured by a Keysight N5224A network analyzer. For Case A with C F = C T = 100 pF, and C S = 2.4 pF, the corresponding measured results are plotted with the simulated ones in Figure 8. Apparently, they agree well with each other, except for some slight discrepancies, which are caused by the fabrication and measured tolerances. Under the condition that the matching is better than 10.0 dB, the measured FBWs are 26.6%, 17.8% with CFs of 2.82 GHz and 4.10 GHz for the first and second passbands, respectively. In addition, over 20-dB insertion loss can be found in the stopband between two passbands from 3.33 GHz to 3.63 GHz, indicating high isolation level. Five TPs for good flatness in the passbands are found at 2.52 GHz, 2.90 GHz, 3.12 GHz, Electronics 2020, 9, 2149 9 of 14 3.80 GHz, and 4.30 GHz, respectively, while five TZs for sharp skirt and high isolation levels are located at 2.12 GHz, 3.34 GHz, 3.46 GHz, 3.59 GHz, and 4.88 GHz. In addition, the group delay within two passbands is no more than 1.78 ns. The overall size of the fabricated filter is 36.0 × 25.0 mm.

Three Independently Tunable Passband Edges
The simulated and measured S-parameters of Case B with CF = 4.7 pF, CS = 2.4 pF, and CT = 100 pF are shown in Figure 9a. By comparing Case A and B, it is apparent that the first passband edge with matching better than 10.0 dB can independently move upwards from 2.44 GHz to 2.73 GHz with the decreases of CF from 100 pF to 4.7 pF, while TZ near the first passband edge also moves upwards from 2.12 GHz to 2.42 GHz for sharp skirt. For the other three passband edges and TZs for sharp selectivity, they are unaltered.
Similar to the first passband edge, the second and third ones also can be independently tunable by controlling the capacitors of CS and CT. In Figure 9b,c, the simulated and measured results under Case C (CF = CT = CS = 100 pF) and D (CF = 100 pF, CS = 2.2 pF, and CT = 2.4 pF) are shown, respectively. Compared with Case A and C, it can be obtained that the second passband edge with matching better than 10 dB moves downwards from 3.19 GHz to 2.96 GHz as CT increases from 2.4 pF to 100 pF, while TZ near the second passband moves downwards from 3.34 GHz to 3.26 GHz for sharp skirt. By comparing Case A and D, it is obvious that the third passband edge with matching better than 10.0 dB will move upwards from 3.73 GHz to 3.89 GHz with the decrease in CT from 100 pF to 2.2 pF, while TZs near the third passband are shifted from 3.59 GHz to 3.62 GHz for sharp skirt. For the rest of the passband edges and other TZs, they are unaltered. Hence, the three independently tunable passband edges can be validated.

Three Independently Tunable Passband Edges
The simulated and measured S-parameters of Case B with C F = 4.7 pF, C S = 2.4 pF, and C T = 100 pF are shown in Figure 9a. By comparing Case A and B, it is apparent that the first passband edge with matching better than 10.0 dB can independently move upwards from 2.44 GHz to 2.73 GHz with the decreases of C F from 100 pF to 4.7 pF, while TZ near the first passband edge also moves upwards from 2.12 GHz to 2.42 GHz for sharp skirt. For the other three passband edges and TZs for sharp selectivity, they are unaltered.
Similar to the first passband edge, the second and third ones also can be independently tunable by controlling the capacitors of C S and C T . In Figure 9b,c, the simulated and measured results under Case C (C F = C T = C S = 100 pF) and D (C F = 100 pF, C S = 2.2 pF, and C T = 2.4 pF) are shown, respectively. Compared with Case A and C, it can be obtained that the second passband edge with matching better than 10 dB moves downwards from 3.19 GHz to 2.96 GHz as C T increases from 2.4 pF to 100 pF, while TZ near the second passband moves downwards from 3.34 GHz to 3.26 GHz for sharp skirt. By comparing Case A and D, it is obvious that the third passband edge with matching better than 10.0 dB will move upwards from 3.73 GHz to 3.89 GHz with the decrease in C T from 100 pF to 2.2 pF, while TZs near the third passband are shifted from 3.59 GHz to 3.62 GHz for sharp skirt. For the rest of the passband edges and other TZs, they are unaltered. Hence, the three independently tunable passband edges can be validated.

Three Independently Tunable Passband Edges
The simulated and measured S-parameters of Case B with CF = 4.7 pF, CS = 2.4 pF, and CT = 100 pF are shown in Figure 9a. By comparing Case A and B, it is apparent that the first passband edge with matching better than 10.0 dB can independently move upwards from 2.44 GHz to 2.73 GHz with the decreases of CF from 100 pF to 4.7 pF, while TZ near the first passband edge also moves upwards from 2.12 GHz to 2.42 GHz for sharp skirt. For the other three passband edges and TZs for sharp selectivity, they are unaltered.
Similar to the first passband edge, the second and third ones also can be independently tunable by controlling the capacitors of CS and CT. In Figure 9b,c, the simulated and measured results under Case C (CF = CT = CS = 100 pF) and D (CF = 100 pF, CS = 2.2 pF, and CT = 2.4 pF) are shown, respectively. Compared with Case A and C, it can be obtained that the second passband edge with matching better than 10 dB moves downwards from 3.19 GHz to 2.96 GHz as CT increases from 2.4 pF to 100 pF, while TZ near the second passband moves downwards from 3.34 GHz to 3.26 GHz for sharp skirt. By comparing Case A and D, it is obvious that the third passband edge with matching better than 10.0 dB will move upwards from 3.73 GHz to 3.89 GHz with the decrease in CT from 100 pF to 2.2 pF, while TZs near the third passband are shifted from 3.59 GHz to 3.62 GHz for sharp skirt. For the rest of the passband edges and other TZs, they are unaltered. Hence, the three independently tunable passband edges can be validated.

Independently Tunable Center Frequency of Lower Passband with Fixed Absolute Bandwidth
As the first and second passband edges can be independently tunable by changing the capacitors of CF and CS, respectively, it is apparent that the center frequency of lower passband also can be independently tunable by suitably selecting these two capacitors, while the corresponding absolute bandwidth is fixed. This reconfigurable property is validated by comparing Case B and C. By gradually decreasing CF from 100.0 pF to 2.4 pF and suitably choosing the capacitor of CS, the center frequency of lower passband can be continuously shifted from 2.71 GHz to 2.97 GHz, while the absolute bandwidth with matching better than 10.0 dB is about 0.49 GHz. For the upper passband, it is fixed. Hence, the fractional tuning range of lower passband is 9.6%, and the corresponding constant FBW is 18.1%.
One thing should be noted: only two reported IEEE journal papers concern the tunable center frequencies of dual-band BPFs with constant absolute bandwidths, which are presented in [9] and [17]. Unfortunately, their constant FBWs are narrow and no more than 9.3%. Hence, the proposed design should be beneficial to exploration of other tunable-center-frequency DWB BPFs with constant absolute bandwidths.

Independently Tunable Bandwidth of Lower Passband with Fixed Center Frequency
Among the reported tunable DWB BPFs, there is no report of the independently tunable bandwidth of lower passband with constant center frequency, which will restrict the development of telecommunication. In this part, this desired reconfigurable property is implemented.
As the first passband edge will move downwards with the increase in CF, and the second one will move upwards with the decrease in CS, the bandwidth of lower passband can be tunable in continue manners by gradually increasing CF and decreasing CS simultaneously, while the corresponding center frequency and upper passband is unchanged. This reconfigurable property can be validated by comparing Case A and E (CF = 4.8 pF, CS = 6.2 pF, CT = 100 pF), whose simulated and measured results are depicted in Figure 10. By suitably decreasing CF from 100 pF to 4.8 pF and increasing CS from 2.4 pF to 6.2 pF, the FBW of the lower passband is varied from 26.6% to 9.9%, and the corresponding center frequency is about 2.83 GHz. Meanwhile, TZs near the first and second passband edges are shifted from 2.12 GHz and 2.40 GHz to 3.34 GHz and 3.29 GHz, respectively. Furthermore, the upper passband is unaltered. Hence, DWB BPF with independently tunable bandwidth and fixed center frequency of lower passband can be designed.

Independently Tunable Center Frequency of Lower Passband with Fixed Absolute Bandwidth
As the first and second passband edges can be independently tunable by changing the capacitors of C F and C S , respectively, it is apparent that the center frequency of lower passband also can be independently tunable by suitably selecting these two capacitors, while the corresponding absolute bandwidth is fixed. This reconfigurable property is validated by comparing Case B and C. By gradually decreasing C F from 100.0 pF to 2.4 pF and suitably choosing the capacitor of C S , the center frequency of lower passband can be continuously shifted from 2.71 GHz to 2.97 GHz, while the absolute bandwidth with matching better than 10.0 dB is about 0.49 GHz. For the upper passband, it is fixed. Hence, the fractional tuning range of lower passband is 9.6%, and the corresponding constant FBW is 18.1%.
One thing should be noted: only two reported IEEE journal papers concern the tunable center frequencies of dual-band BPFs with constant absolute bandwidths, which are presented in [9] and [17]. Unfortunately, their constant FBWs are narrow and no more than 9.3%. Hence, the proposed design should be beneficial to exploration of other tunable-center-frequency DWB BPFs with constant absolute bandwidths.

Independently Tunable Bandwidth of Lower Passband with Fixed Center Frequency
Among the reported tunable DWB BPFs, there is no report of the independently tunable bandwidth of lower passband with constant center frequency, which will restrict the development of telecommunication. In this part, this desired reconfigurable property is implemented.
As the first passband edge will move downwards with the increase in C F , and the second one will move upwards with the decrease in C S , the bandwidth of lower passband can be tunable in continue manners by gradually increasing C F and decreasing C S simultaneously, while the corresponding center frequency and upper passband is unchanged. This reconfigurable property can be validated by comparing Case A and E (C F = 4.8 pF, C S = 6.2 pF, C T = 100 pF), whose simulated and measured results are depicted in Figure 10. By suitably decreasing C F from 100 pF to 4.8 pF and increasing C S from 2.4 pF to 6.2 pF, the FBW of the lower passband is varied from 26.6% to 9.9%, and the corresponding center frequency is about 2.83 GHz. Meanwhile, TZs near the first and second passband edges are shifted from 2.12 GHz and 2.40 GHz to 3.34 GHz and 3.29 GHz, respectively. Furthermore, the upper passband is unaltered. Hence, DWB BPF with independently tunable bandwidth and fixed center frequency of lower passband can be designed. Electronics 2020, 9, x FOR PEER REVIEW 11 of 14

Independently Switchable Lower Passband
Although the switchable dual-band BPFs have been studied extensively, their corresponding passbands are relatively small, as presented in [15][16][17]. In other words, there is no DWB BPF with independently switchable passbands reported. Therefore, the successful design of DWB BPFs with switchable bandwidth should be beneficial to the modern telecommunication.
As mentioned in Case A with CF = CT = 100 pF, and CS = 2.4 pF, there are two passbands with FBWs of 26.6% and 17.8%. Then, the lower passband will be changed into a stopband under the condition of Case F with CF = 1.5 pF, CS = 100 pF, and CT = 100 pF, while the upper one is almost fixed, as depicted in Figure 11. Thus, the lower passband can be independently switchable.

Independently Tunable First Passband Edge of SWB BPF
Considering that the lower passband will be changed into a stopband by selecting the suitable capacitors of CF and CS, and the third passband edge can be independently tunable by controlling the capacitor of CT, SWB BPFs with tunable bandwidth can be designed based on this novel topology. This is verified by comparing Case F and G. As shown in Figures 11 and 12, the first passband edge of SWB BPFs is shifted from 3.76 GHz to 4.07 GHz with the decrease in CT from 100 pF to 1.4 pF, while the other one is fixed about 4.50 GHz. In addition, TZ near the first passband edge of SWB BPFs is varied from 3.58 GHz to 3.76 GHz. Thus, a SWB BPF with tunable-bandwidth range of 7.5% can be designed.

Independently Switchable Lower Passband
Although the switchable dual-band BPFs have been studied extensively, their corresponding passbands are relatively small, as presented in [15][16][17]. In other words, there is no DWB BPF with independently switchable passbands reported. Therefore, the successful design of DWB BPFs with switchable bandwidth should be beneficial to the modern telecommunication.
As mentioned in Case A with C F = C T = 100 pF, and C S = 2.4 pF, there are two passbands with FBWs of 26.6% and 17.8%. Then, the lower passband will be changed into a stopband under the condition of Case F with C F = 1.5 pF, C S = 100 pF, and C T = 100 pF, while the upper one is almost fixed, as depicted in Figure 11. Thus, the lower passband can be independently switchable.

Independently Switchable Lower Passband
Although the switchable dual-band BPFs have been studied extensively, their corresponding passbands are relatively small, as presented in [15][16][17]. In other words, there is no DWB BPF with independently switchable passbands reported. Therefore, the successful design of DWB BPFs with switchable bandwidth should be beneficial to the modern telecommunication.
As mentioned in Case A with CF = CT = 100 pF, and CS = 2.4 pF, there are two passbands with FBWs of 26.6% and 17.8%. Then, the lower passband will be changed into a stopband under the condition of Case F with CF = 1.5 pF, CS = 100 pF, and CT = 100 pF, while the upper one is almost fixed, as depicted in Figure 11. Thus, the lower passband can be independently switchable.

Independently Tunable First Passband Edge of SWB BPF
Considering that the lower passband will be changed into a stopband by selecting the suitable capacitors of CF and CS, and the third passband edge can be independently tunable by controlling the capacitor of CT, SWB BPFs with tunable bandwidth can be designed based on this novel topology. This is verified by comparing Case F and G. As shown in Figures 11 and 12, the first passband edge of SWB BPFs is shifted from 3.76 GHz to 4.07 GHz with the decrease in CT from 100 pF to 1.4 pF, while the other one is fixed about 4.50 GHz. In addition, TZ near the first passband edge of SWB BPFs is varied from 3.58 GHz to 3.76 GHz. Thus, a SWB BPF with tunable-bandwidth range of 7.5% can be designed.

Independently Tunable First Passband Edge of SWB BPF
Considering that the lower passband will be changed into a stopband by selecting the suitable capacitors of C F and C S , and the third passband edge can be independently tunable by controlling the capacitor of C T , SWB BPFs with tunable bandwidth can be designed based on this novel topology. This is verified by comparing Case F and G. As shown in Figures 11 and 12, the first passband edge of SWB BPFs is shifted from 3.76 GHz to 4.07 GHz with the decrease in C T from 100 pF to 1.4 pF, while the other one is fixed about 4.50 GHz. In addition, TZ near the first passband edge of SWB BPFs is varied from 3.58 GHz to 3.76 GHz. Thus, a SWB BPF with tunable-bandwidth range of 7.5% can be designed.
In Figure 13, the photograph of the fabricated filter is given. To vividly demonstrate this topology, the simulated and measured results under different cases are listed in Table 1. One thing should be noted-the insertion loss in the passband is no more than 1.4 dB for all the cases, while the group delay is less than 2.35 ns. To demonstrate the advantages of this design, a comparison with some previous works is presented in Table 2. Obviously, the proposed work can not only be used to design SWB BPFs with tunable bandwidth, but also DWB BPFs with tunable center frequency, tunable bandwidth, and switchable passband. Considering the new reconfigurable properties, i.e., tunable bandwidth of lower passband with fixed absolute center frequency, the proposed work can reduce the design complicity and circuit size of multi-functional wireless communication systems effectively and conveniently. In Figure 13, the photograph of the fabricated filter is given. To vividly demonstrate this topology, the simulated and measured results under different cases are listed in Table 1. One thing should be noted-the insertion loss in the passband is no more than 1.4 dB for all the cases, while the group delay is less than 2.35 ns. To demonstrate the advantages of this design, a comparison with some previous works is presented in Table 2. Obviously, the proposed work can not only be used to design SWB BPFs with tunable bandwidth, but also DWB BPFs with tunable center frequency, tunable bandwidth, and switchable passband. Considering the new reconfigurable properties, i.e., tunable bandwidth of lower passband with fixed absolute center frequency, the proposed work can reduce the design complicity and circuit size of multi-functional wireless communication systems effectively and conveniently.    In Figure 13, the photograph of the fabricated filter is given. To vividly demonstrate this topology, the simulated and measured results under different cases are listed in Table 1. One thing should be noted-the insertion loss in the passband is no more than 1.4 dB for all the cases, while the group delay is less than 2.35 ns. To demonstrate the advantages of this design, a comparison with some previous works is presented in Table 2. Obviously, the proposed work can not only be used to design SWB BPFs with tunable bandwidth, but also DWB BPFs with tunable center frequency, tunable bandwidth, and switchable passband. Considering the new reconfigurable properties, i.e., tunable bandwidth of lower passband with fixed absolute center frequency, the proposed work can reduce the design complicity and circuit size of multi-functional wireless communication systems effectively and conveniently.

Conclusions
In this paper, a novel topology is presented for the design of SWB/DWB BPFs with different reconfigurable properties. This design is based on a dual-wideband passive filtering structure with three TPs in each passband and five TZs in the stopbands, and three capacitors are used as the tuning elements. By controlling the inserted capacitors, it is found that SWB BPFs with tunable bandwidth, and DWB BPFs with tunable center frequency, tunable bandwidths, and switchable passband, can be achieved simultaneously. For verification, a prototype with different capacitors is designed and fabricated. Obviously, the simulated and measured results are in good agreement. Considering that the proposed design owns novel and masses of reconfigurable properties, it is anticipated that this filter can be broadly used in the modern multi-functional telecommunication systems.