A Compact C-Band Bandpass Filter with an Adjustable Dual-Band Suitable for Satellite Communication Systems

: A narrowband dual-band bandpass ﬁlter (BPF) with independently tunable passbands is presented through a systematic design approach. A size-e ﬃ cient coupling system is proposed with the capability of being integrated with additional resonators without increasing the size of the circuit. Two ﬂag-shaped resonators along with two stepped-impedance resonators are integrated with the coupling system to ﬁrstly enhance the quality response of the ﬁlter, and secondly to add an independent adjustability feature to the ﬁlter. The dual passband of the ﬁlter is centered at 4.42 GHz and 7.2 GHz, respectively, with narrow passbands of 2.12% and 1.15%. The lower and upper passbands can be swept independently over 600 MHz and 1000 MHz by changing only one parameter of the ﬁlter without any destructive e ﬀ ects on the frequency response. According to United States frequency allocations, the ﬁrst passband is convenient for mobile communications and the second passband can be used for satellite communications. The ﬁlter has very good in- and out-of-band performance with very small passband insertion losses of 0.5 dB and 0.86 dB as well as a relatively strong stopband attenuation of 30 dB and 25 dB, respectively, for the case of lower and upper bands. To verify the proposed approach, a prototype of the ﬁlter is fabricated and measured showing a good agreement between numerically calculated and measured results.


Introduction
Microstrip technology has been widely used in modern communication systems since it is a mature and highly reliable technology for microwave-and millimeter-wave applications [1][2][3][4][5][6][7][8][9][10][11]. In particular, multiband bandpass filters (BPFs) have been utilized in wireless communication transceivers to Various design approaches for dual-band BPFs have been reported in the open literature. Most of them, however, focused on one or some critical properties at the price of other critical aspects.
In this paper, a straightforward yet systematic design approach which can sufficiently address all (or most of the) critical properties required for narrowband dual-band BPFs is presented. The proposed dual-band BPF provides properties of very good inter-band isolation level, strong attenuation in the stopband and low fabrication cost in a compact size. It can also provide fully tunable passbands, which can be independently adjusted by only one parameter, reducing the complexity of re-tuning the proposed filter for other possible applications.

Proposed Coupling System
The conventional approach to creating a bandpass response is the use of capacitive gaps in the microstrip filters. However, the quality of the passband response can be significantly improved using multiple coupled transmission lines with different electrical lengths and capacitance gaps, leading to some traditional bandpass filters such as end-coupled, comb-line and hairpin-line BP filters [31,60]. Despite their straightforward design approaches, their dimensions are undesirably large due to the large number of coupled lines required for a passband with relatively small insertion loss. In this paper, a new coupling system inspired by the end-coupled lines is proposed, and a systematic miniaturization procedure is presented, which can be used for dual-band bandpass filters with independent passband adjustability. The advantage of the proposed method is that, unlike the abovementioned methods, only one end-coupled structure is required, contributing to a compact configuration. Figure 1a shows a layout of one end-coupled transmission line to create a transmission pole at 7.66 GHz as shown in Figure 1b. The length of the coupled lines in this structure is close to half a guided wavelength at the first resonant frequency, which is inspired by the conventional end-coupled, half-wavelength resonator filters where a weak capacitive coupling is created through the gap between the two adjacent open ends. However, the conventional end-coupled filters are relatively large, due to the end to end orientation of the coupled lines [60]. To reduce the circuit size, the end-coupled lines are bent as shown in Figure 2a, resulting in a dual-band performance as depicted in Figure 2b. It needs to be mentioned that the effective length of coupled lines before and after bending remains almost same, and hence, the locations of the transmission poles remain almost unaffected by bending the coupled lines.
Electronics 2020, 9, x FOR PEER REVIEW 3 of 17 In this paper, a straightforward yet systematic design approach which can sufficiently address all (or most of the) critical properties required for narrowband dual-band BPFs is presented. The proposed dual-band BPF provides properties of very good inter-band isolation level, strong attenuation in the stopband and low fabrication cost in a compact size. It can also provide fully tunable passbands, which can be independently adjusted by only one parameter, reducing the complexity of re-tuning the proposed filter for other possible applications.

Proposed Coupling System
The conventional approach to creating a bandpass response is the use of capacitive gaps in the microstrip filters. However, the quality of the passband response can be significantly improved using multiple coupled transmission lines with different electrical lengths and capacitance gaps, leading to some traditional bandpass filters such as end-coupled, comb-line and hairpin-line BP filters [31,60]. Despite their straightforward design approaches, their dimensions are undesirably large due to the large number of coupled lines required for a passband with relatively small insertion loss. In this paper, a new coupling system inspired by the end-coupled lines is proposed, and a systematic miniaturization procedure is presented, which can be used for dual-band bandpass filters with independent passband adjustability. The advantage of the proposed method is that, unlike the abovementioned methods, only one end-coupled structure is required, contributing to a compact configuration. Figure 1a shows a layout of one end-coupled transmission line to create a transmission pole at 7.66 GHz as shown in Figure 1b. The length of the coupled lines in this structure is close to half a guided wavelength at the first resonant frequency, which is inspired by the conventional endcoupled, half-wavelength resonator filters where a weak capacitive coupling is created through the gap between the two adjacent open ends. However, the conventional end-coupled filters are relatively large, due to the end to end orientation of the coupled lines [60]. To reduce the circuit size, the end-coupled lines are bent as shown in Figure 2a, resulting in a dual-band performance as depicted in Figure 2b. It needs to be mentioned that the effective length of coupled lines before and after bending remains almost same, and hence, the locations of the transmission poles remain almost unaffected by bending the coupled lines.   In order to further investigate the frequency behavior of the proposed structure and predict and control the resonant frequencies, an equivalent lumped circuit model can be extracted for the structure. The use of lumped-element circuit (LC) models for analyzing microwave filters' behavior is a well-known approach and explained in [6,56,61,62]. The effect of the bends on the frequency response of the coupling system can be modeled by six capacitors (Cbend) as illustrated in a simplified lumped-element circuit (LC) model shown in Figure 3a. In the LC circuit, C1, C3, C4 and C6 denote the gap capacitances. C2, C5, C7 and C11 describe the capacitances of the open-end stubs. The inductances of transmission lines are also modeled by L1, L2, L3, L4 and L5, and the bending capacitances are denoted by C8, C9 and C10. The values of the lumped elements are obtained using the procedure outlined in [53,54]  In order to further investigate the frequency behavior of the proposed structure and predict and control the resonant frequencies, an equivalent lumped circuit model can be extracted for the structure. The use of lumped-element circuit (LC) models for analyzing microwave filters' behavior is a well-known approach and explained in [6,56,61,62]. The effect of the bends on the frequency response of the coupling system can be modeled by six capacitors (C bend ) as illustrated in a simplified lumped-element circuit (LC) model shown in Figure 3a. In the LC circuit, C 1 , C 3 , C 4 and C 6 denote the gap capacitances. C 2 , C 5 , C 7 and C 11 describe the capacitances of the open-end stubs. The inductances of transmission lines are also modeled by L 1 , L 2 , L 3 , L 4 and L 5 , and the bending capacitances are denoted by C 8 , C 9 and C 10 . The values of the lumped elements are obtained using the procedure outlined in [53,54], and calculated as follows: C 1 = 0.107 pF, C 2 = 0.73 pF, C 3 = 0.3 pF, C 4 = 0.05 pF, C 5 = 1.289 pF, C 6 = 0.045 pF, C 7 = 7 pF, C 8 = 0.535 pF, C 9 = 7 pF, C 10 = 5 pF, C 11 = 0.65 pF, L 1 = 0.4 nH, L 2 = 0.34 nH, L 3 = 0.5 nH, L 4 = 0.435 nH and L 5 = 0.75 nH. It can be seen from Figure 3b that introducing the bending capacitors improves the passband response, reducing the passband insertion loss from 7.05 to 0.66 dB. The first and second resonant frequencies of the filter shown in Figure 3b can be calculated by equating the input impedance of the equivalent circuit model to zero as shown in (1). As a result, the equations of resonances are obtained as (2) and (3). where Electronics 2020, 9, x FOR PEER REVIEW 5 of 17 (1 + ( Magnitude (dB) The lower passband can be tuned by varying the line gap (A6) since increasing A6 would result in a smaller capacitor, shifting up the resonant frequency as depicted in Figure 4. Additionally, the insertion loss increases by moving the lower passband to higher frequencies. Therefore, for keeping an optimum response, A6 is fixed at 0.1 mm.

Proposed Dual-Band BPF
In order to realize an independently controllable dual passband and to shift the operating frequencies of the filter to the lower bands without scaling the filter layout, which leads to an undesirable large circuit size, a pair of flag-shaped resonators are designed and connected to the aforementioned bended coupling configuration as shown in Figure 5a. Applying the flag-shaped resonators pushes down the lower and upper passbands to 4.42 GHz and 9.5 GHz, respectively, as shown in Figure 5b. Each flag-shaped resonator comprises a high impedance line, a high impedance open stub and a low impedance open-end stub. Each section can be modeled using a series inductor and one shunt capacitor as depicted in Figure 5c. In this model, CH1 and LH1 describe capacitance and inductance of the high impedance line. CL1 and LL1 are capacitance and inductance of the low impedance open-end stub. Additionally, capacitance and inductance of the open stub are presented by CO and LO, respectively. In order to calculate the lumped element values of this LC model, the method described in [6,56,61] can be used, in which the initial values are calculated [60] and then optimized to match the frequency responses of the LC model and the electromagnetic (EM) simulation.

Proposed Dual-Band BPF
In order to realize an independently controllable dual passband and to shift the operating frequencies of the filter to the lower bands without scaling the filter layout, which leads to an undesirable large circuit size, a pair of flag-shaped resonators are designed and connected to the aforementioned bended coupling configuration as shown in Figure  To lower the insertion loss of the second passband, a pair of stepped-impedance resonators, including a high impedance line and a low impedance open-end stub, are added to the BPF. The final geometrical configuration of the proposed BPF is shown in Figure 6a. The EM simulation results of this structure are presented in Figure 6b. The capacitances and inductances of the stepped-impedance lines are displayed in Figure 6c. In the LC model, the capacitance and inductance of the high impedance line are depicted by CH2 and LH2. CL2 and LL2 denote the capacitance and inductance of the low impedance open-end stub, respectively. To lower the insertion loss of the second passband, a pair of stepped-impedance resonators, including a high impedance line and a low impedance open-end stub, are added to the BPF. The final geometrical configuration of the proposed BPF is shown in Figure 6a. The EM simulation results of this structure are presented in Figure 6b. The capacitances and inductances of the stepped-impedance lines are displayed in Figure 6c. In the LC model, the capacitance and inductance of the high impedance line are depicted by C H2 and L H2 . C L2 and L L2 denote the capacitance and inductance of the low impedance open-end stub, respectively. Electronics 2020, 9,

Current Distribution Analysis
The filtering mechanism of the proposed dual-band BPF can be further investigated using the current density distributions at the passband frequencies (4.42 GHz and 7.2 GHz) and at the stopband frequencies (1.75 GHz and 6.3 GHz) as demonstrated in Figure 7. It can be seen that both the open stubs and the resonators along with the bended coupling system experience a strong current flow, resulting in a very small insertion loss in the operating frequencies of the filter (left-side snapshots in Figure 7). However, the bended coupling system does not allow flowing strong currents at out-ofband frequencies (right-side snapshots in Figure 7), leading to large insertion loss outside of the operating frequencies of the filter. As can be seen, the flag-shaped resonators at 4.42 GHz dominantly contribute to the first passband, while, in the case of the second passband, both stepped-impedance and flag-shaped resonators contribute to create the passband.

Current Distribution Analysis
The filtering mechanism of the proposed dual-band BPF can be further investigated using the current density distributions at the passband frequencies (4.42 GHz and 7.2 GHz) and at the stopband frequencies (1.75 GHz and 6.3 GHz) as demonstrated in Figure 7. It can be seen that both the open stubs and the resonators along with the bended coupling system experience a strong current flow, resulting in a very small insertion loss in the operating frequencies of the filter (left-side snapshots in Figure 7). However, the bended coupling system does not allow flowing strong currents at out-of-band frequencies (right-side snapshots in Figure 7), leading to large insertion loss outside of the operating frequencies of the filter. As can be seen, the flag-shaped resonators at 4.42 GHz dominantly contribute to the first passband, while, in the case of the second passband, both stepped-impedance and flag-shaped resonators contribute to create the passband.

Passbands Optimization and Tuning of the Filter
One of the major merits of the proposed dual-band BPFs is their configurable passbands so that they can be tuned throughout the C-band without the need for any active or additional modules. The lower band of the proposed filter can be tuned by varying the capacitive section of the flag-shaped resonators (A14), where decreasing A14 would decrease the capacitive effects, shifting the resonance frequency to higher frequencies, resulting in 600 MHz dynamic range (4.4 GHz to 5 GHz) as shown in Figure 8. The second passband can be adjusted by either varying the capacitive (A21) or inductive (A18) sections of the stepped-impedance resonators. Indeed, increasing A21 or A18 would have the same effect on the upper band, increasing the associated capacitor and inductor, respectively, shifting the upper band to lower frequencies. As shown in Figures 9 and 10, the upper band has a large dynamic range of 1000 MHz (from 7 GHz to 8 GHz).

Passbands Optimization and Tuning of the Filter
One of the major merits of the proposed dual-band BPFs is their configurable passbands so that they can be tuned throughout the C-band without the need for any active or additional modules. The lower band of the proposed filter can be tuned by varying the capacitive section of the flag-shaped resonators (A 14 ), where decreasing A 14 would decrease the capacitive effects, shifting the resonance frequency to higher frequencies, resulting in 600 MHz dynamic range (4.4 GHz to 5 GHz) as shown in Figure 8. The second passband can be adjusted by either varying the capacitive (A 21 ) or inductive (A 18 ) sections of the stepped-impedance resonators. Indeed, increasing A 21 or A 18 would have the same effect on the upper band, increasing the associated capacitor and inductor, respectively, shifting the upper band to lower frequencies. As shown in Figures 9 and 10, the upper band has a large dynamic range of 1000 MHz (from 7 GHz to 8 GHz).

Passbands Optimization and Tuning of the Filter
One of the major merits of the proposed dual-band BPFs is their configurable passbands so that they can be tuned throughout the C-band without the need for any active or additional modules. The lower band of the proposed filter can be tuned by varying the capacitive section of the flag-shaped resonators (A14), where decreasing A14 would decrease the capacitive effects, shifting the resonance frequency to higher frequencies, resulting in 600 MHz dynamic range (4.4 GHz to 5 GHz) as shown in Figure 8. The second passband can be adjusted by either varying the capacitive (A21) or inductive (A18) sections of the stepped-impedance resonators. Indeed, increasing A21 or A18 would have the same effect on the upper band, increasing the associated capacitor and inductor, respectively, shifting the upper band to lower frequencies. As shown in Figures 9 and 10, the upper band has a large dynamic range of 1000 MHz (from 7 GHz to 8 GHz).  The tunable effects of the filter passbands are depicted in Figure 11. As shown in this figure, the fractional bandwidths (FBWs) of both passbands increase slightly as a result of pushing down the first and second center frequencies, while the actual bandwidths remain almost unchanged. It needs to be mentioned that re-prototyping is required for the practical implementation of this tunability.
The tunable effects of the filter passbands are depicted in Figure 11. As shown in this figure, the fractional bandwidths (FBWs) of both passbands increase slightly as a result of pushing down the first and second center frequencies, while the actual bandwidths remain almost unchanged. It needs to be mentioned that re-prototyping is required for the practical implementation of this tunability. Quality factor (Q. factor) is defined as the ratio of operating frequency and bandwidth as shown in (4). Figure 12 shows the Q. factor of the proposed filter as a function of the three physical parameters of A18, A21 and A14. As depicted in this figure, the Q. factor decreases by increasing A18, A21 and A14.
(4) Quality factor (Q. factor) is defined as the ratio of operating frequency and bandwidth as shown in (4). Figure 12 shows the Q. factor of the proposed filter as a function of the three physical parameters of A 18 , A 21 and A 14 . As depicted in this figure, the Q. factor decreases by increasing A 18 , A 21 and A 14 .

Results and Discussions
As shown in Figure 13a, the proposed filter is fabricated on a Rogers Duroid 5880 (Rogers Corporation, Chandler, AZ, USA) substrate with a dielectric constant of 2.2, thickness of 0.508 mm and loss-tangent of 0.0009. The frequency response of the prototyped dual-band BPF is measured by the Agilent N5230A (Agilent Technologies, Santa Clara, CA, USA) network analyzer. The proposed filter simulation was performed using the Advanced Design System 2011.10 (ADS) software, and the EM simulated and experimental results are compared in Figure 13b. According to the measurement, the filter has two passbands with the center frequencies of f1 = 4.42 GHz and f2 = 7.2 GHz, and 3 dB bandwidths of 94 MHz and 83 MHz, respectively. Insertion and return losses at f1 and f2 are about 0.5/17.56 and 0.86/17.9 dB, respectively. The filter provides an excellent out-of-band response, showing a good rejection level of 30 dB in the lower stopband, and a 24 dB isolation level with a 25 dB rejection at upper stopband, which extends up to 14.5 GHz. The measured physical size of the filter is 11.4 mm × 5.8 mm corresponding to 0.23 λg × 0.11 λg, where λg is the guided wavelength at 4.42 GHz. The fabricated filter shows a good selectivity in both bands with sharpness values of 106 dB/GHz and 212 dB/GHz, respectively, calculated using the filter sharpness formula in [61].

Results and Discussions
As shown in Figure 13a, the proposed filter is fabricated on a Rogers Duroid 5880 (Rogers Corporation, Chandler, AZ, USA) substrate with a dielectric constant of 2.2, thickness of 0.508 mm and loss-tangent of 0.0009. The frequency response of the prototyped dual-band BPF is measured by the Agilent N5230A (Agilent Technologies, Santa Clara, CA, USA) network analyzer. The proposed filter simulation was performed using the Advanced Design System 2011.10 (ADS) software, and the EM simulated and experimental results are compared in Figure 13b. According to the measurement, the filter has two passbands with the center frequencies of f 1 = 4.42 GHz and f 2 = 7.2 GHz, and 3 dB bandwidths of 94 MHz and 83 MHz, respectively. Insertion and return losses at f 1 and f 2 are about 0.5/17.56 and 0.86/17.9 dB, respectively. The filter provides an excellent out-of-band response, showing a good rejection level of 30 dB in the lower stopband, and a 24 dB isolation level with a 25 dB rejection at upper stopband, which extends up to 14.5 GHz. The measured physical size of the filter is 11.4 mm × 5.8 mm corresponding to 0.23 λ g × 0.11 λ g , where λ g is the guided wavelength at 4.42 GHz. The fabricated filter shows a good selectivity in both bands with sharpness values of 106 dB/GHz and 212 dB/GHz, respectively, calculated using the filter sharpness formula in [61].
The proposed filter has an acceptable group delay (GD) in both passbands, which is plotted in Figure 14a,b. The maximum variations of GD in the first and second passbands are about 1.33 ns and 1.72 ns, respectively, demonstrating a flat group delay in the two passbands. The proposed filter has an acceptable group delay (GD) in both passbands, which is plotted in Figure 14a In Table 1, a summarized comparison is made between some of the recently reported dual-band BPFs and the proposed one. In this table, the normalized circuit size (NCS) is computed using NCS = (physical size)/ [62,63]. The properties of the proposed filter and some of the recently reported BPFs are listed in Table 1. As can be seen, the proposed filter has the lowest insertion loss in the two passbands, the highest suppression levels in the upper stopbands, and the widest upper stopband as compared with the reported works in [34][35][36][37][38][39][40][41][42][43][44]. It can also be observed that the return loss in passbands is better than the works reported in [36,43,45]. In addition, the presented BPF provides a large tuning range as compared with other works in Table 1. Among the recently reported designs, the proposed BPF offers dual adjustable passbands over the widely used C-band frequency regime for applications Magnitude (dB)  The proposed filter has an acceptable group delay (GD) in both passbands, which is plotted in Figure 14a,b. The maximum variations of GD in the first and second passbands are about 1.33 ns and 1.72 ns, respectively, demonstrating a flat group delay in the two passbands. In Table 1, a summarized comparison is made between some of the recently reported dual-band BPFs and the proposed one. In this table, the normalized circuit size (NCS) is computed using NCS = (physical size)/ [62,63]. The properties of the proposed filter and some of the recently reported BPFs are listed in Table 1. As can be seen, the proposed filter has the lowest insertion loss in the two passbands, the highest suppression levels in the upper stopbands, and the widest upper stopband as compared with the reported works in [34][35][36][37][38][39][40][41][42][43][44]. It can also be observed that the return loss in passbands is better than the works reported in [36,43,45]. In addition, the presented BPF provides a large tuning range as compared with other works in Table 1. Among the recently reported designs, the proposed BPF offers dual adjustable passbands over the widely used C-band frequency regime for applications Magnitude (dB) In Table 1, a summarized comparison is made between some of the recently reported dual-band BPFs and the proposed one. In this table, the normalized circuit size (NCS) is computed using NCS = (physical size)/λ 2 g [62,63]. The properties of the proposed filter and some of the recently reported BPFs are listed in Table 1. As can be seen, the proposed filter has the lowest insertion loss in the two passbands, the highest suppression levels in the upper stopbands, and the widest upper stopband as compared with the reported works in [34][35][36][37][38][39][40][41][42][43][44]. It can also be observed that the return loss in passbands is better than the works reported in [36,43,45]. In addition, the presented BPF provides a large tuning range as compared with other works in Table 1. Among the recently reported designs, the proposed BPF offers dual adjustable passbands over the widely used C-band frequency regime for applications such as satellite modems, transceivers and wireless networking technologies based on the IEEE 802.11 family of standards.

Conclusions
In this paper, a microstrip dual-band BPF with tunable narrow passbands, miniaturized size, sharp response and low-cost fabrication has been designed and fabricated at C-band frequencies.
The proposed filter consists of three subsections including a bended coupling system, flag-shaped resonators and stepped-impedance resonators. The coupling system is based on an end-coupled resonator responsible for creating a weak coupling required for a narrowband response. The quality of the response and the selectivity of the filter is then improved by introduction of flag-shaped and stepped-impedance resonators. The measured results show that the filter has two independent passbands centered at 4.42 and 7.2 GHz with a good isolation level of 24 dB and strong attenuations of 25 and 30 dB in the lower and upper stopbands, respectively. The proposed filter shows excellent selectivity with its sharpness values of 106 and 212 dB/GHz at its lower and upper bands.