An Intrinsically Switched Tunable CABW/CFBW Bandpass Filter

: In this paper, a novel intrinsically switched tunable bandpass ﬁlter based on a dual-mode T-shaped varactor-loaded resonator is presented. The varactors loaded in the T-shaped resonator are capable of efﬁciently tuning the resonant frequencies of the even and odd modes, as well as the transmission-zero frequency. Without any additional RF switches, the passband of the ﬁlter can be intrinsically switched off by adjusting the transmission zero to the resonant frequencies. In the switch-on state, the constant absolute bandwidth (CABW) or constant fractional bandwidth (CFBW) passband can be achieved by controlling the frequency space between the two resonances. For a demonstration, a 0.8–1.1 GHz intrinsically switched tunable bandpass ﬁlter with 74 MHz CABW or 8.5% CFBW was fabricated and tested. In the whole operating band with |S 11 | < 10 dB, the insertion losses for CABW and CFBW are better than 3.3 dB and 3 dB, respectively, and the isolations are better than 20 dB in the switch-off state. The measured results have a good agreement with simulated results, which veriﬁes the design theory. In this paper, a novel intrinsically switched tunable bandpass ﬁlter with CABW/CFBW properties based on dual-mode varactor-loaded T-shaped resonator is presented. The varactors, in which the resonant frequencies are able to be tuned, adjust the transmission zero and switch off the passband, simultaneously. In addition, a feature of tunable passband with CABW/CFBW can be achieved by controlling the resonant frequencies and the spacing between them. As a demonstration, a prototype of a 0.8–1.1 GHz tunable 74 MHz CABW or 8.5% CFBW ﬁlter with intrinsically switchable function is developed and characterized. The proposed design possesses multiple functions only realized by two control voltages, which can simplify the control complexity extensively.


Introduction
Reconfigurable filters have been extensively applied in the frequency-agile and software-defined radio systems due to their adjustable operating performance [1,2]. To meet the requirement of having constant passband characteristics in the whole tuning range, center-frequency-tunable bandpass filters with CABW or CFBW have been reported. Two methods are always used to achieve CABW or CFBW. The first way is to control the coupling strength by using varactors or selecting a proper coupling region [3][4][5][6][7]. The other method is to control the distance between the in-band transmission poles [8,9].
To adapt to complex operating environment, reconfigurable filters with switching capability have aroused a wide attention recently. By using the pin diodes as switches, the proposed filters in [10][11][12][13][14] can be operated in four states. Through utilizing combinations of pin diodes and varactors, the center-frequency-tunable filters can be switched in on/off state or in high/low passband [15,16]. However, it is worth noting that switching the pin diodes requires extra control voltages.
In order to reduce the number of external control variables and simplify the control complexity, intrinsically switched tunable bandpass filters are proposed [17]. In these structures, the off states can be obtained by the tuning elements which are also used to tune the center frequencies, bandwidths or coupling coefficients. Normally, two typical methods are utilized to realize intrinsically switched function. One way to switch off the passband is by changing the varactors embedded between the resonators that can control the coupling coefficients of the filters [17][18][19]. However, the magnetic coupling between the resonators has to be generated in these works in order to cancel the negative electric coupling from the coupling varactors. The other efficient way is to use the transmission zeros to switch off the passbands constructed by the spacing between transmission zeros [20][21][22]. However, these bandpass filters require more cascaded bandstop filters to realize wide out-band suppression.
In this paper, a novel intrinsically switched tunable bandpass filter with CABW/CFBW properties based on dual-mode varactor-loaded T-shaped resonator is presented. The varactors, in which the resonant frequencies are able to be tuned, adjust the transmission zero and switch off the passband, simultaneously. In addition, a feature of tunable passband with CABW/CFBW can be achieved by controlling the resonant frequencies and the spacing between them. As a demonstration, a prototype of a 0.8-1.1 GHz tunable 74 MHz CABW or 8.5% CFBW filter with intrinsically switchable function is developed and characterized. The proposed design possesses multiple functions only realized by two control voltages, which can simplify the control complexity extensively.

Transmission Line Model Analysis
The schematic diagram of the proposed filter is provided in Figure 1a, which consists of a dual-mode T-shaped resonant loaded with two types of varactors (C 1 and C 2 ) and a pair of feed lines. The capacitor C b and resistor R b are applied as dc block and dc bias, respectively. CABW/CFBW properties based on dual-mode varactor-loaded T-shaped resonator is presented. The varactors, in which the resonant frequencies are able to be tuned, adjust the transmission zero and switch off the passband, simultaneously. In addition, a feature of tunable passband with CABW/CFBW can be achieved by controlling the resonant frequencies and the spacing between them. As a demonstration, a prototype of a 0.8-1.1 GHz tunable 74 MHz CABW or 8.5% CFBW filter with intrinsically switchable function is developed and characterized. The proposed design possesses multiple functions only realized by two control voltages, which can simplify the control complexity extensively.

Transmission Line Model Analysis
The schematic diagram of the proposed filter is provided in Figure 1a, which consists of a dual-mode T-shaped resonant loaded with two types of varactors (C1 and C2) and a pair of feed lines. The capacitor Cb and resistor Rb are applied as dc block and dc bias, respectively.
Due to the symmetrical structure, the odd-even mode method is utilized to analyze the proposed filter [23,24]. In order to simplify the analysis process of the dual-mode T-shaped resonator, the basic transmission line model of the proposed resonator is presented in Figure 1b, ignoring the influences of Cb and Rb, where Y1, Y2 and Y3 are the characteristic admittances and θ1, θ2 and θ3 are the electrical lengths. The odd-and even-mode equivalent circuits are illustrated in Figure 1c,d, respectively, the input admittances of the odd-and even-mode can be derived by the following equations: Due to the symmetrical structure, the odd-even mode method is utilized to analyze the proposed filter [23,24]. In order to simplify the analysis process of the dual-mode Tshaped resonator, the basic transmission line model of the proposed resonator is presented in Figure 1b, ignoring the influences of C b and R b , where Y 1 , Y 2 and Y 3 are the characteristic admittances and θ 1 , θ 2 and θ 3 are the electrical lengths.
The odd-and even-mode equivalent circuits are illustrated in Figure 1c,d, respectively, the input admittances of the odd-and even-mode can be derived by the following equations: Y even2 = (Y 1 /2)(j2πfC 2 + jY 2 tanθ 2 )/(Y 2 − 2πfC 2 tanθ 2 ) (4) Under the resonance condition (Im (Y odd ) = 0 and Im (Y even ) = 0), the resonant frequencies can be extracted by Equations (1)- (5). It can be observed that odd-mode resonant frequency f odd is only controlled by C 1 , and the even mode resonant frequency f even is determined by C 1 and C 2 at the same time. Moreover, the transmission zero produced by the shunt stub taped with C 2 can be used not only to improve the selectivity of bandpass filter as the normal way but also to switch off the passband. The input admittance of the shunt stub taped with the varactor C 2 can be derived by: From Equation (6), it is observed that the frequency of transmission zero f zero can be deduced under the condition (Y 2 − 2πfC 2 tanθ 2 = 0), which indicates that f zero can be adjusted by C 2 . Table 1 shows the tuning ranges of f even and f odd with variation of C 1 and C 2 . f odd is independently decided by C 1 , but f even is controlled by C 1 and C 2 simultaneously. With f odd fixed by C 1 , f even varies around f odd by tuning C 2 . As shown in Figure 2, by tuning C 1 and C 2 , the specified frequency space between f even and f odd can be obtained. If f odd is fixed by C 1 , f even can be changed from greater than to less than f odd by adjusting C 2 , and f zero is changed in the same way. Therefore, there is a C 2 such that f odd = f even = f zero for different C 1 (f odd ), as the point A shown in Figure 2, and the passband can be intrinsically switched off at 0.994 GHz when C 1 = 1.1 pF and C 2 = 6.9 pF. Table 1. Tuning range of f even and f odd as C 1 and C 2 vary.
Under the resonance condition (Im (Yodd) = 0 and Im (Yeven) = 0), the resonant frequencies can be extracted by Equations (1)- (5). It can be observed that odd-mode resonant frequency fodd is only controlled by C1, and the even mode resonant frequency feven is determined by C1 and C2 at the same time. Moreover, the transmission zero produced by the shunt stub taped with C2 can be used not only to improve the selectivity of bandpass filter as the normal way but also to switch off the passband. The input admittance of the shunt stub taped with the varactor C2 can be derived by: From Equation (6), it is observed that the frequency of transmission zero fzero can be deduced under the condition (Y2 − 2πfC2tanθ2 = 0), which indicates that fzero can be adjusted by C2. Table 1 shows the tuning ranges of feven and fodd with variation of C1 and C2. fodd is independently decided by C1, but feven is controlled by C1 and C2 simultaneously. With fodd fixed by C1, feven varies around fodd by tuning C2. As shown in Figure 2, by tuning C1 and C2, the specified frequency space between feven and fodd can be obtained. If fodd is fixed by C1, feven can be changed from greater than to less than fodd by adjusting C2, and fzero is changed in the same way. Therefore, there is a C2 such that fodd = feven = fzero for different C1 (fodd), as the point A shown in Figure 2, and the passband can be intrinsically switched off at 0.994 GHz when C1 = 1.1 pF and C2 = 6.9 pF.

Analysis of f C , BW and Q e
According to the filter synthesis method in [25,26], the center frequency f C and bandwidth BW of the passband are estimated by Equations (7) and (8): f C = (f odd + f even )/2 (7) Electronics 2021, 10, 1318 4 of 8 In Figure 3, the weak coupling transmission line responses are investigated. As indicated above, through tuning C 1 and C 2 , the separation between f odd and f even can be suitable for 74 MHz CABW and 8.5% CFBW, respectively.

Analysis of fC, BW and Qe
According to the filter synthesis method in [25] and [26], the center frequency fC and bandwidth BW of the passband are estimated by Equations (7) and (8): BW = feven − fodd (8) In Figure 3, the weak coupling transmission line responses are investigated. As indicated above, through tuning C1 and C2, the separation between fodd and feven can be suitable for 74 MHz CABW and 8.5% CFBW, respectively. The external quality factor Qe of the proposed filter can be extracted by using [26] Qeo/ee = fce/co/Δfe/o±90° (9) Qe = (Qee + Qee)/2 where Qee/eo, fce/co and Δfe/o±90° are the even/odd mode external quality factors, resonant frequencies and bandwidths, respectively. In Figure 4, Qe,CABW,min/max and Qe,CFBW,min/max mean the minimum/maximum curves of Qe to realize 74 MHz CABW and 8.5% CFBW with <12 dB return loss, respectively [26].  The external quality factor Q e of the proposed filter can be extracted by using [26] Q eo/ee = f ce/co /∆f e/o±90 • Q e = (Q ee + Q ee )/2 (10) where Q ee/eo , f ce/co and ∆f e/o±90 • are the even/odd mode external quality factors, resonant frequencies and bandwidths, respectively. In Figure 4, Q e , CABW,min/max and Q e , CFBW,min/max mean the minimum/maximum curves of Q e to realize 74 MHz CABW and 8.5% CFBW with <12 dB return loss, respectively [26].

Analysis of fC, BW and Qe
According to the filter synthesis method in [25] and [26], the center frequency fC and bandwidth BW of the passband are estimated by Equations (7) and (8): BW = feven − fodd (8) In Figure 3, the weak coupling transmission line responses are investigated. As indicated above, through tuning C1 and C2, the separation between fodd and feven can be suitable for 74 MHz CABW and 8.5% CFBW, respectively. The external quality factor Qe of the proposed filter can be extracted by using [26] Qeo/ee = fce/co/Δfe/o±90° (9) Qe = (Qee + Qee)/2 (10) where Qee/eo, fce/co and Δfe/o±90° are the even/odd mode external quality factors, resonant frequencies and bandwidths, respectively. In Figure 4, Qe,CABW,min/max and Qe,CFBW,min/max mean the minimum/maximum curves of Qe to realize 74 MHz CABW and 8.5% CFBW with <12 dB return loss, respectively [26].

Current Density Distribution Analysis
Current density distribution is employed to investigate the effect of being intrinsically switched off [27]. By utilizing the parameters of point A depicted in Figure 2, the filter is switched at 0.994 GHz, and the current density distribution is plotted in Figure 5. As seen, the T-shaped resonator does not allow flowing strong current, representing that the filter' passband is switched off.

Current Density Distribution Analysis
Current density distribution is employed to investigate the effect of being intrinsically switched off [27]. By utilizing the parameters of point A depicted in Figure 2, the filter is switched at 0.994 GHz, and the current density distribution is plotted in Figure 5. As seen, the T-shaped resonator does not allow flowing strong current, representing that the filter' passband is switched off.

Designing Produce
The designing produces are as follows: Step (1) Based on the analysis of even-odd mode and transmission zero, choose the appropriated admittances (Y1, Y2 and Y3), electrical lengths (θ1, θ2 and θ3), and varactors (C1 and C2) and calculate the fC and BW to make sure that the tuning range of fodd, feven and fzero can meet the design requirements of the filter.
Step (2) Calculate the Qe in the tuning range needed for specified return loss and bandwidth.
Step (3) Simulate and extract the Qe in the whole tuning under different space s between the resonant and the feedline.
Step (4) Choose the proper s.

Experimental Verification
An intrinsically switched tunable filter is designed based on a 0.508 mm thick Rogers RO4350B substrate with a relative dielectric constant of 3.

Designing Produce
The designing produces are as follows: Step (1) Based on the analysis of even-odd mode and transmission zero, choose the appropriated admittances (Y 1 , Y 2 and Y 3 ), electrical lengths (θ 1 , θ 2 and θ 3 ), and varactors (C 1 and C 2 ) and calculate the f C and BW to make sure that the tuning range of f odd , f even and f zero can meet the design requirements of the filter.
Step (2) Calculate the Q e in the tuning range needed for specified return loss and bandwidth.
Step (3) Simulate and extract the Q e in the whole tuning under different space s between the resonant and the feedline.
Step (4) Choose the proper s.

Experimental Verification
An intrinsically switched tunable filter is designed based on a 0.508 mm thick Rogers RO4350B substrate with a relative dielectric constant of 3.48 and a loss tangent of 0.0037, where the f C is tuned in the range of 0.8-1.1 GHz and the bandwidth satisfies 74 MHz CABW or 8.5% CFBW. The design parameters of the T-shaped resonant are chosen as Y 1 = 0.01 S, Y 2 = 0.02 S, Y 3 = 0.02 S, θ 1 = 60 • , θ 2 = 22 • and θ 3 = 5 • at 1 GHz. By Equations (9) and (10), the filter's Q e versus f C with different s are extracted in Figure 6, where s is the spacing between resonant and feed line in Figure 1a. It is noteworthy that, with s in range of 0.2-0.25 mm, the values of Q e basically meet the requirements for 74 MHz CABW and 8.5% CFBW shown in Figure 4 at the same time. The simulations are conducted by using SONNET software. After optimization, the physical parameters of the filter are determined as in Table 2. The varactors MA46H201 (the capacitance tuning range is about 0.4-2.2 pF) and MA46H204 (the capacitance tuning range is about 1.8-20 pF) from M/A COM are employed as C1 and C2, which are controlled by voltages V1 and V2, respectively. Cb = 30 pF and Rb = 10 kΩ are used as dc block and dc bias, respectively. The photograph of the proposed intrinsically switched tunable filter is displayed in Figure 7. The prototype circuit size of the proposed filter is about 0.31 The simulations are conducted by using SONNET software. After optimization, the physical parameters of the filter are determined as in Table 2. The varactors MA46H201 (the capacitance tuning range is about 0.4-2.2 pF) and MA46H204 (the capacitance tuning Electronics 2021, 10, 1318 6 of 8 range is about 1.8-20 pF) from M/A COM are employed as C 1 and C 2 , which are controlled by voltages V 1 and V 2 , respectively. C b = 30 pF and R b = 10 kΩ are used as dc block and dc bias, respectively. The photograph of the proposed intrinsically switched tunable filter is displayed in Figure 7. The prototype circuit size of the proposed filter is about 0.31 λg × 0.11 λg, where λg is the guided wavelength at the lowest operating frequency (i.e., 0.8 GHz). The measurements are carried out by the ROHDE&SCHWARZ ZVA24 network analyzer.  The simulations are conducted by using SONNET software. After optimization, the physical parameters of the filter are determined as in Table 2. The varactors MA46H201 (the capacitance tuning range is about 0.4-2.2 pF) and MA46H204 (the capacitance tuning range is about 1.8-20 pF) from M/A COM are employed as C1 and C2, which are controlled by voltages V1 and V2, respectively. Cb = 30 pF and Rb = 10 kΩ are used as dc block and dc bias, respectively. The photograph of the proposed intrinsically switched tunable filter is displayed in Figure 7. The prototype circuit size of the proposed filter is about 0.31 λg × 0.11 λg, where λg is the guided wavelength at the lowest operating frequency (i.e., 0.8 GHz). The measurements are carried out by the ROHDE&SCHWARZ ZVA24 network analyzer.  The simulated and measured frequency responses of the proposed prototype with three reconfigurable states are shown in Figure 8. Figure 8a,b depicts the tuning of the center frequency from 0.8-1.1 GHz with 74 MHz CABW and 8.5% CFBW, respectively. It also can be seen that a transmission zero on the upper band edge increases as the center frequency increases in both Figure 8a,b. The measured 3 dB bandwidth of the CABW filter and 3 dB fractional bandwidth of the CFBW filter are 74 ± 1 MHz and 8.5 ± 0.1%, The simulated and measured frequency responses of the proposed prototype with three reconfigurable states are shown in Figure 8. Figure 8a,b depicts the tuning of the center frequency from 0.8-1.1 GHz with 74 MHz CABW and 8.5% CFBW, respectively. It also can be seen that a transmission zero on the upper band edge increases as the center frequency increases in both Figure 8a,b. The measured 3 dB bandwidth of the CABW filter and 3 dB fractional bandwidth of the CFBW filter are 74 ± 1 MHz and 8.5 ± 0.1%, respectively. The measured insertion losses of the CABW filter and the CFBW filter are better than 3.3 dB and 3 dB, respectively, with measured return losses better than 10 dB. Figure 8c presents the responses of passband in intrinsic switch-off state. As shown, the passband can be switched off at 0.8-1.1 GHz by tuning C 1 and C 2 , and the measured isolations are all better than 20 dB. Comparisons with the previously reported switched tunable filter are listed in Table 3. As can be seen, the proposed filer has all the functions of tuning the center frequency, controlling the bandwidth (CABW and CFBW) and switching off the passband, simultaneously. Moreover, it is worth noting that the number of control voltages used in this work is equal to the order of the filter, which can reduce the control complexity of the design. passband can be switched off at 0.8-1.1 GHz by tuning C1 and C2, and the measured isolations are all better than 20 dB. Comparisons with the previously reported switched tunable filter are listed in Table 3. As can be seen, the proposed filer has all the functions of tuning the center frequency, controlling the bandwidth (CABW and CFBW) and switching off the passband, simultaneously. Moreover, it is worth noting that the number of control voltages used in this work is equal to the order of the filter, which can reduce the control complexity of the design.

Conclusions
A novel intrinsically switched tunable filter based on dual-mode T-shaped resonator embedded with varactors is proposed in this paper. The theoretical basis and characterization of proof-of-concept microstrip prototype have been shown. The proposed filter controlled by only two voltages has the reconfigurable ability of center-frequency tuning, bandwidth controlling and passband intrinsically switching. The proposed filter has the potentiality to be applied in multiband communication systems and reduce its control complexity.