Xiangguan Tan, Yuxia Zhang
©SHUTTETRSTOCK.COM/ANTISHOCK
With the continued development of communication technology, communication systems are required to support ever more operational frequencies and standards, which has resulted in increased complexity, cost, and size of RF front ends. Thus, miniaturized and integrated microwave devices are in high demand. In addition, frequency hopping, which helps overcome the limitations of poor anti-interference and weak security of fixed-frequency communication systems, requires the transceivers to switch to different operating frequencies and modes according to the spectrum environment. At the same time, multifunctional reconfigurable systems can free up scarce spectrum resources by switching to different operational modes depending on the spectrum environment. To leverage these advantages and to meet the aforementioned challenges and requirements of applications, it is important, both from a theoretical and an engineering standpoint, to study the integrated design of multifunctional reconfigurable microwave devices.
In the past few years, reconfigurable microwave devices have developed from single-function reconfigurable to multifunctional fusion reconfigurable. As an important power-dividing/combining device, the coupler is widely used in the design of phase shifters, antenna feed networks, balanced amplifiers, attenuators, mixers, and other devices and circuits. In a balanced power amplifier, the coupler can improve the matching characteristics of the input port and provide a stable power output that does not change with load impedance. In an array antenna, the coupler controls the direction and shape of the beam. In a circulator, the coupler can suppress signal leakage from the transmitter to the receiver and solve the problem of self-interference. Compared with traditional couplers with fixed functions (such as broadband, multiband, and miniaturized couplers) [1], [2], [3], [4], [5], [6], [7], [8], reconfigurable couplers [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30], [31], [32], [33], [34], [35], [36], [37], [38], [39], [40], [41], [42], [43], [44], [45], [46], [47], [48], [49], [50], [55] can switch the operating frequency and mode in real time according to the requirements of dynamic changes in the spectrum. And they can also ease the congestion of radio spectrum resources and other issues. Reconfigurable couplers can be divided into four categories according to their reconfigurable functions: frequency-reconfigurable couplers (FRCs) [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], power-dividing ratio (PDR)-reconfigurable couplers [20], [21], [22], [23], [24], [25], [26], [27], [28], frequency- and PDR-reconfigurable couplers [29], [30], [31], [32], [33], [34], [35], [36], and phase-reconfigurable couplers (PRCs) [37], [38], [39], [40]. However, the aforementioned reconfigurable couplers [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30], [31], [32], [33], [34], [35], [36], [37], [38], [39], [40] are single-function reconfigurable couplers. Compared with the single-function reconfigurable couplers in [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30], [31], [32], [33], [34], [35], [36], [37], [38], [39], and [40], a multifunctional fusion reconfigurable coupler [41], [42], [43], [44], [45], [46], [47], [48], [49], [50], [55] can integrate multiple functions into a single device or circuit, thereby reducing the circuit size, circuit cost, and loss caused by the cascading of different functional devices. At this stage of research, multifunctional fusion reconfigurable couplers mainly include frequency-reconfigurable filtering couplers (FRFCs) [41], [42], [43], [44], [45], [46], [47] and PDR-reconfigurable balanced couplers [48], [49], [50], [55].
This article outlines the recently developed single-function and multifunctional fusion reconfigurable couplers, and then further discusses the progress of the main research directions of these reconfigurable couplers. These couplers may be extended to reconfigurable circuits and system applications in the future.
The center frequency of the FRC is tunable within a certain range while keeping the PDR unchanged. It is often used to design balanced mixers for reconfigurable base stations and reconfigurable reflection phase shifters. There are three main design methods for FRCs. The first method is to replace the ${\lambda}{/}{4}$ transmission line in a traditional coupler with a tunable unit. By adjusting the tunable elements in the tunable unit, the phase of the tunable unit can remain at 90° to realize the FRC. Figure 1(a) shows a representative circuit diagram of this kind of coupler. It can be seen that the tunable unit is realized by using a ${\pi} {-} {\text{type}}$ tunable capacitor-loaded transmission line composed of varactors. The measured center-frequency tuning range is 1.8 ∼ 2.3 GHz (the relative bandwidth is 24%). Similarly, the couplers in [9], [11], and [12] are also designed using this method. When the tunable element is adjusted to change the phase of the tunable unit, the equivalent characteristic impedance of the tunable unit also changes at the same time. However, the isolation and matching characteristics of the coupler will then deteriorate. Therefore, the frequency-tuning range of an FRC based on a tunable unit is limited. The second design method is to design an FRC based on a special circuit structure [13], [14], [15]. When the center frequency is adjusted, the coupler can achieve simultaneous, ideal matching and isolation characteristics. The first 0-dB FRC [13] was realized using two fixed-value capacitors and a varactor to replace the three vertical transmission lines in a traditional two-section branch-line coupler. Its schematic diagram is shown in Figure 1(b). The coupler can be tuned to a frequency-tuning range from 1.2 to 2.4 GHz (67%).
Figure 1. FRCs. (a) An FRC [10] and (b) a 0-dB FRC [13].
The final approach is to design a frequency-reconfigurable rat-race coupler [16], [17] based on the port impedance matching method. The design method for the frequency-reconfigurable rat-race coupler proposed in [16] is briefly summarized as follows. In step 1, the traditional rat-race coupler is represented by a generalized four-port network [as shown in Figure 2(a)]. According to the port matching and isolation conditions of the four-port network, the port-equivalent impedance ${Zeq}_{\text{in}}$ is derived. The port impedance ${Z}_{\text{in}}$ is the impedance looking toward the port, and it satisfies the condition of ${Zeq}_{\text{in}} = {Z}_{\text{in}}^{\ast}{.}$ In step 2, a frequency-reconfigurable matching network is designed to transform the ${Zeq}_{\text{in}}$ to ${Z}_{0}$ across the entire frequency range [(Figure 2(b)]. In step 3, the MN is connected to each port of the four-port network to realize the design of the frequency-reconfigurable rat-race coupler [Figure 2(c)]. Based on this method, a frequency-reconfigurable rat-race coupler was designed [17], which is shown in Figure 3(a). It can be seen that the four-port network consists of two transmission lines ${(}{Z}_{1},{\theta}_{1}{),}$ another transmission line ${(}{Z}_{2},{\theta}_{1}{),}$ and an adjustable transmission line ${(}{Z}_{2},{\theta}_{1} + {180}{).}$ The shunt-adjustable capacitor ${C}_{3}$ is used to realize the MN. In addition, as presented in Figure 3(b), the adjustable transmission line ${Z}_{2}$ is realized by the reconfigurable transmission line, which consists of a tunable capacitor ${C}_{1},$ two tunable capacitors ${C}_{2},$ and two shunt stubs ${Z}_{3}{.}$ Figure 3(c) depicts the frequency of the simulated and measured S-parameters tuning range (1–2.96 GHz). The relative bandwidth is up to 99%.
Figure 2. (a) A four-port network with a port impedance of ${Z}_{\text{in}}{.}$ (b) A port-equivalent impedance with a matching network (MN). (c) A four-port network with an MN.
Figure 3. A frequency-reconfigurable rat-race coupler [17]. (a) A circuit. (b) A tunable transmission line with a 180° phase shift and equivalent reconfigurable transmission line. (c) A simulated and measured $\left|{{S}_{11}}\right|,\,\left|{{S}_{21}}\right|,$ and $\left|{{S}_{41}}\right|{.}$ MN: matching network; EM: electromagnetic.
In addition, recently, dual-band couplers with independently tunable operating frequencies [18], [19] were reported. Figure 4 shows the schematic of a dual-band coupler with independently tunable operating frequencies, which is realized using a coupled line loaded with a varactor to replace the open branch line of a traditional dual-band quadrature coupler [18]. The measured results show that when the upper operating frequency is fixed at 3.4 GHz, the measured lower operating frequency tuning range is from 1.3 to 1.6 GHz (20.7%). And when the lower operating frequency is fixed at 1.55 GHz, the measured upper operating frequency tuning range is from 2.9 to 3.4 GHz (15.8%). At present, there are only a few published papers on dual-band FRCs. In addition, how to effectively broaden the frequency adjustment range is an urgent problem that has yet to be solved. A comparison of measured performance of published FRCs is summarized in Table 1.
Figure 4. A dual-band FRC [18].
Table 1. A performance comparison of several reported FRCs.
In a PDR-reconfigurable coupler the center frequency is fixed, and its PDR is tunable within a certain range. Its application scenarios include reconfigurable beamforming networks of antenna arrays. There are three main design methods for a PDR-reconfigurable coupler. In the first type, the coupler is designed by a tunable unit to replace the ${\lambda}{/}{4}$ transmission line in the traditional coupler. When the PDR changes, the characteristic impedance of the tunable unit is changed by adjusting the tunable element to realize a PDR-reconfigurable coupler. The tunable unit in [20] is realized by a T-type low-pass tunable structure composed of varactors and microstrip line inductors. The measured PDR can be continuously adjusted from −4.2 to −10 dB at 3.5 GHz. However, when the tunable element is used to change the equivalent characteristic impedance of the tunable unit, the equivalent phase of the tunable unit also changes, and then the isolation and matching characteristics of the coupler will be further deteriorated. Therefore, the PDR of the tuning range of a coupler designed using this method is limited. The second method is to switch the transmission line structure, which uses the switch network to select different feed paths to change the PDR [21], [22]. For example, by controlling the p-i-n diode, the PDR of the quasi-lumped coupler can be tuned between four working modes [22]. The disadvantage of this method is that the tuning state of the PDR is limited.
The third design method is to construct a PDR-reconfigurable coupler based on a special circuit structure [23], [24], [25], [26], [27], [28]. When the PDR is tuned, the coupler can achieve good matching and isolation at the same time. The tunable coupler is designed by loading three fixed capacitors at the end and middle of two parallel transmission lines and grounding two varactor diodes in the middle of the transmission line [24], as shown in Figure 5(a). The tuning range of the PDR at the center frequency is from −35 to ∼ 16.2 dB. To broaden the tuning range of the PDR and improve the phase imbalance and insertion loss, an improved reconfigurable coupler with a negative-impedance converter was proposed, which is based on the quadrature coupler in Figure 5(a). The negative-impedance converter is composed of a common-source field-effect transistor with an RLC series feedback structure. This transistor can exhibit negative resistance and capacitance to compensate for the additional phase difference and insertion loss caused by the varactors. Using a negative-impedance converter, the insertion loss is improved by 1 dB, and phase imbalance is improved from 10 to 1°. In Figure 5(b), a PDR-tunable coupler is realized by cascading the phase shifter between branch-line couplers [28]. The PDR tuning range of the coupler is from −25 to ∼ 23.7 dB. However, the size of the coupler may become larger. Table 2 compares the performance of the several reported couplers with reconfigurable PDR.
Figure 5. PDR-reconfigurable couplers in (a) [24] and (b) [28].
Table 2. A performance comparison of several reported PDR-reconfigurable couplers.
With both frequency- and PDR-reconfigurable couplers, the center frequency and PDR of the coupler can be tuned within a certain range. In other words, in the frequency-reconfigurable mode, the PDR of this kind of coupler is fixed and the center frequency can be tuned to a set range. And in the reconfigurable mode of a PDR, the center frequency is fixed and the PDR can be tuned. The design methods are summarized as follows. The first method is to design the reconfigurable coupler based on a tunable transmission line or unit [29], [30], [31]. In the frequency-reconfigurable mode, by adjusting the tunable element, the equivalent characteristic impedance of the tunable transmission line or unit remains unchanged. And the phase always remains at 90° when it changes as the center frequency changes. In the PDR-reconfigurable mode, by adjusting the tunable element, the phase of the tunable transmission line or unit remains unchanged, and its equivalent characteristic impedance changes. A tunable admittance-inverter network composed of a varactor and an inductor was used to replace the ${\lambda}{/}{4}$ transmission line to realize the design of a frequency- and PDR-reconfigurable coupler [31], as shown in Figure 6. In the PDR-reconfigurable mode, the PDR at 1.2 GHz can be continuously adjusted from 0 to 3 dB. In the frequency-reconfigurable mode, the 3-dB coupler can be tuned from 1 to 1.6 GHz (46%). However, this coupler requires 12 tunable elements, and the tuning ranges of the frequency and the PDR are not wide.
Figure 6. The reconfigurable coupler in [31].
In the second type, the couplers are designed as special circuit structures to achieve continuous tuning of the frequency and PDR [32], [33], [34], [35], [36]. The circuit of a frequency- and PDR-reconfigurable quadrature coupler based on lumped elements is presented in Figure 7(a). It consists of 12 fixed inductors ${L}_{1},\,{L}_{2},$ and ${L}_{3},$ and six varactors ${C}_{1},\,{C}_{2},$ and ${C}_{3}{.}$ Among them, two shunt inductors ${L}_{1}$ and a series varactor ${C}_{1},$ and two series inductors ${L}_{2}$ and a shunt varactor ${C}_{2}$ form the tunable low- and high-pass unit, respectively. Four tunable units are cascaded together by inductor ${L}_{3}$ and varactor ${C}_{3}{.}$ Figure 7(b) and (c) shows a picture of the fabricated coupler and the simulated and measured results in frequency-reconfigurable mode. When the frequency is tuned from 1.8 to 4.36 GHz, the fractional bandwidth (FBW) of the 0.5-dB amplitude balance $({FBW}_{{0.5}\,{\text{dB}}})$ and 15-dB return loss and isolation $({FBW}_{{15}\,{\text{dB}}})$ are from 7.3 to ∼ 14% and from 5.2 to ∼ 13%, respectively. As shown in Figure 7(d), in PDR-reconfigurable mode, the measured PDR tuning range is from −16 to ∼ 5 dB (at 3 GHz). Compared with the prior art, this coupler not only has a simpler tuning mechanism (only six varactors) but has better insertion loss flatness characteristics during the process of tuning the frequency. Table 3 compares the measured performance of recently published frequency- and PDR-reconfigurable couplers.
Figure 7. A frequency- and PDR-reconfigurable coupler [35]. (a) A circuit. (b) An image of the fabricated coupler. (c) The simulated and measured results in frequency-reconfigurable mode. (d) The simulated and measured results in PDR-reconfigurable mode. FBW: fractional bandwidth.
Table 3. A performance comparison of several reported frequency- and PDR-reconfigurable couplers.
A traditional coupler can provide a standard phase difference of only 90° or 0/180°. To meet the multistandard requirements of wireless communication, several PRCs [37], [38], [39], [40] have been reported recently. The output phase difference of a PRC is continuously tunable within a certain range, while keeping the frequency and PDR constant. The radiation beam of the beamforming network based on the PRC can be continuously scanned within a certain range. Moreover, the PRC can be used to design the feed network with special functional requirements. The configuration of phase-reconfigurable couplers is shown in Figure 8 [40]. It can be seen that this coupler is realized by cascading the phase-tunable unit between ${\lambda}{/}{8} {-} {\text{coupled}}$ lines. The phase-tuning range of the coupler is from 0 to ∼ 180°. The more phase-tunable units that are cascaded between the coupled lines, the larger the phase-tuning range of the coupler; however, the size of the coupler will become larger and larger. Therefore, it is still necessary to further reduce the size of the coupler on the premise that the phase-tuning range remains unchanged.
Figure 8. A PRC [40].
Figure 9(a) shows the cascaded design of an FRFC. To reduce the mismatch loss and circuit size caused by the cascaded filter and coupler, in [42], the authors propose a reconfigurable filtering coupler with an integrated design, as shown in Figure 9(b). The design of the reconfigurable filtering beamforming network is usually dictated by the FRFC. And the design of an FRFC is usually based on a frequency-reconfigurable resonator to realize the basic unit of a reconfigurable filtering ${\lambda}{/}{4}$ transmission line. When the center frequency changes, by adjusting the tunable element loaded on the resonator, the phase of the basic unit remains unchanged at 90° to realize the frequency-reconfiguration filtering coupler [41], [42], [43], [44]. The first frequency-reconfigurable filtering power divider [41] was realized using a reconfigurable filtering unit based on a reconfigurable resonator to replace the ${\lambda}{/}{4}$ transmission line in a traditional power divider. The center frequency can be continuously adjusted from 0.62 to 0.85 GHz (31%), and the maximum insertion loss is 3 + 2.4 dB. Subsequently, the first frequency-reconfigurable filtering rat-race coupler and quadrature coupler have also been reported [42]. Their working principle is to realize FRFCs using a reconfigurable filtering transmission line with a 90 or −90° phase shift instead of the ${\lambda}{/}{4}$ transmission line in the traditional coupler. The configuration of the frequency-reconfigurable filtering rat-race coupler is shown in Figure 10. Its center-frequency tuning range is from 0.7 to ∼ 1.84 GHz (90%) with an insertion loss of 3 + 2.9 ∼ 3 + 5.3 dB. To reduce the loss of the coupler, a substrate integrated waveguide (SIW) resonator can be used to design the FRFC [45], [46], [47]. When changing the center frequency, the resonant frequency is changed by tuning the gap between the conductor film and the copper pillar using a piezoelectric actuator, thus realizing the FRFC. The coupler in [46] is designed using four SIW evanescent-mode cavity resonators and loading varactors between adjacent resonators. The measured center-frequency tuning range is from 2.31 to ∼ 2.71 GHz (16%). The measured insertion loss is 2.84 ∼ 3.1 dB across the whole frequency tuning range. At present, the additional insertion loss of the FRFC across the entire tuning range is relatively large (>2.3 dB). Thus, effectively reducing the insertion loss is an urgent problem to be solved. A comparison of state-of-the-art reconfigurable filtering couplers is given in Table 4.
Figure 9. Reconfigurable filtering couplers [42]. (a) A cascade design and (b) an integration design.
Figure 10. A reconfigurable filtering rat-race coupler [42].
Table 4. A performance comparison of several reported FRFCs.
Table 5. A performance comparison of several reported balanced couplers.
For the design of increasingly complex microwave integrated circuits, signal crosstalk and common-mode (CM) noise are two important issues that need to be considered. Compared to single-ended circuits, balanced circuits can provide higher resistance to environmental noise and broadband CM rejection. Therefore, the research on passive balanced circuits has always been an academic hot spot. Figure 11(a) depicts a reconfigurable balanced coupler with a cascade design. To reduce the mismatch loss and circuit size caused by the cascade of a balun and a tunable coupler, a tunable balanced coupler with an integrated design is proposed in [50] and shown in Figure 11(b). For the eight-port balanced network [Figure 11(b)], single ports 1 and 4, 2 and 3, 5 and 6, and 7 and 8 constitute balanced ports A, B, C, and D, respectively. The mixed-mode scattering matrix ${(}{S}_{\text{mm}}{)}$ is defined as \begin{align*}{S}_{\text{mm}} = \left[{\begin{array}{cc}{{S}^{dd}}&{{S}^{dc}}\\{{S}^{cd}}&{{S}^{cc}}\end{array}}\right] = \left[{\begin{array}{cccccccc}{{S}_{\text{AA}}^{dd}}&{{S}_{\text{AB}}^{dd}}&{{S}_{\text{AC}}^{dd}}&{{S}_{\text{AD}}^{dd}}&{{S}_{\text{AA}}^{dc}}&{{S}_{\text{AB}}^{dc}}&{{S}_{\text{AC}}^{dc}}&{{S}_{\text{AD}}^{dc}}\\{{S}_{\text{BA}}^{dd}}&{{S}_{\text{BB}}^{dd}}&{{S}_{\text{BC}}^{dd}}&{{S}_{\text{BD}}^{dd}}&{{S}_{\text{BA}}^{dc}}&{{S}_{\text{BB}}^{dc}}&{{S}_{\text{BC}}^{dc}}&{{S}_{\text{BD}}^{dc}}\\{{S}_{\text{CA}}^{dd}}&{{S}_{\text{CB}}^{dd}}&{{S}_{\text{CC}}^{dd}}&{{S}_{\text{CD}}^{dd}}&{{S}_{\text{CA}}^{dc}}&{{S}_{\text{CB}}^{dc}}&{{S}_{\text{CC}}^{dc}}&{{S}_{\text{CD}}^{dc}}\\{{S}_{\text{DA}}^{dd}}&{{S}_{\text{DB}}^{dd}}&{{S}_{\text{DC}}^{dd}}&{{S}_{\text{DD}}^{dd}}&{{S}_{\text{DA}}^{dc}}&{{S}_{\text{DB}}^{dc}}&{{S}_{\text{DC}}^{dc}}&{{S}_{\text{DD}}^{dc}}\\{{S}_{\text{AA}}^{cd}}&{{S}_{\text{AB}}^{cd}}&{{S}_{\text{AC}}^{cd}}&{{S}_{\text{AD}}^{cd}}&{{S}_{\text{AA}}^{cc}}&{{S}_{\text{AB}}^{cc}}&{{S}_{\text{AC}}^{cc}}&{{S}_{\text{AD}}^{cc}}\\{{S}_{\text{BA}}^{cd}}&{{S}_{\text{BB}}^{cd}}&{{S}_{\text{BC}}^{cd}}&{{S}_{\text{BD}}^{cd}}&{{S}_{\text{BA}}^{cc}}&{{S}_{\text{BB}}^{cc}}&{{S}_{\text{BC}}^{cc}}&{{S}_{\text{BD}}^{cc}}\\{{S}_{\text{CA}}^{cd}}&{{S}_{\text{CB}}^{cd}}&{{S}_{\text{CC}}^{cd}}&{{S}_{\text{CD}}^{cd}}&{{S}_{\text{CA}}^{cc}}&{{S}_{\text{CB}}^{cc}}&{{S}_{\text{CC}}^{cc}}&{{S}_{\text{CD}}^{cc}}\\{{S}_{\text{DA}}^{cd}}&{{S}_{\text{DB}}^{cd}}&{{S}_{\text{DC}}^{cd}}&{{S}_{\text{DD}}^{cd}}&{{S}_{\text{DA}}^{cc}}&{{S}_{\text{DB}}^{cc}}&{{S}_{\text{DC}}^{cc}}&{{S}_{\text{DD}}^{cc}}\end{array}}\right] \tag{1} \end{align*}
Figure 11. Reconfigurable balanced couplers [50]. (a) A cascade design and (b) an integration design.
where ${S}_{\text{mm}}$ is the symmetric matrix. The mixed-mode scattering matrix consists of ${S}^{dd},\,{S}^{cc},\,{S}^{dc},$ and ${S}^{cd}.\,{S}^{dd}$ represents the differential-mode (DM) S-parameters. ${S}^{cc}$ represents the CM S-parameters. ${S}^{dc}$ and ${S}^{cd}$ represent the conversion from CM to DM waves and from DM to CM waves, respectively. To achieve a tunable balanced coupler, ${S}^{dd}$ should meet matching and isolation conditions (2a), ${S}^{dc}$ and ${S}^{cd}$ should be suppressed (2b), and ${S}^{cc}$ should meet the condition of total reflection (2c). ${\varphi}_{i}{(}{i} = {1},{2},{3},{4},{5},{6}{)}$ is the phase constant of the S-parameters. \begin{align*}{S}^{dd} & = \left[{\begin{array}{cccc}{0}&{{ue}^{j{\varphi}_{1}}}&{\sqrt{{1}{-}{u}^{2}}{e}^{j{\varphi}_{2}}}&{0}\\{{ue}^{j{\varphi}_{1}}}&{0}&{0}&{\sqrt{{1}{-}{u}^{2}}{e}^{j{\varphi}_{2}}}\\{\sqrt{{1}{-}{u}^{2}}{e}^{j{\varphi}_{2}}}&{0}&{0}&{{ue}^{j{\varphi}_{1}}}\\{0}&{\sqrt{{1}{-}{u}^{2}}{e}^{j{\varphi}_{2}}}&{{ue}^{j{\varphi}_{1}}}&{0}\end{array}}\right] \tag{2a} \\ {S}^{dc} & = {S}^{cd} = {\left[{0}\right]}_{{4}\times{4}} \tag{2b} \\ {S}^{cc} & = \left[{\begin{array}{cccc}{{e}^{j{\varphi}_{3}}}&{0}&{0}&{0}\\{0}&{{e}^{j{\varphi}_{4}}}&{0}&{0}\\{0}&{0}&{{e}^{j{\varphi}_{5}}}&{0}\\{0}&{0}&{0}&{{e}^{j{\varphi}_{6}}}\end{array}}\right] \tag{2c} \end{align*}
The circuit diagram of the first PDR-reconfigurable balanced quadrature coupler is presented in Figure 12. It is designed by loading two types of fixed capacitors $({C}_{0}$ and ${C}_{1})$ at the end and the middle of the four parallel transmission lines. The shunt-grounded varactors $({C}_{d})$ are connected in the middle of the transmission line. The adjustment range of this PDR is from −11.3 to ∼ 10.2 dB at 2 GHz. To reduce phase and amplitude imbalance, a negative-impedance circuit is introduced in the reconfigurable balanced quadrature coupler to compensate for the loss of the varactor and the circuit. Through the use of a negative-impedance circuit, the 3-dB coupling-state insertion loss is improved by 1.2 dB, and the measured phase imbalance is improved from 25 to >2° for all states.
Figure 12. A reconfigurable balanced quadrature coupler [50].
The aforementioned balanced coupler can realize the transmission of DM signals and suppress CM noise, and there is no conversion between DM signals and CM noise. The CM noise is completely reflected at the input port and cannot be transmitted to the output port, but it still exists in the system. Thus, the reflected CM noise can still cause electromagnetic interference [51] and affect overall performance of the system. Therefore, in practical applications, balanced circuits with CM noise-absorption capabilities (such as CM noise-absorptive balanced filters and power dividers [52], [53], [54]) are required. In 2020, the first article on an absorptive PDR-tunable balanced rat-race coupler was published [55]. This article proposed the design method of an absorptive reconfigurable rat-race coupler based on port-equivalent impedance. First, the traditional nonabsorptive balanced rat-race coupler is generally represented by the nonabsorptive eight-port balanced network, and its port impedance is ${Z}_{port}$ [see Figure 13(a)]. The network consists of two lossless reciprocal networks $\left[{{{{Y}_{11}}\atop{{Y}_{12}}}{{{Y}_{12}}\atop{{Y}_{11}}}}\right]$, two inverted lossless reciprocal networks $\left[{{{{Y}_{22}}\atop{{Y}_{23}}}{{{Y}_{23}}\atop{{Y}_{23}}}}\right]$ and $\left[{{{{Y}_{22}}\atop{{-}{Y}_{23}}}{{{Y}_{23}}\atop{{Y}_{22}}}}\right]$, and four transmission lines ${Z}_{3}{.}$ Because this network is a single-symmetric structure, it can be simplified and analyzed using the even-odd-mode method. After derivation, the DM isolation condition of an eight-port balanced network is always satisfied (i.e., ${S}_{\text{AD}}^{dd} = {S}_{\text{BC}}^{dd} = {0}{)}{.}$ The DM PDR is determined by the admittance ratio of the two-port network (i.e., ${\left|{{S}_{\text{AB}}^{dd}}\right|}^{2}{/}{\left|{{S}_{\text{AC}}^{dd}}\right|}^{2} = {\left|{{S}_{\text{AB}}^{dd}}\right|}^{2}{/}{\left|{{S}_{\text{BD}}^{dd}}\right|}^{2} = {Y}_{12}^{2}{/}{Y}_{23}^{2}$). According to the definition of a balanced port, the DM and CM port impedances $({Z}_{\text{p}\text{o}\text{r}\text{t}\_\text{b}\text{a}\text{l}\text{a}\text{n}\text{c}\text{e}}^{dd}$ and ${Z}_{\text{p}\text{o}\text{r}\text{t}\_\text{b}\text{a}\text{l}\text{a}\text{n}\text{c}\text{e}}^{cc})$ seeing into the balanced port with ${Z}_{\text{port}}$ can be calculated. Second, according to the DM matching (2a) and CM reflection conditions (2c), the DM and CM port-equivalent impedances $({Z}_{\text{e}\text{q}\_\text{b}\text{a}\text{l}\text{a}\text{n}\text{c}\text{e}}^{dd}$ and ${Z}_{\text{e}\text{q}\_\text{b}\text{a}\text{l}\text{a}\text{n}\text{c}\text{e}}^{cc})$ of the eight-port balanced network are obtained. The equivalent simplified diagram of the nonabsorptive eight-port balanced network is shown in Figure 13(b) and can be represented by the inner network with ${Z}_{\text{e}\text{q}\_\text{b}\text{a}\text{l}\text{a}\text{n}\text{c}\text{e}}^{\text{dd},\text{cc}}{.}$ With
Figure 13. (a) A nonabsorptive eight-port balanced network. The equivalent diagram of (b) and (c) an absorptive eight-port balanced network. (d) The DM I and (e) a CM-excitation circuit [55].
these two steps, a nonabsorptive balanced rat-race coupler with a reconfigurable PDR can be designed. Third, the absorptive network [Figure 13(c)] is designed based on ${Z}_{\text{e}\text{q}\_\text{b}\text{a}\text{l}\text{a}\text{n}\text{c}\text{e}}^{dd}$ and ${Z}_{\text{e}\text{q}\_\text{b}\text{a}\text{l}\text{a}\text{n}\text{c}\text{e}}^{cc}{.}$ That is to say, under DM excitation, the DM-excitation circuit of the absorptive network [Figure 13(d)] matches the single-port DM-equivalent impedance ${Z}_{\text{e}\text{q}\_\text{s}\text{i}\text{n}\text{g}\text{l}\text{e}}^{dd}\,{(} = {0}{.}{5}{Z}_{\text{e}\text{q}\_\text{b}\text{a}\text{l}\text{a}\text{n}\text{c}\text{e}}^{dd}{)}$ to ${Z}_{0}$ to realize DM signal transmission. Under CM excitation, the CM-excitation circuit of the absorptive network [Figure 13(e)] matches the single-port CM-equivalent impedance ${Z}_{\text{e}\text{q}\_\text{s}\text{i}\text{n}\text{g}\text{l}\text{e}}^{cc}\,{(} = {2}{Z}_{\text{e}\text{q}\_\text{b}\text{a}\text{l}\text{a}\text{n}\text{c}\text{e}}^{cc}{)}$ to ${Z}_{0}{.}$ The CM noise is completely absorbed by the absorptive network. Finally, the designed absorptive network is connected to the balance port of the nonabsorptive reconfigurable balanced rat-race coupler, which is the final step in the design of an absorptive PDR reconfigurable balanced rat-race coupler.
The designed nonabsorptive PDR reconfigurable balanced rat-race coupler [Figure 14(a)] consists of four tunable transmission lines ${Z}_{1}$ and ${Z}_{2}$ with the same phase ${\theta}_{1}{(} = {90}$ at center frequency ${f}_{0}),$ and five transmission lines ${Z}_{3}$ and ${Z}_{4}$ with the same phase ${\theta}_{3}{(} = {180}$ at ${f}_{0}{)}{.}$ During adjustment of the PDR, the equivalent phase of the tunable transmission lines ${Z}_{1}$ and ${Z}_{2}$ remains unchanged, and the characteristic impedance changes. Figure 14(b) shows the final circuit diagram of the nonabsorptive and absorptive reconfigurable balanced rat-race coupler without and with an absorptive network (blue marker), respectively. It can be seen that ${Z}_{1}$ and ${Z}_{2}$ are realized by a tunable unit. The tunable unit consists of two inductors ${L}_{1},$ two inductors ${L}_{2},$ a varactor ${C}_{1}\,({C}_{3}),$ and a varactor ${C}_{2}\,{(}{C}_{4}{)}{.}$ Moreover, the absorptive network is composed of two ${\lambda}{/}{4}$ transmission lines ${Z}_{5},$ two ${\lambda}{/}{4} {-} {\text{coupled}}$ lines ${(}{Z}_{e},{Z}_{o}{),}$ and a grounding resistor $({R}_{1})$ loaded between the coupled lines. A photo of the fabricated absorptive tunable balanced rat-race coupler is shown in Figure 14(c).
Figure 14. A diagram of (a) nonabsorptive and (b) absorptive reconfigurable rat-race couplers. (c) A photo of the fabricated absorptive reconfigurable balanced coupler [55].
Figure 15(a) depicts the measured FBW of the nonabsorptive reconfigurable coupler at the DM with a 0.5-dB amplitude imbalance $({FBW}_{{0.5}\,{\text{dB}}}),$ 15-dB return loss and isolation $({FBW}_{{15}\,{\text{dB}}}),$ and ±5° phase difference ${(}{FBW}_{\pm{5}}{)}{.}$ In the process of PDR adjustment, the $({FBW}_{{0.5}\,{\text{dB}}}),\,({FBW}_{{15}\,{\text{dB}}}),$ and ${FBW}_{\pm{5}}$ are 6 ∼ 14.5%, 19 ∼ 21%, and 8 ∼ 15.2%, respectively. Figure 15(b) shows the measured and simulated CM S-parameters of the nonabsorptive reconfigurable coupler at equal power output. At the center frequency, the CM return loss is close to 0 dB. The measured 15-dB CM insertion loss and isolation bandwidth is up to 1,220 MHz.
Figure 15. Measured results of the nonabsorptive coupler. (a) A DM ${FBW}_{{0.5}\,{\text{dB}}},\,{FBW}_{{15}\,{\text{dB}}},$ and ${FBW}_{{\pm}{5}}{.}$ (b) CM S-parameters with equal power output [55].
Figure 16(a) illustrates the measured ${FBW}_{{0.5}\,{\text{dB}}},\,{FBW}_{{15}\,{\text{dB}}},$ and ${FBW}_{\pm{5}}$ of the absorptive reconfigurable coupler at the DM. During PDR adjustment, the ${FBW}_{{0.5}\,{\text{dB}}},\,{FBW}_{{15}\,{\text{dB}}},$ and ${FBW}_{\pm{5}}$ are 7 ∼ 15.6%, 24 ∼ 33%, and 6 ∼ 23%, respectively. Figure 16(b) shows the measured and simulated CM S-parameters of the absorptive reconfigurable coupler at equal power output. It can be seen that CM matching is achieved, and the CM transmission coefficient is better than −20 dB at the center frequency. The measured 15-dB CM return loss, insertion loss, and isolation bandwidth are up to 1,240 MHz. As the PDR is determined by the characteristic impedance ratio of the transmission line, the proposed reconfigurable balanced rat-race couplers have good amplitude-balance performance.
Figure 16. Measured results of the absorptive coupler. (a) A DM ${FBW}_{{0.5}\,{\text{dB}}},\,{FBW}_{{15}\,{\text{dB}}},$ and ${FBW}_{{\pm}{5}}{.}$ (b) CM S-parameters with equal power output [55].
This article summarized the recently developed single-function reconfigurable couplers (frequency-, PDR-, frequency- and PDR-, and phase- reconfigurable couplers) and multifunctional fusion reconfigurable couplers (i.e., FRFCs and PDR-reconfigurable balanced couplers). The measured performance comparisons with the published reconfigurable couplers are listed in Tables 1–5. Through comparison, it can be seen that there are still many problems to be solved in reconfigurable couplers. First, the design of reconfigurable couplers has developed from single-function reconfigurable to multifunction fusion reconfigurable, and the tuning range needs to be wider. In addition, the reconfigurable implementation of the coupler requires simplification, from multiple types of tuning elements to one type, and the number of tuning elements should be reduced. Finally, there is a need to comprehensively improve the performance of reconfigurable couplers, such as extending the amplitude-balance bandwidth, reducing losses, and achieving CM noise rejection or absorption.
For most reconfigurable couplers, the tunable capacitor is implemented by the voltage-controlled varactor. However, varactors usually have low Q values and large parasitic resistances (up to 1 Ω), which increases the loss of the coupler. And the amplitude-and phase-balance characteristics of the coupler are also affected by parasitic resistors. In the future, low-loss microelectromechanical systems capacitors can be used to replace varactors to reduce circuit loss. In addition, the balanced couplers mentioned in this article can be realized with a single-layer microstrip structure. To further reduce the circuit size of balanced couplers, in the future, they should be realized using integrated circuit technology, which is conducive to integration with other balanced front-end devices and realizes a practical high-density balanced circuit system. Regardless, in the near future, ever more high-performance, multifunctional reconfigurable components and circuit communication systems will be developed and commercialized.
This work has been supported by the National Natural Science Foundation of China (62201324). The authors thank the editors and reviewers of this article for their valuable comments and suggestions, which greatly improved its overall quality.
[1] Y. Liu, S. Jiang, S. Zhu, Y. Tian, and Y. Wu, “Large frequency-ratio dual-band and broad dual-band parallel-line couplers,” IEEE Trans. Compon. Packag. Manuf. Technol., vol. 8, no. 1, pp. 121–131, Jan. 2018, doi: 10.1109/TCPMT.2017.2761991.
[2] L. Jiao et al., “Design methodology for six-port equal/unequal quadrature and rat-race couplers with balanced and unbalanced ports terminated by arbitrary resistances,” IEEE Trans. Microw. Theory Techn., vol. 66, no. 3, pp. 1249–1262, Mar. 2018, doi: 10.1109/TMTT.2017.2778108.
[3] Y. Zhang, Y. Wu, W. Wang, Y. Yang, and L. Ma, “Novel multifunctional dual-band coupled-line coupler with reuse of low-frequency trans-directional and high-frequency contra-directional functions,” IEEE Trans. Circuits Syst., II, Exp. Briefs, vol. 68, no. 6, pp. 1917–1921, Jun. 2021, doi: 10.1109/TCSII.2020.3042503.
[4] M. Liu and F. Lin, “Two-section broadband couplers with wide-range phase differences and power-dividing ratios,” IEEE Microw. Wireless Compon. Lett., vol. 31, no. 2, pp. 117–120, Feb. 2021, doi: 10.1109/LMWC.2020.3041256.
[5] X. Chen, Y. Wang, and Q. Zhang, “Ring-shaped D-band E-plane filtering coupler,” IEEE Microw. Wireless Compon. Lett., vol. 31, no. 8, pp. 953–956, Aug. 2021, doi: 10.1109/LMWC.2021.3082524.
[6] A. Lalbakhsh et al., “Design of a compact planar transmission line for miniaturized rat-race coupler with harmonics suppression,” IEEE Access, vol. 9, pp. 129,207–129,217, Sep. 2021, doi: 10.1109/ACCESS.2021.3112237.
[7] R. Ahamed et al., “A 200-250-GHz phase shifter utilizing a compact and wideband differential quadrature coupler,” IEEE Microw. Wireless Compon. Lett., vol. 32, no. 7, pp. 883–886, Jul. 2022, doi: 10.1109/LMWC.2022.3157790.
[8] S. Li et al., “An ultrawideband GaAs MMIC microstrip directional coupler with high directivity and very flat coupling,” IEEE Trans. Microw. Theory Techn., vol. 70, no. 4, pp. 2271–2279, Apr. 2022, doi: 10.1109/TMTT.2022.3146028.
[9] H.-H. Hsieh, Y.-T. Liao, and L.-H. Lu, “A compact quadrature hybrid MMIC using CMOS active inductors,” IEEE Trans. Microw. Theory Techn., vol. 55, no. 6, pp. 1098–1104, Jun. 2007, doi: 10.1109/TMTT.2007.896815.
[10] E. Lourandakis, M. Schmidt, S. Seitz, and R. Weigel, “Reduced size frequency agile microwave circuits using ferroelectric thin-film varactors,” IEEE Trans. Microw. Theory Techn., vol. 56, no. 12, pp. 3093–3099, Dec. 2008, doi: 10.1109/TMTT.2008.2006807.
[11] S. Y. Zheng, W. S. Chan, and K. F. Man, “Frequency-agile patch element using varactor loaded patterned ground plane,” IEEE Trans. Microw. Theory Techn., vol. 59, no. 3, pp. 619–626, Mar. 2011, doi: 10.1109/TMTT.2010.2098038.
[12] O. D. Gurbuz and G. M. Rebeiz, “A 1.6–2.3-GHz RF MEMS reconfigurable quadrature coupler and its application to a 360° reflective-type phase shifter,” IEEE Trans. Microw. Theory Techn., vol. 63, no. 2, pp. 414–421, Feb. 2015, doi: 10.1109/TMTT.2014.2379258.
[13] F. Lin, S. W. Wong, and Q.-X. Chu, “Compact design of planar continuously tunable crossover with two-section coupled lines,” IEEE Trans. Microw. Theory Techn., vol. 62, no. 3, pp. 408–415, Mar. 2014, doi: 10.1109/TMTT.2014.2300444.
[14] H. Liu, S. Fang, and Z. Wang, “A compact trans-directional coupler with wide frequency tuning range and superior performance,” IEEE Trans. Compon. Packag. Manuf. Technol., vol. 7, no. 10, pp. 1670–1677, Oct. 2017, doi: 10.1109/TCPMT.2017.2692269.
[15] Q. Cui and F. Lin, “Continuously tunable crossover based on HMSIW,” Electron. Lett., vol. 53, no. 24, pp. 1582–1583, Nov. 2017, doi: 10.1049/el.2017.3221.
[16] X. Tan and F. Lin, “A novel rat-race coupler with widely tunable frequency,” IEEE Trans. Microw. Theory Techn., vol. 67, no. 3, pp. 957–967, Mar. 2019, doi: 10.1109/TMTT.2018.2889453.
[17] X. Tan, J. Sun, and F. Lin, “A compact frequency-reconfigurable rat-race coupler,” IEEE Microw. Wireless Compon. Lett., vol. 30, no. 7, pp. 665–668, Jul. 2020, doi: 10.1109/LMWC.2020.2993369.
[18] Y. F. Pan, S. Y. Zheng, Y. M. Pan, Y. X. Li, and Y. L. Long, “Highly reconfigurable dual-band coupler with independently tunable operating frequencies,” IEEE Trans. Ind. Electron., vol. 66, no. 5, pp. 3615–3626, May 2019, doi: 10.1109/TIE.2018.2856196.
[19] Y. F. Pan, S. Y. Zheng, W. Hong, and W. S. Chan, “Highly reconfigurable dual-band coupler with independently tunable frequency and coupling coefficient at the lower band,” IEEE Trans. Ind. Electron., vol. 68, no. 3, pp. 2408–2416, Mar. 2021, doi: 10.1109/TIE.2020.2975459.
[20] S. Y. Zheng, W. S. Chan, and Y. S. Wong, “Reconfigurable RF quadrature patch hybrid coupler,” IEEE Trans. Ind. Electron., vol. 60, no. 8, pp. 3349–3359, Aug. 2013, doi: 10.1109/TIE.2012.2200224.
[21] S.-Y. Wang, D.-Y. Lai, and F.-C. Chen, “A low-profile switchable quadripolarization diversity aperture-coupled patch antenna,” IEEE Antennas Wireless Propag. Lett., vol. 8, pp. 522–524, Mar. 2009, doi: 10.1109/LAWP.2009.2017495.
[22] J.-S. Row and M.-J. Hou, “Design of polarization diversity patch antenna based on a compact reconfigurable feeding network,” IEEE Trans. Antennas Propag., vol. 62, no. 10, pp. 5349–5352, Oct. 2014, doi: 10.1109/TAP.2014.2341271.
[23] M. Zhou, J. Shao, B. Arigong, H. Ren, R. Zhou, and H. Zhang, “A varactor based 90° directional coupler with tunable coupling ratios and reconfigurable responses,” IEEE Trans. Microw. Theory Techn., vol. 62, no. 3, pp. 416–421, Mar. 2014, doi: 10.1109/TMTT.2014.2299522.
[24] F. Lin, “Compact design of planar quadrature coupler with improved phase responses and wide tunable coupling ratios,” IEEE Trans. Microw. Theory Techn., vol. 66, no. 3, pp. 1263–1272, Mar. 2018, doi: 10.1109/TMTT.2017.2783375.
[25] L. Jie, Q. Cui, and F. Lin, “Reconfigurable HMSIW quadrature coupler,” IEEE Microw. Wireless Compon. Lett., vol. 29, no. 10, pp. 648–651, Oct. 2019, doi: 10.1109/LMWC.2019.2937651.
[26] H. N. Chu and T.-G. Ma, “Tunable directional coupler with very wide tuning range of power division ratio,” IEEE Microw. Wireless Compon. Lett., vol. 29, no. 10, pp. 652–654, Oct. 2019, doi: 10.1109/LMWC.2019.2936317.
[27] Y. Yang, Z. J. Hou, X. Zhu, W. Che, and Q. Xue, “A millimeter-wave reconfigurable on-chip coupler with tunable power-dividing ratios in 0.13-µm BiCMOS technology,” IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 67, no. 5, pp. 1516–1526, May 2020, doi: 10.1109/TCSI.2020.2964574.
[28] H. N. Chu and T.-G. Ma, “A coupler with wide power division ratio tuning range and flexible coupling direction,” IEEE Microw. Wireless Compon. Lett., vol. 31, no. 2, pp. 121–124, Feb. 2021, doi: 10.1109/LMWC.2020.3047217.
[29] M. A. Y. Abdalla, K. Phang, and G. V. Eleftheriades, “A compact highly reconfigurable CMOS MMIC directional coupler,” IEEE Trans. Microw. Theory Techn., vol. 56, no. 2, pp. 305–319, Feb. 2008, doi: 10.1109/TMTT.2007.913360.
[30] J. Sun, C. Li, Y. Geng, and P. Wang, “A highly reconfigurable low-power CMOS directional coupler,” IEEE Trans. Microw. Theory Techn., vol. 60, no. 9, pp. 2815–2822, Sep. 2012, doi: 10.1109/TMTT.2012.2204275.
[31] R. Zhang, M. F. Hagag, L. Yang, R. Gomez-Garcia, and D. Peroulis, “A flexible quadrature coupler with reconfigurable frequency and coupling ratio in switchable coupling direction,” IEEE Trans. Microw. Theory Techn., vol. 67, no. 8, pp. 3391–3402, Aug. 2019, doi: 10.1109/TMTT.2019.2918528.
[32] P.-L. Chi and T.-C. Hsu, “Highly reconfigurable quadrature coupler with ideal impedance matching and port isolation,” IEEE Trans. Microw. Theory Techn., vol. 65, no. 8, pp. 2930–2941, Aug. 2017, doi: 10.1109/TMTT.2017.2668412.
[33] X. Shen, Y. Liu, S. Zhou, and Y. Wu, “Coupled-line directional coupler with tunable power division ratio and operating frequency,” IET Microw., Antennas Propag., vol. 11, no. 1, pp. 59–68, Jan. 2017, doi: 10.1049/iet-map.2016.0067.
[34] T. Zhang and W. Che, “A compact reconfigurable coupler with tunable coupling coefficients and frequencies,” IEEE Microw. Wireless Compon. Lett., vol. 27, no. 2, pp. 129–131, Feb. 2017, doi: 10.1109/LMWC.2016.2646904.
[35] X. Tan, J. Sun, and F. Lin, “Design of a simultaneous frequency- and power-dividing ratio-reconfigurable quadrature coupler with simple tuning approach,” IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 67, no. 12, pp. 5510–5519, Dec. 2020, doi: 10.1109/TCSI.2020.3010823.
[36] P.-L. Chi, S.-A. Shang, and T. Yang, “Novel compact coupler with tunable frequency, phase difference, and power-dividing ratio,” IEEE Microw. Wireless Compon. Lett., vol. 31, no. 10, pp. 1119–1122, Oct. 2021, doi: 10.1109/LMWC.2021.3105603.
[37] S. Y. Zheng, “Simultaneous phase- and frequency-tunable hybrid coupler,” IEEE Trans. Ind. Electron., vol. 64, no. 10, pp. 8088–8097, Oct. 2017, doi: 10.1109/TIE.2017.2698423.
[38] H. Zhu and A. M. Abbosh, “A compact tunable directional coupler with continuously tuned differential phase,” IEEE Microw. Wireless Compon. Lett., vol. 28, no. 1, pp. 19–21, Jan. 2018, doi: 10.1109/LMWC.2017.2779819.
[39] B. W. Xu, S. Y. Zheng, W. M. Wang, Y. L. Wu, and Y. A. Liu, “A coupled line-based coupler with simultaneously tunable phase and frequency,” IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 66, no. 12, pp. 4637–4647, Dec. 2019, doi: 10.1109/TCSI.2019.2939931.
[40] Y. F. Pan, S. Y. Zheng, W. S. Chan, and H. W. Liu, “Compact phase-reconfigurable couplers with wide tuning range,” IEEE Trans. Microw. Theory Techn., vol. 68, no. 2, pp. 681–692, Feb. 2020, doi: 10.1109/TMTT.2019.2950001.
[41] L. Gao, X. Y. Zhang, and Q. Xue, “Compact tunable filtering power divider with constant absolute bandwidth,” IEEE Trans. Microw. Theory Techn., vol. 63, no. 10, pp. 3505–3513, Oct. 2015, doi: 10.1109/TMTT.2015.2454731.
[42] F. Lin and H. Ma, “Design of a class of filtering couplers with reconfigurable frequency,” IEEE Trans. Microw. Theory Techn., vol. 66, no. 9, pp. 4017–4028, Sep. 2018, doi: 10.1109/TMTT.2018.2842755.
[43] X. Zhu, T. Yang, P.-L. Chi, and R. Xu, “Novel reconfigurable filtering rat-race coupler, branch-line coupler, and multiorder bandpass filter with frequency, bandwidth, and power division ratio control,” IEEE Trans. Microw. Theory Techn., vol. 68, no. 4, pp. 1496–1509, Apr. 2020, doi: 10.1109/TMTT.2019.2959769.
[44] X. Zhu, T. Yang, P.-L. Chi, and R. Xu, “Novel passive vector-sum reconfigurable filtering phase shifter with continuous phase-control and tunable center frequency,” IEEE Trans. Microw. Theory Techn., vol. 70, no. 2, pp. 1188–1197, Feb. 2022, doi: 10.1109/TMTT.2021.3123615.
[45] B. Lee, B. Koh, S. Nam, T. H. Lee, and J. Lee, “Frequency-tunable filtering power divider with new topology,” IEEE Trans. Compon. Packag. Manuf. Technol., vol. 7, no. 7, pp. 1151–1162, Jul. 2017, doi: 10.1109/TCPMT.2017.2708723.
[46] J. Lai, T. Yang, P.-L. Chi, and R. Xu, “Novel evanescent-mode cavity filter with reconfigurable rat-race coupler, quadrature coupler and multi-pole filtering functions,” IEEE Access, vol. 8, pp. 32,688–32,697, Feb. 2020, doi: 10.1109/ACCESS.2020.2974007.
[47] J. Lai, T. Yang, P.-L. Chi, and R. Xu, “2–2.2 GHz reconfigurable 1 × 4 filtering beamforming network using novel filtering switch-coupler and twisted rat-race coupler,” IEEE Trans. Microw. Theory Techn., vol. 70, no. 4, pp. 2462–2472, Apr. 2022, doi: 10.1109/TMTT.2022.3147194.
[48] Y. Xiao, F. Lin, H. Ma, X. Tan, and H. Sun, “A planar balanced power divider with tunable power-dividing ratio,” IEEE Trans. Microw. Theory Techn., vol. 65, no. 12, pp. 4871–4882, Dec. 2017, doi: 10.1109/TMTT.2017.2722403.
[49] P.-L. Chi and C.-P. Chien, “Balanced-to-balanced power divider with tunable in-phase/out-of-phase power-dividing ratio,” in Proc. Asia-Pacific Microw. Conf., 2018, pp. 1483–1485, doi: 10.23919/APMC.2018.8617588.
[50] F. Lin, “A planar balanced quadrature coupler with tunable power-dividing ratio,” IEEE Trans. Ind. Electron., vol. 65, no. 8, pp. 6515–6526, Aug. 2018, doi: 10.1109/TIE.2017.2786290.
[51] C.-Y. Hsiao, C.-H. Cheng, and T.-L. Wu, “A new broadband common-mode noise absorption circuit for high-speed differential digital systems,” IEEE Trans. Microw. Theory Techn., vol. 63, no. 6, pp. 1894–1901, Jun. 2015, doi: 10.1109/TMTT.2015.2419231.
[52] B. Xia, L.-S. Wu, and J.-F. Mao, “An absorptive balanced-to-balanced power divider,” IEEE Access, vol. 6, pp. 14,613–14,619, Mar. 2018, doi: 10.1109/ACCESS.2018.2815546.
[53] S. Chen, W.-C. Lee, and T.-L. Wu, “Balanced-to-balanced and balanced-to-unbalanced power dividers with ultra-wideband common-mode rejection and absorption based on mode-conversion approach,” IEEE Trans. Compon. Packag. Manuf. Technol., vol. 9, no. 2, pp. 306–316, Feb. 2019, doi: 10.1109/TCPMT.2018.2877803.
[54] W. Zhang, Y. Wu, Y. Liu, C. Yu, A. Hasan, and F. M. Ghannouchi, “Planar wideband differential-mode bandpass filter with common-mode noise absorption,” IEEE Microw. Wireless Compon. Lett., vol. 27, no. 5, pp. 458–460, May 2017, doi: 10.1109/LMWC.2017.2690839.
[55] X. Tan, F. Lin, H. Sun, and Q. Xue, “Planar reconfigurable balanced rat-race coupler with improved amplitude imbalance performance and common-mode noise absorption,” IEEE Trans. Microw. Theory Techn., vol. 68, no. 10, pp. 4276–4289, Oct. 2020, doi: 10.1109/TMTT.2020.3015501.
Digital Object Identifier 10.1109/MMM.2022.3226550