In recent years, with the rapid development of modern wireless communication systems, integrated function RF components have become key devices for multi-communication standards. In the conventional wireless communication system, two indispensable components, power divider [1, 2] and filter [3, 4], are usually cascaded together. However, cascaded devices always lead to large circuit sizes and degraded operating performance. In order to solve this problem, filtering power dividers (FPDs) have received increasing attention, which are multi-function integrated devices that provide both frequency band selection as a filter and power splitting/combining as a power divider. Many FPDs have been proposed, such as microstrip-to-slot transition integrated FPDs [5], substrate integrated waveguide (SIW) resonator cavity based FPDs [6], metamaterial or composite right/left handed transmission lines based FPDs [7], FPD formed by integrating bandpass filter and low-pass filter integrated into a Wilkinson power divider [8], and microstrip multi-mode resonator based FPD [9–11]. However, only a few FPDs with multi-way or multi-band power division have been reported [12–14]. By utilizing the TM₂₀ mode of the square patch and the TE₁₁₀ mode of the SIW cavity resonator, a wideband four-way FPD was proposed in [12]. In [13], a four-way FPD was achieved by introducing coupled lines instead of the quarter-wavelength in conventional Wilkinson power divider. To reduce circuit size and improve operation performance, a four-way FPD was realized based on two looped coupled-lines in [14]. For application of multi-passband, a four-way FPD with reconfigurable characteristics is proposed in [15]. By controlling the varactor, the switchable single/dual/wideband filtering response can be adjusted. The aforementioned works have achieved interesting results, but researches about multi-way multi-band FPD are quite few. To meet the up-to-date development trends, it is meaningful and necessary to explore the design of multi-way multi-band FPD.

In this letter, a new four-way triple-band FPD with sharp frequency selectivity and high port-to-port isolations is presented. By reasonably distributing the first three resonant modes of four triple-mode resonators for each band, the proposed FPD can be operated at three different frequencies of 1.65, 2, and 2.27 GHz. Meanwhile, favorable isolation performances are attained by loading isolated resistors across output feeding lines and adjacent arms of the adopted resonators. For validation, a prototype is designed, fabricated, and tested. The measured results have a good agreement with the simulated results, which prove the concept of the design.

The configuration of the proposed four-way triple-band FPD is shown in Figure 1. As observed, it is mainly composed of four triple-mode resonators, two T-shaped coupled output lines, five microstrip input/output transmission lines, and four isolation resistors. In particular, the employed four triple-mode resonators are located symmetrically on both sides of the common open-ended input transmission line in this design, and two pairs of output transmission lines are placed at both sides of the two T-shaped coupled output lines, respectively. In addition, two of isolated resistors (R ₁, R ₂) are loaded between the inner adjacent arms of two pairs of resonators while the other two isolated resistors (R ₃, R ₄) connect the two open ends of the output line to achieve nice port-to-port isolation. It can distinctly see from the structure that the signal input from Port#1 is first transmitted along the open input line and then evenly coupled to the resonators on both sides of the input line to the T-shaped coupled lines, and finally coupled to output ports (Port#2, Port#3, Port#4, and Port#5) with equal power distribution. Based on the proposed symmetrical circuit structure, the couplings between the resonators and the output lines have the same amplitude and in-phase characteristics. In this way, the desired four-way triple-band filtering power division response can be achieved.

In this design, as shown in Figures 2A, a triple-mode net-type resonator is formed by connecting one net-type open-ended stub, one short-ended stub, and two open-ended stubs, which is inspired by [16, 17]. Because the employed resonator has a symmetrical structure with the reference to the symmetrical plane, the even-/odd-mode analysis method [18] can be applied in analyzing its resonance characteristics. With odd-/even-mode excitation, the symmetrical plane behaves as magnetic/electrical wall. The equivalent circuits for the resonator are shown in Figures 2B,C, respectively. According to transmission line theory, the input admittances of odd-/even-mode equivalent circuits are calculated as Eqs 1, 2: Y i n , o d d = − j Y 1 cot θ 1 (1) Y i n , e v e n = Y 1 − j Y 3 cot θ 3 + j Y 2 tan θ 1 + j 2 Y 1 tan θ 1 2 Y 1 + Y 3 cot θ 3 tan θ 1 − Y 2 tan 2 θ 1 (2) where Y _i (i = 1, 2, 3) denotes the characteristic admittance of each transmission line section. θ i ( = 2 π f L i ε e f f / c , i = 1,2,3 ) represents the related electrical lengths, where c and ε _eff are the light speed in free space and the effective dielectric constant of the substrate. Based on Eqs 1, 2, a triple-mode resonator whose first three resonant modes are even mode, odd mode, and even mode can be designed. Its first three resonance frequencies (f _even1, f _odd1 and f _even2) are derived as Eqs 3 and 4 when Y _in,odd = 0 and Y _in,even = 0. Y 3 cot θ 3 − Y 2 tan θ 2 = 2 Y 1 tan θ 1 ( even-mode ) (3) θ 1 = 90 ° ( odd - mode ) (4) Furthermore, the three resonance frequencies of even-/odd-mode can be roughly estimated as Eq. 5: f even 1 ≈ π f 0 2 ( θ 1 + θ 3 ) , f even 2 ≈ π f 0 θ 1 + θ 2 , f odd = π f 0 2 θ 1 (5) where f ₀ is the center frequency. By setting Y _in,odd = Y _in,even , an inherent transmission zero (TZ) frequency can be deduced by f T Z 0 = π f 0 2 θ 2 . Besides, the other four additional TZs are introduced by two coupled-line prototypes. Figure 3 shows two adopted coupled line sections in the design, i.e., Type A and Type B coupled-line prototypes, which are based on anti-parallel and parallel coupling lines. For the Type A protoype, the frequencies of the two transmission zeros TZ₂ and TZ₃ can be deduced by f T Z 2 = 2 f 0 π arctan 2 Z a Z c e + Z c o and f T Z 3 = 2 f 0 π [ π − arctan 2 Z a Z c e + Z c o ] . Similarly, the frequencies of other two transmission zeros TZ₁ and TZ₄ can also be established near π f 0 2 ( θ 1 + θ 3 ) and π f 0 θ 1 + θ 2 , respectively.

Figure 4 presents the coupling topology and mode distribution of the proposed four-way triple-band FPD. It can be seen from Figure 4A that an incident signal that is fed at Port #1 is divided into two same signals by symmetrically coupling to two pairs of identical triple-mode resonators. Then, by proper exciting the first three resonant modes of the triple-mode resonators and coupling them to the four output ports, four-way filtering power division is realized. In Figure 4A, S and L _1/2/3/4 denote source and loads while Res _1/2/3/4 represents the employed net-type triple-mode resonators. Among them, resonators Res _1/2 and resonators Res _3/4 as well as loads L _1/2 and L _3/4 are symmetrically arranged. Figure 4B is a schematic diagram of the contents of the dotted frame in Figure 4A, which describes detailed mode distribution for multi-band. It can be clearly seen that the corresponding mode contributes to each passband of the triple band. Specifically, each resonator of Res _1/2/3/4 is composed of three resonance modes, which are even mode E ₁₁ (E ₂₁, E ₃₁, E ₄₁), odd mode O ₁₁ (O ₂₁, O ₃₁, O ₄₁), and even mode E ₁₂ (E ₂₂, E ₃₂, E ₄₂), respectively. Among them, the first even modes E ₁₁ (E ₃₁) and E ₂₁ (E ₄₁) of the resonator Res ₁ (Res ₃) and Res ₂ (Res ₄) constitute low passband response. In a similar way, the first odd modes O ₁₁ (O ₃₁) and O ₂₁ (O ₄₁) of the resonator Res ₁ (Res ₃) and Res ₂ (Res ₄) constitute middle passband response. Besides, the second even modes E ₁₂ (E ₃₂) and E ₂₂ (E ₄₂) of the resonator Res ₁ (Res ₃) and Res ₂ (Res ₄) constitute high passband response. Based on the above the coupling topology and mode distribution, a four-way triple-band filtering power divider can be initially implemented. Meanwhile, for achieving good port-to-port isolations, two isolated resistors are elaborately introduced between the inner adjacent arms of two pairs of resonators while the other two isolated resistors are properly placed between the adjacent output lines as shown in Figure 1.

Based on the above analysis, one prototype four-way triple-band FPD was fabricated on a Rogers RO4003C substrate with a relative dielectric constant ε _r = 3.55, thickness h = 0.508 mm, and loss tangent tan δ = 0.0027. The photograph of the fabricated four-way triple-band FPD with size of 66.8 × 35.2 mm² (0.83λ _g × 0.44λ _g ) is shown in Figure 5A. The final optimal layout parameters (in mm) in Figure 1 are: L ₁ = 21.86, L ₂ = 15.62, L ₃ = 2.03, L ₄ = 10.82, L ₅ = 25.44, L ₆ = 27.86, L ₇ = 25.53, L _p = 6.28, L _f1 = 1.36, L _x = 10.81, W ₁ = 0.22, W ₂ = 0.18, W ₃ = 0.23, W _f1 = 0.32, W _f2 = 0.64, g ₁ = 0.14, g ₂ = 0.11, g ₃ = 0.1, r = 0.1, R ₁ = 2000 Ω, R ₂ = 1,000 Ω, R ₃ = 220 Ω, and R ₄ = 220 Ω. The frequency characteristic of the proposed four-way triple-band FPD was studied by the electromagnetic simulator HFSS and the network analyzer Agilent N5244A. The simulation and measured results are shown in Figures 5B,C. Due to the connection loss of the SMA connector, there is a certain discrepancy between the simulation results and the measurement ones. Results indicate that the proposed FPD works at the center frequency of 1.67, 2.10, and 2.26 GHz, with corresponding 3-dB fractional bandwidths of 7%, 12%, and 11%. In addition, as expected, five TZs are generated, at 1.48, 1.76, 2.16, 2.37, and 2.47 GHz, ensuring sharp roll-off skirt and out-of-band harmonic suppression. Meanwhile, the measured insertion losses (ILs) are 7.44, 6.92, 7.02 dB while input return losses (RLs) are better than 17.3, 23.1, and 20.2 for the three passbands, respectively. Besides, the output RLs are better than 17.1, 17.3, and 16.3 dB. Moreover, the three passbands exhibit higher than the 17.0, 16.3, and 17.8 dB isolation for each passband, respectively. Table 1 tabulates the performance comparison between the proposed four-way triple-band FPD and other reported works. It can be seen that our proposed FPD exhibits nice return loss, sharp frequency selectivity with multiple TZs, as well as high port-to-port isolations.

In this letter, a novel triple-band four-way FPD with highly improved performance has been presented. After clearly analyzing its working mechanism, a four-way triple-band FPD is implemented with nice multi-band filtering performance and satisfactory port-to-port isolation. It is believed that the proposed design is very attractive for multi-way multi-band application in wireless multi-communication standard systems.