Benefiting from the better anti-interference and robustness to unwanted and inevitable interference, such as electromagnetic noise, crosstalk, and the other different noise sources, e.g., coupled noise from adjacent circuitry and environmental noise, balanced microwave filters have been attracted much attention and widely used in modern high performance microwave transceivers in past few years [1].

Much efforts have been paid to the desired performances for these circuits of high selectivity and low insertion loss (IL) of differential-mode (DM) filtering function while high common-mode (CM) noise suppression [2]. However, these works are mainly focus on the single DM passband design with desired CM rejection level. The evolving of various modern communication systems providing multi-functional services, multi-band differential filters installed in versatile multimode RF architectures became new requisites [3].

In relation to the satisfied differential BPFs with multi-band characteristics, various technologies and topologies have been proposed, such as planar microstrip resonant structures [4–6], substrate integrated waveguide (SIW) technologies [7], slotline topologies [8], and 3-dimensional dielectric resonators [9]. In the meantime, considering for the circuit miniaturization, microstrip multimode resonant structures, such as the stepped impedance resonators [4], stub loaded resonators [5], and coupled-lines structures [6], are adopted to construct multiband differential BPFs. In addition, some more compact multimode resonators as well as the composite right/left transmission line structure are used for further reducing the circuit size [10]. However, the bandwidths of DM response in above works are narrow case with the relative bandwidths less than 10%, which can not meet the needs of broadband communicate scenarios. To our best knowledge, only one balanced filter with dual-wideband has been publicly reported [11]. However, the filter is constituted by slot-line structure, which needs the dual-layer microstrip process and increases the complexity in fabrication.

A newly dual-wideband balanced bandpass filter based on branch-line structure is proposed in this paper. Through the systematic design and optimization, two desirable wideband DM frequency responses with a good CM suppression within the DM passbands is achieved. The results of electromagnetic (EM) simulation verify the effectiveness of the design method.

Figure 1A portrays the basic topology of the cascaded nth-order dual-band BPF with J inverter, as demonstrated in [12]. B _n (i = 1, 2, 3…) indicates the shunt resonator. The adopted dual-band resonator is shown in Figure 1B, which constructed by shunting two open-circuited branch-lines and one shorted-circuited branch-line [13]. Y and θ indicate the corresponding characteristic admittance and electrical length. The below-line two open- and shorted-circuited branch-lines have same electric length θ _L . Two center frequencies of dual passbands are indicated as f ₁ and f ₂. Imposing the presented dual-band resonator into Figure 1A and replaces B _i, the circuit model of dual-band filter with series dual-band resonators is therefore obtained in Figure 2. All marked electric lengths are determined at f ₁. Note that the first and last admittance inverter can be removed by making J ₀ = 1/Z ₀, where Z ₀ is the terminal characteristic impedance.

For resonator 1 (R1) in Figure 2, five variables, Y _U1, θ _U1, Y _S1, Y _{O 1}, and θ _L1 are used to meet the requirements of the resonant frequencies and slope parameters at the two passbands. According to the classic filter synthesis method [14], it can be written as the following simultaneous equations: Y U 1 ⁡ tan θ U 1 + Y O 1 ⁡ tan θ L 1 − Y S 1 ⁡ cot θ L 1 = 0 , (1) Y U 1 ⁡ tan ( α θ U 1 ) + Y O 1 ⁡ tan ( α θ L 1 ) − Y S 1 ⁡ cot ( α θ L 1 ) = 0 , (2) Y U 1 θ U 1 ⁡ sec 2 θ U 1 + Y O 1 θ L 1 ⁡ sec 2 θ L 1 + Y S 1 θ L 1 ⁡ csc 2 θ L 1 = 2 b 1 , (3) Y U 1 α θ U 1 ⁡ sec 2 ( α θ U 1 ) + Y d α θ L 1 ⁡ sec 2 ( α θ L 1 ) + Y S 1 α θ L 1 ⁡ csc 2 ( α θ L 1 ) = 2 b 2 , (4) b 1 = G g 0 g 1 Δ 1 , b 2 = G g 0 g 1 Δ 2 , (5) where α is the ratio of f ₂ to f ₁, b ₁, b ₂ are the susceptance slope parameters at the resonance frequencies, g _i (i = 0,1,2…) is the low-pass prototype value, and Δ₁, Δ₂ are the relative bandwidths of two passbands, respectively. In addition, the inverter is required to be the same at f ₁ and f ₂, so 1/sin2θ _L1 = 1/sin2αθ _L1 is obtained. The same synthesis method is also applied to design the other resonators in Figure 2.

By solving the Eqs 1–5, a very useful solution is found, i.e., when b ₂ = αb ₁, there is θ U 1 = π α + 1 = 2 θ L 1 , Y S 1 = Y O 1 , (6)

At this time, all uncertain variables can be ascertained based on the desired specifications. Moreover, two parallel open- and short-circuited branch-lines can be equivalent to a short-circuited branch-line in the case of Y _S1 = Y _{O 1}, as the diagram shown in Figure 3A.

Based on the above analysis, a third-order transmission line model (TLM) of dual-band filter is obtained from transformed the Figure 2 and depicted in Figure 3B. Among them, the upper open-circuited branch-line and the below short-circuited branch-line constitute a new dual-band resonator. From the view of structure, it can be regarded as a stepped-impedance resonator. Thus, the overall circuit of Figure 3B is composed by three shunting resonators and two intermediate cascaded transmission lines (TLs). The intermediate cascaded TL is used to behave as the admittance inverter J ₀ in Figure 2 and equal to quarter-wavelength at f _m , where f _m is the average frequency of two passbands, i.e., (f ₁+f ₂)/2. The characteristic admittance Y _j is equal to 0.02 S both for realization of J ₀ and a good impedance matching to signal ports.

Besides, αΔ₂/Δ₁ = 1 is obtained from the condition of b ₂ = αb ₁ and 5) and then, it is known that Δ₂ is positively correlated with Δ₁. Thus, two relative bandwidths of two passbands to be chosen in the later design need to meet this relationship. To further investigation, the variations of Δ₁ versus the Z _U1 (1/Y _U1) and Z _L1 (1/Y _L1) at three different frequency ratios α are portrayed in Figure 4, based on Eqs 1–6. It is observed intuitively that Δ₁ is increasing monotonically as either Z _U1 or Z _L1 is enlarged. However, the required Z _U1 has a smaller value when frequency ratios α is larger in the case of realizing the same Δ₁, as shown in Figure 4A, while Z _L1 remains basically unchanged, as depicted in Figure 4B. Moreover, note that Z _L1 will becomes a ultra small value when Δ₁ is chosen to be a minor value, resulting in a very wide microstrip line and such that enlarge the circuit size. These imply that the proposed structure is more suitable and convenience in designing of larger frequency ratio and a wide bandwidth of dual-band balanced filter.

Based on the analysis in Design Method of Dual-Band Bandpass Filter Section, a third-order dual-wideband balanced BPF is proposed and its TLM is shown in Figure 5A. The desired two passbands are working at 2.52 and 4.65 GHz, respectively.

A newly third-order dual-wideband balanced BPF is developed based on branch-line resonant structure in this work. The comprehensive design method of DM bisection with multi-order filtering response is presented. Besides, the attached stubs on the center plane of the CM bisection are well analyzed for dual-stopband property and such that enhancing the CM suppression. The proposed design method and filtering structure are validated well by the measured results.