# Miniaturized Multiband Bandpass Filters Based on a Single Multimode Resonator Loading Branches

Authors: Jie Luo; Kaibo Shi; Shanshan Gao
Journal: Discrete Dynamics in Nature and Society
 (2022)

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## Abstract

In this paper, the operating mechanism of proposed bandpass filters with a single multimode resonator loaded with branches is introduced. Based on the design procedure, the center frequencies of the proposed bandpass filters can be controlled due to the design freedom. Meanwhile, the proposed bandpass filters (BPFs) feature compact sizes and small insertion loss. To validate the design and analysis, a prototype was fabricated and measured with six passbands centered at 1.23/1.76/2.38/4.24/5.23/6.75 GHz. The measured result of the fabricated filter agrees well with the simulation, which indicates that the proposed structure can serve as a potential candidate for multiband BPF designs.


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## Body

## 1. Introduction

In the modern multiservice wireless communication system, developments in microwave multiband bandpass filters (BPFs) have been gaining much attention for such as GPS, WLAN, WiMAX, and RFID applications.In the past, some research was conducted for the design of multiband BPFs. In [1–6], different quad-band BPFs were realized based on different approaches, Yan et al. used two sets of short-stub-loaded E-Type resonators in [1], Bukuru et al. investigated quad-mode stepped impedance resonator (QMSIR) in [2], Li et al. realized novel quad-band bandpass filters on a basis of the multimode resonator (MMR) using SIRs loaded tapered-line (SIRTL) in [3], Kamma et al. used T-shaped stubs loaded with a modified ring resonator (MRR) in [4], Zhang et al. investigated three-layer stacked structures in [5], Li et al. used two-/tri-section SIRs and stepped impedance inverters in [6]. And in [7–9], some quint-band BPFs were achieved using different structures, in [7], W.Yang used multimode resonators, Liu et al. investigated uniform impedance resonators (UIRs) in [8], Hsu et al. realized a quint-band BPF using five tri-mode stub-loaded SIRs in [9]. It is noted that some works were reported for the case of sext-band application in [10–12], Chen used six pairs of semilumped resonators to achieve a sext-band BPF in [10], Hsu et al. used stepped-impedance resonators in [11], and Ai et al. used a single multimode resonator in [12]. Besides, it is still a challenge to achieve high-performance multiband BPFs with compact size, closely spaced passbands, low insertion loss, high return loss, and sharp skirt to satisfy the whole wireless communication system application demands.In this paper, miniaturized multiband bandpass filters using a single multimode resonator loaded with branches are proposed. To validate the design and analysis, a prototype filter has been fabricated with six passbands centered at 1.23 GHz for GPS, 1.76 GHz for GSM, 2.38/5.23 GHz for WiFi, 4.23 GHz for digital relay system, and 6.75 GHz for RF. The proposed filter has a compact size, low insertion loss, and adjustable frequency response.


## 2. Filter, Design, and Procedure

What is shown in Figure1 should be given here. As shown in Figure 1, θj (j = 1, p1, p2) corresponds to the equivalent electrical length of the microstrip line, while the characteristic impedance of the microstrip line is represented by Zi (i = 1, p1, p2). Explain first the reason, then, give the conclusion ⟶ By increasing the length of the open branch (Z1, θ1), more transmission zeros can be obtained within the specified frequency range, and these transmission zeros can be used to realize the multifrequency response of the BPFs.Figure 1
The proposed symmetrical branch loaded resonator.The characteristics of multimode resonators are analyzed by the odd and even mode method. Figure2(a) shows the even mode equivalent circuit of symmetrical branch loaded resonators, while the odd mode equivalent circuit of symmetrical branch loaded resonators is shown in Figure 2(b). Since the transmission zeros are produced when the resonance frequencies satisfy the transverse resonance condition, the symmetrical branch-loaded resonator needs to satisfy the following formula:(1)ImZl+Zr,e=0,ImZl+Zr,o=0,Zl=Zp1Zinscotθp1jZins+Zp1cotθp1,Zins=−jZ1cotθ1,Zr,e=−jZp2cotθp2,Zr,o=jZp2tanθp2.Figure 2
Symmetrical branch resonator equivalent circuit. (a) Even mode circuit; (b) odd mode circuit.
(a)(b)When the open branch (Z1, θ1) port produces a virtual ground effect, the input impedance can meet the condition Zins = 0. As a result, a set of out-of-band transmission zeros can be obtained because the signals at the input end cannot be directly transmitted to the output port and the signals are all reflected. The positions of these transmission zeros can be calculated by (2). By adjusting the out-of-band transmission zeros fzs of the BPF, the required number of passbands can be obtained within a specified frequency range.(2)cotθ1=0,fzs=nπf02θ1,n=1,3,5....Figure3 presents the equivalent model of the symmetrical branch loaded resonator proposed in this paper. Compared with Figure 1, a short-circuit branch (Zs, θs) is introduced in the middle of the resonator with the purpose of improving the S parameter of the multiband BPFs.Figure 3
The proposed equivalent model of symmetrical branch loaded resonator.By adjusting the characteristic impedance and electrical length of the microstrip line, three passbands of the BPF are generated in the range of [0, 7 GHz] through three groups of resonance points of even mode and odd mode: the first passband is composed of the fundamental resonance frequencyfo1 and fe1, the second passband is composed of the first harmonic resonance frequency fo2 and fe2, and the third passband is composed of the first harmonic resonance frequency fo3 and fe3.Figure4 shows the based tri-band equivalent transmission line model for the proposed BPF. It consists of transmission branches (Zp1, θp1) (Zp2, θp2), an open branch (Z1, θ1), and a short branch (Zs, θs). The proposed BPF shown in Figure 4 can generate three passbands. The center frequencies of the three passbands are represented by f1, f2, and f3, respectively. Ls represent the length of the short branch (Zs, θs). It can be seen in Figure 5 that fe1, fe2, and fe3 all move to the lower frequency band with the increase of parameter Ls, while the positions of fo1, fo2, and fo3 remain unchanged, the passband bandwidth can be changed by adjusting parameter Ls.Figure 4
The based tri-band equivalent transmission line model for the proposed BPF.Figure 5
Variation of frequency with differentLs and L1.
(a)(b)Similarly, in Figure5(b), L1 represents the length of the open branch (Z1, θ1). L1 is adjusted to get the center frequency variation shown in Figure 5(b). With the increase of L1, fo1, fo2, fo3, fe1, fe2, and fe3 all move to the lower frequency. The fo3 and fe3 in the higher frequency move to the lower frequency faster than other resonance frequencies. The center frequency can be adjusted by the fact that the resonance frequency moves at different rates with the change of L1. To validate the proposed design flow, an example tri-band BPF is fabricated. As shown in Figure 6, the measured performances show good agreement with the simulated ones.Figure 6
Simulated and measured results of tri-band BPF.By increasing the number of symmetric open branches, multiple sets of fundamental and higher harmonics can be superimposed. The proposed quad-band multimode resonator based on the asymmetric tree structure is composed of an open branch (Z2, θ2) cascaded in the previous tri-band multimode resonator filter, as shown in Figure 7.Figure 7
The quad-band equivalent transmission line model for the proposed BPF.As shown in Figure8, when the multimode resonator has only the open stub1, the length of the open stub1 can be adjusted to obtain a fundamental resonance at 1.71 GHz and the center frequency of the first harmonic passband at 5.14 GHz. When the multimode resonator has only the open stub2, the length of the open stub2 can be adjusted to obtain a fundamental resonance at 2.19 GHz and the center frequency of the first harmonic passband at 6.44 GHz. When the multimode resonator includes both the stub1 and the stub2, the four passband center frequencies are 1.61 GHz, 2.37 GHz, 5.15 GHz, and 6.87 GHz.Figure 8
The |S11| of the proposed BPF composed of stub1 and stub2.To validate the proposed design flow, an example quad- band BPF is fabricated. As shown in Figure9, good agreements between the measured and simulated performances are also observed.Figure 9
Simulated and measured results of quad-band BPF.From the previous theoretical analysis, it can be concluded that the obtained design method of the multiband BPFs is based on the coupling of fundamental and high-order harmonics of different branches. For example, the quad-band BPF is realized by the dual-band generated by stub1 and the other dual-band generated by stub2. If stub1 is used to realize tri-band and stub2 is used to realize dual-band, the quint-band multimode resonator can be obtained as the model shown in Figure10.Figure 10
The quint-band equivalent transmission line model for the proposed BPF.Similarly, as shown in Figure11, when the multimode resonator has only stub1, adjusting the length of stub1 can achieve the fundamental passband centered at 1.32 GHz, the first harmonic passband centered at 4.01 GHz, and the second harmonic passband centered at 6.54 GHz. If there is only stub2 in the multimode resonator, adjusting the length of stub2 can obtain the fundamental passband centered at 1.71 GHz and the first harmonic passband centered at 5.14 GHz. When the multimode resonator includes both stub1 and stub2, the center frequencies of the five passbands are 1.27 GHz, 1.80 GHz, 4.01 GHz, 5.31 GHz, and 6.82 GHz.Figure 11
The |S11| of the proposed BPF composed of stub1 and stub2.As shown in Figure12, an example quint- band BPF is fabricated, the measurement performances show good agreements with the simulation.Figure 12
Simulated and measured results of quint-band BPF.Finally, the sext-band multimode resonator based on the proposed asymmetric tree structure is composed of an open branch (Z3, θ3) cascaded in the previous quint-band multimode resonator filter, as shown in Figure 13.Figure 13
The equivalent transmission line model for the proposed sext-band BPF.


## 3. Results and Comparisons

The structure of the proposed sext-band BPF is shown in Figure14. An example sext-band BPF is fabricated on a Rogers TMM10 (relative dielectric constant εr = 9.20, loss tangent tanδ = 0.0022) substrate with a thickness of 1.00 mm, as shown in the inset of Figure 12. The dimension values are summarized as follows (all in mm): L1 = 16.73, L2 = 12.57, L3 = 21.10, Lp1 = 4.01, Lp2 = 1.99, Ls = 2.01, W = 0.10 mm. The overall size of the circuit is approximately 0.08λg × 0.07λg, where λg represents the guided wavelength at the first passband.Figure 14
Structure of the proposed sext-band BPF.Measurement of the fabricated filter is performed using an Agilent E8363 B network analyzer. Figure15 shows the simulated and measured S-parameters of the sext-band BPF, and the photograph of the fabricated BPF is also demonstrated in the inset of Figure 15. The measured six passbands are centered at 1.23/1.76/2.38/4.24/5.23/6.75 GHz with 3 dB fractional bandwidth of 29.27%/3.41%/3.78%/5.19%/3.06%/4.45%. The minimum insertion losses of each band are 1.52/1.61/1.43/0.79/0.68/0.87dB.Figure 15
Simulated and measured results of sext-band BPF.The band-to-band isolations are above 70 dB, which generates sharp and deep rejections between the adjacent passbands.The slight difference between the measured and simulated results may result from the nonuniformity of the relative permittivity of the substrate, the fabrication tolerance, and SMA connectors.In order to better evaluate the achieved performance, Table1 presents a performance comparison of the proposed sext-band BPF with some previously reported works. The proposed sext -band BPF in this paper exhibits compact size, high selectivity, and a conveniently adjustable frequency response.Table 1
Comparison with some previous multi-band BPFs.
Ref.Frequency (GHz)Insertion loss (dB)Isolation (dB)Size (λg×λg)[5]1.48/2.49/3.47/4.49/5.781.49/1.78/0.89/1.18/2.47ISO12>34.770.24×0.17 (0.0408)ISO23>27.91ISO34>32.98ISO45>30.88[6]0.59/0.88/1.17/1.48/1.792.79/2.88/2.87/2.58/2.27ISO12>27.890.51×0.05 (0.0255)ISO23>29.97ISO34>35.78ISO45>26.90[7]0.88/1.19/1.37/1.66/1.97/2.392.28/1.99/2.27/2.68/2.19/1.97ISO12>37.980.26×0.15 (0.039)ISO23>19.87ISO34>29.80ISO45>21.92ISO56>14.85[8]0.69/1.98/3.18/4.49/5.77/6.951.29/0.58/0.79/1.06/1.37/2.16ISO12>52.830.16×0.09 (0.0144)ISO23>44.95ISO34>51.72ISO45>41.92ISO56>37.88This work1.23/1.76/2.38/4.24/5.23/6.751.52/1.61/1.43/0.79/0.68/0.87ISO12>70.000.08×0.07 (0.0056)ISO23>70.00ISO34>70.00ISO45>70.00ISO56>70.00


## 4. Conclusions

This paper presents miniaturized multiband BPFs by using a single multimode resonator loaded with branches. The proposed multiband BPFs feature very high design freedom for every single passband. The simulated and measured results have good agreement, which shows that the proposed filters feature compact size and high selectivity. Owing to these merits, the proposed structure could be a good candidate for multiband BPF design.



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