Design of Dual-Band Bandpass Filter Using Dual-Mode Defected Stub Loaded Resonator

A novel approach for designing a dual-band bandpass filter (BPF) using defected stub loaded resonator (DSLR) is presented in this paper. The proposed DSLR consists of two fundamental resonant modes and some resonant characteristics have been investigated by EM software ofAnsoftHFSS.Then, based on two coupledDSLRs, a dual-band response BPF that operates at 2.4GHz and 3.5GHz is designed and implemented for WLAN and WIMAX application. The first passband is constructed by two lower frequencies of the coupled DSLRs and the second passband is produced by two higher ones; the coupling scheme of them is also given. Finally, the dual-band BPF is fabricated and measured; a good agreement between simulation and measurement is obtained, which verifies the validity of the design methodology.


Introduction
Modern development in wireless communication systems has led to an increasing demand for dual-band microwave passive devices.As a key circuit block in dual-band wireless communication, such as for both global system for mobile communications (GSM) and wireless local area networks (WLAN), dual-band bandpass filters (BPFs) have been proposed and exploited extensively [1][2][3][4][5][6][7][8].Two popular methods can be classified to implement dual-band BPFs.One is realized by combining two sets of different resonators with common input and output [1,2], which leads to a relatively large circuit size.Therefore, the other method is by utilizing a multimode resonator (MMR) with controllable resonant frequencies to design the dual-band, such as stepped impedance resonators (SIR) [3,4], stub-loaded resonators [5,6], and ring resonator loaded with open stubs [7,8].Nevertheless, the power capacity of BPF needs to be improved.In [9], resonator conducted in ground plane is proved to own a high power handling.And, recently, various kinds of defects grounded structures have been presented and find their applications in design of dual-band BPFs [10][11][12].
In this paper, a novel dual-band BPF based on dualmode defected stub-loaded resonator (DSLR) is proposed.The resonant property of the DSLR cell with two fundamental resonant modes is researched.Finally, two DSLRs are cascaded to construct a dual-band BPF, and the coupling topology is studied and presented.The measured results validate the proposed design.

Resonant Property of DSLR
The configuration of the proposed defected stub-loaded resonator (DSLR) unit is depicted as the white part on bottom layer in Figure 1, which consists of a defected open-loop resonator and a center loaded defected stub.The DSLR is very similar to the dual-mode stub-loaded resonator (SLR) which is presented in [5] except for the ones where the proposed resonator is realized by etching a SLR on the ground plane. 1 ,  2 , and H and  1 and  2 are indicating the defected physical lengths and widths of every sections of DSLR, respectively, and the open gap width is denoted by .For convenience of design,  2 = 2 1 is assumed in this paper.It should be noted  here that the DSLR can be considered as several slot lines and has opposite impedance characteristics as the microstrip ones.This means a narrow  1 results in a lower impedance, while a wide  2 leads to a higher impedance.
To investigate the resonant property of DSLR, a fullwave EM simulator, Ansoft HFSS 10.0, is used to simulate the resonant cell.For providing the external excitation, a pair of 50 ohm blue microstrip feed lines on the top layer is located in both of the input and output terminal, as shown in Figure 1.The substrate adopted in this paper is FR4 material that has a relative dielectric constant of 4.5 and a thickness of 0.8 mm.
Figure 2(a) illustrates the variation of two resonant modes of DSLR, indicated by mode I and mode II, with different width  of open gap.It can be seen that the frequencies of two modes will increase as the width  of gap decreases.Meanwhile, the transmission curves about the variation of two resonant modes with loaded stub length  are depicted in Figure 2(b).From the figure, it can be observed that only mode II is varied while the first mode remains a constant when  is changing, which results in a conclusion that mode II can be controlled independently.Therefore, for giving the design specifications, it will firstly adjust the physical length of open loop to satisfy the resonant frequency of mode I.Then, tune the length of the center stub to achieve the desired resonant location of mode II.
To investigate the above-mentioned resonant characteristic of the DSLR, even and odd mode theory are used because of the symmetrical structure.Similar to the discussion in [5], the mode I (odd mode) resonant frequency can be expressed as where  = 1, 2, 3, . . .,  is the velocity of light in the free space and  eff denotes the effective dielectric constant of the slot line.Meanwhile, the mode II (even mode) resonant frequency can be calculated as Furthermore, the simulated electric field distributions of the dual-mode DSLR are depicted in Figure 3.It is found that the electric field at mode I is mainly distributed in open loop; the loaded stub does not work in this case.However, it is observed that a significant electric field occurs within the center stub for the second mode, which verifies the validity of Figure 2. In addition, according to the above analysis and discussions in [13], it can be easily obtained that there exists no coupling between the two resonant modes.

Design of Dual-Band Bandpass Filter
Based on the dual-mode DSLR, a dual-mode dual-band BPF that operates at 2.4 GHz and 3.5 GHz for WLAN and WIMAX application is implemented in this paper.To achieve two passbands with controllable bandwidth, two poles existing in each passband are needed.Therefore, as illustrated in Figure 4, two DSLRs are cascaded to obtain the dual-mode dual-band filtering response.As studied in [13], the coupling schematic of the designed dual-band BPF can be ascertained, as depicted in Figure 5.As presented, two of the first modes are coupled to form the first passband while the other two second modes are coupled to produce the second passband.For achieving the desired location of passbands, the dimensions of the DSLR that are shown in Figure 1 are finally optimized as follows:  1 = 14mm,  2 = 10mm,  = 10.3 mm,  = 1.45 mm,  1 = 0.5 mm, and  2 = 1 mm.
Here, a second-order Chebyshev frequency response with 0.1 dB ripple level is designed.The fractional bandwidths of two passbands are 3.3% and 2.9%, respectively.To achieve them, a certain coupling degree, including external and internal one, should be designed appropriately.The lumped circuit element values of the low-pass prototype filter are found to be  0 = 1,  1 = 0.8431,  2 = 0.622, and  3 = 1.3554.Meanwhile, the proposed dual-band filter can be equivalent to the design of two single-band filters independently, because two resonant modes of dual-mode DSLR are decoupled [14].Thus, the coupling coefficients and external quality factors of this filter can be calculated by [15] where subscript 1 represents the first passband and 2 is the second passband.When two coupled DSLRs synchronously are tuned to have a close proximity, the coupling coefficients (  ) can be obtained from the two resonant modes by using EM simulation where   and   are defined to be the higher and lower of the two resonant modes.Thus, by tuning the distance  of two coupled DSLRs, two coupling coefficients will be obtained to meet the desired values,  1 and  2 , simultaneously.Similarly, the   of the proposed filter can be extracted from the following expression: where  0 and Δ ±90 ∘ represent the resonant frequency and the absolute bandwidth between the ±90 ∘ points of  11 phase response.The EM simulator HFSS is used to extract the   for two passbands.Here, a pair of T-shape microstrip feed lines, described by  3 ,  3 , and s, are utilized as the input and output structure.Thus, by adjusting  3 ,  3 , and s, the   of two passbands can be satisfied simultaneously.Finally optimized by Ansoft HFSS, the rest of dimensions can be ascertained as  3 = 14 mm,  3 = 0.5 mm,  = 0.43 mm, and  = 2.8 mm.

Filter Implementation and Results
For demonstration purpose, the designed dual-band BPF using two coupled DSLRs was fabricated and its photograph with top and bottom views is shown in Figure 6.The substrate is chosen as before.The overall size of this filter except for the feed lines is 22.8 × 14 mm 2 (about 0.33  × 0.21  ), where   is the guided wavelength at the center frequency of first passband.Simulation and measurement were carried out using Ansoft HFSS 10 software and Agilent's 8719ES network analyzer, respectively.The simulated and measured transmission responses are illustrated in Figure 7.The simulated results are centered at 2.40 GHz and 3.49 GHz, with 3 dB fractional bandwidths of 3.3% and 2.9%, respectively.In addition, the rejection between two passbands has reached 35 dB, which enhances the isolation of two bands.In the measurements, the two passbands are located at 2.41 GHz and 3.51 GHz, with the fractional bandwidths of 3.2% and 2.8%, respectively.Meanwhile, the measured insertion losses at center frequencies of two passbands are 0.8 dB and 0.9 dB, respectively, which are mainly attributed to the dielectric loss and radiation loss.The return losses of two bands are larger than 17 dB.Some discrepancies between simulation and measurement are caused by the inaccuracy in fabrication and implementation.

Conclusions
A novel dual-band BPF based on dual-mode defected stub-loaded resonator (DSLR) is proposed for WLAN and WiMAX application in this paper.The resonant property of DSLR cell with two fundamental resonant modes is researched.Finally, two DSLRs are cascaded to construct a dual-band BPF, and the coupling topology is studied and presented.The measured results validate the proposed design.The improved power-carrying capacity of the designed dualband BPF can be used to the potential high-power application.

Figure 3 : 3 Figure 4 :
Figure 3: Simulated electric field distributions at two resonant frequencies of DSLR: (a) mode I and (b) mode II.

Figure 5 :
Figure 5: Coupling schematic of the designed dual-band BPF.

Figure 6 :
Figure 6: Photographs of the fabricated DSLR dual-band filter.(a) Top view.(b) Bottom view.

11 Figure 7 :
Figure 7: Simulated and measured results of the proposed DSLR dual-band BPF.