LAI Xin

(Southwest China Institute of Electronic Technology,Chengdu 610036,China)

1 Introduction

The rapid developments in modern wireless communication create a large demand of microwave components with multi-band operations.Therefore,the bandpassfilter(BPF),as a key component filtering unwanted frequencies in RF systems,is necessary to generate two or more frequency bands.In Reference[1],a dual-band BPF is achieved by cascading open-stub structures.And a triband response is achieved by squarering short stub loaded resonators,but the resonant structure is complicated[2].Recently,more and more dual-band and tri-band filters have been realized on stepped impedance resonator(SIR)[3-5]and stub loaded resonator(SLR)[6-9]by their multi-resonant property.In Reference[3],compact miniaturized hairpin resonators which are treated as SIRs are used to design cross-coupled filters with a dual-band response.In Reference[4],a pseudo-interdigital stepped impedance resonators(PI-SIRs)are used to design the bandpass filterwith dual-band response.And the tri-section SIR can be designed to have tri-band performance at desired frequency,which is achieved by tuning its impedance ratio[5].However,the SIR suffers from the dependence of resonant frequencies,which makes the filter design complicated.With the property of freely adjusting the even-mode by tuning the loaded stub without influence on the odd-mode,the symmetrical SLR is widely used to design filterswith multi-band response.In Reference[6-7],the dual-band response is realized by the open stub loaded resonator and short stub loaded resonator respectively.And the unsymmetrical SLR can also realize dual-band response by tuning the stub length and its tap position[8].In Reference[9],a tri-band filter is designed based on the SLR with open and short stubs loaded together,in which the first and third resonant modes are controlled by tuning the lengths of the stubs.In Reference[10],a triband filter is achieved by multimode resonator,but the resonant frequency can′t be easily designed.

Except for the application of multimode resonator,multi-band filter can also be realized by cascaded multiband resonators[11],inwhich proper couplings of each RF passes are accomplished by the special designed coupling structures.In Reference[12-14],the multi-band filters are designed by combing different pass-bands together.In Reference[12],a dual-band filter is realized with SIR and defected SIR,which is fed by a common T-shaped feed line.SIR and half-wavelength resonator are used to form the desired pass-bands which are coupled with the same input and output by the common feed structure[13-14].

As be depicted in the detailed analysis above,independent passband design and simple design procedure is important inmluti-band filter design.In this paper,a triband filter employing shorted stub loaded resonator and DGS resonator is presented,which can design the passband independently.This tri-band filter is realized by combing different controllable passbands together.The SLR generates two resonant modes,which can form the first and the third passbands.The DGS resonator on the back can generate the second passband.A properly designed feed structure is used to provide desired sourceload couplings for the two resonant blocks separately.To verify the proposed approach,a tri-band filter operating at the WLANs 2.45/5.25 GHz and WIMAX band 3.5GHz is designed and fabricated,the measured results exhibit tri-band bandpass responses with high selectivity.

2 Design of Tri-Band Filter

In order to realize the independent passband design,the open stub is used to realize the source and load coupling of the three passband.And benefited from the two resonant structures,the external coupling of the two resonant structures are with little affection on each other.The design method used in this paper can facilitate the multiband filter design.

The geometric structure of the filter is shown in Fig.1(a).The SLR combined with the interdigital feed line realizes the first and the third passbands,and the DGS resonator incorporating slot coupling generates the second passband.In the analysis of the feed structure,it is found that the two external couplings of the two resonant blocks are dependent on different geometric parameters,so the three passbands can be analyzed separately.Based on the analysis,the coupling structure of the proposed triband filter can be described as Fig.1(b).The symbol`R1'and`R2'represent the SLRand DGS resonator respectively.And the superscript`e'and`o'denote the even mode and odd mode of the SLR.

Fig.1 Figure of tri-band filter圖1 三通帶濾波器結(jié)構(gòu)圖

2.1 Analysis of the SLR

The geometric structure of the SLR is shown in Fig.2(a),where Y1,Y2,L1,L2,W1and W2denote the characteristic admittance,lengths and widths of the microstrip line and shorted stub,respectively.Since the shorted stub is shunted at the midpoint of the microstrip line,the even-and odd-mode method can be utilized to analyze the structure.For odd-mode excitation,the equivalent circuit is shown in Fig.2(b),and the resonant condition for the first odd-mode resonant frequency is expressed as

where β represents the phase constant.And observed from Equation(1),the odd-mode is independent to the loaded stubs,which means that the adjusting of stub L2won′t affect the odd resonant mode.For even-mode excitation,we can obtain the equivalent circuit as Fig.1(c),and the resonant condition for the first even-mode resonant frequency can be approximately defined as

Basedon Equation(1)and(2),the stub lengths can be deduced from the fixed even-mode,odd-mode resonant frequencies and characteristic admittance Y1,Y2.In this paper,the odd resonant mode is used to form the passband at 5.25 GHz and the even resonant mode is working at 2.45 GHz.It is also found that the stub length L2decreaseswith the increase of stub impedance,which improves the design flexibility.

Fig.2 Structures of the stub loaded resonator,odd-mode equivalent circuit and even-mode equivalent circuit圖2 枝節(jié)加載諧振器結(jié)構(gòu)與奇模、偶模諧振等效電路

Since the current maximum of the SLR is mainly located in the middle of the SLR at the two resonant modes,magnetic coupling is adopted to generate proper coupling between the two SLRs.The coupling coefficients of the odd mode(M12o)and even mode(M12e)varied with different gapwidth G1are shown in Fig.3(a)together.It is shown in this figure that the coupling coefficients increase while the gap width is decreasing.

Fig.3 Coupling coefficients variation of SLR and DGS resonator圖3 枝節(jié)加載諧振器和缺陷地面結(jié)構(gòu)耦合系數(shù)變化趨勢

2.2 Analysis of the DGS Resonator

The DGS resonator is used as the building block to realize the second passband.As shown in Fig.1,the DGS building block used in this paper is realized by etching the folded split-ring resonator in the ground,its resonant frequency is mainly controlled by the total length of the structure.Owning to the folded structure,this block can realize desired resonant frequency in a compact size.Unlike the microstrip split-ring,the magnetic field maximum of this DGS block is located at the split side while the electric field maximum is located at its opposite side.As shown in Fig.1,the two DGS resonators have a magnetic coupling and the coupling strength is tuned by the gap width G2.The coupling strength M122varied with different G2is shown in Fig.3(b),and desired coupling coefficients can be achieved by adjusting G2.

2.3 Design of the Tri-band Filter

As seen from Fig.1(a),the external coupling of the SLR is realized by the interdigital coupling and that of the DGS resonator is controlled by the overlapped area between the DGS resonator and the feed stub.To analyze the external quality of the DGS resonator,an EM simulation model as shown in Fig.4(a)is used and the external quality varied with geometric parameters is shown in Fig.4(b).The parameter`a'and`b'denote the length of the overlapped area and the relative position,respectively.It is shown in Fig.4(b)that longer overlapped length and bigger relative position result in the stronger external coupling.

Fig.4 EM simulationmodel and external quality under different conditions when c=0.6mm圖4 三維電路仿真模型與不同情況下的外部耦合系數(shù)(c=0.6 mm)

As shown in Fig.1(a),the external qualities of the SLR are provided by the interdigital coupling lines,and the coupling line L3is also used to provide external coupling to the DGS resonator.In order to describe the interaction between the SLRand the DGS resonator,the external qualities of SLRunder different conditions are extracted and shown in Fig.5.In this figure,the external qualities Qeoand Qeevaried with and without the DGS resonator are shown,in which s=0.2 mm,W3=0.3 mm,L4=L5and W5=k=0.6 mm.Seen from the two figures,the external coupling is stronger with longer coupling line length.The DGS Resonator is with little effect on the Qeoof the SLR,and the Qeeunder four conditions are almost the same while the line length is larger than 3 mm.This comparison shows that under some conditions,the external qualities for the two resonant blocks can be designed independently,which provide much more design flexibility.

Fig.5 Qeoand Qeeunder different coupling line lengths圖5 不同耦合長度下的奇模和偶模外部耦合系數(shù)

Based on the analysis of the resonators and the feed structure,a tri-band filter operating at WLAN bands of 2.45/5.25 GHz and WIMAX band of 3.5 GHz is designed.To realize the resonant modes 2.45/5.25GHz,the parameters of SLR are calculated and revised through simulation,which are determined as L1=8.4 mm,L2=5.8 mm,L3=4.4 mm,W1=1 mm and W2=0.4 mm.The gap G1is set as 0.6mm to achieve interior coupling value M12o=0.051 and M12e=0.112 of the two bands.To achieve the response of 3.5 GHz,the parameters of DGS resonator are determined as D1=6.5 mm,D2=4.2 mm,D3=2.25 mm,W5=0.6 mm and d=0.3 mm.The gap G2is0.35 mm to achieve the coupling coefficient M122=0.09.The parameters of the feed line are determined as L4=5.55 mm,L5=6.95 mm,W3=5.55 mm,W4=1.65 mm and S=0.2 mm,which realize Qee=3.9 and Qeo=1.82.With the relative location k=0.53 mm,the Qe2=2.16 of the DGS resonator is obtained.The total size of this filter is 29.5 mm×24 mm.

3 Fabrication

The filter is fabricated on the substrate with relative dielectric constant of 2.65 and height of 1 mm.Simulation and measurement are carried out by Zelad IE3D software and Agilent's 8719ES network analyzer,respectively.The photographs of the fabricated tri-band filter with its front view and back view are shown in Fig.6.And the simulated and measured results are illustrated in Fig.7,which are in good coherence.The measured passbands are centred at 2.47 GHz,3.43 GHz and 5.25 GHz,with the 3 dB fractional bandwidth 6.7%,11.9%and 15.3%,respectively.The minimum insertion losses of the three bands are 1.38 dB,1.25 dB and 0.85 dB respectively.The return losses of the first and second passbands have reached below -13 dB,while that of the third band is below-19 dB.It is noted in the transmission response that the source-load coupling has produced transmission zeros between the adjacent passbands,which improve the selectivity of the tri-band filter.

Fig.6 Front view of the proposed tri-band filter圖6 三通帶濾波器的正面結(jié)構(gòu)

Fig.7 Back view of the proposed tri-band filter圖7 三通帶濾波器的反面結(jié)構(gòu)

Fig.8 Simulated and measured results of the tri-band filter圖8 濾波器響應(yīng)的仿真與實測結(jié)果對比

4 Conclusions

To verify the proposed method,a tri-band filter operating at 2.45/3.5/5.25 GHz is designed,and the measured results have shown good consistence with the simulated ones.Benefited from the designed structure,this three passband have realized independent design.The design approach can facilitate the multi-band filter design in many other areas of the multi-band wireless communication system.

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