IEEE MICROWAVE AND WIRELESS COMPONENTS LETTERS, VOL. 22, NO. 4, APRIL 2012 179

A New Tri-Band Bandpass Filter Based onStub-Loaded Step-Impedance Resonator

Wei-Yu Chen, Min-Hang Weng, Member, IEEE, and Shoou-Jinn Chang, Senior Member, IEEE

Abstract—A tri-band bandpass filter designed based on a stub-loaded step-impedance resonator (SIR) is proposed. The resonantbehavior of the stub-loaded SIR is analyzed. By properly control-ling the impedance ratio �, the length ratio � � and the lengthratio � � of the stub-loaded SIR, the center frequencies are de-signed at 1.575, 2.4, and 3.5 GHz, respectively, corresponding tothe GPS, WLAN and WiMAX applications. Furthermore, a 0 feedstructure is used to provide at least one transmission zero nearpassband edge of each passband, resulting in high selectivity. Ex-perimental results show good agreement with the simulated results.

Index Terms—Filter, step-impedance resonator (SIR), tri-band.

I. INTRODUCTION

S O far, multi-band bandpass filters (BPFs) have been inves-tigated aggressively to satisfy the newly developed multi-

service system and the commercial products. Multi-mode ringresonators, step-impedance resonators (SIRs) and stub-loadedresonators (SLRs) are popular for the design of multi-band BPF[1]–[6]. In [1], a ring resonator with three pairs of degeneratemodes was realized for the tri-band filter by controlling the per-turbations of four open stubs. In [2], a pair of asymmetric SIRswith parallel coupling arrangement was proposed to realize thetri-band responses. However, the symmetry and the selectivityof the passbands still need to be improved. Besides, the circuitsize is also large. In [3], the conventional SIRs and the U-shapeduniform impedance resonators using coupling arrangement wasproposed to realize the tri-band responses. However, there arefive resonators in the circuit layout, resulting in the problem oflarge area. In [4] and [5], a pair of tri-section SIRs also using par-allel coupling arrangement was proposed to realize the tri-bandresponses. However, the tri-section SIRs suffer from the designcomplexity, especially in the analysis of resonant frequencies. In[6], a dual-band filter using SIRs with open-stub line was pro-posed. However, the resonant behavior of SIRs with open-stubline was not investigated. In [7], a tri-band BPF using short andopen SLRs was proposed. In [8], a tri-band BPF based on adual-plane microstrip/defect-ground structure (DGS) was pro-posed. However, the via-hole of short circuit and the DGS struc-ture cause a complex integration in packaging.

Manuscript received November 08, 2011; revised January 10, 2012; acceptedFebruary 02, 2012. Date of publication March 19, 2012; date of current versionApril 11, 2012.

M. H. Weng is with the Opto-electronics System Section, Medical Devicesand Opto-electronics Equipment Department, and Metal Industries Research& Development Center, Kaoshiung 82059, Taiwan. (e-mail: mhweng@mail.mirdc.org.tw).

W. Y. Chen and S. J. Chang are with the Institute of Microelectronics, Depart-ment of Electrical Engineering, Advanced Optoelectronic Technology Center,and Center for Micro/Nano Science and Technology, National Cheng Kung Uni-versity, Tainan 701, Taiwan.

Color versions of one or more of the figures in this letter are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/LMWC.2012.2187884

Fig. 1. Schematic of the proposed tri-band BPF.

Fig. 2. Schematic of the proposed stub-loaded SIR.

In this letter, we proposed a compact tri-band filter designedbased on a stub-loaded SIR for the first time. The resonant be-havior of the stub-loaded SIR, much different with asymmetricSIRs, conventional SIRs and tri-section SIRs, is analyzed anddiscussed.

II. DESIGN PROCEDURE OF THE TRI-BAND BPF

Fig. 1 shows the configuration of the proposed tri-band BPF.It is designed based on two coupled stub-loaded SIRs, twotapped coupling input/output (I/O) ports and 0 feed structureaside the stub-loaded SIR. This simulation work is done byusing the full-wave electromagnetic (EM) simulator. [9]

A. Analysis of Resonant Behavior of Stub-Loaded SIR

To understand the resonant behavior of stub-loaded SIR, theanalysis of resonant modes is required. Fig. 2 shows the config-uration of stub-loaded SIR, which is composed of a typical SIRwith two discontinuities and a stub-loaded section located on thesymmetric plane of SIR. The impedance and electrical length ofthe stub-loaded section are expressed as and , respectively.The input admittance for stub-loaded SIR can be calculated as

(1)

where

(2)

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180 IEEE MICROWAVE AND WIRELESS COMPONENTS LETTERS, VOL. 22, NO. 4, APRIL 2012

Fig. 3. Normalized ratios of the higher resonant frequencies to the fun-damental resonant frequency for the stub-loaded SIR with respect to� � ���� ���� ���� ��� and 0.9.

and are corresponded to the impedance ratio defined as, respectively. The resonant modes

of the stub-loaded SIR can be derived by setting . Thus,the resonant condition can be expressed as

(3a)

(3b)

where (3a) and (3b) are corresponded to the odd- and even-moderesonances of the stub-loaded SIR, respectively. In order to ob-tain more design freedom, the length ratio of the SIR withtwo discontinuities and the length ratio of the stub are alsovaried to adjust the higher order resonant modes over a widefrequency range. The length ratio and the length ratioare, respectively, defined as and

, where is the total length of the SIR section de-fined as , and is the length of the stub. All of the

and are determined for . To simplify the design, letequal to , i.e., . By substituting formulas of length

ratio and the length ratio into (3a) and (3b), several res-onant modes dependent on and can be found.

Fig. 3 shows the normalized ratios of higher resonant fre-quencies to the fundamental resonant frequency for thestub-loaded SIR with and and0.9. In Fig. 3, the odd mode is corresponded to the second res-onant frequency and the fourth resonant frequency ,and the even mode is corresponded to the fundamental reso-nant frequency , the third resonant frequency and thefifth resonant frequency . It is found the resonant modesof the stub-loaded SIR dependent on and different fromthose of typical SIR. It is also can be found that the is lowerthan the while is approaching 0.9 and is varied from 0.2to 0.7. Moreover, the is also lower than the while isapproaching 0.5 and is varied from 0.1 to 1. Consequently,the stub-loaded SIR can achieve the design with very closepassband, and provides a new solution to design the multi-bandfilter. In this study, by mapping the ,

and in the Fig. 3, is explicitlydetermined as 0.3 and is explicitly determined as 0.3 to meetthe requirement of GPS of 1.575 GHz, WLAN of 2.4 GHz andWiMAX of 3.5 GHz. The low impedance of the major sectionand are both set as 28.7 , and the high impedance is thenset as 115 . According to the design chart, the electrical length

, and are decided as 60 , 30 , and 27 , respectively.

B. Tri-Band Filter Design

Two well designed stub-loaded SIRs are employed to formthe tri-band BPF. The 3 dB fractional bandwidths (FBW) ofthe three passbands are set as 5%, 3%, and 5% responding tothe 1.575, 2.4, and 3.5 GHz, respectively. For satisfying filterspecification for the bandwidths of three passbands, the desiredcoupling coefficients and external quality methodologyare performed. The theoretical and are calculated anddefined as [10]

(5)

where FBW is fractional bandwidth, and and are ele-ment values of the filter response function. From the filter spec-ifications, the element values for the low-pass Chebyshev proto-type with 2 dB ripple are found to be ,where for to 2 is the element value.

It is known that the coupling coefficients related with thedesired fractional bandwidths is controlled by the couplingspacing . As proposed in [10], the external quality, , atthe corresponded frequencies, and , with respect to thelength defined by the tapped location to the symmetric plane isanalyzed. The coupling coefficients, , and external quality,

, can be calculated from full-wave simulated transmittedcoefficients, expressed as

(6)

where and are defined to be the higher and lower ofthe two resonant modes, is the resonant frequency, and the

is the bandwidth for the attention of is up 3 dB fromthat at resonance. When meeting the desired coupling coeffi-cients, the coupling spacing can be determined as 0.8 mm.

As shown in Fig. 4, the analysis of center frequencies and ex-ternal quality factors, , are calculated by full-wave EM sim-ulation. It is found that the designed center frequencies atand are independent on . On the other hand, at and

are dominated by the tapped location. The desired tri-bandresponse can be obtained simultaneously by shifting the to in-duce a suitable for the bandwidths of , and , where

is chosen to be 8 mm, leading the to be in turn 35.6, 40.2,56 at 1.575, 2.4, 3.5 GHz, respectively. In addition, the 0 feedstructure is employed to result in a pair of transmission zerosnear each passband edge, based on the theoretical analysis re-ported in [11], which shows high isolation and selectivity.

CHEN et al.: NEW TRI-BAND BPF BASED ON STUB-LOADED SIR 181

Fig. 4. External quality factors of three passbands respect to tapped locationof � (insert plot is the tapped location respect to length of �, material constants:� � ���� ��� � � ������� � � ���� mm, structural parameters: ���� mm, � ���� mm, � ��� mm, � ���� mm, � � � ���� mm, � � ��� mm, � � �� mm, and � � ���� mm).

Fig. 5. Simulated and measured results for the proposed tri-band BPF (insertplot is the photograph of the fabricated BPF).

The sensibility analysis including the variations of couplingspacing ( mm) and width of high impedance sec-tion ( mm) was also simulated, indicating thatthe average variations of bandwidth and center frequency arewithin % and % of three passbands, respectively.

III. EXPERIMENTAL RESULTS

After an optimal design process, the dimensions of the pro-posed structure are chosen as follows: mm,

mm, mm, mm,mm, mm, mm, and mm. The

strip widths of the feed ports are 2.4 mm corresponding to thecharacteristic impedance of 50 . The proposed filter was fabri-cated and measured by an HP8510C Network Analyzer. The in-sert plot in Fig. 5 shows the photograph of the fabricated layout.Fig. 5 shows the simulated and measured results. The measuredpassbands have insertion losses of 1.6 dB, 1.5 dB, and 2.3 dB,return losses of 9 dB, 18.9 dB, and 13.5 dB corresponding to1.575, 2.4, and 3.5 GHz, respectively. It is also verified that dueto the 0 feed structure, transmission zeros at 1.89, 2.65, 3.1and 3.75 GHz are clearly observed, resulting in high band se-

TABLE ICOMPARISONS OF THE PROPOSED FILTER WITH OTHER REPORTED TRI-BAND

FILTERS. (� IS THE FREE-SPACE WAVELENGTH AT THE

CENTER FREQUENCY OF THE FIRST PASSBAND)

lectivity. Table I summarized the comparisons of the proposedfilter with other reported tri-band filters [1], [2], [4], [5], [7], [8].The proposed filter possesses the average advantages of low in-sertion loss and compact size.

IV. CONCLUSION

A tri-band BPF based on a stub-loaded SIR has been pro-posed. The resonant behavior and external quality factor of theproposed stub-loaded SIR is analyzed, providing a design guide-line to realized the tri-band filter. In addition, good passbandselectivity and isolation of each passband can be achieved dueto the appearance of the transmission zeros near each passbandedge.

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