IEEE MICROWAVE AND WIRELESS COMPONENTS LETTERS, VOL. 16, NO. 8, AUGUST 2006 443

A Bandpass Filter Design Using Half-WavelengthStepped Impedance Resonators

With Internal CouplingsKongpop U-yen, Student Member, IEEE, Edward J. Wollack, Senior Member, IEEE, Terence Doiron, Member, IEEE,

John Papapolymerou, Senior Member, IEEE, and Joy Laskar, Fellow, IEEE

AbstractWe propose a new type of microstrip half-wavelength( 2) stepped impedance resonator (SIR) for use in bandpassfilter (BPF) designs. This 2 SIR has an internal coupling sectionthat can be used to generate a coupling coefficient in the filterdesign in addition to couplings between SIRs. It also containsadditional stepped impedance lines that shift and suppress thelowest even-mode resonance frequencies to more than what can beachieved by conventional 2 SIRs. Moreover, a transmission zerois generated close to its fundamental resonance frequency (0

)

which can be used in definition of the filter response. A fourth-order microstrip BPF with 10% bandwidth was constructed usingtwo of the proposed 2 SIRs with a stepped impedance ratio ( )of 0.528. The experimental result shows that the filter can achievelow in-band loss and out-of-band attenuation of 52.6 dB up to30

. The lowest spurious resonance frequency is shifted to 30

asopposed to 2.50

in conventional 2 SIRs with the same value.Index TermsBandpass filters (BPFs), microstrip, transmission

line resonators.

I. INTRODUCTION

MICROWAVE filters are important components in wire-less communication systems. Good microwave filtersshould have an ability to suppress out-of-band signals whileproviding low in-band loss. Moreover, filters should be compactand inexpensive to fabricate.

Stepped impedance resonators are widely used in filter de-signs to suppress spurious response [1][3]. To maximize theout-of-band attenuation, the stepped impedance ratio valueused in the SIR is set to a small value [1], [3]. As a result,the quality factor of the SIR is reduced especially when narrowtraces are used and the in-band insertion loss of the filter usingthis SIR becomes high.

In the previous work [2], we proposed the double split-end4 SIR. The filter constructed using this technique is very

compact, simple to design and provide very good in-band andout-of-band characteristics. However, it requires a grounded ter-mination which increases the filter fabrication complexity.

In this letter, a 2 SIR with internal couplings is introduced.The 2 SIR is integrated with an equivalent impedance in-verter and a transmission zero close to in-band. When used in

Manuscript received March 2, 2006; revised Apri. 25, 2006.K. U-yen, E. J. Wollack, and T. Doiron are with NASA Goddard Space Flight

Center, Greenbelt, MD 20771 USA (e-mail: kuyen@pop500.gsfc.nasa.gov).J. Papapolymerou and J. Laskar are with the School of Electrical and Com-

puter Engineering, Georgia Institute of Technology, Atlanta, GA 30332 USA(e-mail: papapol@ece.gatech.edu).

Digital Object Identifier 10.1109/LMWC.2006.879494

Fig. 1. Theresonator revolution steps starting with (a) the conventional =2SIR, (b) main resonator: the split-folded =2 SIR at center (solid lines) and atsides (dashed line), (c) the final=2 SIR, with stepped impedance stubs inserted,coupled to other SIRs, (d) the SIRs even-mode quarter-circuit model, and (e)the SIRs odd-mode quarter-circuit model.

single-layer filter design without vias, it reduces the size of thefilter footprint significantly. Moreover, an additional steppedimpedance open (SIO) stub is used to control the lowest even-mode resonance of the SIR such that the filter does not requireSIRs with a small value to obtain a wide stop-band band-width. In this letter, we present the result of the filter fabricatedusing the proposed structure. The experimental observations arein reasonable agreement with the theoretical predictions.

II. STEPPED IMPEDANCE RESONATORWITH INTERNAL COUPLING

Consider the conventional 2 SIR, as shown in Fig. 1(a), itconsists of three lines. The line in the middle section has thecharacteristic impedance of . The others have the character-istic impedance of . At , the open-end of the resonator istransformed to a virtual ground at the center of the resonator.Then as shown in Fig. 1(b), both and lines are splitand folded in perpendicular to its structure to produce a morecompact structure. The split and sections have electrical

1531-1309/$20.00 2006 IEEE

444 IEEE MICROWAVE AND WIRELESS COMPONENTS LETTERS, VOL. 16, NO. 8, AUGUST 2006

lengths of and , respectively. As shown in Fig 1(c), theSIRs internal coupling is formed by inserting SIO stubs aroundthe center. The SIO stub is constructed from two lines con-nected in series, each of which has characteristic impedancesof and and electrical lengths of and , respec-tively. These electrical lengths are tuned such that the SIO stubprovides a virtual ground at . When connected to the parallelline with the characteristic impedance of 2 in (1), it forms agrounded-end antiparallel coupler where 2 and 2 are itseven- and odd-mode characteristic impedance

(1)

Using the SIO stub allows the lowest even-mode resonance ofthe SIR to shift away from as discussed in Section III. Sincethe proposed SIR is symmetric in both and axis, it can bemodeled using the quarter of the circuit [see the dark gray areain Fig. 1(c)] in even and odd modes, as shown in Fig. 1(d) and(e), respectively. The fundamental resonance condition of thisSIR is as follows [4]:

(2)

where the stepped impedance ratio is defined asand are the electrical lengths of the line and , respec-tively. The and are chosen such that the antiparallel cou-pler generate transmission zeros frequency at the desired out-of-band location [2], whereas the conditions and

are applied. The minimum length of the 2SIR is used in this letter to reduce the overall filter size (i.e.,

). The split-end sections on the left and the rightside of the SIR have the characteristic impedance of

(3)

where 2 and 2 are even- and odd-mode impedance ofthe opened-end line 2 . They are used for coupling betweenSIRs to form a filter response. The admittance inverter for thiscoupler, which is used for filter designs, is derived in [2].

III. RESONATORS SPURIOUS SUPPRESSIONCAPABILITY FROM SIO STUBS

This letter is focused on the filter design technique usingthe proposed SIR to suppress the lowest spurious resonancefrequency. The filters out-of-band suppression capability de-pends on two factors. First, it depends on the value as it de-fines the separation between and its lowest resonance mode[4]. Second, it depends on the SIO stub which has the inputimpedance as follows:

(4)

where . At , it behaves as a virtual ground atAA in Fig. 1(d), thus 0. The effect of the variable

, and on filter re-sponses as described below.

Fig. 2. Frequency responses of the decibal jS j of fourth-order filters usingthe proposed SIRs with R = 0.528. The nominal design (bold solid line) hasR = R = 0.528; R = 1; = = = 36 . Other responses are ob-tained by only adjusting eitherR (whereR = R = 0.528, and = =36 ) or R and u (where R = 1, and R = 0.528) from the nominal design.

A. Effect of the R VariableThe value in SIRs controls the bandwidth of the filter, as

well as its out-of-band suppression capability, given .First, the bandwidth of the filter relies on to be close to

zero at in order for each 2 SIR in the filter to behave astwo coupled quarter-wavelength ( 4) SIRs. When the SIO stubis combined with the main resonator at AA in Fig. 1(d), atransmission zero frequency is also generated on the lowfrequency side of as shown in Fig. 2 when 1, 0.2, and0 is formed when the opened end of 2 line is transformedto a virtual ground at the connection between 2 and 2lines. approaches zero as decreases to zero.

Second, the attenuation at the lowest spurious frequencyof the filter also relies on the value . As is close to zero,the main resonator behaves close to a 4 SIR and its lowesteven-mode resonance frequency is suppressed.

B. Effect of the and VariableThe and values can be adjusted such that of the SIR

is shifted away from . The maximum separation betweenand is obtained when 2/3 as well as using smallvalue [3]. This effect is demonstrated in Fig. 2 where 1and 1 and where 0.3 and 2/3.

IV. FILTER DESIGN AND IMPLEMENTATION

A fourth-order bandpass filter (BPF) can be constructedas shown in Fig. 3. The filters coefficients are based on anequal-ripple filter prototype. The prototype microstrip filter hasa center frequency at 1.41 GHz and has 10% bandwidth. It willbe used in the NASAs Aquarius satellite to reject out-of-bandspurious response up to 6 GHz while providing rejection fromthe on-board radar instrument at 1.265 GHz. A 0.635-mm-thickRogers Duroid 6010 substrate is used in the design. Overall,the filter has a dimension of 44 mm 35 mm. Its detaileddimension is provided in Table I.

U-YEN et al.: BANDPASS FILTER DESIGN 445

Fig. 3. Physical layout of the fourth-order filter on 0.635-mm-thick RogersDuroid 6010 substrate, Z = 50 .

TABLE IFILTERS DETAIL DIMENSION IN MILLIMETER

Fig. 4. Simulated frequency responses of the decibal jS j of the filter in Fig. 3with a transmission zero placed around f (solid line) and without transmissionzero at f (dashed line). The dotted line is the theoretical filter response usinga transmission line model, including a transmission zero at f .

The internal spacing and the inter-stage spacingshown in Fig. 3 are adjusted to provide the proper filter cou-pling coefficient. Two high impedance 4 lines with the linewidth of and are tapped from the left and right SIR,respectively. , and are set to 0.528, 0.3, and 1, re-spectively, thus 36 20 , and 40 . Fromthe given parameters, of the SIR, the lowest even-modeand odd-mode frequencies can be determined to be at 3 and4 , respectively. The line lengths of and areadjusted such that the coupling sections generate transmissionzeros at 3 3.9 , and 4 , respectively, to optimally rejectthe spurious response of the filter. The line length is ad-justed in coordination with the SIO stubs width andsuch that a transmission zero is generated close to 1.265 GHz.The filter is designed and simulated using Ansoft Designer.The theoretical result in Fig. 4 agrees with the method-of-mo-

Fig. 5. Measured and simulated jS j and jS j in decibal versus frequency ofthe fourth-order BPF in Fig. 3.

ments simulation. Using the propose SIRs alone in filter designcan suppress by more than 20 dB. The filter provides atleast 49 dB of attenuation at 1.265 GHz and has the minimumin-band insertion loss of 1.75 dB, as shown in Fig. 5. The devi-ation of the value from 1.265 GHz is caused by asymmetricparasitic couplings from and to and fromand to as shown in Fig. 3, whereas the parasiticcoupling between and has a negligible effecton . The proposed filter produces a broadband attenuation ofat least 39.7 dB up to 3.9 . The suppression around 4.24was as not optimal as in [3] due to transmission zeroes slightmisplacement.

V. CONCLUSION

A new type of SIR has been proposed. The use of a built-ininternal coupler reduces the number of 2 SIRs required bythe filter design. The proposed SIR also shifts the filters lowestspurious resonance frequency to be higher than the maximumlimit of the conventional 2 SIR. The single-layer microstripfilter prototype demonstrates that both low in-band loss and highout-of-band attenuation can be achieved, simultaneously withthis approach.

REFERENCES[1] K. U-yen, W. J. Wollack, T. Doiron, J. Papapolymerou, and J. Laskar,

The design of a compact, wide spurious-free bandwidth bandpassfilter using stepped impedance resonators, in Proc. 35th Eur. Microw.Conf., Paris, France, Oct. 2005, pp. 925928.

[2] , A planar bandpass filter design with extended rejection band-width using double split-end stepped impedance resonators, IEEETrans. Microw. Theory Tech., vol. 54, no. 3, pp. 12371244, Mar.2006.

[3] J.-T. Kuo and E. Shih, Microstrip stepped impedance resonatorbandpass filter with an extended optimal rejection bandwidth, IEEETrans. Microw. Theory Tech., vol. 51, no. 5, pp. 15541559, May2003.

[4] M. Makimoto and S. Yamashita, Bandpass filters using parallelcoupled stripline stepped impedance resonators, IEEE Trans. Mi-crow. Theory Tech., vol. MTT-28, no. 12, pp. 14131417, Dec.1980.