Collaborative Design of a New Dual-Bandpass 180$^{\circ}$ Hybrid Coupler

$: Collaborative Design of a New Dual-Bandpass 180$^{\circ}$ Hybrid Coupler$
IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 61, NO. 3, MARCH 2013 1053

Collaborative Design of a New Dual-Bandpass180 Hybrid Coupler

Lin-Sheng Wu, Member, IEEE, Bin Xia, Wen-Yan Yin, Fellow, IEEE, and Junfa Mao, Fellow, IEEE

Abstract—A new dual-bandpass 180 hybrid coupler, based onfour properly designed shorted-stub loaded stepped-impedanceresonators, is proposed in this paper. In order to construct thecollaboratively designed coupler/filter, the resonators are cou-pled magnetically and electrically with each other through threeshorted stubs and an open coupled line, respectively. Accordingto the approach of filter synthesis and the derived design equa-tions, the characteristic admittances and electrical lengths of theresonators and coupling sections are determined to achieve thedesired resonant frequencies, external factors, and internalcoupling coefficients for dual passbands. A design procedure isprovided. The design flexibilities for ratios of central frequenciesand achievable bandwidths are explored. The component showsboth filtering and power dividing functions within two specificpassbands, whose good performances are demonstrated by thesimulated and measured results. The two second-order passbandsof a fabricated prototype are located at 2.42 and 5.84 GHz, with4.6% and 5.2% bandwidths, respectively. The insertion losses are1.0 and 1.4 dB over 3-dB power division. The isolations are betterthan 23.5 and 32.8 dB. In both the in-phase and out-of-phase re-sponses, the in-band amplitude and phase imbalances are alwayswithin 1.6–0.6 dB and 6.5 –9.5 , respectively.

Index Terms—Bandpass filter, collaborative design, dual band,180 hybrid coupler, shorted-stub loaded stepped-impedance res-onator (SSLSIR).

I. INTRODUCTION

T HE BANDPASS filter and 180 hybrid coupler are twotypes of important passives to select and divide/combine

RF signals or power in various circuit systems, respectively.They have often been designed with their individual proce-dures and then integrated in cascading geometries, such as thetopology in Fig. 1(a), which leads to the increase of overallcomponent size and losses. In order to develop miniaturizedRF passives with high performances, one collaborative designof filter and 180 hybrid coupler, as shown in Fig. 1(b), hasbeen presented in [1], where a -band bandpass 180 di-rectional coupler is realized with four -mode dielectric

Manuscript received September 04, 2012; revised January 04, 2013; acceptedJanuary 06, 2013. Date of publication February 01, 2013; date of current ver-sion March 07, 2013. This work was supported by the National Basic ResearchProgram of China under Grant 2009CB320204, the National Natural ScienceFoundation of China under Grant 61001014, the China Postdoctoral ScienceFoundation under Grant 201104268, and the Shanghai Postdoctoral ScientificProgram under Grant 11R21414000.The authors are with the Key Laboratory of Ministry of Education of

Design and Electromagnetic Compatibility of High-Speed Electronic Sys-tems, Shanghai Jiao Tong University, Shanghai 200240, China (e-mail:[email protected]; [email protected]; [email protected]).Color versions of one or more of the figures in this paper are available online

at http://ieeexplore.ieee.org.Digital Object Identifier 10.1109/TMTT.2013.2241782

Fig. 1. Schemes to achieve both the functions of 180 hybrid power dividing/combining and bandpass filtering. (a) Cascade of a 180 hybrid coupler and twobandpass filters. (b) Bandpass filtering 180 hybrid coupler.

resonators. In [2], a bandpass rat-race coupler is proposedby using some coupled net-type resonators, with a compactconfiguration and good harmonic suppression obtained. Whencombining a quasi-lumped balun filter and a single-to-commonfilter in low-temperature co-fired ceramic (LTCC), a verycompact bandpass hybrid coupler can be realized [3]. In [4], anLTCC substrate integrated waveguide (SIW) magic-T with athird-order Chebyshev bandpass response has been presentedfor high-frequency applications, where the even and oddresonant modes of each cavity are utilized to get the desiredin-phase and out-of-phase filtering responses, respectively.Both quarter- and half-wavelength microstrip resonators areutilized to construct a compact filter 180 hybrid in [5]. How-ever, it should be indicated that all these 180 hybrid couplersjust have a single-bandpass response.On the other hand, with the rapid development of dual-band

radios, such as GSM/DCS and wireless local area network(WLAN) systems, many miniaturized dual-band passive com-ponents have been reported recently. For dual-band filters, awideband bandpass stub-loaded filter and a narrowband band-stop filter are cascaded to provide two specific passbands [6].In [7] and [8], some synthesis methods have been proposed forthe dual-band filter design with different coupling matrices andtopologies. In [9], some open stubs are employed as resonatorswith dual-band inverters to fulfill the dual-band characteristics.As demonstrated in [10], dual- and triple-bandpass filters canbe constructed by using single-mode and multimode microstripresonators simultaneously. A dual-band filter can be realizedwith two dual-mode ring resonators [11], which can also bebuilt up with only one ring resonator [12] or a patterned patchresonator [13]. Both stepped-impedance resonators (SIRs)[14], [15] and stub-loaded resonators [16], [17] are attractivecandidates as building blocks in dual-band filters, where theirfirst two resonant modes can be utilized to afford the twopassbands. Some methods, as presented in [18] and [19], areproposed especially for realizing dual-band filters with a wideupper stopband. LTCC and SIW dual-band filters have also

0018-9480/$31.00 © 2013 IEEE

1054 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 61, NO. 3, MARCH 2013

been reported in [20]–[23]. A dual-bandpass filter has been re-alized with both SIRs and SIWs [24]. All the above-mentioneddual-band filters have only one input and one output.For dual-band 180 hybrid couplers, the composite right/left-

handed transmission line is firstly applied [25]. By loading openand shorted stubs on a microstrip ring, dual-band operation canbe achieved in the design of some rat-race couplers [26]–[28].Actually, stepped-impedance-stub can provide two desired op-erating bands and helps to miniaturize the coupler simultane-ously [29]. As shown in [30], by loading stubs on a stepped-impedance ring, a dual-band 180 hybrid coupler is realized,even with arbitrary power division ratios. The dual-band 180hybrid ring couplers, built up by a double-sided parallel striplineand ridge SIW, have also been reported in [31] and [32], respec-tively. However, all these dual-band couplers do not have ex-cellent filtering responses, i.e., their frequency selectivities andbandwidths cannot be controlled finely. Therefore, their dualoperating bands cannot be regarded as “dual passbands.”Similar to the case of single-band 180 hybrid coupler/filter,

it is naturally expected that advanced collaborative design ofdual-bandpass 180 hybrid coupler will also be useful. Such anew type of passive component should be able to provide at leastthree functions simultaneously, i.e., in-phase and out-of-phasepower dividing/combining, filtering, and dual-band operation.In this paper, we present the collaborative design of a

new 180 hybrid coupler with a dual-bandpass response.It is based on four properly designed shorted-stub loadedstepped-impedance resonators (SSLSIRs), which are magneti-cally or electrically coupled among one another. Their first twoseries resonant modes are utilized to form the dual passbands.The specific positive and negative internal coupling coefficientsand external factors can be accurately determined by tuningboth the characteristic admittances and electrical lengths for thetwo desired passbands, with the design method and flexibilitiesalso provided for different ratios of central frequencies andbandwidths. The multifunctional performance of our developeddual-band 180 hybrid coupler with suitable bandpass responsehas been demonstrated by both the simulated and measuredresults.

II. ANALYSIS AND DESIGN METHODOLOGY

A. Coupling Scheme of the Dual-Bandpass 180Hybrid Coupler

In this work, the coupling scheme shown in Fig. 2 is utilizedto build up the dual-bandpass 180 hybrid coupler. Similar tothe topology proposed in [1], each port is connected with a res-onator. However, both the dominant and second resonant modesof each resonator are utilized here, and their resonant frequen-cies are designed according to the first and second passbandsof the coupler. The resonators are coupled with their two ad-jacent nodes. The four-port bandpass 180 hybrid coupler canbe synthesized efficiently by modifying the coupling matrix ofa two-port bandpass filter since there are several sophisticatedmethods developed for the synthesis of bandpass filters [33],[34].According to the design theory presented in [1], when a

bandpass 180 hybrid coupler is expected with dual-band equal

Fig. 2. Coupling scheme of the dual-bandpass 180 hybrid coupler.

power divisions, the coupling coefficients and the externalfactors should meet the following requirements:

(1)

(2)

(3)

(4)

where and are two corresponding coupling parametersof a second-order bandpass filter with the specifications of thefirst passband, and are for the second passband, and theother coupling parameters have been marked in Fig. 2. Theycan be determined by the sophisticated theory of filter synthesis.In order to obtain the in-phase and 180 out-of-phase balancedamplitudes between two outputs, the coupling coefficientsand between the second and third resonators have oppositesigns, but the same amplitudes as the other coefficients, whichplay a key role in the realization of the 180 hybrid coupler.For a single passband, the coupled-resonator circuit model

should be extended to the four-port form so as to characterize theresonator-based bandpass 180 hybrid coupler. The reflection,transmission, and isolation coefficients can then be calculatedby

(5a)

(5b)

(5c)

and

(6)

(7)

(8)

(9)

WU et al.: COLLABORATIVE DESIGN OF NEW DUAL-BANDPASS 180 HYBRID COUPLER 1055

Fig. 3. Configuration of the SSLSIR.

(10)

where Ports 1, 2, 3, and 4 are defined in Fig. 2, is the un-loaded factor of each resonator, is the central frequency,and is the fractional bandwidth. The first and last twoidentities in (7) and the first and last two zeros in (8) correspondto the four ports. The elements in the first and last two columnsand rows of represent the coupling coefficients between portsand resonating nodes. The internal and external coupling param-eters in (1) to (4) can be obtained from the elements of thematrixgiven in (9) by [33]

(11)

(12)

For each passband, by obtaining and implementing the cou-pling parameters individually, Ports 2 and 4 can provide twoin-phase outputs when Port 1 is excited and also two out-of-phase outputs when Port 3 is excited. When all the specific cou-pling parameters of dual passbands are finely realized, one de-sired dual-bandpass 180 hybrid coupler will be achieved.

B. SSLSIR

Since each resonator should be coupled with its two adjacentresonators and the two coupling coefficients have the same am-plitude with the same or opposite signs, a symmetric geometryis preferred. Also, there should be enough degrees of freedomfor resonator design since at least four coupling parameters,

, , and , need to be provided. Especially for thesecond and third resonators, two more internal coupling coeffi-cients should be controlled with opposite signs.In our design, a trisection SIR loadedwith two shorted stubs is

employed, as shown in Fig. 3, where , , , and are thecharacteristic admittances of the sections with their electricallengths of , , , and , respectively. For simplification,only the lossless case is considered in the following analysis.From this configuration, it can be seen that the resonator is di-

rectly fed at one end with an external load of . Whenthe imaginary part of the input impedance at the feedingpoint is equal to zero, the corresponding resonance can be cou-pled with such an excitation. The resonating condition is thenwritten as

(13)

Fig. 4. Shorted stub for dual-band magnetic coupling.

where is given by

(14)

The external factors can be calculated by

(15)

where and are the dominant and second resonant frequen-cies, i.e., the central frequencies of the first and second pass-bands, respectively.

C. Magnetic and Electric Couplings Between SSLSIRs

Similar to [14], the dual-band inter-resonator magneticcoupling is realized by a shorted stub at the shorted ends ofSSLSIRs, as shown in Fig. 4. The input susceptance ofthe stub, the residual electrical length , and the value ofthe impedance inverter are given by [35]

(16)

(17a)

(18a)

If the characteristic admittance of the coupling shorted stubis equal to , we have

(17b)

(18b)

The residual electrical length can be absorbed by the -section,i.e., the shorted stub of the SSLSIR.The input impedance looked at from the shorted end

is equal to zero at the resonant frequencies. The reactance slopeparameters and looked at from the shorted endat and are then calculated by

(19)

and

(20)

(21)


Fig. 5. Open coupled line for dual-band electric coupling.

The magnetic coupling coefficient is determined by

(22)

where is the time delay of the shorted stub with the nondis-persive condition assumed. If and are obtainedby filter synthesis, the ratio of two reactance slope parametersshould satisfy

(23)

When (23) is guaranteed, the coupling coefficients of dual pass-bands can be controlled simultaneously by tuning or .The dual-band inter-resonator electric coupling is realized by

a section of open coupled line at the open ends of SSLSIRs,as shown in Fig. 5. It can be equivalent to a -inverter withtwo residual susceptances. The susceptances and of theT-network in Fig. 5 are given by [35]

(24)

(25)

Transforming the T-network into a -network, the values ofand are obtained by

(26a)

(27a)

If and are selected, we have

(26b)

(27b)

The residual susceptance then has the same value as a sectionof open transmission line with the characteristic admittance ofand the electrical length of , which can also be absorbed

by the -section of the SSLSIR in the design.

The input admittance , looked at from the open end, isequal to zero at the resonant frequencies. The susceptance slopeparameters and looked at from the open end atand are calculated by

(28)

and

(29)

(30)

When is small, the value of is almost the same asthe input admittance of the SSLSIR looked at from theright-angle point of the open coupled line. The electric couplingcoefficient is then approximated by

(31)

where is the time delay of the open coupled line also withthe nondispersive condition assumed. If and areobtained by filter synthesis, the ratio of two susceptance slopeparameters should satisfy

(32)

When (32) is guaranteed, the electric coupling coefficients ofthe dual passbands are tuned simultaneously with or .

D. Design of Dual-Bandpass 180 Hybrid Coupler

Four uniform SSLSIRs are utilized to construct thedual-bandpass 180 hybrid coupler, as shown in Fig. 6.When the internal and external coupling parameters of the twopassbands are obtained by the approach of filter synthesis, eachSSLSIR should meet the requirements of (13), (15), (23), and(32) simultaneously. Note that both (13) and (15) include twospecific design conditions. Thus, there are eight independentadmittance and length parameters , , , , , , ,and provided for the six independent design equations. Inthe following design, all the electrical lengths are calculated atthe dominant resonant frequency , i.e., the central frequencyof the first passband.It should be pointed out that there are three more important

things in the design. First, the characteristic admittances andelectrical lengths should be within some realizable ranges. Sec-ondly, the values calculated by the right side of (15) should notvary dramatically within each operating band. Otherwise, thein-band return loss will deviate from the desired values for thedual-bandpass 180 hybrid coupler based on the SSLSIRs, evenwhen the external factors reach their specific values at the twocentral frequencies. Thus, one should carefully explore the de-sign parameters so as to ensure the values obtained from (15)change smoothly. The third one is that a transmission zero


Fig. 6. Schematic diagram of the proposed dual-bandpass 180 hybrid coupler, where ti, tO and tS are the values of , , and , and and .

appears for , , and when the following condition issatisfied:

(33)

where is the frequency ratio of the transmission zero to thefirst central frequency. At , the input impedance of the- and -sections looked at from the four-port conjunction

of a single resonator is equal to zero. However, the transmis-sion zero does not exist in the frequency response of , due tothe open coupled line between the second and third resonators.Therefore, this transmission zero cannot effectively improve theoverall frequency selectivity, but introduce imbalance for theproposed coupler. Thus, it is better to ensure the transmissionzero not too close to the dual passbands, i.e., making the valueof not very close to 1 or .In order to synthesize a dual-bandpass 180 hybrid coupler

with the proposed SSLSIRs, one specific design procedure ispresented as follows.Step 1: According to the design requirements, the coupling

parameters , , , and are determinedby the approach of filter synthesis and (1)–(4).

Step 2: The values of two parameters, such asand , are selected in advance, and then the valuesof other six parameters, , , , , , and , areobtained by solving the six design conditions givenby (13), (15), (23), and (32). It will be shown thatlarger helps to achieve a lower frequency ratioand a larger value of while larger or

helps to provide wider passbands.Step 3: The characteristic admittances , , and are ob-

tained from , , and , respectively.The electrical lengths and are obtained from(22) and (31), respectively. The electrical lengths ofrelated sections of SSLSIRs are reduced byand to compensate the influence of inter-res-onator couplings, according to (17b) and (26b).

Fig. 7. Layout of the proposed dual-bandpass 180 hybrid coupler prototype.

Step 4: The ideal transmission line model is used to predictthe theoretical frequency responses of the couplerfor checking. The in-band return losses are espe-cially concerned. If significant deviations from thedesired performances are observed, we should turnback to Step 2, reselect the values of and ,and then resolve the other structural parameters. Thevalue of should be kept not too close to 1 or

, which can also be achieved by properly se-lecting the preset values of and .

Step 5: The component is implemented with a properlayout, as presented in Fig. 7, and the dimensionsare obtained from the synthesized characteristicadmittances and electrical lengths with the givensubstrate parameters. The influences of discontinu-ities are considered.

Step 6: The configuration of the dual-bandpass 180 hybridcoupler are optimized by using a full-wave commer-cial electromagnetic (EM) solver, such as ANSYSHFSS.


Fig. 8. Theoretical results of the dual-bandpass 180 hybrid coupler with different preset values of and . (a) In-phase response. (b) Out-of-phase response.(c) Amplitude imbalances of the first passband. (d) Amplitude imbalances of the second passband. (e) Phase imbalances of the first passband. (f) Phase imbalancesof the second passband.

E. Theoretical Results of Dual-Bandpass 180 Hybrid CouplerBased on SSLSIRs

A coupler prototype, denoted by C1, is designed to validateour proposed synthesis method. The two central frequencies are

GHz and GHz, both with the in-bandreturn loss better than 15.3 dB and the fractional equal-ripplebandwidth of 5%. The external factors are then synthesizedto be , while the coupling coefficients be-tween SSLSIRs are given by

and .and are then preset, and the other characteristic ad-mittances and electrical lengths of resonators are solved to be

, , ,, , and .

The parameters of the coupling structures are given by, , , ,

and .The theoretical frequency responses are plotted in Fig. 8.

It should be noted that the actual phase differences of theout-of-phase cases are equal to the referred phase imbalances180 in this paper. For the synthesized in-phase response

in Fig. 8(a), has almost the same magnitude as andtheir curves superpose with each other. A transmission zero at3.43 GHz is observed in the responses of , , and , butnot found in . Such a component has good performances


of 0 /180 hybrid power division, bandpass filtering, anddual-band operation. The amplitude and phase imbalancesof the first passband, i.e., 2.39–2.51 GHz, are within 1.0to 0.6 dB and 4.5 to 0.6 , respectively. Those of thesecond passband, i.e., 5.7–6.0 GHz, are within 0.1 to 0.3 dBand 0.2 to 1.2 . The balance performance of the proposedcomponent is not as good as that of nonfiltering 180 hybridcouplers, which is caused by the fast variations of amplitudeand phase introduced by the filtering response.For a conventional single-band rat-race coupler with four 90

arms and an ideal phase inverter, and are given by [36]

(34)

where is the electrical length of each arm and equal to 90 atthe central frequency. The time delay is deduced to be

(35)

where is the central frequency. The group delay at the centralfrequency is then

(36)

It is also found that varies smoothly with the frequency withinthe operating band.However, for a filtering coupler, each arm is replaced by a

second-order filtering structure. The group delay at the centralfrequency can be approximately estimated by [35]

(37)

where is the filter bandwidth, is the order of filteringresponse, and is the correction factor for in-band group-delayestimation. The value of is often chosen as 2 [35]. We thenhave

(38)

If FBW is 5%, will be about 28 times of , and variessignificantly with the frequency, due to the filtering response.Therefore, the group-delay difference between andof the filtering coupler may be much larger than that of a

conventional coupler, which potentially leads to much largerphase imbalance of for the filtering couplerthan that of a conventional coupler.Similarly, its amplitude balance performance is also not as

good as that of conventional couplers. However, the occupiedarea can be saved by using the filtering coupler. Thus, it is atradeoff between area and balance performances. It should alsobe pointed out that cascading a conventional coupler with band-pass filters may also degrade the overall balance performancesof the whole circuit.In order to show the impact of the preselected values of andon the component performances, another prototype, denoted

by C2, is synthesized with the same design requirements. How-ever, the values of and are preset to 0.575 and 45.0 . Thestructural parameters are then obtained to be ,

, , , ,, , , ,

, , and .The theoretical performances of C2 are also plotted in Fig. 8

for comparison. The return loss of the first passband is degradedobviously to 8.5 dB. Its in-band isolation is about 6 dB worsethan that of C1. Its amplitude and phase balance performancesare also not as good as those of C1. The reason is the calculatedright-side value of (15) deceases quickly from 45.8 at 2.39 GHzto 10.9 at 2.51 GHz for C2, while the value only decreases from26.9 at 2.39 GHz to 13.9 at 2.51 GHz for C1. The transmissionzero of , , and is located at 3.09 GHz for C2, closerto the first passband than that of C1. Therefore, the appropriatepreselected and synthesized admittance and length parametersfor C1 are preferred, under the desired design specifications.

F. Design Flexibilities for Ratios of Central Frequencies andFractional Bandwidths

In practical designs, the specific ratios of central frequenciesand fractional bandwidths are usually predetermined by

(39)

(40)

By substituting (12) into (15), it is derived that

(41a)

(41b)

where is the input impedance normalized to .By substituting (11) into (23), we then have

(42)

Similarly, it can be obtained from (11) and (32) that

(43)

For simple analysis, identical normalized parameters are as-sumed for the two passbands simultaneously, i.e.,and , where and . The parameterswithout and with apostrophes are for the first and second pass-bands, respectively. The design equations are then simplified as

(44a)

(44b)

(44c)

Therefore, there are five independent conditions described by(13) and (44) for design.


Fig. 9. Solved structural parameters and achievable fractional bandwidths for the ratios and with different preset parameters of and . (a) andwith and . (b) , , and with and . (c) and with and . (d) and with

and . (e) , , and with and . (f) and with and . In (a) and (d), the red andblue lines (in online version) are for and , respectively. In (b) and (e), the red and blue (in online version) and black lines are for , , and , respectively.In (c) and (f), the red and blue lines (in online version) are for and , respectively.

By further normalizing the characteristic admittances to, we will have three admittance ratios of ,

, and . Together with the four electrical

lengths , , , and at the first central frequency , thereare seven independent structural parameters. When the valuesof and are preset, the other five parameters can be solved


Fig. 9. (Continued.) Solved structural parameters and achievable fractional bandwidths for the ratios and with different preset parameters of and .(g) and with and . (h) , , and with and . (i) and with and . In (g), thered and blue lines (in online version) are for and , respectively. In (h), the red and blue (in online version) and black lines are for , , and , respectively.In (i), the red and blue lines (in online version) are for and , respectively.

from (13) and (44). The design flexibilities for the ratios of cen-tral frequencies and fractional bandwidths can then be explored.By presetting (i) and , the same as

those for the C1 prototype, Fig. 9(a) and (b) shows the values of, , , , and with different ratios of and . If the

maximum and minimum admittance ratios are set to 4.0 and 0.2,respectively, a flexible region can be obtained for design. Thefrequency ratio ranges from 1.8 to 2.8, while the frequencyratio is selected within 0.85 to 2.1. The flexible range ofwill significantly decrease with the increase of .In order to show the influences of the preset and on the

solved values of other parameters and the design flexibilities,the design curves are obtained with (ii) and

and (iii) and . They are plotted inFig. 9(d), (e), (g), and (h) for comparison. Besides the maximumand minimum values of admittance ratios, the flexible region for(iii) is also limited by the condition of and ,which makes the design region more irregular. It is found thatthe achievable range of bandwidth ratio is not much changedwith different values of and , while the frequency ratioranges from 2.3 to 3.0 with , which means the ratio

of two central frequencies will be shifted to higher valueswith smaller preset . It can also be seen from Fig. 9 that thesolved value of is independent from the specific bandwidthratio and the preset value of , and it is determined only bythe required frequency ratio and the preset value of .From (12) and (41), the fractional bandwidth of the first pass-

band is derived as

(45)

Usually, is close to 1, and is set to 50 . The value ofshould be carefully selected to guarantee all the characteristic

admittances satisfy the following condition:

and (46)

where and are theminimum andmaximum realizablecharacteristic admittances of the transmission lines for the dual-bandpass 180 hybrid coupler, respectively. We then have

(47)


The maximum and minimum achievable fractional bandwidth,and , of the first passband can be approximated by

(48a)

(48b)

Note that should be larger than within the flexibledesign region.Here, the minimum and maximum realizable characteristic

admittances, and , are set to 1/200 and 1/25 ,respectively. The evaluated results of the fractional bandwidthsare plotted in Fig. 9(c), (f), and (i) with different preset valuesof and . It is found that the achievable range of (48) variessignificantly from less than 0.5% to more than 60% with the re-quired ratios of central frequencies and bandwidths. It is easy tounderstand that larger or will help to provide wider pass-bands. Further, the maximum and minimum achievable frac-tional bandwidths of the second passband can be estimated bymultiplying and by , respectively.In order to realize a wide passband, the values of and

, provided by the shorted stub and open coupled line, re-spectively, should also be increased. This may lead to relativelylarge values of and . The approximate linear relationshipsbetween the inverter parameters and the operating frequenciesdescribed by (18b) and (27b) cannot then be guaranteed. Somemethods, such as that in [14], should then be introduced to com-plement the errors.The applicable frequency range of the coupled resonator cir-

cuit model for narrowband filters is another limitation on the re-alizable bandwidths of the proposed dual-bandpass 180 hybridcoupler. Thus, as indicated in Section II-C, only the narrowbandcases are analyzed and designed in this paper.

III. RESULTS AND DISCUSSION

As shown in Fig. 10, a 180 hybrid coupler prototype witha dual-bandpass response is fabricated on a Taconic TSM-30substrate, with a relative permittivity of 3.0, a loss tangent of0.0015, and a thickness of 1.016 mm. The design specificationsare the same as those given in Section II-E. The synthesizedadmittance and length parameters of C1 are used to obtain theinitial dimensions with the discontinuities considered. The opti-mized critical dimensions of the component are marked in Fig. 7and listed in Table I. The four SSLSIRs are also illustrated inFig. 7. The overall occupied area of the coupler without fourports is 30.1 28.9 mm , i.e., about 0.41 0.39 , whereis the guided wavelength at 2.45 GHz.The measured and simulated results are plotted in Fig. 11,

with good agreement achieved between them. Both the simu-lated and measured responses are slightly different from the the-oretical results of C1 shown in Fig. 8, which is mainly causedby the influences of discontinuities in the realized coupler, suchas open ends, shorted via-holes, bends, width steps and multi-line conjunctions. However, the performances around the twooperating bands still meet our expectation.The two simulated central frequencies of the coupler proto-

type are 2.43 and 5.82 GHz, and the bandwidths with the re-turn loss better than 15.3 dB are 119 MHz (4.9%) and 299 MHz

Fig. 10. Photograph of the fabricated dual-bandpass 180 hybrid couplerprototype.

TABLE ICRITICAL DIMENSIONS OF THE FABRICATED DUAL-BANDPASS180 HYBRID COUPLER PROTOTYPE (UNIT: MILLIMETERS)

(5.1%), respectively. The corresponding measured values are2.42 and 5.84 GHz with the bandwidth of 112 MHz (4.6%)and 303 MHz (5.2%), respectively. The out-of-band rejectionis better than 20 dB both in simulation as well as measurement.The power leakage between Ports 1 and 3 reaches its maximumsaround the two passbands. The simulated isolation is still betterthan 24.5 and 31.5 dB within the first and second passbands,respectively, while the measured one is better than 23.5 and32.8 dB.To clearly show the dual-bandpass filtering response, the

combined filtering -parameters are plotted in Fig. 11(c), whichare calculated from the simulated and measured results by

(dB)(dB)(dB)

(49)

Both and provide the response of a dual-band bandpassfilter, and each passband is the second-order one. The measuredinsertion losses are about 1.0 and 1.4 dB at the first and secondcentral frequencies, respectively, both agreeing well with the


Fig. 11. Measured (m.) and simulated (s.) frequency responses of the dual-bandpass 180 hybrid coupler prototype. (a) Its in-phase response. (b) Its out-of-phase response. (c) Combined dual-bandpass filtering response.

simulated values of 0.8 and 1.1 dB. The loss differences of 0.2and 0.3 dB are mainly introduced by the SMA connectors usedin measurements.As shown in Fig. 12(a) and (b), the measured in-phase am-

plitude imbalances of the first and second passbands are within1.5–0.4 dB and 0.8–0.0 dB, respectively. The measured

out-of-phase amplitude imbalances of the two bands are within1.6–0.6 dB and 1.4–0.2 dB. The simulated in-phase and

out-of-phase amplitude imbalances in the two passbands varywithin the range of 1.3–1.0 dB.Both the measured and simulated amplitude balance perfor-

mances are degraded slightly, in comparison with the theoret-ical results shown in Fig. 8(c) and (d). The measured varia-tion ranges of the amplitude imbalance within each passbandare close to the simulated ones, but the measured values deviatea little more from 0.0 dB than the simulated results. However,the measured imbalances are always within 1.6–0.6 dB for thetwo passbands, which is still acceptable for many applications.

Fig. 12. Measured (m.) and simulated (s.) imbalances. (a) Amplitude imbal-ances of the first passband. (b) Amplitude imbalances of the second passband.(c) Phase imbalances of the first passband. (d) Phase imbalance of the secondpassband.

The simulated and measured phase imbalances of thefabricated dual-bandpass 180 hybrid coupler are plotted inFig. 12(c) and (d) for comparison. The measured in-phase andout-of-phase imbalances of the first band are from 4.3 to2.1 and 6.5 to 3.5 , respectively, while the measured

values of the second band are from 1.9 to 7.2 and from


TABLE IICOMPARISON BETWEEN MEASURED PERFORMANCES OF THE DUAL-BANDPASS 180 HYBRID COUPLER PROTOTYPE AND PUBLISHED DUAL-BAND COUPLERS

1.6 to 9.5 . The measured phase imbalances are limited from6.5 to 9.5 , which is very close to the variation range from6.2 to 10.2 in our simulation. However, due to the nonideal

characteristics of the configuration, they are both degradedfrom the theoretical range from 4.5 to 1.2 .Table II summarizes the comparison of measured per-

formances between our proposed dual-bandpass 180 hy-brid coupler prototype and the published dual-band 180hybrid couplers. The central insertion losses of our pro-totype are 0.4–0.5 dB higher than the coupler based onstepped-impedance-stub lines [29], which operates at thesimilar frequency bands as ours. The extra loss is due to thedual-bandpass filtering response of the proposed coupler, andit is still smaller than the additionally introduced loss by cas-cading second-order bandpass filters to a nonfiltering coupler.The isolation performance of the bandpass filtering hybridcoupler within its two passbands is comparable to that ofthe nonfiltering counterparts. Although the proposed filteringcoupler has a little worse phase imbalance at the central fre-quencies than the others, its overall imbalance range for the twopassbands is still within the accepted phase imbalance ranges in[25] and [32]. Note that only the phase imbalance informationat the central frequencies is available for the other couplers.The main disadvantage of the presented collaborative proto-

type is its degraded amplitude imbalance, when compared withthe nonfiltering counterparts. This is also caused by the sig-nificant frequency dependence of the dual-bandpass response.Somemethods need to be developed to improve the balance per-formance in the future. However, it is seen from Fig. 1 that theproposed dual-bandpass 180 hybrid coupler can be used to re-place a dual-band 180 hybrid coupler and two dual-bandpassfilters. It should be pointed out that cascading a conventionalcoupler with bandpass filters may also degrade the overall bal-ance performances of the whole circuit. Since the overall occu-pied area will be significantly reduced by using the dual-band-pass 180 hybrid coupler, a tradeoff is now expected to be madebetween the amplitude balance and circuit size.

IV. CONCLUSION

In this paper, a new 180 hybrid coupler has been proposedwith a dual-bandpass filtering response. It is implemented byusing four properly designed SSLSIRs. Their first two resonantfrequencies are located at the expected central frequencies of the

two bands. The magnetic and electric couplings between adja-cent resonators are realized by three shorted stubs and an opencoupled line, respectively, with specific coupling coefficientsprovided for the dual passbands. The resonant frequencies, ex-ternal -factors, reactance, and susceptance slope parametersand internal coupling coefficients are appropriately achieved byfinely tuning both the characteristic admittances and electricallengths of the resonators and the coupling structures. Our de-sign procedure is presented for such a multifunctional coupler,on the basis of the synthesis approach of two-port filters andthe derived design equations of the proposed component. Thedesign flexibilities for ratios of central frequencies and achiev-able bandwidths are carefully analyzed. Further, the influence ofpreselected parameters on the synthesized characteristics is alsoaddressed. The good performances, achieved with the collabo-ratively designed coupler/filter, are demonstrated by the sim-ulated and measured results of the fabricated prototype. Twosecond-order passbands centered at 2.42 and 5.84 GHz, withthe fractional bandwidths of 4.6% and 5.2%, have the centralinsertion losses of 1.0 and 1.4 dB over 3-dB power division,respectively. The in-band isolations are better than 23.5 and32.8 dB for the two specific passbands. In the in-phase andout-of-phase responses, the amplitude and phase imbalancesare always within the ranges of 1.6–0.6 dB and 6.5 –9.5 ,respectively.

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Lin-Sheng Wu (S’09–M’10) was born in 1981. Hereceived the B.S. degree in electronic and informa-tion engineering and M.S. and Ph.D. degrees in EMfields and microwave technologies from ShanghaiJiao Tong University (SJTU), Shanghai, China, in2003, 2006, and 2010, respectively.From August to November 2010, he was a Re-

search Fellow with the Department of Electricaland Computer Engineering, National University ofSingapore (NUS). From February 2010 to January2012, he was a Post-Doctor with SJTU. He is

currently a Lecturer with the Key Laboratory of Ministry of Education ofDesign and Electromagnetic Compatibility of High Speed Electronic Systems,SJTU. Since December 2012, he has been a Research Fellow with NUS. He hasauthored or coauthored over 50 technical papers. His current research interestis mainly focused on novel techniques for microwave integration, passivecomponents, and carbon nanoelectronics.Dr. Wu was a session co-chair of the Asia–Pacific Microwave Conference

(APMC) and IEEEElectrical Design of Advanced Packaging and Systems Sym-posium (EDAPS) in 2011. He is a reviewer of several international journals, in-cluding three IEEE TRANSACTIONS and LETTERS publications.

Bin Xia was born in 1976. He received the B.S.and M.S. degrees in EM fields and microwavetechnologies from the PLA University of Scienceand Technology, Nanjing, China, in 2000, and 2003,respectively, and is currently working toward thePh.D. degree in EM fields and microwave technolo-gies at Shanghai Jiao Tong University, Shanghai,China.FromMay 2003 to November 2005, he was an En-

gineer with the Institute of the General Staff Commu-nication Design, Shenyang, China. Since November

2005, he has been a Lecturer with Zhenjiang Watercraft College, Zhenjiang,China. He is a Reviewer for Progress in Electromagnetics Research (PIER).


Wen-Yan Yin (M’92–SM’98–F’13) received theM.Sc. degree in EM field and microwave techniquefrom Xidian University, Xi’an, China, in 1989, andthe Ph.D. degree in electrical engineering from Xi’anJiao Tong University, Xi’an, China, in 1994.From 1993 to 1996, he was an Associate Professor

with the Department of Electronic Engineering,Northwestern Polytechnic University, Xi’an, China.From 1996 to 1998, he was a Research Fellow withthe Department of Electrical Engineering, DuisburgUniversity, Duisburg, Germany (granted by the

Alexander von Humboldt-Stiftung, Bonn, Germany). In December 1998, hejoined the Monolithic Microwave Integrated Circuit Modeling and PackageLaboratory, Department of Electrical Engineering, National University ofSingapore (NUS), Singapore, as a Research Fellow. In March 2002, he joinedTemasek Laboratories, as a Research Scientist and the Project Leader ofhigh-power microwave and ultra-wideband electromagnetic compatibility(EMC)/electromagnetic interference (EMI). Since April 2005, he has been aProfessor in EM fields and microwave techniques with the School of ElectronicInformation and Electrical Engineering, Shanghai Jiao Tong University,Shanghai, China, where he is currently also the Director and Adjunct Ph.D.He is a Candidate Supervisor with the Center for Microwave and RF Tech-nologies. Since January 2009, he has been with the Center for Optical andElectromagnetic Research, National State Key Laboratory of Modern OpticalInstrumentation, Zhejiang University, Hangzhou, China, as a “Qiu Shi” ChairProfessor. He has authored over 190 international journal papers (over 70IEEE papers). He has authored one international book and 17 book chapters.His chapter, “Complex Media,” is included in the Encyclopedia of RF andMicrowave Engineering (Wiley, 2005). Since 2011, he has been the AssociateEditor of International Journal of Electronic Networks, Devices and Fields.His main research interests include passive and active RF and millimeter-wavedevice and circuit modeling, ultra-wideband interconnects and signal integrity,nanoelectronics, EMC, and EM protection of communication platforms,computational multiphysics, and its application.Dr. Yin has been a guest editor of the IEEE TRANSACTIONS ON COMPONENTS,

PACKAGING AND MANUFACTURING TECHNOLOGY since July 2011. He is anEditorial Board member of the International Journal of RF and MicrowaveComputer-Aided Engineering, Journal of Electromagnetic Waves and Applica-tions (JEMWA), and Progress in Electromagnetics Research (PIER). He wasan IEEE Electromagnetic Compatibility (EMC) Society Distinguished Lecturer(2011–2012). He was the general co-chair of the 2011 IEEE Electrical Designof Advanced Packaging and Systems Symposium (EDAPS’2011), technically

sponsored by the IEEE CPMT Committee. He was also the technical chair ofEDAPS’2006. He is a reviewer for many international journals, including eightIEEE TRANSACTIONS and LETTERS publications. Hewas the recipient of the Sci-ence and Technology Promotion Award of the first class from the local ShanghaiGovernment of China (2005), the National Technology Invention Award of thesecond class from the Chinese Government (2008), and the Best Paper Awardfrom of the 2008 Asia–Pacific Symposium Electromagnetic Compatibility andthe 19th International Zurich Symposium in Singapore.

Junfa Mao (M’92–SM’98–F’12) was born in 1965.He received the B.S. degree in radiation physicsfrom the University of Science and Technologyof National Defense, Changsha, China, in 1985,the M.S. degree in experimental nuclear physicsform the Shanghai Institute of Nuclear Research,Shanghai, China, in 1988, and the Ph.D. degree inelectronic engineering from Shanghai Jiao TongUniversity, Shanghai, China, in 1992.Since 1992, he has been a Faculty Member with

Shanghai Jiao Tong University, where he is currentlya Chair Professor and the Executive Dean of the School of Electronic, Informa-tion and Electrical Engineering. From 1994 to 1995, he was a Visiting Scholarwith the Chinese University of Hong Kong, Hong Kong. From 1995 to 1996, hewas a Postdoctoral Researcher with the University of California, Berkeley, CA,USA. His research interests include the interconnect and package problem ofintegrated circuits and systems, analysis, and design of microwave circuits. Hehas authored or coauthored over 190 journal papers (including 70 IEEE journalpapers) and 120 international conference papers.Dr. Mao is a Chief Scientist of The National Basic Research Program (973

Program) of China. He is a Project Leader of the National Science Foundationfor Creative Research Groups of China. He is a Cheung Kong Scholar of theMinistry of Education, China. He is an Associate Director of the MicrowaveSociety of the China Institute of Electronics. He was the 2007–2009 chair of theIEEE Shanghai Section, the 2009–2011 chair of the IEEE Microwave Theoryand Techniques Society (IEEE MTT-S) Shanghai Chapter. He was the recipientof the National Natural Science Award of China (2004) and the National Tech-nology Invention Award of China (2008), the Best Paper Award of the 2008Symposium of APEMC in conjunction with 19th International Symposium ofZurich EMC.

Collaborative Design of a New Dual-Bandpass 180$^{\circ}$ Hybrid Coupler

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