IEEE MICROWAVE AND WIRELESS COMPONENTS LETTERS, VOL. 22, NO. 2, FEBRUARY 2012 67

Branch-Line Coupler Design Operatingin Four Arbitrary Frequencies

Luca Piazzon, Paul Saad, Student Member, IEEE, Paolo Colantonio, Franco Giannini,Kristoffer Andersson, Member, IEEE, and Christian Fager, Member, IEEE

Abstract—This letter presents a successful design approach fora branch-line coupler operating in four arbitrary frequencies. Anoptimized compensation technique is adopted to fulfill satisfactorymatching, transmission and isolation properties within each oper-ating band. Based on the simple planar microstrip technology, theproposed quad-band coupler has been realized and tested. A re-turn loss better than 16 dB, together with an amplitude imbalancelimited to 0.3 dB and an isolation higher than 17.5 dB, have beenexperimentally measured on each operating band, validating theproposed design methodology.

Index Terms—Balanced, branch-line, coupler, multi-band, pas-sive, quad-band.

I. INTRODUCTION

T HE development of modern communication systemswith frequency agility requires multi-band components,

both active and passive. In this context, for example, the designof multi-band power combiner/splitter, with even or unevensplitter factor, is a challenging subject. Among different passiveplanar combining structures, the branch-line coupler representsone of the most attractive component adopted in microwave andmillimeter-wave applications. Advanced configurations havebeen proposed and investigated to design branch-line couplerswith multi-band behavior. For example, approaches based onthe introduction of suitable stubs in a standard branch-linecoupler structure [1]–[4], or exploiting cross-coupling effects[5] or adopting composite right/left-handed transmission linebased structures [6] have been successfully proposed.

In this letter, the design and experimental results of a quad-band branch-line coupler, with arbitrary operating frequenciesis proposed. Starting from the dual-band transmission line( -TL) topology [7], an optimization technique is adopted toextend its behavior in four arbitrary bands obtaining a quad-band -TL. In contrast to the approach presented in [3], in thiscontribution a different design parameter choice is proposed inorder to simultaneously optimize the achievable performancesat each operating band. At the same time, an alternative stubs

Manuscript received November 10, 2011; accepted December 08, 2011. Dateof publication January 27, 2012; date of current version February 15, 2012.

L. Piazzon, P. Colantonio, and F. Giannini are with the Department ofElectronics Engineering, University of Roma Tor Vergata, Rome 00133, Italy(e-mail: luca.piazzon@uniroma2.it).

P. Saad, K. Andersson, and C. Fager are with the Department of Microtech-nology and Nanoscience, Chalmers University of Technology, Gothenburg,Sweden (e-mail: paul.saad@chalmers.se).

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.2011.2181349

Fig. 1. �-topology of the dual-band ���-TL.

configuration is adopted to more easily extend the implementa-tion for a larger number of operating frequencies. Hence, fourquad-band -TLs are properly combined to realize a quad-band branch-line coupler. The experimental measurement of theproposed topology validate the adopted methodology.

II. DESIGN APPROACH

The design of the quad-band branch-line coupler starts con-sidering the -topology of the dual-band -TL [7], reportedin Fig. 1. It is composed of a series transmission line section,having characteristic impedance , shunted at its ports withtwo purely reactive impedances . This network can repro-duce, simultaneously at two arbitrary frequencies ( and ),the behavior of a -TL having characteristic impedance .To obtain such a behavior, the electrical length of the seriestransmission line has to be 90 at the center frequency,

. Moreover, its characteristic impedance andthe shunting elements have to match the following condi-tions [7]:

(1)

(2)

Computing in (1), being , the topology inFig. 1 allows the realization of a perfect -TL behavior withintwo frequencies.

Introducing in the design four arbitrary frequencies (i.e.,) and defining , three different

values for are derived from (1): , and .Obviously, only a single value can be physically adopted for

in Fig. 1. Consequently, the desired -TL behavior cannotsimultaneously be obtained at the four frequencies. Selecting

, as made in [3], results in the proper -TLbehavior at and only. At and , the network is showinga different equivalent characteristic impedance, with a conse-quent return loss that could be unacceptable. In order to optimizethe return loss simultaneously at all the operating frequencies,an average value for should be adopted. In particular, it is

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68 IEEE MICROWAVE AND WIRELESS COMPONENTS LETTERS, VOL. 22, NO. 2, FEBRUARY 2012

TABLE ITHEORETICAL RETURN LOSS OF THE NETWORK IN FIG. 1 FOR DIFFERENT

APPROACHES TO SELECT THE VALUE OF � , ASSUMING � � �� �

Fig. 2. Topology of the quad-band branch-line coupler.

possible to optimize the return loss among the four frequenciescomputing as the geometric mean between the maximumand minimum values among . Since the maximum value is

, the following relationship is adopted for :

(3)

The values (for , 2, 3, 4) are computed through (2) byusing for the value inferred from (3).

To verify that (3) is the best choice for selecting , a nu-merical example is performed. Four arbitrary frequencies havebeen selected: , ,and . The design parameters of the network inFig. 1, i.e., and , have been computed following differentapproaches, assuming for all of them . Table I re-ports the theoretical return loss resulted from the different ana-lyzed cases. Comparing them, one can observes that, selecting

from (3), the return loss of the network is roughly equallymaximized at the four frequencies, resulting in a better averagecondition. On the contrary, in all the other cases worse levels ofreturn loss are obtained for some frequencies.

The design of a quad-band branch-line coupler can be per-formed by properly combining four quad-band -TL struc-tures (Fig. 1) designed following the above described approach.The resulting structure is reported in Fig. 2, where the character-istic impedances, and , of the opposite lines have to becomputed starting from the characteristic impedance requiredby the opposite lines in a classical single frequency branch-linecoupler (i.e., and ). Analo-gously, represents the parallel combination of the re-spective susceptances derived from and at the fourports of the branch-line coupler. In order to realize the required

susceptance for each frequency, the impedance buffer ap-proach proposed in [8] can be adopted. Such a closed form de-sign method, in fact, allows the realization of arbitrary purely

TABLE IIDESIGN PARAMETERS OF THE QUAD-BAND BRANCH-LINE COUPLER

Fig. 3. (a) Picture of the realized quad-band branch-line coupler. The blackrectangle frames the network based on the Impedance Buffer Methodology. (b)Steps sequence for the design of the network based on the Impedance BufferMethodology.

imaginary loads for arbitrary frequencies. The obtained struc-ture is a fully distributed ladder network. Each stub is adoptedto realize a short circuit condition for one of the operating fre-quencies. The length of the series lines is properly selected tofulfill the desired load at the input port of the network. Such amethod has been preferred to the solution proposed in [3] forits easier implementation. In case of four operating frequencies,the network suggested in [3] requires to collapse in the samenode at least four stubs, with a critical placement issue.

III. TEST DESIGN

In order to verify the approach above described, the de-sign of a quad-band branch-line coupler has been carriedout. The selected operating frequencies were ,

, and . The resultingcenter frequency is . To achieve the branch-linecoupler, it is required to realize two quad-band -TL withcharacteristic impedance , and two quad-band

-TL with characteristic impedance . Table IIsummarizes the computed design parameters.

The actual network has been implemented on a Rogers 5870substrate with a dielectric constant and thickness of0.787 mm. A photo of the realized quad-band branch-line cou-pler is shown in Fig. 3(a). In the same figure, the structure basedon the impedance buffer approach that implement the desiredvalues for is framed. As highlighted in Fig. 3(b),the four frequencies have been controlled in descending order(i.e., from to ). The short circuit condition at , andhas been obtained by means of a open circuit stub, whilea via-hole has been adopted for to reduce the structure size

PIAZZON et al.: BRANCH-LINE COUPLER DESIGN OPERATING IN FOUR ARBITRARY FREQUENCIES 69

Fig. 4. Simulated and measured S-parameters of the quad-band branch-linecoupler.

and to achieve DC rejection. Moreover, referring to Fig. 3(b), thefirst ladder cell (C1) is designed to synthesize the desired sus-ceptance at at the input port of the network. Thesecond ladder cell (C2) is added to synthesize the desired sus-ceptance at at the input port of the network. Thelength of the series line of the second cell is selected accountingfor the effect of C1 at . Conversely, C2 does not affect thebehavior at , due to the short circuit imposed by the stub ofC1. The same approach is followed to design the third (C3) andfourth (C4) cells at and , respectively. The overall size ofthe structure is 6.5 cm 7 cm.

IV. EXPERIMENTAL RESULTS

Fig. 4 reports the measured and simulated S-parameters,showing good agreement. From the experimental results, areturn loss greater than 16 dB at the center frequency of eachband has been registered. At the same time, an isolation higherthan 17.5 dB has been measured. The measured amplitudeimbalance is below 0.3 dB. The quadraturecondition is fulfilled at allfrequencies with a maximum deviation of 1.4 .

Table III summarizes the measured performances at each op-erating frequency, comparing them with the ones simulated withideal elements. Moreover, the average performances with theirdeviations are highlighted in Table III. The high performances(in terms of matching, isolation, amplitude balancing and phasequadrature) and the relatively small deviations confirm the va-lidity of the proposed approach. Finally, for completeness, theregistered bandwidth at and have been

TABLE IIIEXPERIMENTAL PERFORMANCE

reported as well. However, it is to remark that no optimizationwas adopted during the design in order to control the resultingbandwidth.

V. CONCLUSION

The design methodology of quad-band branch-line couplersoperating within arbitrary bands has been presented. The theo-retical approach has been validated by means of the realizationand characterization of an actual prototype. Measured results,well in agreement with simulated ones, confirmed the desiredbehavior, highlighting the advantages and feasibility of the pro-posed design approach.

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