General Compensation Method for a Marchand Balun With an Arbitrary Connecting Segment Between the Balance Ports

IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 61, NO. 8, AUGUST 2013 2821

General Compensation Method for a MarchandBalun With an Arbitrary Connecting Segment

Between the Balance PortsChia-Hui Lin, Cheng-Hsun Wu, Guan-Ting Zhou, and Tzyh-Ghuang Ma, Senior Member, IEEE

Abstract—For a Marchand balun, the output imbalance due tothe inevitable physical separation between the balance ports is aproblem. In this paper, a general compensation method to copewith this imbalance issue is proposedwith rigorous analysis and de-sign formulas. The compensation relies on two intentionally short-ened coupling sections and a pair of short-circuited transmissionlines as the terminations. The proposed method is able to deal witha long connecting segment between the balance ports as long as thecoupling sections are tight enough at the desired frequencies. Thetheory and formulation are first treated using transient analysiswith multiple reflections/couplings between the networks. Designgraphs are summarized and three examples are fabricated, vali-dated, and discussed to demonstrate the design flexibility the pro-posed method provides.

Index Terms—Balance output, coupled lines, Marchand balun,phase compensation, short-circuited transmission line.

I. INTRODUCTION

T HE balance-to-unbalance transformer, abbreviated asbalun, is an indispensable component in circuits and sys-

tems involving balanced and unbalanced signals. Dependingon the operating frequency and application, the balun canbe realized using a number of techniques, such as the ferritematerial [1], active devices [2], lumped elements [3], [4], andtransmission-line sections [5]–[28].The Marchand balun, named after its inventor [5], could be

the most popular balun configuration in microwave frequen-cies. It has been widely used in a variety of applications, in-cluding a doubler [6], mixer [7], and balun filter [8]. In gen-eral, a Marchand balun consists of two quarter-wavelength cou-pled-line sections in cascade, with the terminations being open/short circuited for retrieving balanced signals at the outputs.Impedance transformingMarchand baluns were developed withan isolation network in [9]–[11], and its broadband operationwas feasible by multisection configuration [12], [13], multilayerprocess [7], [14], [15], metamaterial technique [16], or patternedground plane [17]. Inductive termination was used in [18] to

Manuscript received May 07, 2013; revised May 28, 2013; accepted May29, 2013. Date of publication June 25, 2013; date of current version August 02,2013. This work was supported by the National Science Council, Taiwan, underGrant 101-2221-E-011-074 and Grant 101-2628-E-011-007-MY3.The authors are with the Department of Electrical Engineering, Na-

tional Taiwan University of Science and Technology, Taipei 10607, Taiwan(e-mail: [email protected]; [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.2013.2268057

Fig. 1. Practical Marchand balun with a connecting segment between the bal-ance ports.

equalize the even- and odd-mode phase velocities and improvethe balun performance. In the meantime, there are also a signifi-cant number of approaches to miniaturize the large size of a con-ventional balun [19]–[27]. In [19], the filter synthesis techniquewas used for size reduction; a compact balun based on octant-wavelength three-line couplers was discussed in [20].Marchandbaluns using slow-wave synthesized transmission lines [21],[22] and lumped-distributed approaches [23], [24] were recentlyreported with remarkable miniaturization capability. The spiraltransformers, despite their low quality factor, are still a commonway to realize very compact Marchand baluns in integrated cir-cuits [25]–[27].Theoretically, a Marchand balun has perfect amplitude/phase

balance when the electrical separation between the outputports is ideally zero. However, in practical circumstances, theinevitable physical separation between the balance ports alwaysrequires an additional line inserted in between for connection,as indicated in Fig. 1. This additional connecting segment,whose electrical length is around several to several tens ofdegrees, dramatically affects the output balance, as well asinput matching; it could severely degrade the performance ofa Marchand balun. The deterioration becomes worse when anintegration fabrication process is involved such that the porttransitions are large when compared to the balun itself.Some designs in the literature implicitly dealt with this issue.

In [21] and [28], without any formulation, the coupling sectionswere shortened to compensate for this additional connectingline. In [22], an approximate compensation was proposed withthe restriction that the connecting segment must be limited toseveral degrees. To date, none of the compensation methodsdiscussed above can be applied universally. A rigorous anal-ysis and general formulas for the compensation of an arbitraryconnecting segment between the balance ports are required toimprove the circuit performance and design flexibility.In this paper, we propose and analyze a general method to

compensate for the imbalance introduced by the connecting line

0018-9480/$31.00 © 2013 IEEE

2822 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 61, NO. 8, AUGUST 2013

Fig. 2. (a) General structure of a Marchand balun. (b) Transient analysis withmultiple reflections and couplings between the coupling sections and termina-tion networks.

between the outputs of a Marchand balun. Here, the impedancetransforming ratio between the balance output and single-endedinput is fixed at 2:1, a typical Marchand balun without imple-menting an isolation network. The key innovation is to use twointentionally shortened coupling sections along with two ter-mination networks to cope with the mismatch and imbalancedue to the additional segment. In Section II, rigorous formulasare derived based on the analysis of multi-reflections and cou-plings between the coupled-line sections and terminations. De-sign graphs are plotted and discussed. As a proof of concept,three examples are developed, fabricated, and experimentallyverified in Section III. The results are compared and discussedto validate the proposedmethod. The last example, with a foldedlayout arrangement, further demonstrates the additional designflexibility the proposed compensation method can provide.

II. THEORY AND FORMULATION

A. General Structure and Formulation

Fig. 2(a) shows a general Marchand balun using coupledtransmission lines operated at . The line segment repre-sents the additional connection between the output ports dueto practical layout consideration; the two termination networks(load a, b) are accounted for by the input reflection coefficients

and . Throughout this paper, the -parameters of thecoupling sections and will be expressed as and ,respectively.

As indicated in Fig. 2(b), the Marchand balun can be ana-lyzed using signal transients at the center frequency with aninput signal . Each time the signal passing through a couplingsection and arriving at the direct port is multiplied by ofthose coupled lines, while the signal appearing at the coupledport is multiplied by . The connecting line provides anadditional phase delay at . In Fig. 2(b), the red solid arrow(in the online version) represents the signal flow without anyreflection, while the green dashed one (in the online version)indicates the signal experiencing one reflection due to the opencircuit or termination, and so on. For better understanding, thetext attached to each signal flow indicates the additional multi-plicator due to the latest reflection, coupling, or delay transmis-sion. Using the summation of all terms due to multiple reflec-tions and couplings, the -parameters of the Marchand balun,with port 1 excited, are

(1)

(2)

(3)

Except for the first term, the remaining terms in (1)–(3) form ageometric progression with a common ratio of .For an ideal Marchand balun, the connecting line is zero

and the termination networks are shorted to ground. In addition, the -parameters of the

coupled lines at are

(4)

(5)

is the coupling coefficient. By substituting (4) and (5) and theabove conditions ( and ) into (1)–(3)and after manipulation, it is routine to verify that the Marchandbalun will achieve perfect input matching and ideal amplitude/phase balance when dB, a well-known criterion for thedesigns in the literature [9].

B. Proposed Compensation Method

However, with the presence of an extra connecting segment, there is an additional phase delay each time the signal passes

LIN et al.: GENERAL COMPENSATION METHOD FOR MARCHAND BALUN 2823

Fig. 3. (a) Proposed compensation method for a Marchand balun with an ar-bitrary connecting segment . (b) Response of a typical backward-wave cou-pled-line coupler for deriving design equations.

TABLE IDESIRED RESPONSES OF THE SHORTENED COUPLING SECTIONS

through the line; from (1)–(3), the phase delay dramatically de-teriorates the input matching and output balance. To work outa general method to compensate for the additional segment ,we propose a new configuration in Fig. 3(a). In this compensa-tion method, the coupling sections and are shortened suchthat their outputs have an overall phase advance equal to theamount of delay due to the connecting segment . In addi-tion, two short-circuited lines are attached to both sides of thebalun as terminations to complete the compensation. For betterunderstanding, the desired responses of the shortened couplingsections and are summarized in Table I. Here, and arethe center operating frequencies of the sections and , at whichthe electrical lengths become and the associated couplingsreach the maximum values as and , respectively. Thetwo sections need not to be the same, and both andshould be greater than 4.8 dB.

Without loss of the generality, here we use the coupling sec-tion as an example to explain the design procedure. Fig. 3(b)illustrates the response of a typical backward-wave coupled-linesection. Its -parameters are known as [29]

(6)

(7)

is the coupling length.At the center frequency , the coupling section reaches its

maximum coupling with . The output phasesand are 90°and0°,respectively,at this frequency.

To achieve a phase advance for line compensation, it is intu-itive from Fig. 3(b) that the Marchand balun should be operatedat a frequency lower than the center frequency of the couplingsection (i.e., ). Now assuming that the thru and coupledports are always kept in phase quadrature (which is true for apractical design over a wide bandwidth), the additional phaseadvance achieved at the thru and coupled ports can be de-rived from (6) and (7) and Fig. 3(b) at as

(8)

Meanwhile, the same as an ideal Marchand balun(Section II-A), the coupling strength of the shortened sec-tion should be kept at 4.8 dB at (Table I),

(9)

The set of (8) and (9) can be solved to determine the requiredcoupling strength , length , and center frequency

of the coupled-line section for achieving the desired phaseadvance and amount of coupling (4.8 dB) at the operatingfrequency of the balun . The details, including the formulasand design graphs, will be introduced in Section II-C.Now, for a set of solutions , making the sectionsatisfy (8) and (9), its -parameters at can be expressed as

(10)

(11)

(12)


Likewise, for the coupling section , there is another set ofsolutions making its -parameters at equal to

(13)

(14)

(15)

In (10)–(15), the two coupling sections show otherwise idealresponses at , except for the additional phase advance.By substituting (10)–(15) back into (1)–(3) with an additional

constraint that

(16)

the -parameters of the Marchand balun can be rearranged as

(17)

(18)

(19)

Clearly, (17)–(19) are still nonideal as most of the terms areover compensated by an additional phase advance or

, a result of the multiple reflections and couplings at theends of the coupling sections. To deal with this and completethe compensation, two short-circuited transmission lines, eachhaving an electrical length of or , serve as the termina-tion networks, as shown in Fig. 3(a). The input reflection coef-ficients looking into the two networks are

(20)

(21)

By substituting (20) and (21) into (17)–(19), it is routine toverify that all nonideal phase terms are cancelled out and thefinal -parameters of the compensated Marchand balun are ide-ally

(22)

(23)

As long as the coupling sections can be properly designedwith their responses identical to (10)–(15) under the constraintof (16), the proposed method can be applied universally to aMarchand balun with an arbitrary connecting segment betweenthe outputs. It provides more layout flexibility in either printedcircuit board (PCB) or integrated circuit fabrication. The designexamples for validation will be illustrated in Section III.

C. Design Graphs for the Coupling Sections

This section provides the formulas and design graphs of thecoupling sections for achieving the desired phase advance (or ) at . First of all, (8) and (9) can be rearranged as

(24)

(25)

Clearly, is not a linear function of , as the two termsare related to each other through the trigonometric functions;the negative sign in (25) could be removed directly since thecoupling length is always a positive value. By substituting (25)into (24), we have

(26)

For a given value of , (26) becomes a transcendental equa-tion and can be solved numerically or graphically for . With

, has one and only one solution.By substituting back into (25), the required coupling

length at could be determined. As indicated in Fig. 3(b),since the frequency is a linear function of the coupling length,the center frequency of the coupling section or can be de-rived by

(27)

With the knowledge of the center operating frequency andmaximum coupling strength, the coupled-line sections canbe designed routinely using the conventional technique for aquarter-wavelength coupler [29].For easy reference, Fig. 4(a) and (b) plots the design graphs

calculated using (25)–(27); here, the system impedance at theunbalance port is set to 50 . Fig. 4(a) shows the required max-imum coupling and normalized center frequencyversus the desired phase advance ; Fig. 4(b) depicts themaximum coupling versus the coupling length at. is also known as the length of the short-circuited termi-

nated line. Taking dB as a figure of merit, the proposedmethod can be used to compensate for a connecting segment upto 70° with and (or ).With even tighter coupling [shadow region in Fig. 4(a)], the ap-plicable compensation range can be further augmented.

III. DESIGN EXAMPLES AND DISCUSSION

Using the formulas and design graphs, three examples are de-veloped, fabricated, and measured in this section for validation.The first example, which is referred to as the single-sided com-pensation, uses the coupling section only for phase adjust-ment. The double-sided compensation is discussed and com-pared in the second balun. In the final example, the Marchandbalun is folded to demonstrate the additional flexibility of the


Fig. 4. Design graphs for the coupling sections in the compensated Marchandbalun. (a) Maximum coupling and normalized center frequency versus the de-sired phase advance. (b) Maximum coupling versus the coupling length at .

Fig. 5. Cross-sectional view of the CPW broadside coupler with dielectricoverlays.

proposed method facilitates. For brevity, all designs were de-veloped using broadside coupled coplanar waveguides (CPWs)on a double-layer 0.508-mm RO4003C substrate (and ) at GHz; nevertheless, the pro-posed balun can be also realized in planar form if multi-con-ductor couplers such as the interdigital or Lange couplers couldbe incorporated [30]. To improve the directivity of the CPWcoupling sections, the dielectric overlay technique [31] was im-plemented. A cross-sectional view of the coupler is depicted inFig. 5. For easy reference, Fig. 6 shows the design graphs for theCPW broadside coupler, including the even-/odd-mode charac-teristic impedances and coupling coefficient versusand .

Fig. 6. Design graphs for the CPW broadside coupler with dielectric overlays.

A. Single-Sided Compensation

The schematic of the first design example is shown inFig. 7(a); the connecting line between the coupling sections is

. In this example, only the coupling section (left) isused for phase compensation; i.e., the coupling section (right)should be designed with and dB.For phase compensation, the electrical length of the short-

circuited line and the phase advance of the coupling sectionare both . From (25) and (26), with , thecoupling length is 61.5 at and the maximum coupling

is calculated as 4.05 dB; the center frequency of thecoupling section , from (27), is 2.64 GHz . Thedesign parameters are summarized in Fig. 7(a).Fig. 7(b) depicts the layout of the single-sided compensated

Marchand balun. The overall size is 49.4 20.7 mm . With thedouble-layer process, the connecting segment isrealized by a grounded coplanar waveguide (CPWG) with thelength mm. For a 50- line, the trace and slot widthsof the CPWG are mm and mm. The CPWbroadside coupling sections are designed using Fig. 6 for thedesired electrical properties. The parameters are mm,

mm, and mm for the section andmm, mm, and mm for the section .

The short-circuited line is also realized by the CPWG. To reducethe parasitic coupling between the termination network and theinput feed line, the short-circuited CPWG is bent intentionallywith mm, mm, and mm for

. The line impedance is also fixed at 50 . All shortcircuits are achieved by connecting the signal trace directly tothe ground; the open circuit is realized by a tapered aperturewith mm and mm. The dielectric overlayhas a width mm, and the rows of vias suppress thepotential surface waves.


Fig. 7. (a) Schematic and (b) circuit layout of the single-sided compensatedMarchand balun.

TABLE IISIMULATED PARAMETERS OF THE COUPLING SECTIONS IN THE

SINGLE-SIDED COMPENSATED MARCHAND BALUN

The compensated Marchand balun was simulated and opti-mized for parasitic effects using the EM simulator HFSS. Thenonideal short-/open-circuited termination can be accounted forby an additional equivalent segment or , whose lengthcan be predicted in advance using the approximate formulasin [32]. However, a fine-tuning process on the compensatedshort-circuited termination is still necessary to take into consid-eration the parasitic coupling between the terminated segmenton the bottom layer and the I/O lines on the top layer. Table IIsummarizes the simulated parameters of the two coupling sec-tions at the center frequency of the Marchand balun andthat of the coupling section . Both sections show goodmatching and high directivity at with the coupling coeffi-cients close to the ideal value (4.8 dB). At 2.64 GHz, the sectionreaches its maximum coupling, also close to the theoretical

value of 4.05 dB.The simulated and measured -parameters, phase differ-

ences, and amplitude imbalances are shown in Fig. 8(a) and

Fig. 8. Simulated and measured: (a) -parameters and (b) phase differencesand amplitude imbalances of the single-sided compensated balun. (c) Compar-ison of the output balances between the single-sided compensated and uncom-pensated baluns.

(b); a photograph of the fabricated sample is shown as an inset.The of the uncompensated balun (with two 90 couplingsections and a 23 connecting line) is also shown in Fig. 8(a)for comparison. The measured results, taken by an AgilentN5242A network analyzer, agree well with the simulatedones. The slight discrepancy can be attributed to the in-house


fabrication, specifically the dielectric overlay. At the centerfrequency GHz , the measured and ofthe balun are 3.5 and 3.1 dB, while the phase differencebetween the outputs is 180.7 .Fig. 8(c) further compares the phase differences and ampli-

tude imbalances of the compensated and uncompensated baluns.Clearly from the figures, the proposed scheme dramatically im-proves the balun performance in terms of either the output bal-ance or input matching. With the criteria of dB,

dB, and , thefractional bandwidths of the compensated and uncompensatedbaluns are 29% 1.65 2.17 GHz and 0%, respectively. Thesomewhat narrower bandwidth, when compared to a typical de-sign 55 70 is likely a result of the unequal responses ofthe coupling sections and , specifically the unequal slopes of

with respect to frequency [see Fig. 3(b)]. A double-sidedcompensated balun with identical responses of the two sectionscould tackle the problem easily; the details will be discussed inSection III-B.

B. Double-Sided Compensation

The schematic of the double-sided compensated balun isshown in Fig. 9(a); for demonstration, the connecting segmentis selected as mm . In this example, the twocoupling sections are designed with equal responses using

. The design graphs in Fig. 4 can beapplied again to determine the electrical parameters. Using(26), the maximum coupling of both sections is 4.15 dB,while the coupling length from (25) is 63.5 at . With(27), the center frequency for maximizing the couplingis 2.55 GHz. Using Fig. 6, the dimensions of the couplingsections are mm, mm, and

mm.The complete circuit layout is shown in Fig. 9(b). The overall

size is 51.8 20.7 mm . For the termination networks, bothshort-circuited lines are 50 with an electrical length of 21.5 .The short-circuited line on the left side is realized by the CPWGwith mm, mm, and mm,while that on the right side, due to the open aperture, is de-signed using the CPW with mm, mm,and mm. The linearly tapered aperture is charac-terized by mm and mm; the width of thedielectric overlay is 4.7 mm.Table III summarizes the simulated electrical parameters of

the coupling sections at the center frequency of the Marchandbalun and that of the coupling sections . Allvalues are very close to the predicted ones using the formulasin Section II. Fig. 10(a) and (b) illustrates the simulated andmeasured -parameters, phase differences, and amplitudeimbalances of the double-sided compensated balun, whileFig. 10(c) compares the output balances of the compensatedand uncompensated baluns. The agreement between the simu-lated and measured results is pretty good.From the figures, the balun performance is significantly

ameliorated. Without the compensation, the impedance band-width does not coincide with the bandwidth having balancedoutputs; in addition, the shifts to the lower frequencyside, a common phenomenon observed in many designs [9],

Fig. 9. (a) Schematic and (b) circuit layout of the double-sided compensatedMarchand balun.

TABLE IIISIMULATED PARAMETERS OF THE COUPLING SECTIONS IN THE

DOUBLE-SIDED COMPENSATED MARCHAND BALUN

[21]. Using the proposed method, the Marchand balun remainswell behaved with dB, dB,and from 1.32 2.48 GHz, orequivalently, a fractional bandwidth up to 64%. At the centerfrequency, the measured and are both 3.2 dB,while the phase difference deviates from the ideal value byonly 1 .The proposed scheme, without much effort by using two

shortened coupling sections and termination networks, pro-vides excellent output balance with an operating bandwidthcomparable to an ideal design.

C. Compensation With Folded Configuration

The final example is shown in Fig. 11. In this design, the com-pensated balun is folded on purpose such that the input/outputports are opposite to one another to facilitate connection in cas-cade. The connecting line has an electrical length ofwith mm, mm, and mm. The


Fig. 10. Simulated and measured: (a) -parameters and (b) phase differencesand amplitude imbalances of the double-sided compensated balun. (c) Compar-ison of the output balances between the double-sided compensated and uncom-pensated baluns.

two coupling sections are designed to have slightly different re-sponses with and . The coupling sec-tion , with , is exactly the same as that in theprevious example and the design details are omitted for sim-plicity. The required parameters of the coupling section , on theother hand, can be calculated using (25)–(27) as dB,

Fig. 11. Circuit layout of the folded compensated Marchand balun.

TABLE IVSIMULATED PARAMETERS OF THE COUPLING SECTIONSIN THE FOLDED COMPENSATED MARCHAND BALUN

at , and GHz. The dimensions aremm, mm, and mm.

Table IV summarizes the simulated parameters of the twocoupling sections. The coupling strengths of both sections arenearly 4.8 dB at the center frequency of the balun ; for thesection , the coupling strength increases to the nominal max-imum value of 4.15 dB at 2.55 GHz, while the maximum cou-pling occurs at 2.79 GHz with dB for section. The short-circuited line connected to section is the same asthat in the previous example, while the short-circuited CPW linefor terminating the section has an electrical length of 25.5with mm, mm, and mm.The linearly tapered aperture is defined by mm,

mm and mm. To reduce the parasiticcoupling between the connecting segment and output traces,the output lines are bent intentionally with mm and

mm. The overall circuit dimension is 26.6 20 mm .The simulated and measured -parameters, phase differ-

ences, and amplitude imbalances of the folded compensatedbalun are shown in Fig. 12(a) and (b); a photograph is shownas an inset. A comparison of the output balances betweenthe compensated and uncompensated baluns is depicted in


Fig. 12. Simulated and measured: (a) -parameters and (b) phase differencesand amplitude imbalances of the folded compensated balun. (c) Comparisonof the output balances between the folded compensated and uncompensatedbaluns.

Fig. 12(c). The agreement is once again very good. At 1.8 GHz,the measured and are 3.1 and 3.2 dB, while thephase difference is 181 . With the criteria of dB,

dB, and , thebandwidth of the folded compensated Marchand balun is from1.32 2.58 GHz, or a fractional bandwidth of 70%.The last example clearly demonstrates the additional flexi-

bility the proposed method provides in practical designs: with

opposite input/output arrangement using shortened couplingsections and a long connecting segment in between.As a summary, the flexibility that the balance ports could be

placed apart without performance degradation is definitely anattraction. Its adaptability is especially suitable for multilayerfabrication process such as themonolithicmicrowave integratedcircuit (MMIC) or low-temperature co-fired ceramic (LTCC) inview of circuit integration with a number of components in closeproximity.

IV. CONCLUSION

In this paper, a new compensation method for a Marchandbalun with an arbitrary connecting segment between the outputshas been developed and rigorously analyzed. The design exam-ples, with comparable performance to the ideal case, clearly val-idate the proposed approach. The phase compensation is com-pleted with two shortened coupling sections together with ter-mination networks. According to the formulation, without mucheffort the proposed method can be used to compensate for a longsegment up to 70 with a pair of typical 3-dB coupled-line cou-plers; it can also increase the design flexibility as the balun couldbe integrated with other circuits easily. To the best of the au-thors’ knowledge, this is the first general compensation methodin the open literature to cope with the output imbalance due tothe physically separated balance ports. Developing an alterna-tive compensation scheme with an arbitrary impedance trans-forming ratio would be a crucial topic worthy of future study.Widening the operating bandwidth using advanced techniquesis another interesting issue deserving further investigation.

ACKNOWLEDGMENT

The authors would like to express their sincere gratitude toProf. C.-C. Chang, National Chung Cheng University, ChiayiCounty, Taiwan, for her valuable suggestion.

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Chia-Hui Lin was born in Nantou, Taiwan, in 1986.He received the B.S. and M.S. degrees in electricalengineering from the National Taiwan University ofScience and Technology, Taipei, Taiwan, in 2009 and2011, respectively.In 2011, he joined the Advantech Corporation,

Taipei, Taiwan, where he is currently an SI Engineer.His research interests include passive and activemicrowave circuit design and antenna designs.

Cheng-HsunWu (S’11) was born in Yunlin, Taiwan,in 1986. He received the B.S. degree in electricalengineering from the National Taiwan University ofScience and Technology, Taipei, Taiwan, in 2009,and is currently working toward the Ph.D. degreeat the National Taiwan University of Science andTechnology.His research interests include active integrated an-

tennas and microwave passive circuit designs.Mr. Wu was the Honorable Mentioned winner of

the Student Paper Competition of the 2011 IEEE In-ternational Symposium on Antennas and Propagation, Spokane, WA.

Guan-Ting Zhou was born in Tainan, Taiwan,in 1990. He received the B.S. degree in electricalengineering from the National Taiwan University ofScience and Technology, Taipei, Taiwan, in 2012,and is currently working toward the Ph.D. degreeat the National Taiwan University of Science andTechnology.His research interests include microwave passive

circuit design and its applications.

Tzyh-GhuangMa (S’00–M’06–SM’11) was born inTaipei, Taiwan, in 1973. He received the B.S. andM.S. degrees in electrical engineering Ph.D. degreein communication engineering from National TaiwanUniversity, Taipei, Taiwan, in 1995, 1997, and 2005,respectively.In 2005, he joined the faculty of the Department of

Electrical Engineering, National Taiwan Universityof Science and Technology, Taipei, Taiwan, where heis currently a Full Professor. His research interests in-clude miniaturized microwave circuit designs, inno-

vative phased arrays, ultra-wideband antennas, and RF identification (RFID).Dr.Mawas the recipient of the Poster Presentation Award of the 2008 Interna-

tional Workshop on Antenna Technology (iWAT), Chiba, Japan, the Best PaperAward of 2011 International Workshop on Antenna Technology (iWAT), HongKong, the 2010 Dr. Wu Da-Yu Award of the National Science Council, the mostoutstanding research award for young researchers in Taiwan. In 2010, he wasalso the recipient of a certificate from the IEEE TRANSACTIONS ON ANTENNASAND PROPAGATION for his exceptional performance as an article reviewer during2009–2010. He was the advisor of the Honorable Mention winner of the IEEEAP-S 2011 Student Paper Competition. In 2012, he was the recipient of the Ex-cellent Young Engineer Award of the Chinese Institute of Electrical Engineeringand was bestowed the title of Distinguished Professor of the National TaiwanUniversity of Science and Technology.

Documents

General Compensation Method for a Marchand Balun With an Arbitrary Connecting Segment Between the Balance Ports