Miniaturized Quasi-Lumped Coupled-Line Single-Section and Multisection Directional Couplers

2924 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 58, NO. 11, NOVEMBER 2010

Miniaturized Quasi-Lumped Coupled-LineSingle-Section and Multisection

Directional CouplersKrzysztof Wincza and Slawomir Gruszczynski

Abstract—A class of lumped-element coupled-line directionalcouplers has been investigated. The paper discusses the influenceof the number of coupler’s subsections on the overall couplers’performance. The design procedure for calculating elements ofthe coupler for the chosen coupling C and the number of coupler’ssubsections has been proposed. The design procedure has beenexperimentally verified by the measurements of a single-sectiondirectional coupler. Also, an asymmetric two-section coupler notreported in the literature has been designed using a lumped-ele-ment technique, and the experimental results are shown.

Index Terms—Directional couplers, lumped-element couplers,multisection couplers.

I. INTRODUCTION

D IRECTIONAL couplers are well-known components inmicrowave engineering. Typically, these networks are de-

signed and manufactured in microstrip or stripline technologyand are composed of either sections of transmission lines or sec-tions of coupled lines. Other competitive technique for direc-tional couplers’ realization is the lumped-element technique. Inthis approach, sections of transmission lines or coupled trans-mission lines are replaced by a network composed of lumpedcapacitors and inductors. This technique of directional couplers’realization has its advantages, such as the possibility of minia-turization, which is important especially for lower frequencyranges, and independence of the coupler’s parameters on thesubstrate chosen for the design. The lumped-element techniqueis well suited and often used for networks’ realization in ad-vanced technologies such as low-temperature cofired ceramic(LTCC) or monolithic microwave integrated circuit (MMIC)technique [1]–[6]. The principles of design of the lumped-el-ement branch line couplers have been comprehensively investi-gated and the design procedures for various realizations of suchnetworks have been shown in [7]. As it is known, such net-works feature relatively narrow bandwidth in contrast to the cou-pled-line couplers for which a bandwidth of one octave is easily

Manuscript received April 01, 2010; accepted August 04, 2010. Date of pub-lication October 07, 2010; date of current version November 12, 2010.

The authors are with the Faculty of Electrical Engineering Auto-matics, IT and Electronics, AGH University of Science and Technology,30-059 Cracow, Poland (e-mail: [email protected]; [email protected]).

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

Digital Object Identifier 10.1109/TMTT.2010.2078970

obtainable from a single-section circuit. A number of papers re-port results of investigation regarding the design of lumped-el-ement coupled-line directional couplers. In [1] and [2], one canfind the designs of 3-dB coupled-line directional couplers inwhich a direct single-section equivalent circuit of coupled lineshas been realized in MMIC technology. In both cases, however,the simplicity is reflected in poor performance of the transmis-sion-coupling characteristics, which limit the bandwidth of thedesignated coupler. In [8], coupled-line directional couplers de-signed in LTCC technology were presented in which coupledinductors were replaced by a connection of uncoupled ones. Theproposed modification, however, limits the operational band-width of the couplers. In [9], a 3-dB directional coupler hasbeen designed with the use of planar spiral transformer tech-nique. The achieved transmission-coupling characteristics arebroadband and are in agreement with the ones obtained with thestandard distributed coupled transmission-line technique. Thepresented approach involves a two-subsection equivalent cir-cuit. Similarly, in [10], a two-subsection equivalent circuit hasbeen employed for the design of a 3-dB quadrature hybrid inGaAs monolithic technology for application in phase shifters,down-converters, and I-Q converters. In [11], an exemplary de-sign of a weak-coupling 24-dB directional coupler designedusing a multilayered organic packaging structure is presented.In this case, the achieved directivity is low due to the fact thatthe obtained isolation is about 25 dB.

In this paper, we present our investigation into the design oflumped-element broadband directional couplers. The influenceof the number of subsections in a lumped-element equivalentcircuit on the coupler’s overall performance has been investi-gated. A simple procedure for calculation of capacitors and in-ductors for arbitrary values of coupling and an arbitrary numberof subsections has been proposed.

In order to verify the presented analysis, a single-section3-dB directional coupler, the equivalent circuit of whichis composed of four elementary subsections, has been de-signed, manufactured, and measured. Moreover, a broadbandtwo-section directional coupler has been experimentally inves-tigated. The presented results prove the possibility of designingbroadband high-performance directional couplers using thelumped-element technique.

II. SINGLE-SECTION DIRECTIONAL COUPLER

The goal of the research is to investigate the propertiesof coupled-line directional couplers designed with the useof the lumped-element technique versus classic coupled-line

0018-9480/$26.00 © 2010 IEEE

WINCZA AND GRUSZCZYNSKI: MINIATURIZED QUASI-LUMPED COUPLED-LINE SINGLE-SECTION AND MULTISECTION DIRECTIONAL COUPLERS 2925

Fig. 1. (a) Generic schematic of a lumped-element coupled-line directional coupler divided into � subsections. (b) Quasi-lumped realization of a subsection withthe use of the symmetrical coupled-line model.

distributed-element directional couplers with emphasis on theoperational bandwidth. The lumped-element equivalent circuitof a coupled-line directional coupler is shown in Fig. 1(a). Thevalues of lumped elements can be found once the coupling ofthe directional coupler, the center frequency , and the numberof subsections chosen for the realization are specified. Weassume that the conditions of ideal coupler realization are met[12], i.e., inductive and capacitive coupling coefficients areequal and the coupled lines are terminated with the properimpedances ( for 1, 2, where , 1,2, is the characteristic impedances of terminating lines, and

, 1, 2, is the characteristic impedance of linein the presence of line , 1, 2, ).At first, we can derive the expressions for capacitance and

inductance elements of the and matrices which describethe properties of coupled lines. These parameters can be foundas

(1)

(2)

(3)

(4)

Having found the values of and , one can calculate thevalues of elements of the directional coupler shown in Fig. 1(a)as

(5)

(6)

(7)

where is the length of the coupler, is thefree-space velocity of light, and coupling of coupled inductorsequals the initially chosen coupling of the directional coupler

.The equivalent circuit of a subsection of the lumped-element

directional coupler can be also represented in a form shownin Fig. 1(b), where coupled inductors have been replaced byan electrically short section of coupled lines at

. Having assumed that the velocities of normal propagatingmodes equal and the physical length of the cou-pled-line section equals , the even and odd modal impedancesof the coupled-line section can be found as

(8)

(9)

where , and the electrical length of the section equals

(10)

Introduction of a coupled-line section realizes the requiredcoupled inductors but also contributes to the self and mutual ca-pacitances, therefore, the correcting capacitances andneed to be subtracted from original values and ; thesevalues can be expressed as

(11)

(12)

For these calculations, a homogeneous air-filled structureis assumed since the values of self and mutual inductancesof coupled lines are invariant with regard to the dielectricproperties. Once the geometry of coupled lines is found in a


Fig. 2. Frequency characteristics of the 3-dB directional coupler analyzedusing the schematic shown in Fig. 1(a) for which � � �.

TABLE IVALUES OF LUMPED SELF AND MUTUAL CAPACITANCES, SELF INDUCTANCES,

EVEN- AND ODD-MODE IMPEDANCES, AND ELECTRICAL LENGTH OF

THE COUPLED-LINE SECTION AND CORRECTING CAPACITANCES FOR

THE DIRECTIONAL COUPLER SHOWN IN FIG. 2 FOR � � ��, � � �,� � 6.6 mm, AND � � 1 GHz

homogeneous medium, one can include dielectric propertieswhich will modify only correcting capacitances so that newvalues can be obtained and , knowing the even- andodd-mode phase velocities for the chosen structure

(13)

(14)

The necessary numerical calculations of the required cou-pled-line section in a chosen dielectric structure can be per-formed using numerical software such as the one presented in[13].

The properties of a lumped-element coupled-line couplerhave been investigated with the use of the schematic shown inFig. 1(a). Fig. 2 shows the normalized frequency characteristicsof a directional coupler for which and

3 dB were chosen. Identical results are obtainedwhen each subsection from Fig. 1(a) is modified as shown inFig. 1(b). The values of lumped elements and the coupled-linesection parameters have been listed in Table I (for 0.707,

, 6.6 mm, and 1 GHz).One can see that such an approach allows for realization of

directional couplers having properties of distributed coupled-line couplers in a wide frequency range. The influence of thechosen number of subsections on the coupler’s properties is

Fig. 3. Return losses of the 3-dB directional coupler analyzed using theschematic shown in Fig. 1(a) for � � 1, 2, 3, 4, and 5.

Fig. 4. Isolation of the 3-dB directional coupler analyzed using the schematicshown in Fig. 1(a) for � � 1, 2, 3, 4 and 5.

presented in Figs. 3 (return loss) and 4 (isolation). As can beseen, the properties of the coupler are very poor for butimprove rapidly for larger ; therefore, broadband operation isensured by the choice of for which return losses and isolationof the directional coupler are acceptable in wide frequency range(i.e., 0 to ). For as low as 3, the return losses and isolationof the 3-dB coupler are better than 25 dB, which is sufficientfor typical applications. The isolation and return losses can beslightly improved when the and parameters are tunedfrom the theoretical values.

The difficulty in the design of quasi-lumped coupled-line di-rectional couplers is to realize coupled inductors. In more ad-vanced technologies such as LTCC or MMIC—where it is pos-sible to realize multilayer circuits—a coupled spiral inductorcan be designed in order to achieve high inductance per unitsquare. In our investigation, we have focused on planar direc-tional coupler realization, hence coupled inductors are designedas short sections of broadside coupled lines.

To verify experimentally the presented theoretical investiga-tion, a single-section 3-dB directional coupler with the couplingimbalance of 0.6 dB has been designed. For the de-sign, and the center frequency 1.2 GHz havebeen chosen. Theoretical frequency characteristics of the ideal


Fig. 5. Frequency characteristics of the 3 � 0.6-dB directional coupler ana-lyzed using the schematic shown in Fig. 1(a) for which � � �.

Fig. 6. Cross section of the dielectric structure used for the design of quasi-lumped coupled-line directional couplers.

lumped-element coupler are shown in Fig. 5. For further elec-tromagnetic analysis, a dielectric structure shown in Fig. 6 hasbeen assumed. The structure consists of a thin 25 m lam-inate layer on which elements of the coupler areetched.

In order to maximally miniaturize the circuit, the coupledstrips’ width has been chosen as narrow as possible (techno-logical limitations) to obtain the highest self-inductance per unitlength which gives the shortest length of the coupled lines, andthe dielectric thickness has been chosen to obtain coupling perunit length greater than desired. The strip offset was tuned in away to achieve appropriate coupling (tuning the offset does notinfluence the self inductance). In the presented design, the width

0.09 mm of coupled lines was assumed. The designeddirectional coupler has been electromagnetically analyzed andoptimized in order to reduce the overall size (meandering of thecoupled-line sections). Fig. 7 shows the layout of the designedcoupler in which all elements are clearly marked. The overallarea of the designed coupler (without 50- transmission lines)equals 17.6 mm . This is half of the size of a standard coupled-line directional coupler designed in a homogeneous broadsidecoupled-line technique using laminates with dielectric constant

and the layer thicknesses 1.52 0.025 1.52 mm. Forsuch a case, the area of only coupled lines equals 38.4 mm .

Fig. 8 shows the electromagnetically calculated frequencycharacteristics of the designed coupler. As it is seen a very good

Fig. 7. Layout of the designed single-section 3-dB directional coupler, thestructure of which has been divided into � � � subsections.

Fig. 8. Frequency characteristics of the designed 3 � 0.6 dB directional cou-pler. Results of electromagnetic analysis.

agreement between theoretical and electromagnetic calculationshas been obtained.

The designed coupler has been manufactured and measured.Fig. 9 presents a photograph of the etched structure of the quasi-lumped directional coupler. For the purpose of measurement,the thin laminate was attached to a measurement fixture madeof a standard microwave thick laminate having input and output50- microstrip lines. A rectangular hole in the measuring fix-ture has been made in a way to ensure that the coupled-linestructure has a cross section that is consistent with the one pre-sented in Fig. 6.

The results of measurement of the designed coupler are pre-sented in Figs. 10–12. The obtained return losses of the designedcoupler are better then 30 dB and isolation is better than 20 dBin a wide frequency range. The measured phase characteristicdiffers from the theoretical value of 90 by less than 7 , andthe dissipation losses are about 0.25 dB measured at the centerfrequency. It is important to comment that the upper and lowerground-planes shown schematically in Fig. 6 have no influenceon the couplers’ behavior since the overall dimensions of the


Fig. 9. Photograph of the thin laminate on which the traces of the designedcoupler are etched.

Fig. 10. Frequency characteristics of the designed 3 � 0.6-dB directionalcoupler.

Fig. 11. Differential phase characteristics of the designed 3 � 0.6-dB direc-tional coupler.

network are small in comparison to the distance of the assumedair layer 5 mm.

A very important advantage of the design of quasi-lumpedcouple-line directional couplers is that the condition of idealcoupler realization, i.e., equalization of inductive and capaci-tive coupling coefficients, can always be fulfilled! Since the ca-pacitive and inductive elements are independently designed, anarbitrary dielectric structure can be chosen. This is opposite tothe solutions presented in, e.g., [14]–[16], where special carehad to be taken while choosing the dielectric structure together

Fig. 12. Measured dissipation losses of the designed 3 � 0.6-dB directionalcoupler.

Fig. 13. Frequency characteristics of a two-section asymmetric 3 � 0.5-dBdirectional coupler analyzed using the schematic shown in Fig. 1(a), in whicheach of the two sections has been divided into � � � subsections.

with coupled-line geometry in order to achieve good propertiesof the directional coupler.

III. ASSYMETRIC MULTISECTION DIRECTIONAL COUPLER

In the next step, multisection directional couplers as pro-posed in [17] and [18] with the exemplary physical realizationspresented in [19]–[21] have been investigated using thequasi-lumped technique. In this approach, each of the sec-tions of the multisection directional coupler is independentlydesigned with the use of the presented method. The couplingcoefficients of coupled-line sections (even-mode impedances)are taken directly from [17] or [18]. For the purposes of investi-gation, a two-section asymmetric directional coupler for whicha center frequency 1.4 GHz, the coupling imbalance of

0.5 dB and the number of subsections for each sectionof the coupler have been assumed. The theoreticalcharacteristics of the designed coupler are presented in Fig. 13and are in agreement with those obtained using distributedcoupled-line sections regarding the transmission and coupling.It should be noted that the frequency characteristics of thedistributed multisection directional couplers differ slightly


Fig. 14. Layout of the designed two-section asymmetric 3� 0.5-dB directionalcoupler in which each of the two sections has been divided into � � � subsec-tions.

Fig. 15. Frequency characteristics of the designed two-section asymmetric 3� 0.5-dB directional coupler.

from the characteristics of lumped-element multisection direc-tional couplers in the sense that zero-coupling frequency ofthe former is lower (zero-coupling frequency is the frequencyfor which coupling equals 0 and transmission equals 1, whichcorresponds to the frequency at which the electrical length ofeach section equals 180 —see Fig. 13). The difference dependson the number of subsections . The larger is, the smallerthe difference in zero-coupling frequency is. For the case of

the zero-coupling frequency is reduced by afactor of 0.9, 0.955, 0.975, and 0.985 respectively. Layout ofthe designed two-section 3-dB directional coupler is presentedin Fig. 14, in which weakly and strongly coupled sections areindicated. The results of measurement of the designed couplerare presented in Fig. 15. In this case, the coupling–transmissionimbalance of the designed coupler differs from the theoreticalone since no equal ripple character is obtained due to manu-facturing inaccuracy. However, the results of the experiment

Fig. 16. Results of the sensitivity analysis of transmission, coupling, and isola-tion characteristics of the two-section asymmetric 3 � 0.5-dB directional cou-pler shown in Fig. 13, in which each of the lumped capacitors’ and inductors’values has been assumed to have normal distribution and deviation equal to 2%.

Fig. 17. Differential phase characteristics of the designed two-section asym-metric 3 � 0.5-dB directional coupler.

prove the possibility of realization of broadband multisectiondirectional couplers with the proposed technique. To illustratethe influence of manufacturing accuracy on the directional cou-pler frequency characteristics, a sensitivity analysis has beenperformed, the results of which are shown in Fig. 16. For thispurpose, the ideal lumped-element directional coupler—shownin Fig. 13—has been analyzed with the assumption that valuesof the lumped elements have a normal distribution and deviationequal to 2% (which has been evaluated based on the manufac-turing accuracy equal to 10 m and actual dimensions of themanufactured coupler).

The return losses of the designed coupler are better than20 dB, and isolation is better than 15 dB in the frequency range0.5–2.5 GHz. The measured phase characteristic in compar-ison to the theoretical one is shown in Fig. 17 and is in closeagreement. In this case, no constant differential phase shift hasbeen achieved since the designed coupler is an asymmetric one[17]. Fig. 18 shows the measured dissipation losses which donot exceed 0.4 dB at the center frequency.

The necessity of equalization of inductive and capacitive cou-pling coefficients in the case of multisection couplers is even


Fig. 18. Measured dissipation losses of the designed two-section asymmetric3 � 0.5-dB directional coupler.

more difficult to fulfill in a classic distributed coupled-line cou-pler design [15], whereas it is easily obtained using the pre-sented technique, which is its main advantage next to the possi-bility of miniaturization.

IV. CONCLUSION

In this paper, a novel approach for the realization ofquasi-lumped coupled-line directional couplers has beenshown. Simple formulas derived from a basic coupled-linedirectional coupler theory are presented. It has been shownthat as little as three subsections are sufficient for realizationof directional couplers having proper frequency response in awide frequency range.

The main advantages of the presented technique are givenhere.

• Possibility of miniaturization: in the case of the manufac-tured single-section directional coupler, a miniaturizationby a factor of over two has been achieved in comparisonto the coupler realized in a typical broadside coupled-linetechnique.

• Possibility of designing directional couplers in commonlyused MMIC, and LTCC techniques.

• Possibility of designing coupled-line directional couplersin an arbitrarily chosen dielectric structure with the possi-bility of equalization of capacitive and inductive couplingcoefficients and, therefore, the possibility of achievinggood isolation and good return losses of the designed cou-pler in a wide frequency range. This is the most importantadvantage.

The presented theoretical analysis has been verified by thedesign and measurements of the single-section 3-dB and thetwo-section asymmetric 3-dB directional couplers, which havenot been previously reported in literature. In both cases, the ob-tained frequency responses of the directional couplers are inagreement with theoretical ones in a wide frequency range, thusproving the possibility of realization of wideband coupled-linedirectional couplers using the quasi-lumped-element technique.

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Krzysztof Wincza was born in Walbrzych, Poland,on May 27, 1979. He received the M.Sc. degree andthe Ph.D. degree in electronics and electrical engi-neering from the Wroclaw University of Technology,Wroclaw, Poland, in 2003 and 2007, respectively.

In 2007, he joined the Institute of Telecommunica-tions, Teleinformatics and Acoustics, Wroclaw Uni-versity of Technology, Wroclaw, Poland. In 2009, hejoined the Faculty of Electrical Engineering Auto-matics, IT and Electronics, AGH University of Sci-ence and Technology, Cracow, Poland, where he be-

come an Assistant Professor. He has authored or coauthored 41 scientific papers.Dr. Wincza was the recipient of The Youth Award presented at the 10th Na-

tional Symposium of Radio Sciences (URSI) and the Young Scientist Grantawarded by the Foundation for Polish Science in 2001 and 2008, respectively.

Slawomir Gruszczynski was born in Wroclaw,Poland, on December 14, 1976. He received theM.Sc. degree and the Ph.D. degree in electronics andelectrical engineering from the Wroclaw Universityof Technology, Wroclaw, Poland, in 2001 and 2006,respectively.

From 2001 to 2006, he was with the Telecom-munications Research Institute, Wroclaw Division,where he was involved in numerous projects formilitary applications. In 2005, he joined the Insti-tute of Telecommunications, Teleinformatics and

Acoustics, Wroclaw University of Technology, Wroclaw, Poland, becomingan Assistant Professor in 2006. In 2009, he joined the Faculty of ElectricalEngineering Automatics, IT and Electronics, AGH University of Science andTechnology, Cracow, Poland. He has authored or coauthored 45 scientificpapers, including journal, conference, and symposium papers.

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Miniaturized Quasi-Lumped Coupled-Line Single-Section and Multisection Directional Couplers