dc6.pdf

994 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 58, NO. 4, APRIL 2010

A Design Method for Microstrip DirectionalCouplers Loaded With Shunt Inductors for

Directivity EnhancementSeungku Lee and Yongshik Lee, Member, IEEE

Abstract—An accurate design method is proposed for directivityenhancement of microstrip directional couplers loaded with shuntinductors. The parasitic effects of junction discontinuities in var-ious parts of such microstrip directional couplers have critical ef-fects especially on the directivity, and therefore they must be takeninto account. Without proper modeling of these parasitic effects,directivity enhancement becomes extremely difficult especially forweak coupling levels. The demonstrated method of analysis can beapplied to obtain exact designs of all previous microstrip direc-tional couplers that are loaded symmetrically with series and/orshunt reactance for directivity enhancement, regardless of the cou-pling levels. Based on the proposed method, a 20-dB microstrip di-rectional coupler is designed at 2.4 GHz. A maximum directivityof 56 dB has been measured, which is an improvement of 48 dBover a conventional microstrip directional coupler. A 16.3% band-width at 2.4 GHz has been measured in which the directivity re-mains above 20 dB, while the maximum variation in the couplinglevel is 0.5 dB. This is the first work to demonstrate directivity ofmore than 50 dB for a 20-dB microstrip directional coupler.

Index Terms—Directional coupler, directivity enhancement,isolation enhancement, microstrip directional coupler, parallelcoupled line, parallel coupled-line coupler, parasitic effect, 20-dBcoupler.

I. INTRODUCTION

V ARIOUS techniques have been proposed to overcomethe inherent problem of microstrip directional couplers,

which is poor directivity. Among them, the method of reactiveloading such as those in [1]–[8] have been a popular choicedue to its relatively simple design procedure, compared withthe methods of distributed compensation [9]–[12] and othertechniques utilizing delay lines [13], spur lines [14], or reflectedpower cancellation [15]–[17].

However, the reactively compensating methods have beendemonstrated experimentally for relatively tight coupling levels

Manuscript received February 24, 2009; revised December 04, 2009. Firstpublished March 15, 2010; current version published April 14, 2010. This workwas supported by the Low Observable Technology Research Center and theDefence Nano Technology Application Center Programs of the Defense Ac-quisition Program Administration and the Agency for Defense Development ofKorea under Contract UD080040GD and Contract UD090088JD.

The authors are with the Department of Electrical and Electronic Engineering,Yonsei University, Seoul 120-749, Korea (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.2010.2042544

only. For instance, [1] and [2] utilize series inductors for direc-tivity enhancement of directional couplers with a relatively tightcoupling level of 10 dB only. This is perhaps due to the designequations that are based on approximate analysis, making themvalid only for tight coupling levels. On the other hand, thedesign equations for the capacitive-compensation techniques in[3] and [4] are accurate. Also, they have a strong advantage ofproviding a superior directivity-enhanced bandwidth, since thecompensating capacitors are seen in the odd mode only but notin the even mode. However, the experimental results are shownfor a fairly tight coupling level of 7 dB only.

Directivity enhancement becomes a much more difficult taskfor weakly coupled directional couplers [18], especially withreactive loading. The most important issue is the parasitic ef-fects related to junction discontinuities that have never been in-vestigated. The effects on the directivity of such couplers maybe detrimental especially for weak coupling levels at high fre-quencies, Therefore, they must be taken into account in the de-sign equation through proper modeling. Otherwise, intensivelayout optimization through time-consuming full-wave simula-tions may be required.

This paper expands the previous work by the authors [8] andfully investigates the design method for microstrip directionalcouplers loaded with shunt inductors for directivity enhance-ment. In Section II and III, a design method is demonstrated fora generalized structure that provide flexibility in design process.Performance depending on the location of loading is investi-gated in detail. In Section IV, the proposed method is comparedwith other reactively compensating methods. Advantages anddisadvantages in various aspects are discussed. In Section V, theparasitic effects are discussed that can be detrimental, especiallyfor loosely coupled couplers that operate at high frequencies. Anew set of design equations is derived to include the capacitancethat model the parasitic effects. In Section VI, experimental re-sults for a 20-dB coupler centered at 2.4 GHz are provided. Fi-nally, conclusion follows in Section VII.

II. MICROSTRIP DIRECTIONAL COUPLER LOADED

WITH SHUNT INDUCTORS

Shown in Fig. 1 are the schematics of a conventional and theproposed microstrip directional couplers. In the proposed direc-tional coupler, the conventional directional coupler is dividedinto three sections and, between two sections of each strip, isloaded with two identical shunt inductors. Maintaining a sym-metric structure is an important factor since an ideal coupler

0018-9480/$26.00 © 2010 IEEE

LEE AND LEE: DESIGN METHOD FOR MICROSTRIP DIRECTIONAL COUPLERS LOADED WITH SHUNT INDUCTORS 995

Fig. 1. Schematics of: (a) conventional and (b) proposed microstrip directionalcouplers.

Fig. 2. Even- and odd-mode equivalent circuit of proposed microstrip direc-tional coupler.

with ideal isolation and matching performance can be realizedif and only if the structure is symmetric [4].

The even- and odd-mode electrical lengths of both couplersin Fig. 1 are such that the lengths are effectively at the de-sign frequency. The proposed coupler in Fig. 1(b) is the generalstructure for the couplers in [8], where the inductors are locatedat the center , and in [6], where the inductorsare located at the ports .

Applying the even- and odd-mode analysis between ports 1and 3, the proposed four-port coupler can be simplified to a setof two identical two-port networks, as shown in Fig. 2. Then,an additional even- and odd-mode analysis between ports 1 and2 (or ports 3 and 4) is applied, the equivalent circuits of whichare shown in Fig. 3 for all four modes. The input impedance ofeach mode in Fig. 3 are

(1)

(2)

(3)

(4)

The -parameters of the two-port even- and odd-mode equiv-alent circuits in Fig. 2 can be expressed by the input impedances

(5a)

(5b)

(5c)

(5d)

Fig. 3. Equivalent circuits of proposed directional coupler: (a) even mode(ports 1 and 3) followed by even mode (ports 1 and 2); (b) even mode (ports1 and 3) followed by odd mode (ports 1 and 2); (c) odd mode (ports 1 and3) followed by even mode (ports 1 and 2); and (d) odd mode (ports 1 and 3)followed by odd mode (ports 1 and 2).

The -parameters of the four-port coupler in Fig. 1(b) can beexpressed by those of the two-port even- and odd-mode equiv-alent circuits in Fig. 2. The relationships are [19]

(6a)

(6b)

(6c)

(6d)

where the subscripts and denote even and odd modes, re-spectively.

Thus, the condition for infinite directivity is. and can be expressed in terms of the even- and

odd-mode -parameters in (5) as

(7a)

(7b)

where is the system impedance.Therefore, the following two conditions are obtained for in-

finite directivity, or :

(8)

(9)

With (5), these conditions can be simplified further to

(10)

(11)

Applying (1)–(4) to (10), the following equation is obtainedfor the inductance :

(12)


where

With the even-mode impedance , the odd-modeimpedance of the original directional coupler and thelocation of loading, , , , and , the inductance thatprovides infinite directivity can be obtained. Also, this condi-tion guarantees not only an isolation null, but also a perfectmatch at the same frequency. To the author’s experience, (12)yields positive solutions for all practical cases.

Equation (11) implies that the system impedance of theproposed directional coupler is no longer the same as the systemimpedance of its conventional counterpart, .This is a common phenomenon for reactively loaded directionalcouplers. Reactively loading a directional coupler improves itsdirectivity but, at the same time, alters the system impedanceand, therefore, the actual coupling level .

In order to maintain the original system impedance andthe coupling level before and after loading, (10), (11), and theequation for the coupling level in (6c) must be solvedsimultaneously. However, the resulting are nonlinear equationsthat are difficult to solve analytically. As an alternative, an itera-tive solution method can be applied, which is discussed in detailin Section III.

Fig. 4 shows the inductance , system impedance , andthe coupling level depending on the location of loading for cou-plers with various coupling levels at 2.4 GHz. The substrate has

3.5, 0.76-mm thickness, 0, and 35- m coppercladding. The figure shows the actual parameters of the initialdesign, which are altered due to loading. The figure also showsthe design parameters of the final design which has the samesystem impedance and the same coupling level as the originalunloaded coupler. The final design is obtained by the iterativesolution method in Section III.

For instance, for a 20-dB coupler with inductors loaded atthe center , the initially calculated inductance is5.771 nH from Fig. 4(a). However, the loaded inductors changethe system impedance from 50 to

96.54 [Fig. 4(b)], resulting in an actual couplinglevel of 17.82 dB [Fig. 4(c)] in a 96.54 system.To compensate for the changes in the system impedance andthe coupling level, the iterative solution method in Section IIIis applied. In the final design, the coupled line needs to be de-signed to have a coupling level of 22.03 dB [Fig. 4(c)] in a

23.78 system [Fig. 4(b)]. When this coupled lineis loaded with 2.504-nH inductors [Fig. 4(a)], the resulting isa coupler with perfect matching, infinite directivity, and exact

20 dB coupling at 2.4 GHz in a 50-system.

Fig. 4. (a) Calculated inductance ��, (b) system impedance �� , and (c) cou-pling level �� as a function of location of loading for various coupling levels.Actual parameters of initial design � � and design parameters of final design

� �.

The results in Fig. 4 indicate that there is no optimum locationfor inductive loading. As can be seen in Fig. 4(a), the minimuminductance is required when the coupler is loaded at the center

, regardless of the coupling level. This is a greatadvantage since lower inductance generally indicates higherand higher self-resonant frequency [20], [21]. Moreover, whenloaded at the center, the actual inductance is half of the valuein Fig. 4(a) since the two shunt inductors can be combined. Onthe other hand, the change in is at its maximum when theinductors are located at the center of the coupler ,while it is at its minimum when they are loaded at the ports

.Fig. 4 suggests that, for very tight coupling, the changes

in the system impedance and the coupling level may be suf-ficiently small to be neglected. However, as the coupling


Fig. 5. (a) Directivity and (b) coupling levels for 5-dB and 30-dB couplers, asa function of location of loading.

becomes weaker, the changes may be sufficiently substantialthat they must be compensated for. This is especially true whenthe inductors are loaded at the center since the change inis the largest. This may be problematic, especially for weakcoupling levels. For a 30-dB coupler, for instance, the coupledline must be designed to have 17.02 , which may betoo low to implement. This can be overcome by loading theinductors at different locations. For instance, for , thecoupled line can be designed to have a much more practicalsystem impedance of 31.34 .

Shown in Fig. 5 are the circuit simulation results for 5-dB and30-dB directional couplers at 2.4 GHz on the same substrate,when the inductors are loaded at the center , at thequarter lengths , and at the end . Ascan be seen, all couplers show nearly infinite directivity withspecified coupling levels at the design frequency. For a verytight coupling level of 5 dB, the three locations show nearly thesame directivity bandwidths, while the coupling bandwidth isthe smallest when loaded at the center. However, as the cou-pling becomes weaker, there is a notable change in the trend.For a very weak coupling level of 30 dB, not only the directivitybandwidth, but also the coupling bandwidth are the smallestwhen the inductors are loaded at the center. The same phenom-enon is observed for loose coupling levels of practical range. Byloading the inductors at other locations, wider bandwidths canbe obtained.

Therefore, the generalized structure in Fig. 1(b) provides adegree of freedom in designing directivity-enhanced microstripcouplers by loading with shunt inductors. One can choose the

optimum location of loading, depending on the design parame-ters such as the inductance and/or the directivity and couplingbandwidths.

III. ITERATIVE SOLUTION METHOD

The iterative solution method serves to obtain the design pa-rameters of the proposed coupler that provide infinite directivitywhile maintaining the system impedance and the coupling levelbefore and after loading. The method compensates for the dif-ferences between the designed and the ac-tual and between the designed and the ac-tual coupling repeatedly, until the differences become neg-ligible. The required inductance is recalculated after each itera-tion stage.

To avoid confusion, the system impedance of theoriginal coupler is denoted as in this section. This leads tothe following relationships between the even-/odd-mode imped-ances and the coupling level :

(13a)

(13b)

Initially, the coupler is designed for a system impedanceof 50 . The initial even- and odd-mode impedances and

electrical lengths of the coupled line are calculated accordingly.Then, the compensating inductance is calculated with (12).From these initial parameters, the actual system impedancein (11) is calculated.

Due to the inductive loading, the actual system impedanceis now different from the designed system impedance .

This leads not only to a poor matching performance, but also toa coupling level in (6c) that is different from the couplinglevel before loading, given by . Moreover, the isolation nullmay not be obtained.

In the first iteration stage, is adjusted in proportion tothe initial . For instance, suppose that the actual afterthe inductive loading is 96.54 while the designed is50 . In this case, the designed in the second stage isset to 50 50/96.54 25.9 . Then the even-/odd-modeimpedances in (13) are adjusted accordingly, and the actualsystem impedance as well as all other electrical parametersare recalculated. Since the recalculated is 55.69 with

25.9 after the first iteration, in the second iterationis now set to 50 25.9/55.69 23.25 . In this way, isadjusted iteratively until converges to 50 . Similarly, theactual coupling level is solved iteratively until it convergesto the original coupling level . In general, the differencebetween the initial and 50 becomes large as the couplinglevels become weaker, requiring more iteration steps.

Based on the proposed method, a 20-dB microstrip direc-tional coupler with a center frequency of 2.4 GHz is designed.A lossless RF-35 substrate with 3.5, 0.76-mm thickness,and 35- m copper cladding is used as the substrate. LineCalcin ADS [22] is utilized to compute the electrical parameters ofthe coupled line. For simplicity, the compensating inductors are


TABLE IDESIGN OF PROPOSED 20-dB COUPLER AT 2.4 GHz WITH INDUCTORS LOADED AT CENTER

Fig. 6. Circuit simulation results for initial and final 20-dB coupler design inTable I for � � 50 �. Results for conventional 20-dB coupler also shown forcomparison.

loaded at the center of the coupled lines, i.e., inFig. 1(b).

Table I summarizes the calculated parameters of the cou-pler after each iteration stage. After only six iterations, and

converged to 50 and 20 dB, respectively, with negligibleerrors for a coupler with a coupling level as weak as 20 dB.The iterative solution method enables to maintain the systemimpedance and the coupling level before and after loading, ina relatively simple manner. It is not a time-consuming processsince any types of simulations or optimizations are not requiredafter each iteration stage.

Fig. 6 shows the circuit simulation results for the initial andfinal designs of the 20-dB directional coupler in Table I. As evi-denced by the figure, the performance of the initial design is farfrom the specified. This is mostly due to the system impedance,

96.5 that is nearly twice as high as the initial systemimpedance 50 . However, the isolation and couplinglevels of the final design at the design frequency meet the speci-fied, which validates the proposed design method. Although di-rectivity is remarkably improved over its conventional counter-part, the matching bandwidth is narrower than the conventionalcoupler, restricting the proposed method for wideband applica-tions.

In rare occasions when the difference between the even-and odd-mode effective dielectric constants are very large forextremely weak coupling levels, the actual system impedance

may be an imaginary number. In this case, the

Fig. 7. Various reactively compensating methods of directivity enhancement.Lumped-element values for 20-dB couplers at 2.4 GHz are: (a) 1.90 nH in [1],(b) 0.16 nH in [2], (c) 80.4 fF in [3] and 82.1 fF in [5], and (d) 112.6 fF in [4]for circuit simulation results shown in Fig. 8.

iterative solution method cannot be applied due to the absenceof initial . However, as seen in Fig. 4, the method providesvalid solutions for all practical coupling levels, regardless ofthe loading locations.

IV. COMPARISON WITH OTHER REACTIVELY

COMPENSATING METHODS

Shown in Fig. 7 are other popular reactively compensatingmethods of directivity enhancement for microstrip directionalcouplers. With the design equations in the corresponding lit-erature, 20-dB directional couplers at 2.4 GHz are designedon the same substrate as that used in Section III. For compar-ison, a 20-dB coupler is designed also by the proposed method.

is chosen since it provides the largest couplingbandwidth. For the method in [3] and [4], the iterative solutionmethod is applied to take into account the changes in the effec-tive dielectric constants.

Circuit simulation results in Fig. 8 show that most of themethods in Fig. 7 provide directivity enhancement over the con-ventional counterpart. On the other hand, only the conventionaland proposed methods and the methods in [3] and [4] providethe specified coupling level of 20 dB at the design frequency of2.4 GHz. Circuit simulation results for the method in Fig. 7(b)are not shown since the design equations in [2] yields negativeelectrical lengths for the coupled-line section.

The design equations in [1] for the method in Fig. 7(a) areonly approximate and are valid only for relatively tight cou-pling levels. For a coupling level as weak as 20 dB, as seen


Fig. 8. Comparison with other reactively compensating methods for 20-dBcouplers. Results for the method in Fig. 7(b) are not included since the designparameter is nonphysical. (a) Directivity. (b) Coupling.

in Fig. 8, a peak in the directivity is not observed while a rel-atively large deviation in the coupling level is seen. Since thestructure in Fig. 7(b) is symmetric, accurate design equationscan be obtained by applying the demonstrated analysis methodin Section II and III.

The design equations in [5] for the method in Fig. 7(c) do notprovide optimum performance. Although directivity enhance-ment is obtained over the conventional coupler in a very widebandwidth, a prominent peak in the directivity is not seen, andthe specified coupling level is not obtained at the design fre-quency. On the other hand, accurate performance is obtainedwith superior directivity bandwidth with the improved designequations in [3] for the same method in Fig. 7(c) as well as withthose in [4] for the method in Fig. 7(d) that utilize only one ele-ment. The superior directivity bandwidths of these methods aredue to the compensating capacitors that are seen in the odd modeonly.

However, from a practical point of view, the capacitivecompensating methods in [3]–[5] suffer from the difficultiesthat the capacitor must be placed in the narrow gap of thecoupled lines. Otherwise, it requires intensive layout opti-mization through time-consuming full-wave simulations tocompensate for the parasitic effects associated with the linesthat connect the capacitors with the coupled line. Moreover, therequired capacitance of 80.4 and 112.6 fF for the methods inFig. 7(c) and (d), respectively, for a 20-dB coupler at 2.4 GHzindicate that the capacitance may be too low to be practicalat higher frequencies. Most importantly, these relatively low

Fig. 9. Microstrip implementation of the proposed directional coupler.

Fig. 10. Circuit and full-wave simulation results for proposed 20-dB direc-tional coupler at 2.4 GHz, with inductors loaded at center.

capacitance levels become more problematic when the parasiticeffects, which will be discussed in Section V, are considered.

Indeed, nearly infinite directivity as well as the exactcoupling level at the design frequency are obtained for the pro-posed method. Although the directivity bandwidth of proposedmethod is narrower compared with the methods in [3] and [4],the proposed method provides a coupling bandwidth that islarger than these methods. Moreover, the freedom in the loca-tion of loading provides more flexibility in the design process.Most importantly, shunt inductors can be easily implementedby grounded stubs in shunt, which makes the proposed methodis far more practical especially at high frequencies.

V. MODELING OF PARASITIC EFFECTS

Fig. 9 shows the microstrip implementation of a proposedcoupled line with the inductors that are loaded at the center, in-cluding the 50- feeding line at each port. The shunt inductorsare realized with grounded stubs in shunt. Shown in Fig. 10 arethe full-wave simulation results from the High Frequency Struc-ture Simulator (HFSS) [23] for the final design of the 20-dB cou-pler in Table I, including the feed line at each port. For compar-ison, the circuit simulation results for the same design in Fig. 6are repeated in this figure. As can be seen, no major difference isseen between the circuit and the full-wave simulation results, ex-cept for the isolation performance that is dramatically degradedin the full-wave simulations.

The major reason is due to the parasitic effects related withjunction discontinuities in various parts of the actual circuit,which are not included in the circuit simulations. For the coupler


Fig. 11. Equivalent circuit of the proposed coupler including capacitors thatmodel dominant parasitic effects, when the coupler is loaded at center and con-nected to feeding lines. The feeding lines are not shown.� � �� in Fig. 1(b).

in Fig. 9, the dominant ones can be modeled as capacitors be-tween the two stubs and between the feeding lines connected toports 1 and 3 and to ports 2 and 4. Therefore, the equivalent cir-cuit of proposed coupler in Fig. 1(b) can be modified to includethese capacitors, as shown in Fig. 11. With parasitic capacitanceof 20 fF and 70 fF, the circuit simulation resultsare now in excellent agreement with the full-wave simulationresults, as shown in Fig. 10.

The capacitances and in Fig. 11 play the exact samerole as does the compensating capacitance in Fig. 7(c) and (d),respectively. They compensate for the odd-mode phase veloc-ities, which in turn alters and of the coupler. In gen-eral, these capacitance are very small, only about several tensof femtofarads.

However, as seen in Section IV, the compensating capaci-tance for a 20-dB coupler at 2.4 GHz is 80.4 fF for the methodin Fig. 7(c) and 112.6 fF for the method in Fig. 7(d). The com-pensating capacitance values of such levels at 2.4 GHz indi-cate that the parasitic capacitance of the order of several tensof femtofarads can be detrimental on the directivity of a cou-pler. More importantly, as the coupling weakens and/or the op-erating frequency increases, the compensating capacitances inFig. 7(c) and (d) become even lower, indicating that the para-sitic effects become more eminent.

The effects of junction discontinuities on the directivity is acommon problem not only for reactively loaded directional cou-plers, but also for the directional couplers utilizing other tech-niques for directivity enhancement [13], [14]. The directivityis affected the most, but the system impedance is also al-tered. However, the importance of parasitic effects on the direc-tivity of directivity-enhanced couplers have never been investi-gated. This is because their effects are not prominent in mostof the previous reactively compensated microstrip directionalcouplers, perhaps due to their relatively tight coupling levelsand/or relatively low operating frequencies. For instance, in [8],the parasitic effects are negligible due to its relatively tight cou-pling level of 10 dB and the relatively low operating frequencyof 0.9 GHz. However, the results in Fig. 10 indicate that the par-asitic effects cannot be ignored for a 20-dB coupler at 2.4 GHzand that they can be modeled properly with capacitors.

As a rule of thumb, when the capacitance that models theparasitic effects are comparable to the compensating capaci-tance, they must be included in the design equations. Other-wise, proper performance may be obtained only through inten-

Fig. 12. Fabricated 20-dB directional couplers: proposed (left) and conven-tional (right).

sive layout optimization via time-consuming full-wave simula-tions.

Accordingly, the design equations for the proposed direc-tional coupler in (1)–(4), (11), and (12) must be modified to in-clude the capacitance that model the parasitic effects. For the di-rectional coupler in Fig. 11, in which the coupled line is loadedat the center , the modified design equationsare

(14)

(15)

(16)

(17)

(18)

where

The iterative solution method in Section III also needs to beapplied to compensate for the changes in the system impedance

and the coupling level due to the inductiveloading as well as parasitic effects.

VI. EXPERIMENTAL RESULTS

For experimental verification, an inductively loaded 20-dBdirectional coupler at 2.4 GHz is fabricated in an RF-35 sub-strate with 3.5, 0.76-mm thickness, and 35- m coppercladding. The inductors are realized with 75- stubs, groundedby via holes of 0.25-mm radius. Fig. 12 shows a photograph ofa fabricated directivity-enhanced directional coupler. For com-parison, a conventional 20-dB directional coupler is also fabri-cated in the same substrate, as shown in the same figure.


TABLE IIFINAL DESIGN PARAMETERS

Since the parasitic effects are fully characterized, a 20-dBcoupled-line coupler in Table I is redesigned to include capaci-tances and in Fig. 11 that model parasitic effects, withinitial values of 20 and 70 fF, respectively. Then, the iterative so-lution method in Section III is applied to meet 50 and

20 dB. The final even-/odd-mode impedances, the totallength of the coupled line, and the inductance that load the lineare 34.70 , 30.24 , 18.39 mm, and 2.53 nH, respectively. Thelarge differences between these design parameters and those inTable I (25.75 , 21.97 , 18.08 mm, and 1.252 nH) in whichthe parasitic effects are not taken into account and which can beobtained also from the design equations in [8] and after applyingthe iterative solution method, indicate how large the impact ofparasitic effects are on the overall performance of a coupler at2.4 GHz with a coupling level as weak as 20 dB. The change inthe parasitic capacitance may be relatively large, even for smallchanges in the layout. The capacitances and in the finaldesign are 15 and 40 fF, respectively.

Finally, the design is optimized in a full-wave simulator,HFSS [23], to compensate for other parasitic reactance in-cluding the via hole effects that are not exactly modeled inFig. 11. The final design parameters are summarized in Table IIalong with those for the conventional 20-dB directional coupler.

The fabricated couplers are measured in the 1–4-GHz rangewith an MS4624D vector network analyzer from Anritsu.Electronic calibration is achieved with a 36584KF calibrationmodule. Fig. 13(a) shows the full-wave simulated and measuredresults for the proposed coupler, which are in excellent agree-ment. A maximum isolation of more than 76 dB with a couplinglevel of 20.1 dB have been measured at 2.41 GHz. Fig. 13(b)shows the measured and simulated directivity and couplinglevels of the proposed and conventional 20-dB directionalcouplers. A maximum directivity of 56 dB has been measuredfor the proposed coupler, whereas the directivity of the conven-tional coupler remains under 9.5 dB in the measured range. Forthe proposed coupler, the directivity remains above 20 dB in a16.3% bandwidth, from 2.25 to 2.65 GHz, in which the max-imum variation in the coupling level is 0.5 dB. In this frequencyrange, the minimum and maximum directivity improvementsof the proposed coupler are 12 and 48 dB, respectively, overthe conventional counterpart. For the conventional directionalcoupler, the maximum variation of the coupling level is 0.2 dBin the same frequency range. This suggests that improvement inthe coupling level bandwidth of the proposed coupler remainsas future work.

VII. CONCLUSION

This paper presents an accurate design method for microstripdirectional couplers, loaded with shunt inductors for directivity

Fig. 13. Full-wave simulated and measured results. (a) �-parameters of pro-posed coupler. (b) Directivity and coupling levels of proposed and conventionalcouplers.

enhancement. Complete design equations are derived for ageneralized structure, providing more design flexibility whendesigning such couplers. Also, the demonstrated iterative so-lution method enables to maintain the system impedance andthe coupling level before and after reactive loading. Moreover,by properly modeling the dominant parasitic effects as capaci-tors, improved design equations are derived to provide properperformance. Among various reactively compensating methodsof directivity enhancement, the proposed method is the mostpractical method especially for weak coupling levels at highfrequencies.

Based on the proposed design method, a 20-dB microstripdirectional coupler loaded with shunt inductors at 2.4 GHzis designed and fabricated. A maximum directivity of 56 dBhas been measured, which is an improvement of 48 dB overa conventional microstrip directional coupler. This is the firstwork to demonstrate directivity of more than 50 dB for a20-dB microstrip directional coupler. The directivity remainsabove 20 dB in a 16.3% bandwidth, with a maximum variationof 0.5 dB in the coupling level. Without proper modeling ofparasitic effects, the superior directivity performance would nothave been possible for a coupling level as weak as 20 dB. Al-though the proposed method is capable of providing the largestcoupling bandwidth among various reactively compensatingmethods, the coupling as well as matching bandwidths are


narrow, compared to the conventional counterpart. Improve-ment in these bandwidths remains as future work.

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Seungku Lee was born in Seoul, Korea, in 1982. Hereceived the B.S. and M.S. degrees from Yonsei Uni-versity, Seoul, Korea, in 2008 and 2010, respectively.

He is currently with the Radio CommunicationResearch Center, Yonsei University. His currentresearch interests include multiband planar circuitsfor microwave applications.

Mr. Lee was the recipient of the Bronze Awardin the Samsung Human-Tech Paper Competition in2008 and the Silver Award in 2010.

Yongshik Lee (S’00–M’04) was born in Seoul,Korea. He received the B.S. degree from YonseiUniversity, Seoul, Korea, in 1998, and the M.S. andPh.D. degrees in electrical engineering from TheUniversity of Michigan at Ann Arbor, in 2001 and2004, respectively.

In 2004, he was a Post-Doctoral Research Asso-ciate with Purdue University, West Lafayette, IN.From 2004 until 2005, he was with EMAG Technolo-gies Inc., Ann Arbor, MI, as a Research Engineer.In September 2005, he joined Yonsei University,

Seoul, Korea, as an Assistant Professor. His current research interests includepassive and active circuitry for microwave and millimeter-wave applicationsand electromagnetic metamaterials.

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