3674 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 60, NO. 12, DECEMBER 2012
Coupled Line 180 Hybrids With Lange CouplersVeljko Napijalo, Member, IEEE
Abstract—This paper presents 180 coupled line hybrids withnoninterspersed inputs/outputs, which utilize Lange couplers. Itdemonstrates that, due to the near-TEM properties of the cou-plers, the asymmetry in power division found in previous work canbe removed. A novel hybrid topology with increased layout flexi-bility and reduced substrate area is proposed and theoretically an-alyzed. Test circuits for the novel hybrid were designed to operateat 8 GHz and fabricated using low-temperature co-fired ceramictechnology. Imperfections of the fabrication process have affectedthe coupled conductors of Lange couplers. A suitable simple modelto account for the differences from the properties assumed in thedesign has been found. Samples have been measured with one portterminated in a grounded resistor, and the influence of termina-tion was de-embedded from measured results. The de-embeddedresults are in good agreement with simulations.
Index Terms—Hybrid couplers, Lange couplers, low-tempera-ture co-fired ceramic (LTCC), multilayer technology, rat race.
I. INTRODUCTION
H YBRID couplers are four-port circuits used for splittingor combining microwave signals. When signals are si-
multaneously applied to the inputs of a 180 hybrid, the sumwill be formed at one output port , while the difference willbe formed at the other output port . A detailed descriptionof a conventional 180 hybrid (rat race) can be found in [1].Numerous improvements of the conventional hybrid have beenreported mainly dealing with increasing the bandwidth [2]–[12],size reduction [13]–[21], simultaneous size reduction and sup-pression of the harmonic response [22]–[24], and dual band op-eration [25]–[30].A new direction of improvements has been introduced re-
cently focusing on the development of 180 hybrids with nonin-terspersed input/output ports. Such a property can be beneficialwhen laying out complexmicrowave circuit. The rearrangementof a layout of the conventional microstrip 180 hybrid to obtainnoninterspersed ports has been described in [31], while in [32],a similar idea was implemented in a low-temperature co-firedceramic (LTCC) technology.A microstrip coupled line 180 hybrid coupler presented in
Fig. 1 was introduced in [33]. It comprises two identical direc-tional couplers. One connection between the couplers is direct,the other one is made using a 180 phase shifting line. In a mul-tilayer technology such as LTCC, couplers can be realized as
Manuscript received April 05, 2012; revised August 11, 2012; accepted Au-gust 24, 2012. Date of publication October 09, 2012; date of current versionDecember 13, 2012.The author is with the Faculty of Technical Sciences, University of Novi Sad,
Novi Sad 21000, Serbia (e-mail: [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.2012.2217980
Fig. 1. Electrical schematic of a 180 coupled line hybrid.
broadside coupled lines and a hybrid with noninterspersed in-puts/outputs can be obtained [34]–[36].If non-TEM couplers are used to construct a coupled line hy-
brid, the only practical choice is to design an over-coupled hy-brid with two frequencies of equal power division asymmetri-cally located with respect to the operating frequency [34]. Thisproperty arises from different velocities of the even and oddmode on non-TEM coupled lines. Single frequency of equalpower division (the canonical response) or symmetrical over-coupling is possible only when couplers are TEM.Near-TEM Lange couplers [37]–[42] are used in this paper to
construct hybrids with the canonical and symmetrical over-cou-pled response. Combining two different types of Lange cou-plers, hybrids with noninterspersed ports are obtained withoutrewiring described in [34]–[36].A coupled line hybrid from Fig. 1 is conveniently laid out
with couplers arranged perpendicularly to each other [33]–[36].A modified hybrid schematic resulting in a more flexible hybridcircuit is introduced and analyzed here. Test samples for the newhybrid have been fabricated using an LTCC technology. Fabri-cated conductors constituting Lange couplers have been foundto have a semi-elliptical cross section in contrast to the rectan-gular assumed in the design. Furthermore, the conductors wereimmersed into a ceramic substrate instead of resting on the topsurface. A simple model for such conductors is proposed andapplied to electromagnetic (EM) simulations. Measured -pa-rameters are presented and compared with EM simulations.
II. COUPLED LINE 180 HYBRID WITH LANGE COUPLERS
A. Application of Lange Couplers in Coupled Line Hybrid
Two properties of Lange couplers presented in Fig. 2 are im-portant from the perspective of this paper. The first one is thenear-TEM property, which is crucial for controlling power di-vision in 180 coupled line hybrids [34]. The second propertyof interest can be anticipated if Fig. 2 is viewed as an integralpicture. When an “unfolded” and a “folded” Lange coupler arealigned, as in the figure, and connected together in a straightfor-ward manner (an input port of one coupler to an adjacent outputport of the other), the remaining inputs are located on the topside of the figure and the outputs are located on the bottom side.Therefore, the combination of Lange couplers from Fig. 2 can be
NAPIJALO: COUPLED LINE 180 HYBRIDS WITH LANGE COUPLERS 3675
Fig. 2. Lange couplers in microstrip technology. (a) Unfolded Lange coupler.(b) Folded Lange coupler.
Fig. 3. Coupled line 180 hybrid with Lange couplers in LTCC technology.
directly used to construct a hybrid with noninterspersed inputsand outputs following the electrical schematic given in Fig. 1.A layout of such a hybrid is shown in Fig. 3 where non-
planar connections between coupled conductors are located onan inner layer of amultilayer substrate. Therefore, wire bonding,inherent to the conventional microstrip Lange couplers, can beavoided. In other words, the hybrid circuit from Fig. 3 can befabricated using a single multilayer process, e.g., LTCC.
B. Design of Hybrid With Lange Couplers
As a first step in the design of the coupled line hybrid withLange couplers, an ideal Lange coupler has been designed usingan EM simulator [43] for the operating frequency of 8 GHz.The ideal coupler circuit, where the connections between theconductors were made through EM ports, is shown in Fig. 4(a).A multilayer LTCC stack was selected comprising 12 layers ofa dielectric material with a relative dielectric constant ,a dielectric loss tangent , and a nominal layerthickness m. Perfect conductors with zero thicknesshave been assumed. The suitable coupling ratio of 7.56 dB [34]has been obtained with a conductor width m and aseparation distance m. The length of the coupler was
m.In the next design step, models of the realistic connections
were added to the EM model of the ideal hybrid. As illustratedin Fig. 3, details of connection arrangements at the ports of twoLange couplers are different. Nonplanar connections were re-alized on the inner layer with m, m
Fig. 4. Connection details of coupled conductors in Lange couplers.
[see Fig. 4(b)] using short traces with the minimum width rec-ommended for the particular LTCC process 100 m . Thediameter of vias was 100 m, and the diameter of via padswas 200 m. New models for Lange couplers have been sim-ulated using [43]. Simulations reveal different maximum cou-pling value and a shift of the maximum with respect to theoperating frequency compared to the values obtained for theideal coupler. The differences can be attributed to the effectsof discontinuities [44], [45] introduced when connections wereadded.Individual Lange couplers were then connected together ac-
cording to Fig. 3 and the integrated hybrid circuit was opti-mized. Two manual EM optimizations have been carried outto obtain one hybrid with the canonical response and the otherwith over-coupling of approximately 1 dB. The goals have beenachieved with m, m, and m,
m, respectively. For both of the hybrids, the length ofthe Lange coupler was m and the approximate totallength of bent phasing line was 7600 m. The width of phasingand terminal lines was m.
C. Simulated Parameters of Hybrid With Lange Couplers
Transmission -parameters corresponding to the canonicaland over-coupled hybrids are shown in Fig. 5(a) and (b), re-spectively. According to the discussion presented in [34], whereresults of similar EM simulation contained large asymmetry,symmetrical responses from Fig. 5 were possible only becauseLange couplers with near-ideal TEM properties have been usedin this study.For the canonical hybrid, the insertion loss of 3 0.5 dB
corresponds to the frequency range of approximately6.8–9.2 GHz. For the over-coupled hybrid, the insertionloss of 3.1 0.6 dB corresponds to the frequency range ofapproximately 6.4–9.5 GHz. Phase imbalance of both of thehybrids, specified as 5 variation form the nominal values, isin the frequency range of 7.6–8.4 GHz.It can be deduced from Fig. 6 that differences between the
canonical and over-coupled hybrid are not significant. The re-turn loss for both of the hybrids is better than 15 dB in the fre-quency range of 6.7–9.5 GHz, and the isolations are better than20 dB within the range of 6.3–9.8 GHz.
III. MODIFIED COUPLED LINE 180 HYBRID
In coupled line 180 hybrids presented in [33]–[36], and inprevious sections of this paper, directional couplers are perpen-dicular to each other. For a number of application this is ade-quate as terminal lines can be bent to meet various layout re-quirements. However, more flexibility when using the hybridin a complex circuit can be obtained if directional couplers can
3676 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 60, NO. 12, DECEMBER 2012
Fig. 5. Results of EM simulation for hybrids from Fig. 3. (a) Transmission-parameters of a hybrid with the canonical response. (b) Transmission -pa-rameters of a hybrid with over-coupled response.
be positioned differently, e.g., in a line. This requires the directconnection between the couplers to be replaced with a short seg-ment of a transmission line, as shown in Fig. 7. Such a modi-fication introduces significant changes in the hybrid circuit andrequires a new theoretical analysis. The circuit shown in Fig. 7can be analyzed analytically carrying out the analysis based onthe matrix method, similar to the analysis described in [34].In the analysis, the directional couplers are assumed to have
TEM properties, i.e., . The requirement for thesimultaneous port match leads to the equation for the electricallength of the coupled section at the operating frequency
(1)
where impedances and are the respective even- and odd-mode impedance of the coupled line, is the normalizingimpedance 50 , and is selected to be .On the other hand, the following equation is obtained by
equating expressions for and (equal power division):
(2)
Fig. 6. Results of EM simulation for hybrids from Fig. 3. (a) , , ,and . (b) and .
Fig. 7. Electrical schematic of a modified 180 coupled line hybrid.
where
(3)
For a single frequency of equal power split, (2) must take a formof a linear equation
(4)
i.e., the quadratic term must vanish. This will be the case if
(5)
NAPIJALO: COUPLED LINE 180 HYBRIDS WITH LANGE COUPLERS 3677
Comparing (4) and (5), it can be concluded that the frequencyof equal power split coincides with the frequency of perfectmatch. The solution of (5) gives a relation
(6)
where normalized impedances andhave been introduced. Replacing this result into (1), a relationbetween electrical length of short transmission line and elec-trical length of coupled section can be obtained
(7)
The coupling at a frequency where electrical length of thecoupler is 90 is
(8)
Using (6) and expressing the result in logarithmic units, the lastequation becomes
(9)
When the electrical length is different from 90 , the couplingof the coupled line TEM coupler is
(10)
Finally, the coupling at the operating frequency is found to be
(11)
Functional dependencies of directional coupler parametersto the electrical length are plotted in Fig. 8. The electricallength of coupled line section can be approximated as alinear function of . Coupling has an approximate value of7.67 dB in a relatively wide range of (the same value as
in the original hybrid from [34]). For , couplingis less than 4.0 dB and can be easily realized using a Langecoupler.For an over-coupled hybrid, (2) must be solved with
. The frequencies of equal power split can be calculatedfrom the following expression:
(12)
These frequencies are located asymmetrically with respect tothe operating frequency where the electrical length is . Itmeans that, when over-coupled, the hybrid from Fig. 7 musthave asymmetric power division with respect to the operatingfrequency.
Fig. 8. Directional coupler parameters for a modified 180 coupled line hybrid.
IV. MODIFIED HYBRID WITH LANGE COUPLERS
A. Hybrid Circuit Design Using 2.5-D EM Simulator
A hybrid circuit with Lange couplers arranged in a line is pre-sented in Fig. 9. Such a hybrid has been designed for the oper-ating frequency of 8 GHz using 2.5-D EM simulations [43]. Thesame dielectric layer stack as in Section II-B was used. For theinitial design, the conductor thickness has been neglected, andthe value for the conductivity was 2.0 10 S/m. The dimen-sions were chosen as in the hybrid presented in Fig. 3. Due tothe complex layout of the hybrid, it was necessary to adjust iter-atively a shape and the length of the added line in conjunctionwith other elements of the circuit. The shape has been adjustedto minimize various discontinuities along with the tuning of theline length to reduce parasitic coupling between the added lineand the phasing line on one side, and between the parallel seg-ments of the phasing line on the other.The other dimensions of the hybrid were optimized by
manual iterative process using the conclusions of the theoret-ical analysis, which has resulted in a minimal number of EMsimulations. Lengthening of has been followed by shorteningof and adjusting and to increase the coupling of Langecouplers. However, the maximum value for the coupling ofthe Lange coupler was limited by the minimum permissibledistance between the conductors on the top layer 100 m .In particular, this relates to the distance between a via padand a neighboring conductor (if m, the minimumvalue for is 150 m). Therefore, the maximum value of
3678 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 60, NO. 12, DECEMBER 2012
Fig. 9. Modified 180 coupled line hybrid with Lange couplers aligned in aline.
Fig. 10. Partitioning of a modified 180 coupled line hybrid circuit into ele-ments suitable for comparison with theoretical analysis ( m,
m, m, m, m, m,m, m, m, m, and
m).
was limited. The length of the phasing line has been adjustedindependently to give required phase ratios and isolation atthe center frequency. The hybrid with optimal performancehas been obtained with m, m, and
m. The other dimensions are given in Fig. 10. The-parameters of the hybrid after optimization are presented inFig. 11.Neglecting the conductor thickness in the case of Lange cou-
plers can introduce a significant error [40]. To fine tune the hy-brid circuit in the final design step, the influence of finite con-ductor thickness of m has been analyzed using three3-D EM simulators [47]–[49], which has resulted in three signif-icantly different values for the over-coupling. As over-couplingcould not be estimated at this stage with sufficient confidence, ithas been decided to fabricate samples as designed with a 2.5-DEM simulator.
B. Comparison Between 2.5-D EM Design and Theory
After the desired performance of the hybrid has beenachieved, the hybrid circuit was partitioned in order to comparethe values of electrical parameters of the optimized circuitwith the values that follow from the theoretical analysis. Thepartitioning is illustrated in Fig. 10. From subsequent 2.5-DEM simulations of the parts, approximate values of , ,and can be calculated from the phases of the transmission-parameters.The theoretical analysis presented in Section III uses the even
and odd characteristics of a pair of coupled lines to derive the
Fig. 11. Results of EM and circuit (CKT) simulation for hybrids from Fig. 9.
important relations between hybrid parameters. These quanti-ties cannot be defined for the four coupled conductor structureof the Lange coupler. However, average even- and odd-modecharacteristics can be calculated from -parameters of a sectionof four coupled lines that are connected at the ports according tothe use in the Lange coupler. A circuit similar to the one shown
NAPIJALO: COUPLED LINE 180 HYBRIDS WITH LANGE COUPLERS 3679
TABLE ICOMPARISON BETWEEN HYBRID PARAMETERS OBTAINEDTHROUGH EM SYNTHESIS AND THEORETICAL ANALYSIS
in Fig. 4(a) with m, m, and mhas been EM simulated and the average even- and odd-modeimpedances, and , respectively, have been calculated usingthe method described in [46] and used in [34].Using the value of normalized even-mode impedance
obtained by the method described in the previous paragraph,and a value of obtained from circuit partitioning, all ofthe other hybrid parameters can be calculated using formulasderived in Section III. The results are presented in the secondrow of Table I. The remaining values of hybrid parametersobtained by circuit partitioning are presented in the third row.Agreement between the two sets of values is very good.In order to examine the possibility to design the hybrid using
a microwave circuit simulator, the ideal schematic from Fig. 7has been created with the electrical parameters of the transmis-sion lines, as shown in Table I. The response of the ideal circuitis shown in Fig. 11 and compared with 2.5-D EM simulations.The position of return-loss minima is almost exactly at the op-erating frequency for circuit simulation, and very close to theoperating frequency for EM simulations. A similar conclusionholds for the isolation minima. The differences in the magni-tudes between ideal circuit and EM analysis and the frequencyshift is due to the presence of various discontinuities in the EMmodel. For the same reason, the frequencies of equal power di-vision are different. Nonetheless, the agreement between thesimulators can be considered as very good. Therefore, besidequalitative usefulness during EM synthesis, theoretical analysiscould have quantitative significance for hybrid design. Wheretechnology limitations are not restrictive as explained, it can beused as an alternative to the iterative process to directly derivethe circuit elements from Fig. 10.
C. Comparison Between Lange Coupler Hybrids and Rat Race
For the sake of the comparison with a known structure, a con-ventional microstrip hybrid has been designed for the same di-electric substrate and operating frequency. The comparison ofthe hybrids is presented in Table II. The area occupied by theLange coupler hybrid circuit presented in Fig. 4 is similar tothe one of the conventional hybrid, and the bandwidths are sim-ilar as well. In such circumstances, for applications where re-solving a complex circuit layout without affecting performancelevel is important, e.g., in mixers, frequency multipliers, or an-tenna array feeding networks, the Lange coupler hybrid fromFig. 3 presents a better choice than the rat race, as it has noninter-spersed input/output ports. For the applications where slightlynarrower bandwidths can be tolerated, the hybrid from Fig. 9can be used instead providing a 22% smaller footprint than the
TABLE IICOMPARISON OF DIMENSIONS AND EM SIMULATED BANDWIDTHS
FOR A RAT-RACE HYBRID AND LANGE COUPLER HYBRIDS
Fig. 12. Fabricated sample circuits for modified 180 coupled line hybrid withLange couplers: type 1: grounded with vias; type 2: grounded with a radial stub.
rat race in addition to noninterspersed input/output ports. Sucha tradeoff can lead to significant space saving when integratingcomplex circuits comprising several hybrids, e.g., I/Q mixersand six-port receivers. Additional space saving will be possibleif the phasing line is meandered. EM simulations results indi-cate that more than 40% size reduction compared to the rat-race is possible without any worsening of the performance fromFig. 11.Comparing with the coupled-line hybrid presented in [34], the
hybrids presented in this paper have wider bandwidth and sim-pler construction (a multilayer crossing between the directionalcouplers is required there to obtain noninterspersed ports).
D. Hybrid Sample Circuits
Test circuits of the hybrid from Fig. 9 have been devised forthe measurements using coplanar waveguide probes. Similarlyto the case described in [34], the measurement facilities avail-able had only three probe arms so only three ports were acces-sible for measurements, while the fourth port was terminatedby soldering a shunt surface mount device (SMD) 50- re-sistor. The number of -parameters that can be measured whena port is terminated with a resistor is restricted. In order tocircumvent the restriction, two identical sample circuits werefabricated—type 1 a where port 1 is terminated into resistorgrounded using vias, and type 1 b where port 2 is terminatedin the same way. This arrangement, shown in Fig. 12, enabled
3680 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES, VOL. 60, NO. 12, DECEMBER 2012
Fig. 13. Measured and EM simulated [47] transmission -parameters. Nota-tion 1 a, 1 b, 2 a, and 2 b in accordance with Fig. 12.
measurements of all -parameters of a hybrid, except isolationbetween ports 1 and 2. On test circuits 2 a and 2 b, the resistorgrounding has been realized using a radial stub merged with re-sistor pad.A number of additional test circuits have been fabricated,
measured, and the results adequately processed to calculate thereflection coefficients of grounded resistors. Reference [34, eqs.(16) and (17)] have been used to de-embed measured resultswhere the influence of the terminations cannot be neglected, inaccordance with the discussion presented there.
Fig. 14. Measured and EM [47] simulated and . Notation 1 a, 1 b, 2 a,and 2 b in accordance with Fig. 12.
V. MEASURED RESULTS AND DISCUSSION
The measured magnitudes of transmission -parameters arepresented in Fig. 13. The measured value of over-coupling,taken as the maximum difference between and insidethe overlapping range, was approximately 2.4 dB for samples1 a and 1 b, and 2.7 dB for 2 a and 2 b. As predicted by(12), power division of the hybrid with such a large amountof over-coupling is asymmetrical with respect to operatingfrequency. The difference of 0.3 dB comes from fabricationtolerances, measurement errors, and neglecting the influence ofnonideal terminations. It is actually a result of much smallershifts of individual and traces in opposite directions.Measured phases of the transmission -parameters are shownin Fig. 13(c). At the operating frequency, they are 177.8 and0.3 .Measured and are presented in Fig. 14, while de-em-
bedded values of and are presented in Fig. 15. De-em-bedded values of are presented in Fig. 16.Except for the over-coupling, the characteristics of the hybrid
are as predicted in Section IV. Phase imbalance, return loss, andisolation bandwidths, according to the definitions from Table II,are 12%, 26%, and 37%, respectively, very similar to the valuesobtained using 2.5-D EM simulations.A high value of over-coupling is a consequence of two major
factors. The first one is linked to inconclusive results of 3-DEM analysis, which prevented any fine tuning of hybrid trans-mission -parameters prior to the fabrication. The second oneis related to the occurrence of critical differences in the fabrica-tion process, which leads to a significant increase in a value ofa coupling coefficient in Lange couplers.In addition to dimensional inaccuracy ( m,m, and m has been measured on the samples),
the conductors on the top surface were completely immersedinto ceramics. A cross section of immersed conductors has beenfound to be semi-elliptical, as shown in Fig. 17(c).A suitable EM model for the semi-elliptical cross section has
been found in a form of a rectangular one. To determine ade-quate values of and for the model, several 2-D quasi-static
NAPIJALO: COUPLED LINE 180 HYBRIDS WITH LANGE COUPLERS 3681
Fig. 15. De-embedded and EM simulated [47] and . Notation 1 a, 1 b,2 a, and 2 b in accordance with Fig. 12.
Fig. 16. De-embedded and EM simulated [47] . Notation 1 a, 1 b, 2 a, and2 b in accordance with Fig. 12.
Fig. 17. Cross sections of coupled conductors in Lange couplers. (a) Zerothickness. (b) As in EM simulations prior to fabrication. (c) As measured onfabricated samples. (d) Equivalent of (c) for EM modeling.
EM simulations have been carried out using LINPAR [50]. Cou-pling coefficients were calculated from even- and odd-mode im-pedances using (8). The results are presented in Table III. For thecase where the dimensions, cross section, and dielectrics weremodeled as on fabricated samples, i.e., as in Fig. 17(c), the cou-pling was approximately 1.6 dB larger than for the infinitely thinconductors from Fig. 17(a). Approximately the same value wasobtained when the conductors had rectangular cross section andnominal dimensions and were immersed into ceramic material,as illustrated in Fig. 17(d). The difference in effective dielectricconstants between the four cases presented in Table III has beenfound negligible.Results of the EM simulations using updated models are pre-
sented in Figs. 13–16 and are in good agreement with measuredresults, especially in regard to over-coupling. This suggests a
TABLE IIICOMPARISON OF 2-D EM SIMULATIONS OF A PAIR OF COUPLED
CONDUCTORS WITH DIFFERENT CROSS SECTION
choice for a 3-D EM simulator and a modeling method to finetune over-coupling in the future designs.
VI. CONCLUSION
Two 180 coupled line hybrids have been presented and de-signed to operate at 8 GHz. The first structure has been con-structed using Lange couplers along with a schematic knownfrom previous work. Due to near-ideal TEM properties of thecouplers, asymmetry in the hybrid response has been removed.The second hybrid structure has been obtained by modifyingthe original schematic to increase layout flexibility. In the mod-ified topology, Lange couplers were arranged in a line and ahybrid footprint was reduced by 22% compared to the conven-tional rat-race coupler with further possibilities for size reduc-tion explained. The theoretical analysis of a modified structurepresented can be applied more generally, e.g., to design a hybridwith parallel TEM couplers.Both hybrids presented have noninterspersed input/output
ports and do not require subsequent wire bonding as multilayerLTCC technology has been used for fabrication, allowingnonplanar connections between the conductors to be realizedon an inner layer. The multilayer crossing between the couplersrequired in previous work has been removed, resulting in asimpler layout.Modeling of coupled conductors having a semi-elliptical
cross section with conductors having a rectangular cross sectionhas been applied to increase the efficiency of EM simulations.Measured results are in good agreement with EM simulation.
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Veljko Napijalo (M’88) was born in Belgrade,Serbia, in 1962. He received the Dipl. Ing., M.Sc.,and Ph.D. degrees in electrical engineering from theUniversity of Belgrade, Belgrade, Serbia, in 1987,1994 and 2010, respectively.In 1987, he joined the Institute of Microwave
Technology and Electronics, IMTEL, Belgrade,Serbia, where he was involved with the design ofactive and passive microwave circuits and devel-opment of the automated measurement methods formicrowave circuits and systems. During this time,
his research interest was in the field of numerical electromagnetics appliedto microwave planar circuit design. From 2001 to 2009, he was with TDKElectronics Ireland, Dublin, Ireland, where he was involved in modeling ofembedded LTCC passive circuits, research and development of active andpassive LTCC components for 24-GHz applications, and advanced electronicpackaging methods. He is currently with the Faculty of Technical Sciences,University of Novi Sad, Novi Sad, Serbia, where he is involved in research onmicrowave circuits in ceramic, polymer, and flexible technologies. He authoredor coauthored over 30 papers published in journals or presented at conferences.He holds two U.S. patents.Dr. Napijalo has been a member of the European Microwave Association
