Dual-band artificial transmission lines branch-line coupler

Dual-Band Artificial Transmission LinesBranch-Line Coupler

Giuseppina Monti, Luciano Tarricone

Department of Innovation Engineering, University of Lecce, Via Monteroni, 73100, Lecce, Italy

Received 10 November 2006; accepted 19 March 2007

ABSTRACT: By using short-circuited Composite Right/Left-Handed Transmission Lines as

loading stubs, and Purely Right-Handed Artificial Transmission Lines, a Dual-Band Branch-

Line coupler is presented. The adoption of such technologies adds degrees of freedom with

respect to other already proposed design techniques, thus allowing the development of a

very compact device, and a larger flexibility in the choice of the two operating frequencies

and corresponding bandwidths. VVC 2007 Wiley Periodicals, Inc. Int J RF and Microwave CAE 18:

53–62, 2008.

Keywords: branch-line coupler; artificial transmission line; composite right/left-handed transmis-

sion line; dual-band

I. INTRODUCTION

Branch-Line couplers (BLC) are quadrature hybrids

widely employed in microwave and millimeter-wave

applications representing key components in balanced

mixers, frequency discriminators, (de)modulators,

and power amplifiers. Unfortunately, due to the elec-

trical length of the Transmission Lines (TLs) equal to

908, conventional BLCs exhibit narrow bandwidths

and a large circuit area. Consequently their applica-

tion to multi/wide-band systems as well as to systems

demanding small size devices is limited.

To address these problems several design techni-

ques have been proposed such as the use of quasi-

lumped elements [1] to obtain both broadband behav-

iour and size reduction or the use of Composite

Right/Left-handed (CRLH) Transmission Lines (TLs)

to design a dual-band BLC [2, 3].

Distributed planar design techniques which allow to

obtain DB performance have been also proposed; among

these, some examples are a BLC made of unequal length

branches [4], a three-Branch Line Coupler (3-BLC), in

which a third branch is added to the two branches of a

conventional BLC [5], and a stub-loaded BLC [6].

In this article, this last approach is employed, par-

ticularly the proposed Dual-Band BLC consists of a

purely right-handed artificial TLs loaded with short

circuited stubs in CRLH technology.

The use of artificial TLs, results in reduced-size

devices with a more flexible frequency response with

respect to the same devices designed by using

conventional right-handed TLs [7]. This leads to a

dual-band BLC whose operating frequencies and cor-

responding bandwidths can be easily customized.

To verify the proposed design strategy, two BLCs

are presented with operating frequencies respectively

equal to: (960, 1600) MHz, (900, 2700) MHz.

The article is structured as follows: first the funda-

mentals of the artificial TLs here employed are given

in Section II; later on the proposed BLC is described

in Sections III and IV. Finally, circuital and full-wave

simulation results are given and discussed in Section

V, and some conclusions drawn in Section VI.

Correspondence to: G. Monti; e-mail: [email protected],[email protected].

DOI 10.1002/mmce.20266Published online 26 September 2007 in Wiley InterScience

(www.interscience.wiley.com).

VVC 2007 Wiley Periodicals, Inc.

53

ARTIFICIAL TRANSMISSION LINES

Artificial TLs are periodic networks whose unit cell

consists of a TL of length d, much shorter than the TL

wavelength, loaded with series or shunt elements, so

that the network acts as an effectively homogeneous TL.

Depending on the loading element the line exhibits a

purely right-handed or a CRLH behavior. Particularly,

by using as loading element a shunt capacitance C (see

Fig. 1a) an artificial TL can be obtained, whose charac-

teristic impedance and phase velocity are given by:

Z0ATL ¼ L0

ðC0 þ C=dÞ

� �1=2

;

mpATL ¼ L0 C0 þC

d

� �� 1=2

) /ATL ¼ Ndx0

mpATL

¼ Ndx0 L0 C0 þC

d

� �� 1=2

: ð1Þ

Where L0 and C0 are the distributed inductance and

capacitance of the loaded TL. The use of this line in

place of conventional TL leads to very compact de-

vices [7, 8]. Indeed, from (1) it can be derived that

the same electrical length can be achieved with a

physically shorter structure with respect to those

required by the loaded TL.

Alternatively, an artificial TL with a CRLH [2, 3,

9] behavior can be designed by using the unit cell

showed in Figure 1c. In this case, the loading element

consists of a series capacitance, C, and a shunt in-

ductance, L; the phase delay corresponding to the

unit cell is given by:

bd ¼ bTLd þ bLHd ¼ x½L0C0�1=2d

� 1

x½LC�1=2¼ �/RH � /LH: ð2Þ

One of the most attractive properties of a CRLH

line is highlighted in Figure 1d which compares the

corresponding phase delay with that of a conven-

tional right-handed TL.

For a purely right-handed TL, we have only two

degrees of freedom, consequently its parameters are

fully determined by imposing a matching condition

to an impedance Z0 and a phase delay /1 at x1:

/RH;1 ¼�x1½L0C0�1=2

Z0 ¼L0

C0

� �1=2

8>><>>: )L0 ¼ðZ0Þ2C0; C0 ¼

/RH;1

x1d

� �:

ð3Þ

For a balanced CRLH TL, made of N unit cells, in

the same conditions assumed for the purely right-

handed TL, we have:

/1 ¼ N �x1½L0C0�1=2d þ 1

x1½LC�1=2

n oZRH ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiL0=C0

pffiffiffiffiffiffiffiffiffiffiffiffiffiL0=C0

p¼

ffiffiffiffiffiffiffiffiffiL=C

p

8>>>><>>>>:

: ð4Þ

From (4) it is evident that one more degree of free-

dom is available. As demonstrated in [2, 3], this prop-

erty can be used to design the CRLH line to satisfy a

Figure 1. (a) Unit cell of an artificial TL obtained by

periodically loading a conventional TL with a shunt ca-

pacitance and corresponding realization in microstrip tech-

nology. (b) Left-handed unit cell and corresponding para-

sitic reactances (i.e., CRLH medium unit cell); (c) CRLH

medium unit cell here employed for the design of the

BLC loading stubs. (d) Phase delay of a purely right-

handed TL ( ) and a CRLH TL ( ). One more degree of

freedom is available for the CRLH TL allowing the possi-

bility to achieve a dual-band behavior.

54 Monti and Tarricone

International Journal of RF and Microwave Computer-Aided Engineering DOI 10.1002/mmce

matching condition to an impedance Z0 and to have

two specified phase delays, /1 and /2, respectively at

x1 and x2. In this way, the dual-band behavior can

be easily achieved by using CRLH lines in place of

conventional right-handed TLs.

In the following, it will be shown as this same

property can be used to design a stub-loaded BLC

with a flexible frequency response by using CRLH

TLs as loading elements.

Figure 3. Equivalence between a quarter wavelength TL

and a TL with electrical length yL loaded with L/C ele-

ments realized by means of a short-circuited stub.

Figure 2. (a) Conventional BLC circuit schematic. (b) BLC loaded by short-circuits.

STUB LOADED BLC

Figure 2a shows the circuit schematic of a conven-

tional BLC. It consists of four quarter-wavelength

TLs at the center frequency of interest (f0) resulting

in a large device which can operate at any odd har-

monics of the design frequency (f1, 3f1, 5f1, etc.)

On the basis of the equivalence between a (�908)-TL and a (yL)-TL loaded with shunt distributed L/Celements (Fig. 3), some design techniques have been

proposed to achieve dual-band performance [6] or,

alternatively, a reduced-size BLC [10], by an appro-

priate choice of ZL, yL, and Y (see Fig. 3).

For dual-band operation purpose, the equivalence

must be satisfied at two arbitrary frequencies (f1, f2);

introducing the fractional bandwidth d:

d ¼ 2Dff0

¼ f2 � f1f2 þ f1

; f0 ¼ f1 þ f22

:

as demonstrated in [6], this can be obtained by fixing:

hLðf1Þ¼^ hL1 ¼ np2ð1�dÞ

hLðf2Þ¼^ hL2 ¼ np2ð1þdÞ

() hLðf0Þ ¼

hL1 þhL2

2¼ n

p2;

ZL ¼ Z0

cos ndp2

� �� ;Y ¼

tanðndp=2ÞZL

; f ¼ f1

� tanðndp=2ÞZL

; f ¼ f2

8<: ; n ¼ 1; 3; 5; . . . ð5Þ

Consequently, a dual-band BLC can be obtained

by using the circuit schematic showed in Figure 2b.

Right-handed Loading Stubs

In conventional right-handed TL technology, the

loading L/C elements can be realized by means of

�908 open-ended stubs or with �1808 short-circuited

stubs (see Fig. 2b), whose characteristic impedance,

must be fixed to satisfy the matching condition

expressed in (5) [6].

From a theoretical point of view both these solu-

tions (�908 open-ended stubs or �1808 short-

Dual-Band Artificial TLs Branch-Line Coupler 55


circuited stubs) can be used to design a dual-bandBLC with any couple of operating frequencies (f1,f2); however, by considering that realizable values ofthe line impedances are in the range of (30 X, 90–120 X), open ended stubs allow to design dual-bandBLCs with a fractional bandwidth in the range of(0.3–0.5), while short-circuited stubs allow to obtainvalues of d in (0.2, 0.3).

This is due to the values of the loading stub im-

pedance which quickly changes with d. In the follow-

ing, it will be shown that this limitation can be over-

come by using CRLH loading stubs in place of con-

ventional right-handed stubs.

CRLH LINES AS LOADING STUBS

By using CRLH technology, the loading elements

can be realized by means of short-circuited stubs; by

imposing the equivalence between the stub input ad-

mittance and Y given in (5), we have:

hCRLH;1 ¼^hCRLHðf1Þ ¼ hLHðf1Þ þ hRHðf1Þ¼

^hLH;1 þ hRH;1

hCRLH;2 ¼^hCRLHðf2Þ ¼ hLHðf2Þ þ hRHðf2Þ¼

^hLH;2 þ hRH;2

(!

ZCRLH tanðhCRLH;1Þ ¼tan ndp

2ð ÞZA

; f ¼ f1

ZCRLH tanðhCRLH;2Þ ¼ � tan ndp2ð Þ

ZA; f ¼ f2

8<: ) hCRLH;2 ¼ np� hCRLH1; n ¼ 0; 1; . . . ð6Þ

Observing Figure 1d it is evident that at low fre-

quencies the CRLH line exhibits a positive phase

delay. Indeed, from (2) it can be derived:

hCRLH > 0 ) /RH < /LH ) 0 < x <1

½L0Cd�1=2

Consequently, (6) can be satisfied by fixing

hCRLH;2 ¼ �hCRLH1, which, by using (2) and the bal-

anced condition expressed by the third equation of

(4), leads to the following relations:

hLH;1 ¼ x2

x1

hLH;2

hRH;1 ¼ x1

x2

hRH;2

hRH;2 þ hLH;2 ¼ �hRH;1 � hLH;1

8>>>>><>>>>>:

)hCRLH;1 ¼ 2d

1�d hLH2;

hCRLH;2 ¼ � 2d1�d hLH2;

8><>:

hRH;1 ¼ �hLH2;

hRH;2 ¼ �hLH1;

8><>: ) L0C ¼ 1

x1x2

: ð7Þ

From (7) it is evident that one degree of freedom

is available, which can be used to satisfy the matching

condition between the input impedance of the CRLH

stub input impedance and Y:

tan2

1 � dhLH2

� �¼ Z0

1 þffiffiffi2

p � 1

sin dp2

� �ZCRLH

: ð8Þ

Consequently, a dual-band BLC can be obtained

with any value of d in the range of (0.2–0.5), and,

if needed, this interval can be also extended. Fur-

thermore, as clarified in the following section,

interesting effects on the two bandwidths can be

observed.

Effects on Bandwidth

Let us introduce the relative bandwidths correspond-

ing to the two operating frequencies:



Bandwidth1ð2Þ%¼^Df1ð2Þf0

� �3 100: ð9Þ

where Df is the range of frequencies in which the

scattering parameters of the coupled ports satisfy the

following relations:

jðS21ÞdB � ðS31ÞdBj � 1dB; jangðS21Þ � angðS31Þj2 ½90� � 10��:

By using right-handed stubs as loading elements,

as one can see from Figure 1d, Bandwidth1 and

Bandwidth2 are fully determined by the fractional

bandwidth desired:

Df1 ¼ Df2 ) Bandwidth2 ¼ f1f2

Bandwidth1

¼ ð1 � dÞð1 þ dÞBandwidth1:

So, by considering that typical achievable values

of Bandwidth1 are in the range of 10–20%, a BLC

with right-handed stubs is not well suited for systems

needing high values of the fractional bandwidth and

at the same time high values of Bandwidth2 (one pos-

sible example being Wireless Local Area Network-

applications).

Similar considerations can be developed for the

BLC proposed in [2, 3] Indeed, in this case it can be

derived that:

d#CRLH

df

jf1

d#CRLH

df

jf2

¼ ð1 � 2d2Þð1 þ dÞð1 þ 2d2Þð1 � dÞ

< 1;

8d < 0:5 ) Df1 < Df2 ) Bandwidth2 < Bandwidth1

This limitation can be overcome by using the

design technique here proposed. Indeed, for a CRLH

line satisfying (7), we have:

d#CRLH

df

� �jf1¼ 1

f1ð#RH;1 � #LH;1Þ

¼ � 1

f1

f2f1þ 1

� �#LH;2 / #LH;2

d#CRLH

df

� �jf2¼ 1

f2ð#RH;2 � #LH;2Þ

¼ � 1

f2

f2f1þ 1

� �#LH;2 / #LH;2 ð10Þ

Consequently, alternatively to the approach pro-

posed in the previous section, the CRLH stubs can be

designed by fixing hLH;2 to customize the frequency

derivatives of hCRLN at f1 and f2, and by using (8) to

find ZCRLH.

Furthermore, from (10), it can be derived that:

d#CRLH

df

jf1

d#CRLH

df

jf2

¼ ð1 þ dÞð1 � dÞ ¼

f2f1

8#LH;2:

TABLE I. Line Parameters (Microstrip Line dimensions are in Millimeters)



As demonstrated by the full-wave simulation results

reported in the next section, this allows to obtain Df2 >Df1 resulting in larger values of Bandwidth2 with

respect to the previously mentioned design techniques.

Size Reduction

Another attractive feature of the proposed DB BLC

derives from the use of the purely right-handed artifi-

cial TLs in the design of the BLC. Indeed, as demon-strated in [7, 8], this allows the optimization of thearea occupied by devices with a rectangular/ringshape in which most of the interior surface is unoccu-pied.

Particularly, in the case of the BLC here consid-ered, they are attractive not only for the electricallength (which allows the size reduction) but also forthe characteristic impedance of the loaded TL

Figure 4. (a) Circuit schematic of the proposed artificial TL BLC with a fractional bandwidth

equal to 0.24 (0.5). (b–e) Layout comparison: stub-loaded BLCs in purely right-handed technol-

ogy (c, e), BLCs obtained by using the proposed design strategy (b, d).



required to synthesize a desired value of Z0ATL and

/ATL.

Indeed, referring to Figure 2b and letting Z0 the

normalization impedance adopted at the BLC port,

values lower than 1.5 Z0 and Z0 are respectively

required for ZA and ZB to achieve a fractional band-

width in the range of (0.2–0.5) ([6]). As an example,

fixing Z0 to its typical value of 50 X, by using the

first equation of (5) we have: ZA [ [50X,75X], ZB [[35X,50X].

With reference to conventional TLs realized in

microstrip technology, these values would require

large strip widths which, as one can see from (1), can

be reduced by using artificial TLs.

RESULTS

To verify the assertions made in the previous section,

in the following we report the results obtained by

means of circuital and full-wave simulators for two

BLCs with a fractional bandwidth respectively equal

to (0.24, 0.5).

The BLC lines (Line A and B of Fig. 2b) have

been designed by using two artificial TLs whose pa-

rameters have been determined by using (1); while,

for the loading stubs two CRLH unit cells (see Fig.

1c) have been used and the corresponding parameters

fixed to satisfy (3–4) and (7–8). The values obtained

in this way for L and C have been approximated by

Figure 5. Circuital simulation results of the 2 proposed

ATL BLCs: amplitude of the scattering parameters

achieved for a fractional bandwidth respectively equal to

0.24 (a) and to 0.5 (b).

Figure 6. Comparison between the full-wave simulation results obtained for the artificial TL

BLC working at (960, 1600) MHz by using Ansoft Designer and Zeland: amplitude of the scat-

tering parameters respectively in the first (a, b) and in the second (c, d) band.



considering those available as Surface Mounted

Components (particularly we refer to the Panasonic

data sheet: Nonmagnetic Cor Types, ELJ series,

inductors and Multilayer Ceramic Chip, ECJ series,

capacitors).

TLs have been designed in microstrip technology

on a ROGERS Corp. substrate (TMM3 substrate:

er ¼ 3.27 6 0.032, tgd ¼ 0.002, thickness ¼ 0.508mm;

conductor: copper); the microstrip and lumped ele-

ments parameters are given in Table I.

Figure 4 shows the circuit schematic and layoutsobtained for the proposed BLCs compared with thosecorresponding to the stub-loaded BLCs designed in con-ventional right-handed technology; in this case, depend-ing on the value of d, different circuit schematics havebeen used (i.e., the loading elements are short circuitedstubs for d ¼ 0.24, whilst they are open-ended stubs ford ¼ 0.5). Defining the Planar Surface Ratio (PSR) asthe ratio between the area occupied by the proposedBLC and the corresponding right-handed stub-loaded

BLC, a PSR respectively equal to (0.4, 0.45) has beenobtained corresponding to size reductions of (60, 55)%.

Figure 5 shows the BLCs scattering parametersobtained by means of a circuital simulator. To verifythese results, full-wave simulations have been alsoperformed taking in account both the substrate andthe metal loss. Particularly, the layouts showed inFigure 4 have been simulated by means of two wellknown commercial simulators: Ansoft Designer [11,12] and Zeland [13–15]; the results obtained in thisway to the BLC working at (960, 1600) MHz arecompared in Figure 6 and summarized in Table II.

It is evident that they are in good agreement: in

both cases values greater than 11% have been

obtained for the second pass-band.

Similar performance has been obtained for the

BLC working at (900, 2700) MHz. The correspond-

ing full-wave results are reported in Figure 7; in this

case the relative bandwidths are: Bandwidth1 ¼ 16 %,

Bandwidth2 ¼ 10 %, confirming the broadening effect

TABLE II. Dual-Band BLC at (960, 1600) MHz: Full-Wave Results

Ansoft Designer

½S21; S31� 2 ½�2:95;�3:95�dB for f 2 ½888; 996�MHz ) f01 ¼ 927 MHz;BW1 ¼ 8:4%

½S21; S31� 2 ½�3:09;�4:09�dB for f 2 ½1580; 1770�MHz ) f02 ¼ 1675 MHz;BW2 ¼ 11:3%

Zeland

½S21; S31� 2 ½�3:3;�4:3�dB for f 2 ½902; 971�MHz ) f01 ¼ 936:5 MHz;BW1 ¼ 7:4%

½S21; S31� 2 ½�3:01;�4:01�dB for f 2 ½1580; 1770�MHz ) f02 ¼ 1647:5 MHz;BW2 ¼ 11:84%

Figure 7. Full-wave simulation results obtained by using Ansoft Designer for the artificial TL

BLC working at (900, 2700) MHz: amplitude of the scattering parameters respectively in the

first (a, b) and in the second (c, d) band.



which can be obtained in the second band by using

the design strategy here proposed.

CONCLUSION

On the basis of artificial TLs technology a dual-band

branch-line coupler has been proposed; results of cir-

cuital and full-wave simulation demonstrate that

operating frequencies with a ratio (f2/f1) in the range

of [1.5, 3] can be obtained. With respect to the exist-

ing approaches, the advantage of the proposed design

strategy consists in a compact size combined with

values of the bandwidth in the second pass-band

greater than 9%, thus leading to devices which are

well suited for current multi-band communication

systems (Table III).

References

1. T. Kaway, Y. Kokubo, and I. Ohta, Broadband

lumped-element 180-degree hybrids utilizing lattice

circuits, IEEE MTT-S Dig 1 (2001), 47–50.

2. I. Lin, C. Caloz, and T. Itoh, A branch-line coupler with

two arbitrary operating frequencies using left-handed

transmission lines, IEEE MTT-S Dig 1 (2003), 325–328.

3. I.-H. Lin, M. DeVincentis, C. Caloz, and T. Itoh, Ar-

bitrary dual-band components using composite right/

left-handed transmission lines, IEEE Trans Micro-

wave Theory Tech MTT-52 (2004), 1142–1149.

4. F.-L. Wong and K.-K. M. Cheng, A novel planar

branch-line coupler design for dual-band applications,

IEEE MTT-S Dig 2 (2004), 903–906.

5. C. Collado, A. Grau, and F. De Flaviis, Dual-band

Planar Quadrature Hybrid with enhanced bandwidth

response, IEEE Trans Microwave Theory Tech MTT-

54 (2006), 180–188.

6. K.-K.M. Cheng and F.-L. Wong, A novel approach

to the design and implementation of dual-band com-

pact planar 908 branch-line coupler, IEEE Trans

Microwave Theory Tech MTT-52 (2004), 2458–2463.

7. G. Monti and L. Tarricone, Reduced-size broadband

ATL-CRLH rat-race coupler, Proc 36th European

Microwave Conf, 2006, Manchester, UK, pp. 125–128.

8. K.W. Eccleston and S.H.M. Ong, Compact planar

microstripline branch-line and rat-race couplers, IEEE

Trans Microwave Theory Tech MTT-51 (2003), 2119–

2125.

9. K. Iyer and G.V. Eleftheriades, Negative refractive

index metamaterials supporting 2-D waves, IEEE

MTT-S Dig 2 (2002), 1067–1070.

10. T. Yun, K.-B. Kim, and J.-C. Lee, Investigation on

size reduction of a branch-line power divider using

shunt-stub, Proc Asia-Pacific Conf 1 (2005), 4.

11. http://www.ansoft.com.

12. N.A. Stutzke, D.S. Filipovic, Four-arm 2nd- mode

slot spiral antenna with simple single-port feed,

Antenna Wireless Propag Lett 4 (2005), 213–216.

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14. L.K. Yeung and K.-L. Wu, A compact second-order

LTCC bandpass filter with two finite transmission ze-

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52 (2004), 1082–1086.

TABLE III. Circuital Simulation Results Summary

CRLH Short

Circuited Stub

RH Short/Open

Circuited Stubs

f1 f2 f1 f2

(960, 1600) MHz, d ¼ 0.24, PSR ¼ 0.4225, Size reduction ¼ 58%

jðS21ÞdB � ðS31ÞdBj � 1dB (914–992)

MHz, 10%

(1486–1713)

MHz, 14.2%

(817–976)

MHz, 16%

(1527–1679)

MHz, 9%

jphaseðS21Þ � phaseðS31Þj 2 ½90� � 10�� (860–1007)

MHz, 16%

(1470–1794)

MHz, 20.8%

(841–1040)

MHz, 21%

(1520–1719)

MHz, 12.3%

(Isolation/ret. loss) < �15 dB (920–985)

MHz, 7%

(1525–1672)

MHz, 9.2%

(908–1004)

MHz, 10%

(1556–1650)

MHz, 6.4%

(900, 2700) MHz, d ¼ 0.5, PSR ¼ 0.37, Size reduction ¼ 63%

jðS21ÞdB � ðS31ÞdBj � 1dB (833–965)

MHz, 14.7%

(2555–2812)

MHz, 9.6%

(813–991)

MHz, 19.7%

(2608–2786)

MHz, 6.6%

jphaseðS21Þ � phaseðS31Þj 2 ½90� � 10�� (775–984)

MHz, 24%

(2548–2919)

MHz, 14%

(743–1007)

MHz, 30%

(2593–2856)

MHz, 9.6%

(Isolation/ret. loss) < �15 dB (850–946)

MHz, 10.7%

(2593–2807)

MHz, 5.8%

(833–960)

MHz, 14%

(2640–2767)

MHz, 4.7%



BIOGRAPHIES

Giuseppina Monti was born in Lecce,

Italy, in 1975. She received the Laurea

degree in telecomunication engineering

(with honors) from the University of Bo-

logna, Italy, in 2003, and is currently

working toward the Ph.D. in telecomuni-

cations engineering at the University of

Lecce (Italy).

Luciano Tarricone was born on May

24, 1966, in Galatone Lecce, Italy. He

received the Laurea degree in electronic

engineering (with honors) and the Ph.D.

degree from Rome University ‘‘La Sapi-

enza,’’ in 1989, and 1994, respectively.

In 1990, he was with the Italian National

Institute of Health Laboratories as a Vis-

iting Researcher in charge of European

draft standards for EMI interferences with implanted devices.

From 1990 to 1992, he was with IBM Rome Scientific Centers in

Italy as a Researcher. From 1992 to 1994, he was with IBM Eu-

ropean Center for Scientific and Engineering Computing in

Rome, involved in supercomputing for several scientific applica-

tions. Between 1994 and 1997, he was a researcher of EM Fields

at the University of Perugia, Department of Electronic and Infor-

mation Engineering. Between 1997 and 2001, he was a senior

researcher and a Professore Incaricato of EM Compatibility at the

same university. In 2001, he moved to the University of Lecce,

where he has been an associate professor since 2002. He has

authored about 170 scientific papers and five books. His main

contributions are in the area of the modelling of microscopic

interactions of EM fields and biosystems, and in numerical meth-

ods for efficient CAD of MW circuits and antennas. He is cur-

rently involved in the finite-difference time-domain (FDTD)

analysis of human–antenna interaction, graph-theory methods for

the enhancement of numerical EM techniques, novel CAD tools

and procedures for MW circuits, EM parallel computing, and

metamaterials.



Dual-band artificial transmission lines branch-line coupler

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