A Computationally Efficient Technique for Prototyping Planar Antennas and Printed Circuits for...

INV ITEDP A P E R

A Computationally EfficientTechnique for PrototypingPlanar Antennas andPrinted Circuits forWireless ApplicationsThis paper presents an accurate and efficient algorithm for prototyping

microstrip antennas and circuits, using moderate memory and CPU time

for solutions.

By Raj Mittra, Life Fellow IEEE, Giacomo Bianconi, Chiara Pelletti, Member IEEE,

Kai Du, Simone Genovesi, Member IEEE, and Agostino Monorchio, Fellow IEEE

ABSTRACT | In this paper, we present a novel procedure for an

efficient and accurate electromagnetic simulation of microstrip

circuits and printed antennas etched in layered media. The

proposed approach, based on a new algorithm referred to

herein as the equivalent medium approach (EMA), is applied for

a rapid design of the preliminary desired circuit prototype. The

illustrated technique yields reliable results and reduces the

computational time in comparison with the conventional meth-

od of moments (MoM). Some examples that demonstrate the

accuracy and the efficiency of the described procedure are

included.

KEYWORDS | Characteristic basis function method (CBFM);

characteristic basis functions (CBFs); method of moments

(MoM)

I . INTRODUCTION

Rapid prototyping plays an extremely important role in the

design of antennas and related planar circuits for wireless

communications. While there are a number of software

modules commercially available for this task, often they

are found to be not as reliable as desired, because they are

based on approximate equivalent circuit models for variouscircuit components comprising the antenna system.

Consequently, it becomes necessary to resort to the use

of more sophisticated simulation techniques that are nu-

merically rigorous, albeit computer intensive. Further-

more, optimizing the dimensions of antennas and circuits

to enhance the performance of the system is frequently

desired, and this often exacerbates the problem since the

simulation must be run a large number of times to achievethe performance goal. As a result, it is highly desirable to

develop an accurate yet efficient technique, both in terms

of memory and central processing unit (CPU) time to ex-

pedite the design process as much as possible. The purpose

of this paper is to introduce a technique that strives to

accomplish both of these goals. As explained below, the

paper addresses these issues by first introducing an ap-

proach that bypasses the time-consuming step of evaluat-ing the Sommerfeld integrals (SIs) [1], either directly or by

using the discrete complex image method (DCIM) [2]–[5],

which has been extensively employed to reduce the

Manuscript received July 28, 2011; revised January 5, 2012; accepted January 27, 2012.

Date of publication March 23, 2012; date of current version June 14, 2012.

R. Mittra is with the Electromagnetic Communication Lab, Pennsylvania State

University, University Park, PA 16802 USA and also with the King Fahd University of

Petroleum and Minerals, Dhahran 31261, Saudi Arabia (e-mail: [email protected]).

G. Bianconi, C. Pelletti, and K. Du are with the Electromagnetic Communication

Lab, 319 EEE, Pennsylvania State University, University Park, PA 16802 USA

(e-mail: [email protected]; [email protected]; [email protected]).

S. Genovesi and A. Monorchio are with the Microwave and Radiation Laboratory,

Department of Information Engineering, University of Pisa, Pisa 56122, Italy

(e-mail: [email protected]; [email protected]).

Digital Object Identifier: 10.1109/JPROC.2012.2187769

2122 Proceedings of the IEEE | Vol. 100, No. 7, July 2012 0018-9219/$31.00 �2012 IEEE

computational burden associated with the direct compu-tation of the integral. In addition, the proposed method

employs a recently introduced algorithm, called the char-

acteristics basis function cethod (CBFM) [6], to reduce the

matrix size in the context of the method of moments

(MoM). This strategy not only helps to speed up the com-

putation, but also opens up the possibility of parallelization

of the algorithm [7], with a view to enhancing its speed still

further. Our emphasis in this paper is to introduce thereader to the underlying concepts of the techniques men-

tioned above, and we present a few examples of antenna

and circuit designs to illustrate the application of the pro-

posed methods.

II . EQUIVALENT MEDIUM APPROACH

One of the most widely used algorithms for the electro-magnetic analysis of printed microwave circuits and

antennas is based on the MoM formulation [8] employed

in conjunction with the dyadic Green’s function (DGF).

The MoM derives a matrix equation for the weight coeffi-

cients of the Rao–Wilton–Glisson (RWG) or rooftop basis

functions, used to represent the induced currents on the

circuit being analyzed. When the circuit is located in a

stratified medium, the corresponding spatial domainGreen’s function can be expressed in terms of SIs [1]

that are very time consuming to evaluate. Alternatively,

the SI can be cast in a closed form by using the DCIM [2]–

[5], which improves the computational efficiency. In this

work, we introduce a new approach, referred to herein as

the equivalent medium approach (EMA) [9], for simulat-

ing microstrip circuits etched in layered media that pro-

vides an alternative to the DCIM. In the following section,we will briefly review the DCIM which has been imple-

mented, in conjunction with conventional MoM, referred

to hereafter as the reference algorithm.

III . DISCRETE COMPLEX IMAGEMETHOD AND EQUIVALENTMEDIUM APPROACH

Without loss of generality, we consider the case where the

background medium is stratified along the z-axis and is

terminated by a perfectly conducting ground plane at the

bottom (see Fig. 1). In the context of MoM, a circuit or an

antenna printed on this type of stratified medium is ty-

pically analyzed by employing the DGFs [2]–[5], [10]–

[14]. One of these approaches, namely the mixed-po-

tential integral equation (MPIE) approach [14], utilizesboth the electric and magnetic DGFs to express the elec-

tric and magnetic fields generated by the induced cur-

rents. To evaluate the DGFs, an equivalent transmission

line along the axis normal to the stratification is intro-

duced to express the spectral domain Green’s functions in

terms of currents and voltages defined on the equivalent

network.

Then, for source and observation points located at z0

and z, respectively, the spatial-domain Green’s function

fð�; zjz0Þ can be expressed in terms of the spectral coun-

terpart Fðk�; zjz0Þ by using the following relationship:

fð�; zjz0Þ ¼ 1

2�

Z1

0

Fðk�; zjz0ÞJ0ðk��Þk� dk� (1)

where J0 is the Bessel function of the first kind of order 0,

� is the horizontal distance in a cylindrical coordinatesystem, and k� is the wave number in the �-direction. The

procedure described above, though general, and applica-

ble to a multilayered structure with an arbitrary number

of layers, is computing intensive since the evaluation of

SIs is time consuming [15]–[19]. Given this background, it

is not surprising that a number of different approaches to

speed up the computation of SIs have been proposed.

Among these, the DCIM [2]–[5] is particularly appealingsince it allows expressing analytically the SIs. By resorting

to the generalized pencil of function (GPOF) method

[20], it is then possible to cast the spatial domain Green’s

functions in closed form. Using the two-level approach

reported in [5], the spatial domain Green’s function can

be expressed as

fð�; zjz0Þ ¼XN1

n¼1

a1ne�jkir1n

r1nþXN2

n¼1

a2ne�jkir2n

r2n(2)

where

r1n ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffix2 þ y2 � �2

1n

qr2n ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffix2 þ y2 � �2

2n

q(3)

Fig. 1. Grounded dielectric structure (left) and equivalent

grounded homogeneous medium (right).

Mittra et al.: A Computationally Efficient Technique for Prototyping Planar Antennas and Printed Circuits

Vol. 100, No. 7, July 2012 | Proceedings of the IEEE 2123

and a1;2n, �1;2n, N1, and N2 are the coefficients and thenumber of exponentials, respectively, obtained with GPOF

method.

Though the DCIM definitely represents an improve-

ment over the purely numerical integration approach for

evaluating the SI, the improvement can be inadequate,

especially when the Green’s function has to be evaluated

either at many different frequencies and/or for many

different combinations of the vertical coordinates z and z0,i.e., the observation and source locations. Furthermore,

the DCIM returns a large number of complex images for

certain geometries, and results in a severe degradation of

the numerical performance. Although some techniques

[21]–[27] have been recently proposed for the analysis of

general printed structures at a fixed frequency and planar

microstrip devices at multiple frequencies, the difficulties

faced in the evaluation of the SI have not yet been eli-minated altogether.

In this work, we propose an alternative approach, re-

ferred to herein as the EMA [9]. It is based on the premise

that the original, stratified medium can be replaced by an

equivalent, semi-infinite, and homogeneous grounded med-

ium, as shown in Fig. 1. It is worthwhile to point out that

the Green’s function for the equivalent medium can be

determined analytically, since it is simply composed of thecontribution of the direct and reflected rays from the

source in the presence of the ground plane. Not entirely

unexpectedly, the key step in this procedure is an accurate

determination of the effective dielectric constant, which

can either be computed analytically for simple cases or

derived numerically for more complex geometries. For a

single-layer problem, the effective dielectric constant can

be easily calculated [28] but when the dielectric substrateis multilayered, the effective dielectric constant must be

determined by first solving the problem of an open-ended

microstrip line residing on the multilayered substrate. The

current distribution in the center region of the line, where

it is free from edge-truncation effects, is expressed in

terms of complex exponentials via the use of the GPOF

technique in order to extract the "eff value from the ima-

ginary part of the propagation constant associated with thefundamental mode along the line.

We can now introduce another timesaving strategy,

namely, the fast matrix generation (FMG) scheme, which

is implemented in conjunction with the EMA [29]–[33].

Since the repeated numerical evaluation of the integrals

involving the DGFs is the prime contributor to the matrix

fill time, the use of the FMG helps to speed up this step

considerably. Thus, using this approximation, we can ex-press the impedance matrix elements in a closed canonical

form, and generate the MoM matrix in a fast and efficient

manner, while preserving its accuracy. Furthermore, the

previous FMG formulation can be easily generalized to the

case of the equivalent semi-infinite medium (Fig. 1, right)

by simply using the image theory to account for the current

distribution induced on the ground plane.

The FMG procedure enables us to evaluate a consid-erable fraction of the impedance matrix entries analyti-

cally, which, in turn, reduces the fill time of the MoM

matrix significantly. In Section IV, we will show how we

combine the EMA algorithm, the FMG scheme, and the

characteristic basis function method (CBFM) for fast

prototyping of microstrip circuits and antennas.

IV. CBF METHOD COMBINED WITH EMA

The CBFM [6], [7], [34]–[36] is an efficient technique that

has been employed both for the analysis of monolithicmicrowave integrate circuits (MMICs), as well as for

scattering problems involving 3-D objects.

The CBFM algorithm begins by partitioning the origi-

nal microstrip circuit into several sections, commonly re-

ferred to as blocks. An example is shown in Fig. 2.

Next, we construct two types of high-level basis func-

tions, referred to as the characteristic basis functions

(CBFs) (though higher order basis functions can also beincluded), for the purpose of representing the current

distribution induced on the circuit in each block. The first

of these, called the primary CBFs, is the solution for the

current distribution induced on an isolated section, i.e.,

without the inclusion of the mutual coupling effects be-

tween the blocks, that are accounted for via the use of

secondary CBFs.

The generation of the primary CBFs starts by definingappropriate interfaces (inner ports) between adjacent

blocks and considering each section in isolation such that

the coupling between the blocks is neglected. The number

of primary CBFs for each block is related to the number of

interfaces associated with the section under consider-

ation. For instance, the ith block in Fig. 2 is characterized

by two primary CBFs, since this block has two interfaces.

In order to avoid an edge effect in the induced currentdistribution, the fictitious sources are shifted away slightly

from the block edges by introducing a small extension.

The matrix equation relating the voltage gap sources,

Fig. 2. Division of the overall region domain into N blocks. A couple

of generic blocks involved in the primary and secondary CBF

evaluation are colored in dark gray.

Mittra et al. : A Computationally Efficient Technique for Prototyping Planar Antennas and Printed Circuits

2124 Proceedings of the IEEE | Vol. 100, No. 7, July 2012

applied at the block interfaces, and the primary CBFs canbe expressed as

Zii� J

i;n¼ Vi;n;

i ¼ 1; 2; . . . ;Mn ¼ 1; 2; . . . ;Ni

(4)

where Zii

is the impedance matrix corresponding to the ithextended block, J

i;nis the nth current distribution asso-

ciated with the ith section, Vi;n is the nth source of block i,M is the block number, and Ni is the number of primary

CBFs defined over the ith block. After solving the extended

isolated problem, only the partitions of the CBFs entriesbelonging to the original blocks, and not extended ones,

are retained.

As mentioned earlier, the secondary CBFs are needed

to describe the electromagnetic coupling between differ-

ent blocks. Specifically, a secondary CBF represents the

current distribution induced on a particular block due to

the primary CBFs residing on a different block (see Fig. 2).

The secondary CBFs are generated by solving the linearsystem of equations

Zii� J

i;n¼ Z

ij� J

j;m;

i; j ¼ 1; 2; . . . ;M; i 6¼ jn ¼ Ni þ 1;Ni þ 2; . . . ;Ntot

i

m ¼ 1; 2; . . . ;Nj

(5)

where Zii

is the block-diagonal matrix associated with theith section, Z

ijis the off-diagonal matrix which accounts for

the coupling effects between the block i and j, Nj is the

number of primary CBFs defined for the jth block, and Ntoti

is the total number of CBFs for the ith block.

The level of coupling between the various sections is

determined by a number of parameters such as the geom-

etries of the blocks and the frequency of operation. We can

therefore take a clue from the physics of the problem anddiscard the CBFs in a dynamic manner through a thresh-

olding scheme. To implement this procedure, we apply the

singular value decomposition (SVD) algorithm and retain

at most K linearly independent CBFs by choosing a thresh-

old, which is typically on the order of 0.001. The afore-

mentioned procedure enables us to reduce the number of

employed CBFs and, hence, the matrix size, with little

compromise of the accuracy of the solution.The resulting current distribution J can then be

expressed as

J ¼XNtot

1

n¼1

�1;nJ1;nþXNtot

2

n¼1

�2;nJ2;nþ � � � þ

XNtotM

n¼1

�M;nJM;n

(6)

where the �i;j is the weight associated with the CBF Jij, i.e.,

the jth CBF of the ith block.

The final step in this process is the generation of thereduced matrix Z

R, whose dimensions are ðNtot � NtotÞ,

where Ntot is the total number of CBFs, including both the

primaries and the secondaries. The reduced matrix is

generated by applying the Galerkin testing procedure with

the CBFs as basis and testing functions

ZR� � ¼ VRZR ¼ IT � Z � I VR ¼ IT � V (7)

where Z is the MoM impedance matrix, I is the matrix

comprising all the CBFs, and V is the vector associated

with the analyzed input port. Typically, the dimension of

the reduced matrix in the CBFM approach is much smaller

than that needed in the conventional MoM formulation,

and the reduced matrix can be dealt with directly via lowerand upper (LU) decomposition, bypassing all convergence

issues associated with iterative techniques.

The underlying concept upon which the CBMoM/EMA

algorithm is based is relatively simple: construct the CBFs

as well as the associated matrix equation for the unknown

expansion coefficients for an equivalent Bhomogeneous[medium, characterized by the associated effective dielec-

tric constant. In the event the block under consideration iscomposed of traces of different widths, the effective di-

electric constant for the block is evaluated by using an

averaging process. As expected, the proposed technique

leads to considerable timesaving when compared to the

conventional approach, thanks to the analytical nature of

the associated Green’s function. It has been shown in [37]

that the variation of the effective dielectric constant is

quite significant near the transverse electric (TE) surfacewave bandgaps for high impedance surfaces realized by

using sinusoidal-modulated periodic structures. We are

currently developing a more rigorous approach which will

take into account the mentioned variation of the effective

dielectric constant, to further improve the accuracy of the

proposed technique. What is not so obvious though, and

what has been discovered through extensive numerical

experimentations with a variety of different circuit andantenna configurations, is that the CBMoM/EMA tech-

nique yields accurate results even when large variations in

the widths of the metal traces are considered. Our experi-

ments have demonstrated (see Section V) that the

CBMoM/EMA results are far superior, in terms of accu-

racy, in comparison to simple circuit-based approximations

such as those generally implemented in commercial codes

for rapid prototyping. Furthermore, typically, the differ-ences between the conventional results from MoM utiliz-

ing the DCIM or SI-based formulations, and those derived

by using either the finite element method (FEM) or the

finite difference time domain (FDTD) algorithms, are ty-

pically larger than the difference between the conven-

tional MoM and the CBMoM/EMA results for both the

return loss or radiation characteristics. This leads us to



observe that the CBMoM/EMA is well suited for rapid

prototyping of antennas and circuit configurations,

because it offers considerable timesaving in comparison

to conventional full-wave techniques, with little loss of

accuracy introduced by the simplification.

V. NUMERICAL RESULTS

To illustrate the CBMoM/EMA procedure, we first analyze

a four-stage, stepped-filter problem (see Fig. 3). The filteris modeled at the highest frequency by using 575 un-

knowns, and this number remains unchanged over the

entire frequency band of interest. The microstrip circuit

has been partitioned into nine blocks, so that the widths of

the metal traces vary as little as possible. The results for

the S-parameters are shown in Figs. 4 and 5, where the

CBMoM/EMA results are compared with those obtained

by using three independent commercial codes, whichemploy the MoM, FEM and the equivalent circuit (EC)

approaches.

The EC method is not as general as the others, though

it is still applicable to this type of geometry. It is apparent

that our technique generates results that are much more

accurate than those obtained by using the EC approxima-

tion. We also note that the difference between the FEMand MoM results is larger than the corresponding differ-

ence between MoM and the proposed EMA, even near the

resonances. This result is quite significant since the sim-

ulations with finite methods are usually much more time

consuming than they are with the conventional MoM. Yet,

the EMA approach reduces the MoM-simulation time

significantly, but yields results that are much closer to the

MoM than does the corresponding FEM simulation of thesame problem geometry.

In Table I, we list the value of the three resonance

frequencies obtained by using the CBMoM/EMA, the

MoM, the FEM, and the EC. The relative differences be-

tween the CBMoM/EMA, the FEM, and the EC results

from the MoM reference algorithm obtained by using the

equation below are also included in Table I

Rel: fn(%) ¼ 100 � jfmethod � f MoMj

f MoM: (8)

Next, in order to demonstrate the wider applicability of

the proposed technique compared to conventional EC

algorithms for a single dielectric layer, we analyze three

geometries that are difficult to handle by using the ECapproach, though the CBMoM/EMA can simulate them

with relative ease. The first test example comprises a two-

stub filter printed on a multilayered dielectric environ-

ment (see Fig. 6). The microstrip circuit has been modeled

by using 861 RWG basis functions and divided into two

blocks when analyzed with the CBMoM/EMA. The corre-

sponding S-parameter results in the frequency range of

Fig. 3. Geometry of the proposed four-stage stepped-filter.

Fig. 4. Comparison between the S11-parameter magnitude for the

stepped-filter problem.

Fig. 5. Comparison between the S21-parameter magnitude for the

stepped-filter problem.



2.0–4.25 GHz are illustrated in Fig. 7. We note that theproposed technique is able to accurately predict the stop-

band of the filter, which ranges from 2.85 to 3.70 GHz.

For the next example, we address the problem of a

patch antenna (see Fig. 8).

The antenna is designed for operation at 2.40 GHz, and

is printed on a substrate whose permittivity and thickness

are 2.2 and 1.57 mm, respectively. A quarter-wavelength

transformer is used to match the antenna input impedanceto a 50-� system. The total number of unknowns for the

problem is 1081, when the mesh employed is uniform. The

antenna is divided into three blocks and the corresponding

S-parameters are calculated from 2.0 to 3.0 GHz (Fig. 9). It

Table 1 Resonance Frequency Value for the Four-Stage Stepped Filter

Fig. 6. Geometry of the two-stub microstrip problem.

Fig. 8. Geometry of the proposed patch antenna.

Fig. 7. Comparison between the S-parameter magnitude of

the two-stub filter calculated by using the CBMoM/EMA,

the MoM, and the FEM approach.

Fig. 9. Comparison between the S11-parameter magnitude of the

patch antenna problem.



is worthwhile to note here that, although the CBMoM/

EMA is an approximate method and the analyzed geometry

is characterized by large width variations of the metal

traces, the results generated by the conventional MoM and

by the proposed approach are still in very good agreement.

In fact, the percentage difference in the predictedresonance frequency, computed by using (8), is 0.83%

for the CBMoM/EMA and 3.35% for the FEM.

The final problem analyzed is a patch antenna array

shown in Fig. 10. The antenna is etched on the same

dielectric layer as in the previous example. The problem

geometry is divided into 33 blocks and discretized by using

a total of 6677 RWG basis functions. The principal-plane

radiation patterns and the current distribution along theinput feed line at 2.5 GHz are displayed in Figs. 11–13. It is

evident that the proposed technique generates accurate

results both for the radiation patterns and for the cur-

rent distribution of the patch array antenna.

In order to provide a measure of the computational

efficiency of the proposed approach, we introduce a quan-

tity which we call the relative time (RT), defined as the

ratio between the CPU time required by the CBMoM/EMA

and that needed to generate the results by using theconventional MoM. The RTs for the four examples inves-

tigated are 20.75%, 37.9%, 37.37%, and 30.25%, respec-

tively. Of course, in comparison, the RT between the FEM

and the conventional MoM is higher, and the accuracy of

the FEM is usually lower than that of the MoM for this

type of problems. For instance, in this case, the FEM

commercial code requires a peak memory usage of 16.6 GB

and the RT (considering the ratio between the CBMoM/EMA and the FEM CPU time) is less than 20% on an

eight-processors machine.

Fig. 10. Geometry of the proposed patch antenna array.

Fig. 11. Radiation pattern obtained via the CBMoM/EMA and

the conventional MoM at 2.5 GHz on the H-plane.

Fig. 12. Radiation pattern obtained via the CBMoM/EMA and

the conventional MoM at 2.5 GHz on the E-plane.

Fig. 13. Comparison between the results for the current

distribution along the middle of the input feed line at 2.5 GHz.



VI. CONCLUSION

In this paper, we have presented an efficient algorithm,

called the CBMoM/EMA, for rapid prototyping of micro-strip circuits and antennas etched on layered media.

The CBMoM/EMA, which can be employed for a pre-

liminary design, replaces the stratified medium with a

semi-infinite homogeneous grounded slab whose Green’s

functions can be derived analytically.

The method is shown to have far better accuracy than

the EC approach, and is more general as well, since the EC

cannot be easily applied to either antenna problems or tomultilayered geometries. The obtained EMA solutions

agree well with those generated by using the conventional

MoM, and offer considerable time advantages over the

MoM-only approach. Furthermore, the CBMoM/EMA re-

sults are almost always closer to those of the conventional

MoM than are the FEM results. The RT advantage of the

EMA makes it a desirable choice for rapid prototyping of

planar antennas and circuits encountered in wirelessapplications. h

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ABOUT THE AUT HORS

Raj Mittra (Life Fellow, IEEE) received the B.Sc.

degree from the University of Agra, Agra, India, in

1950, the M.Sc. degree from the Institute of

Radiophysics in 1953, and the Ph.D. degree from

the University of Toronto, Toronto, ON, Canada,

in 1957.

He specializes in the design of electromagnetic

systems such as radars, satellite antennas, com-

munication systems, microwave, and millimeter

wave integrated circuits and instruments for

remote sensing and geophysical prospecting. His role in the design of

these systems is primarily in the development of special-purpose

computer programs and algorithms that are capable of solving problems

that are well beyond the reach of commercially available computer

codes. He has graduated over 110 Ph.D. students and has mentored over

60 postdoctorates and visiting scholars who have specialized in the areas

of computational electromagnetics, antennas, sensing, metamaterials,

integrated circuits, and electronic packaging. He has published over 1000

technical papers and more than 30 books or book chapters related to

electromagnetics. He has directed short courses on pioneering electro-

magnetics topics held at universities around the world and in-house at

many companies, extending the reach of his knowledge beyond his

classroom. He has attracted the best and brightest to study under him,

and his students’ thesis work has often transferred to industry with

lasting impact, providing more efficient and cost-effective design

solutions. Further information may be found at the website: http://

www.personal.psu.edu/rxm53/. He is currently Director of the Electro-

magnetic Communication Lab at Pennsylvania State University, Univer-

sity Park. He also holds a Chair Professorship (Adjunct) at King Fahd

University of Petroleum and Minerals, Dammam, Saudi Arabia, and a

similar position at the YunTze University, Taiwan. He is a Principal

Scientist and President of RM Associates, a consulting company founded

in 1980, which provides services to industrial and governmental

organizations, both in the United States and abroad.

Giacomo Bianconi received the M.S. degree

(summa cum laude) in telecommunication engi-

neering and the Ph.D. degree in information

engineering from the University of Pisa, Pisa, Italy,

in 2007 and 2011, respectively.

In 2008–2010, he was a Visiting Scholar at the

Electromagnetic Communication Laboratory,

Pennsylvania State University (Penn State), Uni-

versity Park, where he is currently a Research

Associate at the Electromagnetic Communication

Laboratory. His research is focused on frequency-domain methods for

efficiently solving microwave circuits and antennas etched on layered

media.

Chiara Pelletti (Member, IEEE) received the

Laurea degree in telecommunication engineering

and the Ph.D. degree in information engineering

from the University of Pisa, Pisa, Italy, in 2007 and

2011, respectively.

She was a Visiting Scholar at the Electromag-

netic Communication Laboratory, Pennsylvania

State University (Penn State), University Park, in

2007, 2009, and 2010. In 2008, she joined the

Microwave and Radiation Laboratory, University

of Pisa. She is currently a Research Associate at the Electromagnetic

Communication Laboratory, Pennsylvania State University. Her main

research interests include the development of efficient frequency- and

time-domain numerical techniques for the solution of electromagnetic

scattering at low frequencies, as well as the analysis and design of

frequency-selective surfaces.

Kai Du received the B.S. and M.S. degrees in radio

electronics from the University of Science and

Technology of China (USTC), Hefei, Anhui, China,

in 1992 and 1995, respectively, the M.S. degree

in mathematics from Purdue University, West

Lafayette, IN, in 1997, and the Ph.D. degree in

engineering science and mechanics from the


versity Park, in 2001.

He works as a Research Associate in the De-

partment of Electrical Engineering at Penn State. He is also an active

engineering consultant for several electronic design companies.

Simone Genovesi (Member, IEEE) received the

Laurea degree in telecommunication engineering

and the Ph.D. degree in information engineering

from the University of Pisa, Pisa, Italy, in 2003 and

2007, respectively.

Since 2003 he has been collaborating with the

Electromagnetic Communication Laboratory,


versity Park. From 2004 to 2006, he was a Re-

search Associate at the ISTI, National Research

Council of Italy (ISTI-CNR), Pisa, Italy. He is currently a Research Associate

at the Microwave and Radiation Laboratory, University of Pisa. His re-

search is focused on metamaterials, antenna optimization, and evolu-

tionary algorithms.



Agostino Monorchio (Fellow, IEEE) received the

Laurea degree in electronics engineering and the

Ph.D. degree from the University of Pisa, Pisa,

Italy, in 1991 and 1994, respectively.

During 1995, he joined the Radio Astronomy

Group, Arcetri Astrophysical Observatory, Italy, as

a Postdoctoral Research Fellow. He has been

collaborating with the Electromagnetic Communi-

cation Laboratory, Pennsylvania State University

(Penn State), University Park, and he is an Affiliate

of the Computational Electromagnetics and Antennas Research Labora-

tory. He has been a Visiting Scientist at the University of Granada,

Granada, Spain, and at the Communication University of China, Beijing,

China. In 2010, he was affiliated with the Pisa Section of the National

Institute of Nuclear Physics (INFN). He is currently an Associate Professor

in the School of Engineering, University of Pisa, and Adjunct Professor at

the Italian Naval Academy of Livorno. He is also an Adjunct Professor in

the Department of Electrical Engineering, Penn State. He is active in a

number of areas including computational electromagnetics, microwave

metamaterials, antennas and radio propagation for wireless networks,

active antennas, and electromagnetic compatibility.

Prof. Monorchio has been a reviewer for many scientific journals and

he has been supervising numerous research projects related to applied

electromagnetics.



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