delft university of technology pulsed em field, close

Delft University of Technology

Pulsed EM field, close-range signal transfer in layered configurations - A time-domainanalysis

Lager, IE; Voogt, V; Kooij, BJ

DOI10.1109/TAP.2014.2307588Publication date2014Document VersionAccepted author manuscriptPublished inIEEE Transactions on Antennas and Propagation

Citation (APA)Lager, IE., Voogt, V., & Kooij, BJ. (2014). Pulsed EM field, close-range signal transfer in layeredconfigurations - A time-domain analysis. IEEE Transactions on Antennas and Propagation, 62(5), 2642-2651. https://doi.org/10.1109/TAP.2014.2307588

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https://doi.org/10.1109/TAP.2014.2307588

https://doi.org/10.1109/TAP.2014.2307588

2642 IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 62, NO. 5, MAY 2014

Pulsed EM Field, Close-Range Signal Transfer inLayered Con gurations—A Time-Domain Analysis

Ioan E. Lager, Senior Member, IEEE, Vincent Voogt, and Bert Jan Kooij

Abstract—The pulsed electromagnetic (EM)- eld propagationin con gurations that are of relevance for the radiation fromintegrated antennas is examined. The investigated con gura-tions consist of layered structures with material parameters thatare typical for integrated circuits fabricated in complementarymetal–oxide semiconductor technology, and are excited via small,conducting, current-carrying loops. Space-time expressions of theEM- eld quantities are derived by using the modi ed Cagniardmethod. After validating it by means of comparisons with ana-lytical results, the devised framework is used for examining theradiated eld in the proximity of a chip. This study is instrumentalfor the analysis and design of close-range digital signal transfer.

Index Terms—Electromagnetic radiation, time-domain analysis.

I. INTRODUCTION

T HE EXPLOSIVE digital data exchange in nomadic appli-cations is the driving force behind ever faster wireless data

transfer, with rates of 10 Gb/s (or higher) being deemed possible[1]. Offering such performance, while conforming to the inter-national spectrum regulations, pushes the capacity of the radiochannel to its physical limits.Due to its intrinsically localized, low-power operation,

the close-range, interchip, digital signal transfer constitutes aclass of wireless applications that optimally make use of theradio channel’s physical capacity, while precluding collisionwith spectrum regulations. These applications are most oppor-tunely implemented by means of the pulsed electromagnetic(EM)- eld signal transfer. This approach is, moreover, requi-site to situations requiring a combination of communication,localization, and imaging [2].The feasibility of the (close-range) pulsed EM eld, wireless

transfer was demonstrated in [3] for a basic, yet illustrative, in-terchip digital communication setup. Amore realistic con gura-tion, accounting for the typical (layered) structure in integratedcircuits (ICs), was preliminarily examined in [4]. The relevantspace-time Green’s functions were obtained via the modi edCagniard method (the “Cagniard-DeHoop method”) [5]–[7], a

Manuscript received July 18, 2013; revised February 04, 2014; acceptedFebruary 11, 2014. Date of publication February 21, 2014; date of currentversion May 01, 2014.The authors are with the Faculty of Electrical Engineering, Mathematics

and Computer Science, Delft University of Technology, Delft 2628 CD,the Netherlands (e-mail: [email protected]; [email protected];[email protected]).Color versions of one or more of the gures in this paper are available online

at http://ieeexplore.ieee.org.Digital Object Identi er 10.1109/TAP.2014.2307588

mathematical instrument with increasingly wider use in ultraw-ideband (UWB) antenna studies [8], [9].This paper presents for the rst time a detailed, time-do-

main (TD) analysis of the EM eld radiated by an integratedloop antenna, as habitually realized in (Bi)complementarymetal–oxide semiconductor (CMOS) technology. The frame-work bares some similarity with approaches in the widelyinvestigated class of frequency-domain formulations for theanalysis of layered structures [10]–[23]. However, by em-ploying a causality preserving formulation, the avenue chosenin this paper offers de nite conceptual advantages for the studyof digital wireless transfer that involves pulsed, as opposedto time-harmonic, signals. The proposed methodology is,moreover, highly versatile, being suitable for studying various(model) layered con gurations. Nonetheless, for maintainingthe focus on the close-range wireless transfer, its formulation istailored in this paper to the analysis of the free-space EM- eldpropagation in the near- eld region, with aspects such as thefar- eld, free space radiation (as required by electromagneticcompatibility studies), or the in-slab, guided propagation (asrequired by crosstalk estimation) being left deliberately outsidethe scope of the analysis.In the following sections, a realistic model con guration isrst devised. Expressions of the space-time, EM- eld quanti-ties in the free space outside the integrated circuit (IC) are sub-sequently derived, with technical details being elaborately ex-plained in the Appendices. The obtained formulation is rst val-idated against analytic results concerning the eld radiated bya small, conducting, current-carrying loop in free space, andis subsequently employed for examining the EM radiation ofa CMOS integrated-loop antenna. Conclusions round off theaccount.

II. MODEL CONFIGURATION

The model con guration employed in this study mimicks aCMOS integrated (loop) antenna fabricated via the process de-scribed in [24]. The relevant antenna is sandwiched between avery low conductivity layer and an insulating passivationlayer with matched permittivity. This compound is deposited ontop of a conductive Si substrate. In a rst approximation,can be taken as an insulator; this allows coalescing the oxideand passivation layers into one slab, with the antenna being im-mersed parallel to the slab’s faces. Furthermore, the losses inthe substrate are suf ciently high to completely damp out anyre ection from interfaces underneath it.Based on this, the con guration in Fig. 1 (baring simil-

itude with the one in [25]) is devised. With reference to a

0018-926X © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

LAGER et al.: PULSED EM FIELD, CLOSE-RANGE SIGNAL TRANSFER IN LAYERED CONFIGURATIONS 2643

Fig. 1. Model con guration concerning the pulsed EM eld radiated by a trans-mitting wire loop in a three media layered structure.

TABLE IELECTROMAGNETIC PROPERTIES OF THE MEDIA IN

THE MODEL CONFIGURATION

right-handed, orthogonal Cartesian frame with coordinates, the model consists of a conductive substrate

; an insulating (dielectric)slab , ; and freespace . The values of theelectric permittivity , magnetic permeability , and conduc-tivity are given in Table I, and the material parameters for Siand the compound /passivation slab are chosen based on[26]. The wave speeds in , , 2, 3, are . Atransmitting wire loop, of vanishing wire diameter and vectorialarea , is located in . Without loss of generality,its reference center is taken at , .The loop is electrically small with respect to the pulse’s spatialextent , with being the (conventional) pulsewidth, andis fed at its Kirchhoff port by a pulsed electric current ,with denoting the time coordinate. This analysis is con ned todetermining EM- eld quantities in . The observation pointis then taken at , with and,correspondingly, the relative position vector is .Hereafter, , , 2, 3, denotes partial differentiation

with respect to , and denotes partial differentiation withrespect to .

III. SPACE-TIME EXPRESSIONS OF THE EM-FIELDQUANTITIES IN FREE SPACE

The expressions of the EM- eld quantities, that is, the electricand magnetic eld strengths, are now derived.

Only the steps that are essential for understanding the formu-lation will be presented, with details concerning the discussedframework being available in [27].

Fig. 2. Explicative for the waves in the model con guration in Fig. 1.

A. Field Quantities

Since the transmit loop antenna is electrically small, it is as-similated to a vertical magnetic dipole located at its referencecenter. In line with [28], [29, Sec. 2.2.2], the TE-polarized EMeld radiated by the magnetic dipole is expressed inside eachsubdomain of continuity , 1, 2, 3, as

(1)

(2)

with the potential function satisfying the dissipativewave equation1

for (3)

With reference to Fig. 2, three types of waves are distin-guished: 1) incident waves, denoted by the superscript “i,” thatis, the ones propagating away from the source and not inter-acting with any of the interfaces; 2) re ected waves, denotedby the superscript “r,” that is, the ones re ected at interfaces;3) transmitted waves, denoted by the superscript “t,” that is, theones transmitted through interfaces. The relevant superscriptsare complemented for the re ected and transmitted waves bythe corresponding interface identi er. Note that since andare semi-in nite half-spaces, no re ected waves exist in them.With these notations, the potential function is given by

forforfor .

(4)

The incident potential functions (with support in ) are [4]

(5)

where is the magnetic moment. Theother potential functions in (4) follow from by accountingfor the relevant re ection and transmission coef cients.1For brevity, the explicit statement of the and dependence is henceforth

dropped.


B. Boundary Conditions

For guaranteeing the standard interface boundary conditionsapplying to and , the following interface boundary condi-tions are enforced at and [28]:

(6)

(7)

(8)

(9)

C. Spectral Domain Representations

Equations (1)–(9) are now subjected to a Laplace transformwith respect to the time coordinate , followed by an -scaledFourier transform with respect to the space coordinatesand . The Laplace transform of an arbitrary, causal function

is given by2

for (10)

where the choice for , is requisite, via Lerch’stheorem [30], [31, Sec. II.6] for ensuring the uniqueness of theinverse transformation. The scaled Fourier transform is givenby

(11)

with , . Note that theaforementioned choice for is again bene cial, allowing to se-lect conveniently , , . The inversescaled Fourier transform then follows as:

(12)

By applying the spectral domain transformations in (10) and(11), (3) results in

(13)

with the propagation coef cient being

(14)2Since all physical quantities dealt with in this paper have bounded values,

the condition suf ces for ensuring the absolute convergence of theLaplace integral.

As stated in Section II, the analysis is restricted to observa-tion points in . Consequently, solving (13) and applying thespectral domain transformed relations (5)–(9) yields

(15)

where is a counter for the double re ections at the interfacesand , is the Laplace transform of , is the

transmission coef cient at

(16)

with

(17)

being the re ection coef cient at .

(18)

is the re ection coef cient at and

(19)(20)(21)

From (15), it can be readily inferred that is obtained asan in nite superposition of two types of “generalized rays” [9],namely “rays” that originate from incident waves propagatingupward and downward (in the and directions, respec-tively), and their multiple re ections at the interfaces. Note thatthere is one “ray” originating from the upward incident wavethat does not undergo any re ection.Substitution of (15) into the spectral domain counterparts of

(1) and (2) yields the spectral domain eld quantities

(22)(23)(24)(25)(26)(27)


By applying the inverse Fourier transform (12) to (22)–(27), therelevant components are expressed generically as

for

(28)where the combination of superscripts and indices1, 2, 3 refers to the relevant EM- eld quantity components and

represents the corresponding Green’s functions3

(29)

with being the ray functions (s/m)

(30)

(31)

for 1, 2, 3 and .

D. Time-Domain EM-Field Quantities

The Cagniard–DeHoop method [5]–[7] is now applied for theinverse transformation to the time domain. To this end, a changeof variables , with ,

(32)(33)

is rst applied in (29), following from via polarmapping. The substitution of (32) and (33) in (14) yields

with for(34)

where

for (35)

Note that does not depend on . Furthermore, (27) doesalso not depend on ; this is consistent with the required ro-tational symmetry of . By now using the change of variables

in (29), it is found that

(36)

that contains one single integral along the imaginary axis.The next step in the Cagniard–DeHoop method is deforming

the integration path for the -integral to a suitably chosen con-tour, the goal being to derive an expression from which the in-3From (24), it is evident that 0. This condition will be hereafter

implicitly accounted for.

verse Laplace transform can be inferred by inspection. This pro-cedure requires the ray functions to be independent of . How-ever, from (18), (30), and (31) it is clear that does dependon due to the nonzero conductivity in .For handling the -dependence, is rewritten as

for

(37)where

(38)

is the instantaneous response of the re ection coef cient (an-independent quantity) and

for

(39)with denoting the Bromwich path and

. The variable in (37) can be interpreted as a time relax-ation due to the losses in . By using the procedure describedin Appendix B, is expressed as

(40)

with being introduced in (58), that transforms (36) into

(41)

where

(42)

with or for or , respectively, and isthe Dirac delta distribution. Note that is an independentquantity.To recognize a Laplace transform in (41), the following

parametrization is introduced:

with (43)

that deforms the integration path for the -integral into the“Cagniard-DeHoop” contour , withbeing its intersection with the real axis (see Appendix A fordetails). Equation (43) induces a mappingwith as its inverse. Furthermore, let

with and (44)


The real parameter is the time coordinate consisting of twodistinct real constituents, that is, that corresponds to the stan-dard application of the Cagniard–DeHoop method—the loss-less time parameter, and the time relaxation that was intro-duced in (37). Accordingly, is assimilated tothe ray’s arrival time at the observation point. Note that (43)implies that . With these prerequisites, the proce-dure discussed in Appendix C yields

(45)

At this point, the Green’s functions can be transformed backto the time domain by inspection as

(46)

with denoting the Heaviside step function. Finally, thespace-time expressions of the EM- eld quantities are obtainedby accounting for the inverse Laplace transform in (28) as

(47)

Once the expressions of the free-space-radiated EM- eldquantities were established, the received equivalent Thévenincircuit generator voltage can be derived by using the method-ology developed in [32].

IV. ILLUSTRATIVE NUMERICAL EXPERIMENTS

The formulation derived at Section III was implemented in aMatlab code.After discussing some basic software implementation

choices, the code will be rst validated by using the analyticexpressions of the EM eld radiated by a small, conducting,current-carrying loop in free space (see [33, Sec. 26.9 and26.10] and [34]) and then employed for examining the modelcon guration in Fig. 1. This section is concluded by stressingthe computational and conceptual advantages yielded by theEM- eld analysis framework advocated in this paper.

A. Implementation Aspects

1) Spatial Sampling: In view of the con guration’s rotationalsymmetry, the EM- eld quantities are evaluated at

, with . This case is representative for arbitraryobservation points.

2) Excitation: The exciting electric current is takenas the time derivative of the unipolar, power-exponential (PE)pulse [35]

for (48)

where is the rst peak magnitude in , is the pulsezero-crossing time (corresponding to the pulse rise time of thePE pulse), is the initial rise power of the PE pulse (which isrelated to the high-frequency asymptotic falloff in its Bode plot),and is the normalization constant

(49)

In all experiments, is taken to be an integer and larger than4. This prevents any jump discontinuity at the pulse’s onset inthe time derivatives intervening in the eld expressions. The(conventional) pulsewidth follows from equating:

(50)

that results into

(51)

where denotes the Euler gamma function. The chosenfeeding pulse carries no net electric charge. The time Laplacetransform of (48) is

(52)The numerical experiments are carried out for a transmittingloop with (for circular loops, this amountsto a diameter of 0.2 mm, a dimension that is consistent with thedevices studied in [36]). The pulse is taken to have the parame-ters 5 and 0.1 ns, the latter yielding via (51) a pulsespatial extent 9 mm that concurs with the radiator beingelectrically small.3) Computation of the EM-Field Quantities: With reference

to (44), (46), and (47), the following elements are essential forthe computation of the EM- eld quantities:• determining , the relevant points follow from solvinga quadratic equation;

• evaluating an integral over , the integration limits are ob-tained via the mapping ;

• evaluating an integral over , the lower integration limitsare obtained via the mapping ;

• determining the arrival times ;• evaluating a convolution integral.The integrals over use either an adaptive integration scheme

(thequadlMatlab function) or the trapezoidal rule (thetrapzMatlab function). Note that coordinate stretching is employed


for circumventing the singularity of the integrand in (47). Allequations, including the ones needed for constructing the map-pings, are solved numerically.The convolution integrals are implemented using the

trapezoidal rule. For minimizing the computational effort,is oversampled by means of the interp Matlab

function (using the interpolation scheme in [37, Sec. 8.1]).By denoting as the relevant time integration step,this strategy allowed sampling at intervals up to

without signi cant loss of accuracy in the integrals’evaluation when compared with sampling. More imple-mentation details can be found in [27, Ch. 7].

B. EM Field Radiated by a Small, Conducting,Current-Carrying Loop in Free Space

The rst experiment concerns a comparison of the resultsevaluated by means of the present method for, with the corresponding values following from the analytic

expressions for the EM eld radiated by a small, conducting,current-carrying loop in free space. The “direct ray,” that is,the one corresponding to and , is accounted for,exclusively, this being equivalent to removing the re ectionsfrom the lower half-space. In the plots, the eld quantities arenormalized with respect to and

, with the superscript “av” desig-nating “analytical values.” Furthermore, the normalized arrivaltime retarded, time coordinate , withis employed.The results corresponding to are shown

in Fig. 3. From the plots, it is evident that the discussed methodaccurately replicates the analytic results. An extremely reduceddeviation manifests itself at late times as a result of numericalerror accumulation in the evaluation of the convolution inte-grals. The same excellent agreement with the analytical resultsis obtained at any location, as shown in [4].

C. EM Field Radiated by an Integrated Antenna in a LayeredCon guration

The second experiment concerns the evaluation of theEM- eld quantities in the considered layered con guration at

, that is, close to grazing angles, and at, that is, close to broadside. (see Figs. 4).

The eld quantities are computed by taking the rays up to4 (10 rays). The normalization in the plots is similar with thatemployed in Section IV-B, with denoting, in this case, thedirect ray’s arrival time.Comparing Figs. 3 and 4 illustrates the modi cations re-

sulting from the addition of the dielectric layer, the changesbeing mainly visible in the magnetic behavior. The radiatedpulse is still clearly recognizable, which is bene cial for signaltransfer applications. The signatures in Fig. 4 showa lower in uence of the rays re ected from the conductivehalf-space. They are also evidence of the magnetic eld’s ip-ping that is characteristic for the near- and intermediate- eldregions [34].

Fig. 3. Comparison between the results determined with the present formu-lation and the corresponding analytical results at .The arrival time is, in this case, . The eld quantities are normal-ized with respect to the analytical values. (a) Normalized , (b) normalized, and (c) normalized .

It is noted that the total computation time amounted in thiscase to 55 min on an IntelCoreDuo CPU at 3-GHz computer,with 79% of the time being used for calculating the integralsover and , 19.5% for determining , and 1.5% for allother tasks. Measures for reducing the computation times arecurrently explored.


Fig. 4. EM- eld quantities at (mm) and(mm), evaluated with eight generalized rays. (a) ;(b) ; (c) .denotes the arrival time retarded and time coordinate, with being the directray’s arrival time. The shape of the exciting pulse is provided for comparison.

The presented examples attest the method’s ability to provideaccurate results with a very high (in fact, arbitrary) time resolu-tion, irrespective of the sampling point’s location and devoid ofany correlation with spatial parameters, such would be the casewith purely numerical techniques. This feature is instrumentalfor carrying out system performance prediction, especially in

the case of pulse shapes with very fast rising and fall off timesas the ones employed in this paper.More numerical examples, not included here for brevity, are

available in [27].

D. Computational and Conceptual Advantages of theProposed FormulationThe results discussed in Sections IV-B and C provide the

grounds for comparing the presented method with established,purely computational techniques. Evidently, this method doesnot offer the same exibility as general-purpose software pack-ages. Its applicability is restricted to the class of con gurationsthat can be mapped on the one in Fig. 1. However, this limita-tion is balanced by some categoric advantages:• it offers arbitrary spatial and temporal resolution;• it allows determining the EM- eld quantities at speci clocations without the need to examine complete domains;

• it does not suffer from numerical artifacts, most notablyfrom spurious re ections from boundaries and the effectof incongruent electric and magnetic interfaces;

• it offers valuable insight into the modeled phenomena.The fact that the method allows determining the radiated

EM- eld quantities at arbitrary locations and with excellenttemporal resolution is pivotal for performance prediction andaccurate electromagnetic interference or signal integrity es-timation in digital signal-transfer systems. Furthermore, thisfeature represents a cogent argument for using these results asbenchmarks for EM computational packages.

V. CONCLUSIONPulsed EM- eld propagation was examined in con gurations

that are of relevance for complementary metal–oxide semicon-ductor integrated antennas. By using the modi ed Cagniardmethod, space-time expressions of the EM- eld quantitiesin layered structures with realistic material parameters wereobtained. The obtained results were shown to be in excellentagreement with ones following from analytical expressions thatare available for free-space propagation. Once the method’saccuracy was established, it was employed for analyzing acon guration that is illustrative for the close-range, pulsed EMeld, (digital) signal transfer. This formulation has the abilityto provide highly accurate results with practically arbitrarytemporal resolution, recommending it as an expedient analysisand design instrument.

APPENDIX

A. Cagniard-DeHoop Contour FeaturesFor being able to infer the Laplace transform by inspection,

an opportune parametrization was introduced in Section III-Dvia (43). This de nes the so-called “Cagniard-deHoop” contour

(see Fig. 5). Its intersection with the realaxis (denoted by “D” in the gure) follows from the expression:

for (53)

for . Note that and , as given in (34), are alsoreal in this case. Solving (53) gives that, when lledin (43), induces a mapping . By observing that in the


Fig. 5. Cagniard–DeHoop contour .

con guration under investigation , (34) implies,upon taking , that . By now invokingSnell’s refraction law at (see Fig. 1) it follows that [27]:

(54)

with denoting the refraction angle in andthe incidence angle in . It is clear that

, corresponding to (grazing angles). Nonetheless,(34) yields in this case that, in turn, renders (53) singular.This situation is excluded in this paper by always accounting fora nonvanishing vertical shift from of the observation points(a choice that is justi ed by the fact that a receiving antennacannot be located at that interface).The conditions in (34) require a branch cut in the -plane

along .The aforementioned discussion allows concluding thatnever intersects that branch cut.

B. Handling the -Dependence of

The Cagniard–DeHoop method is standardly applied tolossless, layered con gurations. Nonetheless, the nonzeroconductivity in results in an -dependence of [see(18), (30) and (31)] that needs to be removed before invokingthe Cagniard–DeHoop formalism. The strategy adopted tothis end is reminiscent of that in [38], with the conceptualextension of carefully investigating its applicability conditions.For clarity, all manipulations in this Appendix are performed ina complex -plane, with and being identi ed in the relevantexpressions in the main text, as applicable.To begin with, is rewritten as

for

(55)in which

(56)

is the instantaneous response of the re ection coef cient (a -in-dependent quantity) and

(57)with Br denoting the Bromwich path and

. Note that is constructed such that it satis esJordan’s lemma in the complex -plane. To evaluate the integralin (57), the integral path is closed with a semicircle to the leftof Br, the corresponding integral vanishing in view of Jordan’slemma. Subsequently, (18) is rewritten as

(58)with , that induces a branch cut interconnectingthe branch points and . By means of Cauchy’stheorem, the integral along Br is then equal to the integral alonga closed contour enclosing that branch cut. This contour integralis evaluated by a change of variable according to

(59)

that, in turn, implies that

(60)

(61)

Using these expressions transforms (57) as

(62)

with the contribution of to the integral vanishing since

(63)

The expression in (62) lends itself to a straightforward numer-ical quadrature (e.g., by using standard Matlab functions) and isused in the main text.It must be noted that changing the integration path in (41)

from the imaginary -axis to has repercussions on thelocation of the branch point . As long as 0,(14), (32), (33), and (35) ensure that and that, inturn, implies that , with . However, for ,is, in general, complex. Nonetheless, it can be easily shown

that

(64)Since , it is clear that is always nonzeroand, thus, and are nite. Consequently, even


when 0, its value is nite, and in (55) can betaken large enough for ensuring the absolute convergence ofthe integral that, in turn, ensures the existence of the relevantLaplace transform.

C. Transformation of the Integrals in the Green’s Function

By examining the ray function (41) it can be established thatare and are , with de-

noting the Landau order symbol [33, p. 1019]. Consequently,does not satisfy the conditions required by Jordan’s

lemma. For handling the integral along the imaginary -axisin that equation, use is then made of the arti ce

, with being an arbitrary parameter, that, for, allows rewriting (41) as

(65)

This transformation may result in introducing a singularity at0 [see (44)]. However, apart from the fact that is de ned

such that it never equals zero, it can be shown that the contri-bution of the residue corresponding to this singularity vanishes(the relevant residue is a polynomial of degree one in that isthen subject to a second-order derivative).With the new integrand conforming to the conditions required

by Jordan’s lemma, the relevant integrals on the arcs of radiusconnecting and in Fig. 5 vanish. Con-

sequently, by invoking Cauchy’s theorem, the integral along theimaginary -axis can be replaced by an integral along thepath. Furthermore, a change of variableswith the Jacobians

(66)(67)

[see (43) and (44)], and using Schwarz’s re ection principle andchanging the order of integration transforms (65) into

(68)

Since all existence conditions of the intervening integralshave now been established, can commute with theintegral. Straightforward algebra then yields

(69)

and this expression is used in the main text.

ACKNOWLEDGMENT

The authors would like to thank Prof. A. T. de Hoop for theinstrumental conceptual clari cations and conducive technicaladvice that were received throughout the effectuation of the re-ported research.

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Ioan E. Lager (SM’14) was born in Bras ov, Ro-mania, on September 26, 1962. He received theM.Sc.degree in electrical engineering from the TransilvaniaUniversity, Bras ov, Romania, in 1987, the Ph.D. de-gree in electrical engineering from the Delft Univer-sity of Technology, Delft, the Netherlands, in 1996,and a second Ph.D. degree in electrical engineeringfrom the Transilvania University in 1998.He successively occupied research and academic

positions with the Transilvania University and theDelft University of Technology, where he is currently

Associate Professor. In 1997, he was Visiting Scientist with Schlumberger-DollResearch, Ridge eld, CT, USA. He has a special interest in bridging thegap between electromagneticeld theory and the design, implementation,and physical measurements of wireless systems. His research interests covercomputational electromagnetics and antenna engineering, with an emphasis onpulsed- eld electromagnetic propagation and nonperiodic (interleaved) arrayantenna architectures.Dr. Lager is active in several antenna engineering European networks, pri-

marily in the “VISTA” COST Action.

Vincent Voogt was born in ’s-Gravenzande, theNetherlands, in 1990. He received the B.Sc. andM.Sc. degrees in electrical engineering from theDelft University of Technology, Delft, the Nether-lands, in 2011 and 2013, respectively.

Bert Jan Kooij was born in Amersfoort, the Nether-lands, on February 11, 1959. He received the B.Scand M.Sc. degrees in electrical engineering, and thePh.D. degree in technical sciences fromDelft Univer-sity of Technology, Delft, The Netherlands, in 1984,1986, and 1994, respectively.Since 1987, he has been a member of the scienti c

staff of the Electromagnetic Research Group, DelftUniversity of Technology, where he has carried outresearch and taught classes in the area of electromag-netics, as well as acoustics, wave propagation, and

scattering problems. During a three-month period in 1996, he was a VisitingScientist at Ecole Supérieure d’Electricité (Supelec), Gif sur Yvette, France.He has worked on transient wave propagation problems in the eld of elastody-namics and electromagnetics. His current research interests are the computationof inverse wave- eld problems employing iterative techniques based on errorminimization and space time-domain wave- eld modeling.Since 2010, he has been a member of the Microwave, Sensing, Signals and

Systems Group, Delft University of Technology.

delft university of technology pulsed em field, close

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