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Hindawi Publishing CorporationInternational Journal of Antennas and PropagationVolume 2013 Article ID 873234 17 pageshttpdxdoiorg1011552013873234

Research ArticleCompact Slotted Printed Antennas for Dual-BandCommunication in Future Wireless Sensor Networks

Constantine G Kakoyiannis and Philip Constantinou

Mobile Radio Communications Laboratory National Technical University of Athens Zographos Polytechnic Campus9 Iroon Polytechniou Street 15773 Athens Greece

Correspondence should be addressed to Constantine G Kakoyiannis kkakmobilentuagr

Received 13 August 2012 Revised 25 October 2012 Accepted 20 December 2012

Academic Editor Fan Yang

Copyright copy 2013 C G Kakoyiannis and P ConstantinouThis is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

Inverted-F antennas (IFAs) are a primary choice to implement the radiating system of portable devices A tried and tested idea canremain topical if proven useful in modern applications This paper shows that printed IFAs (PIFAs) are capable of forming robustcompact dual-band radiating systems for wireless microsensors with an adjustable spacing between bands Reactive tuning wasapplied by inductively loading the structures with prefractal slots inductive slot loading degenerates higher-order resonances andincreases the fractional bandwidth (FBW)The current distributions revealed that most of the element area is used for radiation atboth resonances In radiation terms the antennas provide satisfactory gains and high efficiencies (ge82) A simple figure ofmerit isused to compare the performance of the three PIFAs head to head Operation at 25 GHz and 55GHz indicated that changes in slotgeometry almost double the FBW The proposed antennas serve both the 515ndash535GHz U-NII and the 58GHz ISM bands at thelower band their size is less or equal to the half-wavelength dipoleThis study of dual-band antennas also showed that the aggregateFBW of a PIFA is bounded by degenerating higher-order modes the designer redistributes whatever bandwidth is available by theantenna itself to the desired bands

1 Introduction

11 Background and Motivation For the past fifteen yearsinverted-F antennas have been a major design vehicle forthe implementation of radiating systems for portable devices[1ndash8] IFAs use image theory as their basic miniaturizationtechnique through a shorting wall or pin that ties themto the ground plane (GNDP) The planar version of IFAsinherits the cavity features of microstrip patch antennasthus its bandwidth is inherently limited Extensive antennaandor GNDP alteration has been applied through slots andslits to excite more radiating modes The printed version ofIFAs is not shaped like a cavity thus it is significantly morebroadband

Dual-band printed and planar IFAs have drawn signifi-cant attention in the existing literature [9ndash21] Starting fromlegacy applications like PCMCIA cards [9] the use of dual-band PIFAswas extended to (i) wireless LAN communicationfor laptop computers in the 24- and 5258-GHz bands

[11ndash13 15 16 20] (ii) mobile phone antennas operating at9001900MHz [14] (iii) dual-band communication at 26 and55GHz [17] (iv) mobile phones equipped withWLAN capa-bility operating at DCSISM frequencies [18] and (v) dual-band antennas printed on USB dongles serving as multibandantennas [19] In the case of portable computers (laptops)printed antennas are usually installed under the lid on theback side of the screen [20] Furthermore printed dual-bandantennas can be readily applied toWLANrouters Finally in arecent study Li et al [21] proposed a reconfigurable structurethat can be transformed from a double planar IFA into ameandered loop antenna by means of a PIN diode switchThe two modes of operation enable the antenna to achievecomplementary operating bands in the 079ndash256GHz range

This paper addresses the design of dual-band PIFAs forwireless sensor nodes It aims to show that by properlyapplying inductive loading in the form of prefractal slotsprinted IFAs are capable of producing robust compact dual-band radiating systems for wireless microsensors with an

2 International Journal of Antennas and Propagation

adjustable spacing between bands One could argue thatdual-band antennas find no use in wireless sensor networks(WSNs) because dual-band WSNs do not exist the secondintegrated transceiver that is required along with its periph-eral passive components bring extra complexity cost andenergy consumption for a wireless microsensor So it is bestto wait until very large scale integration (VLSI) technologymatures to the point of single-chip dual-band integratedtransceivers However the above arguments do not hold fortwo reasons On one hand dual-band communication isinherent in real-world WSN deployments the microsensorsimplement various algorithms for example routing local-ization virtual array formation and improved connectiv-ity and coverage These algorithms depend on GPS signalreception hence a second communication band comes intoplay On the other hand dual-band single-chip integratedtransceivers are already here Cho et al [22] designed anenergy-efficient dual-band fully integrated transceiver forbody sensor network applications in the 30ndash70MHz andMICS (402ndash405MHz) bandsThus it is anticipated that dual-band communication will become vital in future wirelesssensor networks

To the best of the authorsrsquo knowledge the only existingstudy on dual-band antennas that target wireless sensors isthe work of Mendes et al [10] We comment on this work inSection 4 along with the rest of the relevant literature

12 Theoretical Considerations Boyle [5 23] and Boyle andLigthart [24] used superposition and divided the operationof the antenna into the balanced (nonradiating) and theradiating mode One of their key findings was that the PCBlength has a strong effect on antenna quality factor 119876 the119876 is minimized when the length is close to the 1205822- or 120582-antiresonance Hence the bandwidth (BW) which is relatedto the quality factor 119876 is strongly affected by the length ofthe GNDP Furthermore in the case of dual-band PIFAs thewidth of the two bands is not independent to improve BWat the lower resonance the higher resonance BW must bedegraded

Referring to the internal workings of dual-band slottedplanar IFAs [1 25] Boyle suggested that slots in the antennatop plate between the feed and short pins allow independentvariation of the impedance transformation and shunt reac-tance [5 23 24] Furthermore slots in the top plate can tunea planar inverted-L antenna (ILA) that is naturally resonantbetween the lower and upper resonance If the slot is too longthe lower BW is degraded if the slot is too short the upperBW is degraded

The technique of degenerating higher-order radiatingmodes by inductive loading of the antenna with slots appliesequally well in the case of nonadjacent frequency bandsThis has been shown for planar IFAs by Liu et al [25] andBoyle and Ligthart [23 24] Angelopoulos et al [9] showedthat this response is also feasible with printed IFAs theauthors of [9] presented an application of the slot-loadingconcept which involved a dual-band PIFA comprised of two1205824 monopoles coupled and separated by an L-slot It wassuggested that each monopole radiates in its own resonance

frequency (245525GHz) when fed by a single feeding portconnected to the smaller monopole It was also theorizedthat the function of the L-slot was to form a gap for higherfrequency currents which at the same time is not wideenough to disturb the lower resonance The work describedherein will demonstrate that in general this is not the case

13 Scope and Structure of the Paper Based on our expe-rience with multimode single-band printed IFAs [26] wehave attempted to design microsensor-oriented PIFAs whichshould satisfy the following specifications

(1) Display a bandwidth at least equal to 100MHz inthe vicinity of 25 GHz thus a fractional bandwidthFBW119881ℓge 4

(2) Display a bandwidth at least equal to 200MHz at thelower end of the 5-6GHz range A good applicationexample is the U-NII 515ndash535GHz band whichfeatures a fractional bandwidth FBW

119881119906= 38

(3) Achieve the previous two specifications withoutexceeding the electrical size 119896119886 of the half-wave-length dipole (119896119886)

1205822= 1205872 rad at the lower band

(4) Achieve a mean total radiation efficiency over bothbands at least equal to 80 that is 119899total ge minus1 dB

The paper describes the design of printed inverted-Fantennas that have been inductively loaded by four differentpre-fractal slotsThe first three slot topologies were discussedin detail in [26] they are the simple generalized and dualgeneralized Koch curves of the second iteration The fourthslot resembles the quadratic type 2 Koch curve its propertiesare described in Section 34 The effect of the size of theground plane on both frequency bands was also investigatedThe reactive loading imposed by the pre-fractal slots notonly surpassed the specifications but also outperformed theresults of several prior studies Section 2 discusses design andmodelling issues Section 3 displays an array of numericalresults produced by accurate computational models of thefour slotted antenna configurations Section 4 discusses theresults Section 5 presents measurement results harvestedfrom a prototype antenna Finally Section 6 concludes thepaper

2 Antenna Design andElectromagnetic Modelling

Out of the four antennas that were designed the first threewere inductively loaded by slots shaped after the followingpre-fractal curves

(1) the Koch curve of the second iteration (abbreviatedherein as ldquoK2rdquo) [26]

(2) the generalized Koch curve of the second iteration(abbreviated herein as ldquoGK2rdquo) [26] and

(3) the dual generalized Koch curve of the second itera-tion (abbreviated herein as ldquoD-GK2rdquo) [26]

Apart from [26] the properties of Koch curve variants arealso described in [27ndash30] thus the details are omitted here for

International Journal of Antennas and Propagation 3

119909

119910

119911

119882ind

119882short

119871ind119882feed

119882slot

119889fs

119871fs

119871slo

t

119871PI

FA

119882PIFA

119882strip

119882gnd

119871gnd

Figure 1 Parametric breakdown of the printed IFA loaded with an embedded Koch-shaped slot The substrate is transparent showing theground plane on the bottom layer The nomenclature of parameters is a simplified version of the one used in [26]

brevity The fourth antenna was loaded by a quadratic type2 Koch curve of the second iteration (abbreviated herein asldquoMK2rdquo) which is described in Section 34

The antennas were designed to operate about the centrefrequencies 119891

0ℓ= 25GHz and 119891

0119906= 525GHz where the

correspondingwavelengths are1205820ℓ= 120mmand120582

0119906≃ 571

mmThe 2-layer PCBs are made of Taconic TRF-45 material(120576119903= 438 and tan 120575

119890= 00028 at 25 GHz) The substrate is

119867sub = 163mm thick and it is loaded with 1 oz copper oneach side [31] Higher frequencies at the upper band demandthe use of a good quality substrate that features low-lossand well-controlled relative permittivity TRF-45 combineslow-loss with an FR4-compatible printing process In thissystem model the size of the PCB represents the whole sizeof the sensor node On the top layer we etched the printedantenna and the 31mm-wide microstrip line that excites itOn the bottom layer there is a continuous copper claddingthat serves as the ground plane (GNDP) of both antenna andmicrostrip line The GNDP was removed below the antennaAssuming that the PCB in Figure 1 is an autonomous nodethen all radiofrequency (RF) and baseband integrated circuitsand discrete components would be soldered on the bottomlayer in an actual implementationThis structure can be easilytransformed to uniplanar (single-sided PCB) by changingthe feed to coplanar waveguide (CPW) The use of ground-backed CPW would double the available space for RF andbaseband electronics

The antennas were designed and simulated by meansof a transient solver which is part of a full-wave EMsimulator that uses the finite integration technique (FIT) toreformulate Maxwellrsquos integral equations into the so-calledldquoMaxwell Grid Equationsrdquo In the time domain by applyingYeersquos spatial discretization and time-stepping scheme FITresults in the same set of equations as FDTD [32 33] Thestructures were excited by a wideband Gaussian pulse (DC-7GHz) A spatially adaptive hexahedral mesh discretized theobjects Finer meshing was applied inside the substrate tocapture the large gradients of the E-field the same appliesacross the microstrip feed on the main arm and inside

the dielectric of the SMA connector The simulator stoppedwhen the initial system energy decayed by 40 dB This trade-off between simulation speed and FFT truncation error wasslightly in favour of speed The maximum cell size at 7GHz(smallest wavelength) was set at 120582

7GHz20 The solvablespace was terminated at four Berenger PML layers with adistance-to-boundary equal to 120582

3GHz8 The antennas didnot exhibit topological symmetry thus did not satisfy therequired boundary conditions of electric and magnetic fluxfor the placement of ldquomagnetic wallsrdquo which would lower thecomputational burden The complexity of the models variedin the range 370ndash495 times 103 Yee cells Complexity depends onthe size of the PCB and the level of detail exhibited by theantenna element Narrow copper traces and narrow objectspacing contribute greatly to complexity The MK2 modelexhibited 28ndash33 greater complexity compared to the otherthree model due to its inherently finer structure Simulationsetup settings are summarized in Table 1

3 Proposed Radiating Structures andNumerical Results

Thedesign of the four slotted antennas is based on themanualoptimization procedure and design guidelines that werereported in [26] The controlling parameters of the antennasconverged to the values listed in Table 2 The nomenclatureof parameters shown in Figure 1 is a representative of all fourstructures

Table 2 lists at the bottom parameters 119871 ind and 119882ind Inorder to achieve a well-balanced input impedance in bothoperating bands there is a need to compensate the capacitivepart of the impedanceThe imaginary part119883in(119895120596) assumedlarge negative values because the common length of thefeeding and shorting stubs119871 fs is short due to high-frequencyupper band thus the main arm of the PIFA approaches theground plane far more than it did in the case of the multi-mode single-band counterparts [26] To mend this problemthe last segment of the microstrip feed line whose lengthequals 119871 ind was narrowed from 119882strip down to 119882ind The


0

0 1 2 3 4 5 6 7

Inpu

t refl

ectio

n co

effici

ent (

dB)

Frequency (GHz)

minus40

minus30

minus20

minus10

Figure 2The computational model of the dual-band K2 PIFA in perspective and the magnitude of its input reflection coefficient in the rangeDC-7GHz

Table 1 Settings applied to the FIT-TS solver [32 33] during thesimulations of the slotted PIFAs

Slotted PIFA simulation setupExcitation signal Gaussian pulse DC-7 GHzSpatial discretization Hexahedral nonuniformConvergence condition 40 dB energy decayMaximum cell size at 119891max 120582min20

Absorbing boundary conditions 4-layer PMLMinium distance to PMLboundary 120582

3GHz8

Computational complexity(D-)(G)K2 (370ndash385) times103 Yee cells

Computational complexity MK2 495 times 103 Yee cells

narrowed segment inserts extra inductance in series with119885in(119895120596) and makes up the simplest matching circuit

It is also noted that the design procedure verified themanual optimization algorithm given in [26] but with oneimportant difference excluding parameters 119871PIFA and 119871 slotthe other six parameters affect the response of the antennain the two frequency bands in opposite ways For examplea change in 119889fs that improves matching and resonance inthe lower band worsens the performance in the upper bandand vice versa Inevitably parameter values were chosen in acompensatory manner

During simulations for the virtual prototyping an auto-mated calculation of the electrical size of antennas wasrequired Thus the automated estimation of the radius of thecircumscribing sphere was based on the simplified expression

119886 =1

2

radic1198822

strip + (119882PIFA + 119871 fs + 119871gnd)2

(1)

which produces slightly larger electrical sizes than the actualones

This section demonstrates through accurate computa-tional models (virtual prototypes) the electrical performanceof the four slotted PIFAs

31 Dual-Band PIFA Loaded by the Koch Slot The firstantenna that was designed is inductively loaded by a Koch-shaped slot of the second iteration which has been describedin [26] and also in [27ndash30] The computational model andthe broadband magnitude of the input reflection coefficientare depicted in Figure 2 Antenna dimensions starting with119871 slot were adjusted so as to obtain resonances at the desiredbandsThe high-frequency upper band leads to a significantlysmaller slot compared to the one in [26] the side length ratioof the outline of the K2 slot remains constant as dimensionsvary thus the slot is much shorter allowing for the design ofa PIFA with a significantly narrower main arm The feedingline is offset with respect to the longitudinal symmetry axisof the PCB Application of the offset feed further facilitatesmatching and resonance in both bands The key numericalresults of the K2 PIFA are listed in Table 4The antennameetsall four specifications but the figure ofmerit assumes negativevalues in decibels In the lower band the low FoM values aredue to the reduced bandwidth whereas in the upper bandthey result from the increased electrical size in the 5-6GHzrange the K2 PIFA is electrically large (119896119886 gt 2 rad)

The Smith charts in Figure 3 were derived after placingthe reference plane of the scattering parameters at thebeginning of the SMA end launch connector The chartsindicate that the compensatory dimensions that were chosenfor the K2 antenna produce a frequency response that iswell-balanced between inductive and capacitive reactanceFurthermore in the lower band the input resistance is equallydistributed below and above 50Ω whereas in the upper bandwe mostly get 119877in lt 50Ω

The surface current distributions (SCDs) in Figure 4 showconcurrent maxima of current density at every point on thePCB Concurrent maxima are physically unrealisable due tothe phase shift along the structure but they are useful foridentifying ldquohotrdquo and ldquocoldrdquo regions The SCDs indicate that(i) in the lower frequency band practically the whole extent ofthemain arm radiates and (ii) in the upper band themain armradiates mainly along the K2 slot whereas a discontinuousimage forms on the ground plane with a greater overalllength In both bands return currents are strong along all foursides of the GNDP


0 (minus1876119890 minus 031 minus3063119890 minus 015) ohm

02

04

0608 1

15

2

3

45

10

S-parameter smith chart

02 04 06 08 1 15 2 3 4 5 10

minus02

minus04

minus06minus08 minus1

minus15

minus2

minus3minus4minus5

minus10

4 (3627 minus2928) ohm

(a)

02

04

0608 1

15

2

3

45

10


02 04 06 08 1 15 2 3 4 5 10

minus02

minus04


minus15

minus2

minus3minus4minus5

minus10

3 (9633 minus1621) ohm7 (1994 383) ohm

(b)

Figure 3 Smith chart of the complex reflection coefficient of the dual-band K2 PIFA in the overlapping frequency ranges DC-4 GHz and3ndash7GHz

0 48

944

157

241

355

509

169

(Am)

Curr

ent (

peak

)(119891=25)

[1]

(a)

Curr

ent (

peak

)

216

649

453

308

2012612

0

(Am)

(119891=525)

[1]

(b)

Figure 4 Surface current distributions of the dual-band K2 PIFA at 25 GHz and 525GHz


Table 2 Values of parameters that determine the design of the fourproposed dual-band PIFAs All dimensions are in millimetres

Dimension K2 GK2 D-GK2 MK2119871 sub times119882gnd 57 times 37 54 times 358 54 times 362 60 times 336

119871gnd times119882gnd 40 times 37 40 times 358 40 times 362 40 times 336

119871PIFA times (119882PIFA + 119871 fs) 240 times 77 233 times 78 232 times 76 212 times 81

119882strip 31 31 31 31119889fs 25 21 22 15119871 slot 103 89 89 67119871PIFA 240 233 232 216119871 fs 24 14 15 15119882slot 05 05 06 03119882PIFA 53 64 61 66119882short 05 04 04 04119882feed 10 11 06 09119871 ind 62 61 64 62119882ind 17 19 23 19The first row denotes the extent of the PCB the second row denotes the sizeof the ground plane and the third one denotes the extent of the antennaelement

32 Dual-Band PIFA Loaded by the Generalized Koch SlotThe second antenna that was designed is inductively loadedby a generalized Koch-shaped slot of the second iterationwhich has been described in [26] The computational modeland the broadband magnitude of the input reflection coef-ficient are depicted in Figure 5 The antenna resonates at25 GHz 514GHz and 571 GHzThis means that by a simplechange in slot geometry the reactive loading produces asecond 119878

11minimum in the 5-6GHz range As a result the 5-

6GHz range meets the VSWR criterion practically in its fullextent The key numerical results of the K2 PIFA are listed inTable 4

The Smith charts in Figure 6 indicate that the compen-satory dimensions that were chosen for the GK2 antennaproduce a frequency response that is well-balanced betweeninductive and capacitive reactance Furthermore in the lowerband the input resistance is equally distributed below andabove 50Ω whereas in the upper band we mostly get 119877in lt50Ω Finally the 119878

11minimum at 571 GHz is not a resonance

in the strict sense but appears as a result of the small loop thatthe curve traces

The surface current distributions in Figure 7 show con-current maxima of current density at every point on the PCBIn the lower frequency band the same comments as in the K2case apply At 514GHz the main arm radiates mostly alongthe GK2 slot whereas a discontinuous image forms on theground plane with greater overall length At 571 GHz themain arm radiates uniformly (not focused around the slot)whereas a strong image forms on the ground plane away fromthe slot

33 Dual-Band PIFA Loaded by the Dual Generalized KochSlot The third antenna was inductively loaded by the dualgeneralized Koch-shaped slot of the second iteration whichhas been described in [26] This particular version of the

Koch pre-fractal shape exhibits lower variations in height andthus produced an antenna with slightly narrower main armThe computational model and the broadband magnitude ofthe input reflection coefficient are depicted in Figure 8 Theantenna resonates at 25 GHz 511 GHz and 577GHz that isthe dual of the generalized Koch slot preserves the second 119878

11

minimum in the 5-6GHz rangeThe key numerical results ofthe K2 PIFA are listed in Table 4

The Smith charts in Figure 9 indicate that the compen-satory dimensions that were chosen for the D-GK2 antennaproduce a frequency response that is well-balanced betweeninductive and capacitive reactance Furthermore in the lowerband the input resistance is equally distributed below andabove 50Ω whereas in the upper band we mostly get 119877in lt50Ω Finally the 119878

11minimumat 577GHz appears as a result

of the small loop traced by the curve which produces an extraresonance

The surface current distributions in Figure 10 show con-current maxima of current density at every point on the PCBAt 25 GHz and 511 GHz the same comments as in the K2 andGK2 cases apply At 577GHz the main arm radiates in anexceptionally uniform manner almost ignoring the presenceof the slot whereas a strong image forms on the ground planeaway from the slot

34 Dual-Band PIFA Loaded by the Quadratic Koch SlotThe fourth antenna was inductively loaded by the quadraticKoch-shaped slot of the second kind and second iterationThis particular version of the Koch pre-fractal shape is alsoknown in the literature as the Minkowski sausage The curveis produced by an iterative function system (IFS) [26ndash30] asillustrated in Figure 11 an initial straight segment is dividedinto 119899 equally long consecutive segments Then each one ofthe 119899 minus 2middle segments is replaced by a Π-shaped brokenline The straight segments of the broken line are equal inlength to the initial subdivisions In order for the curve topreserve its self-avoidance a sequence of proper and invertedPi shapes is created In this way during the first iteration ofthe pre-fractal curve the initial straight segment takes on theshape of a meander line Thus we are working with a hybridmeander-Koch curve and this is where the abbreviationldquoMK2rdquo for the 119894 = 2 iteration came from It is easily proventhat with every new iteration the updated curve comprises3119899 minus 4 straight segments where 119899 is the number of segmentscomprising the previous iteration Therefore the Haussdorfdimension for 119894 = +infin is equal to

119863MK =ln (3119899 minus 4)ln (119899)

(2)

and is maximized when the initial straight segment is dividedinto 119899opt = arg max119863MK = 4 subdivisions 119863MKmax =

15 The increased complexity of the MK2 curve leads totwo geometrical differences with regard to the previous threeantennas (i) the current covers a longer path as it traversesthe initial part of the main arm thus length 119871PIFA turns outto be 86ndash117 shorter when compared to the correspondinglengths of the previous three antennas (ii) the width of theMK2 slot had to be reduced by a factor of two to facilitate


0

0 1 2 3 4 5 6 7

Inpu

t refl

ectio

n co

effici

ent (

dB)

Frequency (GHz)

minus25

minus20

minus15

minus10

minus5

Figure 5 The computational model of the dual-band GK2 PIFA in perspective and the magnitude of its input reflection coefficient in therange DC-7GHz

02

04

0608 1

15

2

3

45

10


02 04 06 08 1 15 2 3 4 5 10


minus02

minus04


minus15

minus2

minus3minus4minus5

minus10

4 (3792 minus3927) ohm

(a)

02

04

0608 1

15

2

3

45

10


02 04 06 08 1 15 2 3 4 5 10

minus02

minus04


minus15

minus2

minus3minus4minus5

minus10

3 (2322 minus2507) ohm7 (1493 2443) ohm

(b)

Figure 6 Smith chart of the complex reflection coefficient of the dual-band GK2 PIFA in the overlapping frequency ranges DC-4GHz and3ndash7GHz

fabrication The computational model and the broadbandmagnitude of the input reflection coefficient are depicted inFigure 12 The antenna resonates at 245GHz 524GHz and588GHz The meander-Koch slot preserves the second 119878

11

minimum however the matching meets the VSWR criteriononly approximately in the 5-6GHz range The key numericalresults of the K2 PIFA are listed in Table 4

The Smith charts in Figure 13 indicate that the compen-satory dimensions that were chosen for the MK2 antennaproduce a frequency response that is well-balanced betweeninductive and capacitive reactance Furthermore in the lowerband we get an input resistance 119877in gt 50Ω whereas in theupper band we obtain119877in lt 50Ω Finally in this case it is the

11987811

minimum at 524GHz that appears as a result of a smallloop traced by the curve

The surface current distributions in Figure 14 show con-current maxima of current density at every point on thePCB At 25 GHz the same comments as in the previous threecases apply At 524GHz and 588GHz themain arm radiatesmostly in the vicinity of the slot whereas a strong imageforms on the ground plane along the full extent of the mainarm

35 Study of Ground Plane Effect The effect of the size of theground plane was studied in the same manner as in [26 34]The most important findings are briefly summarized here


Figure 7 Surface current distributions of the dual-band GK2 PIFA at 25 GHz 514GHz and 571 GHz

0

0 1 2 3 4 5 6 7

Inpu

t refl

ectio

n co

effici

ent (

dB)

Frequency (GHz)

minus25

minus20

minus15

minus10

minus5

Figure 8 The computational model of the dual-band D-GK2 PIFA in perspective and the magnitude of its input reflection coefficient in therange DC-7GHz

The width of the ground plane should be at least largeenough to accommodate the main arm of the PIFA Further-more small extensions are also required towards the open-circuited end of the PIFA the substrate and ground planeshould be extended by 8 le 119908

1le 10mm Towards the

short-circuited end of the PIFA the substrate and groundplane should be extended by 3 le 119908

2le 5mm Changes

in 1199081affect both resonances significantly so this parameter

must be chosen carefully Changes in1199082only affect the upper

resonance the lower one is practically insensitive Note thatthe values suggested above are frequency-dependent

The results presented in Sections 31ndash34 correspond tothe common ground plane length 119871gnd = 40mm Thiscommon length is equal to 1205823 at 25 GHz and 31205824 at55 GHz Table 3 lists the ranges of ground length thatproduce maximum absolute bandwidth and total efficiency

for each antenna and frequency band It seems that optimallycompensatory ground length equals 1198711015840gnd = 32mm Thislength is equal to 027120582 at 25 GHz and 059120582 at 55 GHz The40 mm-long ground plane was chosen because it maximizesthe obtainable bandwidth at the lower band

4 Discussion

41 Performance of the Four Slotted PIFAs The results givenin Section 3 lead to conclusions and comparisons with priorstudies First it is important to note that in the generalcase the whole structure is used at both resonances forradiation Unlike what was suggested in prior studies [9] thecurrent distributions indicate that the slot does not dividethe antenna element in two separate radiators that is itdoes not facilitate the creation of two resonant current paths


02

04

0608 1

15

2

3

45

10


02 04 06 08 1 15 2 3 4 5 10

0 (minus1876119890 minus 031 minus3064119890 minus 0154 (3543 minus3516) ohm

minus02

minus04


minus15

minus2

minus3minus4minus5

minus10

) ohm

(a)

02

04

0608 1

15

2

3

45

10


02 04 06 08 1 15 2 3 4 5 10

3 (1464 minus2226) ohm

minus02

minus04


minus15

minus2

minus3minus4minus5

minus10

7 (1329 3341) ohm

(b)

Figure 9 Smith chart of the complex reflection coefficient of the dual-band D-GK2 PIFA in the overlapping frequency ranges DC-4GHzand 3ndash7GHz

Figure 10 Surface current distributions of the dual-band D-GK2 PIFA at 25 GHz 511 GHz and 577GHz


1 2

3

Figure 11 The first two iterations 119894 = 0 rarr 2 of the hybrid meander-Koch curve for the optimum case of 119899 = 4 subdivisions

0 1 2 3 4 5 6 7

Inpu

t refl

ectio

n co

effici

ent (

dB)

Frequency (GHz)

0

minus10

minus20

minus30

Figure 12 The computational model of the dual-band MK2 PIFA in perspective and the magnitude of its input reflection coefficient in therange DC-7GHz

Table 3 Comparison of well-performing GNDP lengths between the four dual-band printed IFAs in terms of bandwidth and efficiency

K2 GK2 D-GK2 MK2Band (GHz) 2-3 5-6 2-3 5-6 2-3 5-6 2-3 5-6Maximum BW (GHz) 023 096 018 140 019 120 018 100at 119871gnd (mm) 36ndash40 28 36ndash44 28 32ndash44 32ndash40 32ndash44 28Maximum 119899total () 88 87-88 83 91 84 88ndash90 84 87-88at 119871gnd (mm) 32ndash36 28ndash32 32ndash44 28ndash32 28ndash44 20ndash36 28ndash48 28

Table 4 Comparison of electrical performance between the four dual-band printed IFAs in each frequency band

K2 GK2 D-GK2 MK2Band (GHz) 2-3 5-6 2-3 5-6 2-3 5-6 2-3 5-6119891119888(GHz) 2530 5310 2500 5410 2500 5410 2450 5450

BW119881(GHz) 0231 0598 0182 1000 0191 1050 0182 0950

FBW119881

0091 0113 0073 0185 0076 0193 0074 0174119876 73 59 91 36 87 34 90 38119896119886 (rad) 160 335 156 338 157 341 150 320119866max (dBi) 20 42 20 43 20 44 21 46119899rad 094 097 094 097 094 097 094 097119899total 087 082 083 086 084 087 083 084FOM (dB) minus31 minus56 minus41 minus33 minus39 minus31 minus39 minus34

119876119903(dB) +89 +78 +99 +57 +97 +54 +98 +59

119876119905(dB) +92 +86 +104 +62 +102 +59 +104 +66


02

04

0608 1

15

2

3

45

10


02 04 06 08 1 15 2 3 4 5 10

4 (4762 minus5423) ohm0 (minus1876119890 minus 031 minus3063119890 minus 015) ohm

minus02

minus04


minus15

minus2

minus3minus4minus5

minus10

(a)

02

04

0608 1

15

2

3

45

10


02 04 06 08 1 15 2 3 4 5 10

3 (3304 minus314) ohm7 (1091 2279) ohm

minus02

minus04


minus15

minus2

minus3minus4minus5

minus10

(b)

Figure 13 Smith chart of the complex reflection coefficient of the dual-band MK2 PIFA in the overlapping frequency ranges DC-4GHz and3ndash7GHz

Figure 14 Surface current distributions of the dual-band MK2 PIFA at 25 GHz 524GHz and 588GHz

Rather it provides the proper reactive loading (or ldquotuningreactancerdquo) for a single-resonant PIFA to become dual bandThe computational models corroborate Boylersquos theoreticaltreatment [5 23 24]

Referring to the results tabulated in Table 4 the fourdual-band PIFAs meet the specifications that were set for thefractional bandwidth the electrical size and the mean totalradiation efficiency The choice of a low-loss substrate leads


(a)

1 2 3 4 5 6 7

SimulatedMeasured

0

Frequency (GHz)

minus10

minus20

minus30

minus40

Inpu

t refl

ectio

nco

effici

ent 11987811

(dB)

(b)

Figure 15 (a) Prototype dual-band PIFA reactively loaded by a K2 slot (b) Comparison of numerical and experimental magnitudes of thereflection coefficient at the input to the dual-band K2 PIFA

22192165137

11082405490275

0minus473minus945minus142minus189minus236minus284minus331minus378

120601

120579

TypeApproximationMonitorComponentOutputFrequencyRad efficTot efficGain

119910

119909

enabled (kR≫ 1)ff_026000 [1]AbsGain26minus01735 dBminus03442 dB

Farfield

2197 dB

(dB)

(a)

43438

326271217163109

05430

minus446minus891minus134minus178minus223minus267minus312minus357



Farfield

4344 dB

(dB)

120601

120579

119909

119911

119910

(b)

Figure 16 Numerically estimated three-dimensional gain patterns of the K2 PIFA at (a) 26GHz and (b) 54GHz Notice the differentamplitude scales (both are given in dBi)

to mean radiation efficiencies in the range 94ndash97 that isminus03 le 119899rad le minus01 dB All eight FoM levels take on negativevalues in decibels In the lower band the low FoM values aredue to the reduced bandwidth whereas in the upper bandthey result from the increased electrical size in the 5-6GHzrange all four slotted PIFAs are electrically large (119896119886 gt 2 rad)a fact that is also attested by the corresponding mean gainvalues (gain averaged over each band)The expression for thedimensionless figure of merit in decibels is repeated here forconvenience

FOM = 10 + 10 log (119899total)

+ 10 log (FBW) minus 10 log (119896119886) (3)

Karilainen et al [35] suggested the use of the radiationquality factor 119876

119903 for the comparison of overall performance

of antennas featuring different shapes volumes and resonantfrequencies

119876119903=119876

119899rad (4)

Taking mismatch losses also into account the totalradiation quality factor 119876

119905 is proposed here in order to

evaluate the performance of the antenna system

119876119905=

119876

119899total (5)

The values of the dimensionless 119876119903and 119876

119905in decibels

are also tabulated in Table 4 (actually the former is given as119876119899rad)Thegoal of any given design is tomaximize FOMandminimize both 119876

119903and 119876

119905 All three metrics paint the same


30

210

60

240

90

270

120

300

150

330

180 0

SimulatedMeasured

0

1

2

minus1

minus2

minus3

(a)

30

210

60

240

90

270

120

300

150

330

180 0

SimulatedMeasured

0

5

minus5minus10

minus15

minus20

(b)

Figure 17 Comparison of numerical and experimental gain pattern cuts at 26GHz recorded at the principal planes (a) 120601 = 0 and (b) 120579 = 1205872Notice the different radial scales (both are given in dBi)

30

210

60

240

90

270

120

300

150

330

180 0

SimulatedMeasured

0246

minus10minus8minus6minus4minus2

(a)

30

210

60

240

90

270

120

300

150

330

180 0

SimulatedMeasured

0

5

minus5

minus10

minus15

minus20

(b)

Figure 18 Comparison of numerical and experimental gain pattern cuts at 54GHz recorded at the principal planes (a)120601 = 0 and (b) 120579 = 1205872Notice the different radial scales (both are given in dBi)


Table 5 Aggregate absolute and fractional bandwidths achieved bythe four proposed dual-band PIFAs

K2 GK2 D-GK2 MK2BW119881ℓ+ BW

119881119906(GHz) 0829 1182 1241 1132

FBW119881ℓ+ FBW

1198811199060204 0258 0269 0248

picture with regard to the differential overall performance ofthe four proposed slotted PIFAs

Table 5 lists the aggregate bandwidth absolute and frac-tional that was achieved by each PIFA By comparison ofthese bandwidth values to the ones given in [26] one con-cludes that there exist clear indications that the cumulativeabsolute bandwidth of each antenna is significantly increasedHowever this is a superficial conclusion and it results fromthe high centre frequency of the upper band which is morethan double the centre frequency of the lower band Themost appropriate indicator of impedance bandwidth is thefractional bandwidth Table 5 indicates that the aggregateFBW that an antenna either a single-band or a multi-bandone can yield is strictly limited Therefore it is not actuallyfeasible to extractmore bandwidth froman antenna by simplytriggering more and more resonances The aggregate FBWof any given antenna is also given in the sense that it is anintrinsic quality of that particular antenna configurationTheonly aspect that the designer can actually influence is how theavailable fractional bandwidth will be distributed amongstthe desired frequency bands

42 Comments on Prior Studies and Performance ComparisonAs mentioned in Section 11 the only existing study on dual-band antennas for wireless sensors is the work of Mendeset al [10] They designed a chip-size multilayered planarIFA for operation at 24 and 57GHz It achieved 50MHzof bandwidth at 24GHz (21 fractional) and 170MHz at57GHz (30) The overall size of the radiator was 6mm times

85mm times 45mm The circumscribing sphere had a radius1198861= 57mm which corresponds to an electrical size equal

to (119896119886)1= 029 rad ≪ 1 rad The definition of electrical

size is given in [26 34] Based on data reported in [10] thequality factor of the chip-size planar IFA was estimated at119876 = 316 However the lower bound on 119876 that is the well-knownChu-Harrington-McLean limit is equal to119876

ℓ119887= 376

One possible explanation for the discrepancy is the effect ofthe coaxial connector on this electrically small antenna Theantenna operates in dipole mode hence there exist radiatingcurrents on the outer sheath of the coaxial connector If this isindeed the case then the connector must be included in thecircumscribing sphere The height of the antenna increasesfrom 45mm to 145mm and the electrical size becomes(119896119886)1015840

1= 045 rad ≪ 1 rad The lower bound on 119876 becomes

1198761015840

ℓ119887= 132 hence no violation occursMoving on to the comparison Table 6 lists the electrical

sizes fractional bandwidths and aggregate fractional BWsthat were obtained from the literature survey Note that theestimation of all electrical sizes was based on the assumptionthat the whole extent of the finite GNDP contributes to the

radiationmechanismThe same policywas applied to the fourslotted PIFAs (see Table 4) It is also the reason why the workof Wong and Chen [20] was excluded from the comparisonall results reported therein had the antenna mounted onthe lid of a laptop which provided the antenna with anelectrically large ground plane All other structures discussedherein involve strictly finite GNDPs hence the comparisonwould not be meaningful

The aggregate bandwidths listed in Table 6 range between5-32 since the listed PIFAs vary in size from electricallysmall to electrically very large All bandwidths were calcu-lated at VSWR = 192 1 that is at a reflection level equal tominus10 dB The aggregate bandwidths of the four slotted PIFAsdescribed herein compare favourably with those reported inprior worksThe twelve referenced studies can be divided intothree main categories

(1) PIFA structures that are electrically larger and stillproduce a smaller aggregate bandwidth compared tothe four slotted PIFAs [9 16ndash18]

(2) PIFA structures that are electrically smaller and pro-duce a smaller aggregate bandwidth compared to thefour slotted PIFAs either because they are smaller orbecause they are planar IFAs [10 11 14 15 21] and

(3) PIFA structures that are electrically smaller but man-age to produce greater aggregate bandwidths com-pared to the four slotted PIFAs [12 13 19]

The design of the four slotted PIFAs opted for maxi-mization of the bandwidth of the lower resonance hence theantennas reported herein perform worse compared to designapproaches that maximized the upper band or both More-over the electrical size of the slotted PIFAswas influenced notonly by the maximization of the lower bandwidth but also bythe need for available real-estate on the PCB to solder the RFand baseband electronics of the wireless sensors Last but notleast the dual-band technique reported herein also achievesdesign simplicity and low cost of fabrication

5 Measurement Results

Figure 15(a) depicts a fabricated dual-band printed IFA thathas been reactively loaded with a Koch-shaped slot of thesecond iteration (K2)The antenna was fabricated on TRF-45laminated substrate [31] Parameter values are in accordancewith Table 2

Measurements were conducted in an fully anechoicchamber (far-field test site) suitable for antenna characteri-zation in the range 08ndash40GHz The reference antenna wasspaced by 47m from the antenna under test (AUT) that isby approximately 39120582 at 25 GHz Both AUT and referenceantenna were connected through low-loss coaxial cables tothe ports of an E8358A vector network analyzer (VNA)[36] which recorded the complex scattering parameters Thesettings that were applied to theVNAare listed in Table 7Themeasurements were done over two consecutive 3GHz-widebands


51 Measured Input Impedance The result illustrated inFigure 15(b) firstly shows that there is a lower-frequencyband exhibiting a resonance at 119891

0ℓ= 2610GHz a centre

frequency 119891cℓ = 2618GHz and an operational bandwidthBWℓ= 0235GHz The corresponding fractional bandwidth

is FBWℓ= 0090

At the same time an upper operating band exists in the5-6GHz range It exhibits a resonance at 119891

0ℎ= 5395GHz

a centre frequency 119891cℎ = 5428GHz and an operationalbandwidth BW

ℎ= 0575GHz The corresponding fractional

bandwidth is FBWℓ= 0106

The results stated above lead to an aggregate absolutebandwidth equal to BW

ℓ+ BW

ℎ= 0810GHzThe aggregate

fractional bandwidth is equal to FBWℓ+ FBW

ℎ= 0196

The results reported in this section compare favourablywith the corresponding numerical results listed in Tables 4and 5 The relative error in centre frequencies is equal to+35 and +22 for the lower and upper band respectivelySimilarly the differences in absolute bandwidth are +17and minus38 whereas the errors in fractional bandwidth readminus11 and minus53 Finally the deviation in aggregate absoluteand fractional bandwidth is minus23 and minus39 respectively

52 Measured Far-Field Patterns The far-field patterns ofthe K2 PIFA were measured at 26 and 54GHz For theconvenience of the reader the computed three-dimensionalpatterns of the antenna at these two frequencies are illustratedin Figure 16 The antenna lies on the 119909119910-plane as shownby the coordinate system in Figure 16 The surface currentsdepicted in Figures 4 7 10 and 14 indicate that the radiatingcurrents feature strong119909- and119910-componentsTheorthogonalcurrents are phased randomly Thus as anticipated the fourprinted IFAs are elliptically polarized in the general caseTherefore the gain amplitudes given in Figure 16 correspondto the vectorial sum of the 120579- and 120601-components of the E-field

The far-field measurements discussed here report on theresults that were harvested from the 120601 = 0 and 120579 =

1205872 principal planes The reference antenna was a linearlypolarized standard-gain horn hence the 120579 (vertical) and120601 (horizontal) components of the far field were measuredseparately The results are grouped in Figures 17 and 18 thegain amplitudes again correspond to the vectorial sum of the120579- and 120601-components of the E-field

At 26GHz there is good agreement between computedand measured patterns especially in the 120579 = 1205872 cut Thedirections of maxima and minima have been predicted withconsiderable accuracy In the 120601 = 0 cut the measuredmaximum IEEE gain lags the computed one by 01 dB (19 dBiversus 20 dBi) On the other hand in the 120579 = 1205872 cutthe measured maximum gain exceeds the computed one by02 dB (21 dBi versus 19 dBi) A deviation on the order ofplusmn02 dB lies within the measurement uncertainty of the VNA[36] which can be estimated by the instrument settings listedin Table 7

At 54GHz the agreement between computed and mea-sured patterns becomes worse particularly in the 120601 = 0

cut Significant null filling is observed together with angular

shifting of the side lobes The deviant behaviour is attributedto radiation from the feed cable which amplifies the 120579-component and to scattering from the mounting pole andtripod according to the 21198632120582 rule the reactive and radiatingnear field of the antenna occupies twice the space when firingin the upper band Nevertheless in the 120601 = 0 cut themeasured maximum IEEE gain exceeds the computed oneby 09 dB (49 dBi versus 40 dBi) On the other hand in the120579 = 1205872 cut the measured maximum gain lags the computedone by 12 dB (32 dBi versus 44 dBi)

6 Conclusion

Dual-band communication can play a significant role in cur-rent and future wireless sensor networks Given the scarcityof relevant proper radiators this paper described how printedantennas can be efficiently designed as simple compactdevice-integrated dual-band antennas During the evolutionof modern antennas the planar IFA inherited the propertiesof the microstrip ldquopatchrdquo antenna while the printed IFAinherited those of the printed monopole Printed monopolesare well-known wideband radiators patch antennas are notReactive tuning of printed IFAs was applied in the formof four slotted configurations in order to exert as muchaggregate bandwidth as possible for use in two well-knownunlicensed bands

Electrical performance was characterized throughnumerous computed results Slot loading showed a potentialto increase the impedance bandwidth compared to priorimplementations in terms of achievable FBW

119881 The study of

SCDs revealed that most of the area of the element is usedfor radiation at both resonances In radiation terms theantennas provided satisfactory gains and high efficiencies(ge82) A simple figure of merit was used to compare theperformance of the three PIFAs head to head The finalcomparison displayed in an emphatic way that modernantenna design is an art of compromise

By exploring the potential for operation at 25 GHz and55GHz it was discovered that a simple change in slot geom-etry can almost double the achievable operational bandwidthThus the proposed antennas not only serve the 515ndash535GHzU-NII band but also the 5725ndash5875GHz ISM band Theproposed dual-band structures exhibited at the lower bandan electrical size less or equal to that of the half-wavelengthdipole Nonetheless these antennas can indeed be consideredcompact even though they are not electrically small per sesince their dual-band capability enables them to do the jobof two and even three separate antennas Meanwhile aneducated choice of substrate can enable the combination ofease of fabrication and high radiation efficiency even at mid-C-band

Yet another important design element that this studyof dual-band antennas highlighted is that the aggregatefractional bandwidth of a PIFA is bounded within certainlimits and by degenerating higher-order radiating modesthe designer merely re-distributes whatever bandwidth isavailable by the antenna itself to the desired frequency bands


Table 6 Electrical sizes fractional bandwidths and aggregate fractional bandwidths from the literature survey

Reference work Lower band Upper band119896119886 (rad) FBW 119896119886 (rad) FBW Aggr FBW

Angelopoulos et al [9] 303 0086 647 0063 0149Mendes et al [10] 045 0021 107 0030 0051Moon et al [11] 079 0041 190 0145 0186Cho et al [12] 060 0057 139 0261 0318Nakano et al [13] 111 0041 265 0282 0323Azad and Ali [14] 113 0070 236 0033 0103Cho et al [15] 133 0045 302 0162 0207Wang et al [16] (spiralled tail) 197 0057 422 0144 0201Wang et al [16] (coupling element) 194 0098 415 0128 0226Michailidis et al [17] 172 0095 359 0137 0232Chan et al [18] 209 0109 283 0036 0145Yu and Choi [19] 114 0187 251 0153 0340Li et al [21] (IFA mode) 116 0085 304 0078 0163

Table 7 Settings applied to the network analyzer during themeasurement of the K2 PIFA

Network analyzer settingsSpan (Cal + Meas) 1ndash4GHz and 4ndash7GHzIF bandwidth 5 kHzNumber of points 601 (Δ119891 = 5MHz)Sweep time 128msec (manual)Averaging (full span) 32 (15 dB)

Acknowledgments

C Kakoyiannis thanks Dr T Zervos and Dr A Alexan-dridis both with the Wireless Communications LaboratoryInstitute of Informatics and Telecommunications NCSRldquoDemokritosrdquo Athens Greece for assisting with the antennameasurements that were conducted in the anechoic facilityof the institute The authors wish to acknowledge TaconicAdvanced Dielectric Division (Mullingar Ireland and Cheo-nan South Korea) for donating the TRF-45 laminated sub-strate which was used for design and fabrication of all anten-nas described hereinThis work is part of the ldquoMAGELLANrdquoresearch project implemented within the framework of theldquoTHALISrdquo Research Programme (NSRF 2007ndash2013) and co-financed by the Greek Ministry of Education and ReligiousAffairs Culture and Sports and the European Union

References

[1] P S Hall E Lee and C T P Song ldquoPlanar inverted-Fantennasrdquo in Printed Antennas for Wireless Communications RWaterhouse Ed chapter 7 pp 197ndash228 John Wiley amp SonsChichester UK 2007

[2] B S Collins ldquoHandset antennasrdquo in Antennas for PortableDevices Z N Chen Ed chapter 2 John Wiley amp SonsChichester UK 2007

[3] Y C Vardaxoglou and J R James ldquoMobile handset antennasrdquoinAntenna Engineering Handbook J L Volakis Ed chapter 36McGraw-Hill New York NY USA 4th edition 2007

[4] Z Ying M Ohtsuka Y Nishioka and K Fujimoto ldquoAntennasfor mobile terminalsrdquo inMobile Antenna Systems Handbook KFujimoto Ed chapter 5 pp 213ndash320 Artech House NorwoodMass USA 3rd edition 2008

[5] K Boyle ldquoMultiband multisystem antennas in handsetsrdquo inMultiband Integrated Antennas for 4GTerminals D A Sanchez-Hernandez Ed chapter 2 pp 33ndash52 Artech House NorwoodMass USA 2008

[6] M Martınez-Vazquez E Antonino-Daviu and M Fabedo-Cabres ldquoMiniaturized integrated multiband antennasrdquo inMultiband Integrated Antennas for 4GTerminals D A Sanchez-Hernandez Ed chapter 5 pp 151ndash186 Artech House Nor-wood Mass USA 2008

[7] Y Rahmat-Samii J Guterman A A Moreira and C PeixeiroldquoIntegrated antennas for wireless personal communicationsrdquo inModern Antenna Handbook C A Balanis Ed chapter 22 pp1079ndash1142 John Wiley amp Sons Hoboken NJ USA 2008

[8] K Fujimoto ldquoAntennas formobile communicationsrdquo inModernAntenna Handbook C A Balanis Ed chapter 23 pp 1143ndash1228 John Wiley amp Sons Hoboken NJ USA 2008

[9] E S Angelopoulos A I Kostaridis and D I Kaklamani ldquoAnovel dual-band f-inverted antenna printed on a PCMCIAcardrdquo Microwave and Optical Technology Letters vol 42 no 2pp 153ndash156 2004

[10] P M Mendes A Bartek J N Burghartz and J H CorreialdquoNovel very small dual-band chip-size antenna for wirelesssensor networksrdquo in Proceedings of the IEEE Radio andWirelessConference (RAWCON rsquo04) pp 419ndash422 Atlanta Ga USASeptember 2004

[11] J I Moon D U Sim and S O Park ldquoCompact PIFA for245GHz dual ISM-band applicationsrdquo Electronics Letters vol40 no 14 pp 844ndash846 2004

[12] Y J Cho S H Hwang and S O Park ldquoPrinted antenna withfolded non-uniformmeander line for 245GHzWLANbandsrdquoElectronics Letters vol 41 no 14 pp 786ndash788 2005

[13] H Nakano Y Sato H Mimaki and J Yamauchi ldquoAn invertedFL antenna for dual-frequency operationrdquo IEEETransactions onAntennas and Propagation vol 53 no 8 pp 2417ndash2421 2005

[14] M Z Azad and M Ali ldquoA miniaturized hilbert PIFA for dual-bandmobile wireless applicationsrdquo IEEE Antennas andWirelessPropagation Letters vol 4 no 1 pp 59ndash62 2005


[15] Y J Cho Y S Shin and S O Park ldquoInternal PIFA for 245GHzWLAN applicationsrdquo Electronics Letters vol 42 no 1 pp 8ndash92006

[16] Y S Wang M C Lee and S J Chung ldquoTwo PIFA-relatedminiaturized dual-band antennasrdquo IEEETransactions onAnten-nas and Propagation vol 55 no 3 pp 805ndash811 2007

[17] E Michailidis C C Tsimenidis and E G Chester ldquoParametricstudy of dual and wide band PIFArdquo in Proceedings of theIET Seminar on Wideband Multiband Antennas and Arrays forDefence or Civil Applications pp 145ndash159 London UK March2008

[18] P W Chan H Wong and E K N Yung ldquoDual-band printedinverted-F antenna for DCS 24GHZ WLAN applicationsrdquoin Proceedings of the Loughborough Antennas and PropagationConference (LAPC rsquo08) pp 185ndash188 Loughborough UKMarch2008

[19] Y Yu and J Choi ldquoCompact internal inverted-F antenna forUSB dongle applicationsrdquo Electronics Letters vol 45 no 2 pp92ndash94 2009

[20] K L Wong and W J Chen ldquoSmall-size microstrip-coupledprintedPIFA for 245258 GHzWLANoperation in the laptopcomputerrdquo Microwave and Optical Technology Letters vol 51no 9 pp 2072ndash2076 2009

[21] Y Li Z Zhang J Zheng Z Feng and M F Iskander ldquoAcompact hepta-band loop-inverted F reconfigurable antennafor mobile phonerdquo IEEE Transactions on Antennas and Prop-agation vol 60 no 1 pp 389ndash392 2012

[22] N Cho J Bae and H J Yoo ldquoA 108mW body channelcommunicationMICS dual-band transceiver for a unified bodysensor network controllerrdquo IEEE Journal of Solid-State Circuitsvol 44 no 12 pp 3459ndash3468 2009

[23] K Boyle Antennas for multi-band RF front-end modules [PhDthesis] Delft University of Technology Delft The Netherlands2004

[24] K R Boyle and L P Ligthart ldquoRadiating and balanced modeanalysis of PIFA antennasrdquo IEEE Transactions on Antennas andPropagation vol 54 no 1 pp 231ndash237 2006

[25] Z D Liu P S Hall and D Wake ldquoDual-frequency planarinverted-F antennardquo IEEE Transactions on Antennas and Prop-agation vol 45 no 10 pp 1451ndash1458 1997

[26] C G Kakoyiannis A Kyrligkitsi and P ConstantinouldquoBandwidth enhancement radiation properties and ground-dependent response of slotted antennas integrated into wirelesssensorsrdquo IETMicrowaves Antennas and Propagation vol 4 no5 pp 609ndash628 2010

[27] C Puente J Romeu and A Cardama ldquoFractal-shaped anten-nasrdquo in Frontiers in Electromagnetics D Werner and R MittraEds chapter 2 pp 48ndash93 IEEE Press New York NY USA2000

[28] J P Gianvittorio and Y Rahmat-Samii ldquoFractal antennas anovel antenna miniaturization technique and applicationsrdquoIEEEAntennas and PropagationMagazine vol 44 no 1 pp 20ndash36 2002

[29] D H Werner and S Ganguly ldquoAn overview of fractal antennaengineering researchrdquo IEEE Antennas and Propagation Maga-zine vol 45 no 1 pp 38ndash57 2003

[30] W J Krzystofik ldquoPrinted multiband fractal antennasrdquo inMulti-band Integrated Antennas for 4G TermInals D A Sanchez-Hernandez Ed chapter 4 pp 95ndash150ArtechHouseNorwoodMass USA 2008

[31] Advanced PCB Materials Product Selection Guide TaconicPetersburgh NY USA 2010

[32] T Weiland M Timm and I Munteanu ldquoA practical guide to3-D simulationrdquo IEEE Microwave Magazine vol 9 no 6 pp62ndash75 2008

[33] I Munteanu M Timm and T Weiland ldquoItrsquos about timerdquo IEEEMicrowave Magazine vol 11 no 2 pp 60ndash69 2010

[34] C G Kakoyiannis and P Constantinou ldquoRadiation propertiesand ground-dependent response of compact printed sinusoidalantennas and arraysrdquo IET Microwaves Antennas and Propaga-tion vol 4 no 5 pp 629ndash642 2010

[35] A O Karilainen P M T Ikonen C R Simovski et al ldquoExper-imental studies on antenna miniaturisation using magneto-dielectric and dielectric materialsrdquo IET Microwaves Antennasand Propagation vol 5 no 4 pp 495ndash502 2011

[36] Agilent PNA Series RF Network Analyzers E835678AE880123A N338123A Data Sheet Agilent Technologies IncSanta Rosa Calif USA 2006

International Journal of

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Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



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Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

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Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



adjustable spacing between bands One could argue thatdual-band antennas find no use in wireless sensor networks(WSNs) because dual-band WSNs do not exist the secondintegrated transceiver that is required along with its periph-eral passive components bring extra complexity cost andenergy consumption for a wireless microsensor So it is bestto wait until very large scale integration (VLSI) technologymatures to the point of single-chip dual-band integratedtransceivers However the above arguments do not hold fortwo reasons On one hand dual-band communication isinherent in real-world WSN deployments the microsensorsimplement various algorithms for example routing local-ization virtual array formation and improved connectiv-ity and coverage These algorithms depend on GPS signalreception hence a second communication band comes intoplay On the other hand dual-band single-chip integratedtransceivers are already here Cho et al [22] designed anenergy-efficient dual-band fully integrated transceiver forbody sensor network applications in the 30ndash70MHz andMICS (402ndash405MHz) bandsThus it is anticipated that dual-band communication will become vital in future wirelesssensor networks

To the best of the authorsrsquo knowledge the only existingstudy on dual-band antennas that target wireless sensors isthe work of Mendes et al [10] We comment on this work inSection 4 along with the rest of the relevant literature

12 Theoretical Considerations Boyle [5 23] and Boyle andLigthart [24] used superposition and divided the operationof the antenna into the balanced (nonradiating) and theradiating mode One of their key findings was that the PCBlength has a strong effect on antenna quality factor 119876 the119876 is minimized when the length is close to the 1205822- or 120582-antiresonance Hence the bandwidth (BW) which is relatedto the quality factor 119876 is strongly affected by the length ofthe GNDP Furthermore in the case of dual-band PIFAs thewidth of the two bands is not independent to improve BWat the lower resonance the higher resonance BW must bedegraded

Referring to the internal workings of dual-band slottedplanar IFAs [1 25] Boyle suggested that slots in the antennatop plate between the feed and short pins allow independentvariation of the impedance transformation and shunt reac-tance [5 23 24] Furthermore slots in the top plate can tunea planar inverted-L antenna (ILA) that is naturally resonantbetween the lower and upper resonance If the slot is too longthe lower BW is degraded if the slot is too short the upperBW is degraded

The technique of degenerating higher-order radiatingmodes by inductive loading of the antenna with slots appliesequally well in the case of nonadjacent frequency bandsThis has been shown for planar IFAs by Liu et al [25] andBoyle and Ligthart [23 24] Angelopoulos et al [9] showedthat this response is also feasible with printed IFAs theauthors of [9] presented an application of the slot-loadingconcept which involved a dual-band PIFA comprised of two1205824 monopoles coupled and separated by an L-slot It wassuggested that each monopole radiates in its own resonance

frequency (245525GHz) when fed by a single feeding portconnected to the smaller monopole It was also theorizedthat the function of the L-slot was to form a gap for higherfrequency currents which at the same time is not wideenough to disturb the lower resonance The work describedherein will demonstrate that in general this is not the case

13 Scope and Structure of the Paper Based on our expe-rience with multimode single-band printed IFAs [26] wehave attempted to design microsensor-oriented PIFAs whichshould satisfy the following specifications

(1) Display a bandwidth at least equal to 100MHz inthe vicinity of 25 GHz thus a fractional bandwidthFBW119881ℓge 4

(2) Display a bandwidth at least equal to 200MHz at thelower end of the 5-6GHz range A good applicationexample is the U-NII 515ndash535GHz band whichfeatures a fractional bandwidth FBW

119881119906= 38

(3) Achieve the previous two specifications withoutexceeding the electrical size 119896119886 of the half-wave-length dipole (119896119886)

1205822= 1205872 rad at the lower band

(4) Achieve a mean total radiation efficiency over bothbands at least equal to 80 that is 119899total ge minus1 dB

The paper describes the design of printed inverted-Fantennas that have been inductively loaded by four differentpre-fractal slotsThe first three slot topologies were discussedin detail in [26] they are the simple generalized and dualgeneralized Koch curves of the second iteration The fourthslot resembles the quadratic type 2 Koch curve its propertiesare described in Section 34 The effect of the size of theground plane on both frequency bands was also investigatedThe reactive loading imposed by the pre-fractal slots notonly surpassed the specifications but also outperformed theresults of several prior studies Section 2 discusses design andmodelling issues Section 3 displays an array of numericalresults produced by accurate computational models of thefour slotted antenna configurations Section 4 discusses theresults Section 5 presents measurement results harvestedfrom a prototype antenna Finally Section 6 concludes thepaper

2 Antenna Design andElectromagnetic Modelling

Out of the four antennas that were designed the first threewere inductively loaded by slots shaped after the followingpre-fractal curves

(1) the Koch curve of the second iteration (abbreviatedherein as ldquoK2rdquo) [26]

(2) the generalized Koch curve of the second iteration(abbreviated herein as ldquoGK2rdquo) [26] and

(3) the dual generalized Koch curve of the second itera-tion (abbreviated herein as ldquoD-GK2rdquo) [26]

Apart from [26] the properties of Koch curve variants arealso described in [27ndash30] thus the details are omitted here for


119909

119910

119911

119882ind

119882short

119871ind119882feed

119882slot

119889fs

119871fs

119871slo

t

119871PI

FA

119882PIFA

119882strip

119882gnd

119871gnd




0ℓ= 25GHz and 119891



0119906≃ 571












0

0 1 2 3 4 5 6 7

Inpu

t refl

ectio

n co

effici

ent (

dB)

Frequency (GHz)

minus40

minus30

minus20

minus10





3GHz8






119886 =1

2

radic1198822

strip + (119882PIFA + 119871 fs + 119871gnd)2

(1)








02

04

0608 1

15

2

3

45

10


02 04 06 08 1 15 2 3 4 5 10

minus02

minus04


minus15

minus2

minus3minus4minus5

minus10

4 (3627 minus2928) ohm

(a)

02

04

0608 1

15

2

3

45

10


02 04 06 08 1 15 2 3 4 5 10

minus02

minus04


minus15

minus2

minus3minus4minus5

minus10

3 (9633 minus1621) ohm7 (1994 383) ohm

(b)


0 48

944

157

241

355

509

169

(Am)

Curr

ent (

peak

)(119891=25)

[1]

(a)

Curr

ent (

peak

)

216

649

453

308

2012612

0

(Am)

(119891=525)

[1]

(b)

















11







119863MK =ln (3119899 minus 4)ln (119899)

(2)




0

0 1 2 3 4 5 6 7

Inpu

t refl

ectio

n co

effici

ent (

dB)

Frequency (GHz)

minus25

minus20

minus15

minus10

minus5


02

04

0608 1

15

2

3

45

10


02 04 06 08 1 15 2 3 4 5 10


minus02

minus04


minus15

minus2

minus3minus4minus5

minus10

4 (3792 minus3927) ohm

(a)

02

04

0608 1

15

2

3

45

10


02 04 06 08 1 15 2 3 4 5 10

minus02

minus04


minus15

minus2

minus3minus4minus5

minus10

3 (2322 minus2507) ohm7 (1493 2443) ohm

(b)



11



11987811






0

0 1 2 3 4 5 6 7

Inpu

t refl

ectio

n co

effici

ent (

dB)

Frequency (GHz)

minus25

minus20

minus15

minus10

minus5





2le 5mm Changes






4 Discussion



02

04

0608 1

15

2

3

45

10


02 04 06 08 1 15 2 3 4 5 10


minus02

minus04


minus15

minus2

minus3minus4minus5

minus10

) ohm

(a)

02

04

0608 1

15

2

3

45

10


02 04 06 08 1 15 2 3 4 5 10

3 (1464 minus2226) ohm

minus02

minus04


minus15

minus2

minus3minus4minus5

minus10

7 (1329 3341) ohm

(b)




1 2

3


0 1 2 3 4 5 6 7

Inpu

t refl

ectio

n co

effici

ent (

dB)

Frequency (GHz)

0

minus10

minus20

minus30






BW119881(GHz) 0231 0598 0182 1000 0191 1050 0182 0950

FBW119881


119876119903(dB) +89 +78 +99 +57 +97 +54 +98 +59

119876119905(dB) +92 +86 +104 +62 +102 +59 +104 +66


02

04

0608 1

15

2

3

45

10


02 04 06 08 1 15 2 3 4 5 10


minus02

minus04


minus15

minus2

minus3minus4minus5

minus10

(a)

02

04

0608 1

15

2

3

45

10


02 04 06 08 1 15 2 3 4 5 10

3 (3304 minus314) ohm7 (1091 2279) ohm

minus02

minus04


minus15

minus2

minus3minus4minus5

minus10

(b)






(a)

1 2 3 4 5 6 7

SimulatedMeasured

0

Frequency (GHz)

minus10

minus20

minus30

minus40

Inpu

t refl

ectio

nco

effici

ent 11987811

(dB)

(b)


22192165137

11082405490275


120601

120579


119910

119909


Farfield

2197 dB

(dB)

(a)

43438

326271217163109

05430




Farfield

4344 dB

(dB)

120601

120579

119909

119911

119910

(b)



FOM = 10 + 10 log (119899total)

+ 10 log (FBW) minus 10 log (119896119886) (3)




119876119903=119876

119899rad (4)




119876119905=

119876

119899total (5)


119905in decibels


119903and 119876



30

210

60

240

90

270

120

300

150

330

180 0

SimulatedMeasured

0

1

2

minus1

minus2

minus3

(a)

30

210

60

240

90

270

120

300

150

330

180 0

SimulatedMeasured

0

5

minus5minus10

minus15

minus20

(b)


30

210

60

240

90

270

120

300

150

330

180 0

SimulatedMeasured

0246


(a)

30

210

60

240

90

270

120

300

150

330

180 0

SimulatedMeasured

0

5

minus5

minus10

minus15

minus20

(b)





119881119906(GHz) 0829 1182 1241 1132

FBW119881ℓ+ FBW

1198811199060204 0258 0269 0248







ℓ119887= 376



1198761015840
















is FBWℓ= 0090


0ℎ= 5395GHz





ℓ+ BW



ℎ= 0196









6 Conclusion



119881 The study of










Acknowledgments


References








































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










119909

119910

119911

119882ind

119882short

119871ind119882feed

119882slot

119889fs

119871fs

119871slo

t

119871PI

FA

119882PIFA

119882strip

119882gnd

119871gnd




0ℓ= 25GHz and 119891



0119906≃ 571












0

0 1 2 3 4 5 6 7

Inpu

t refl

ectio

n co

effici

ent (

dB)

Frequency (GHz)

minus40

minus30

minus20

minus10





3GHz8






119886 =1

2

radic1198822

strip + (119882PIFA + 119871 fs + 119871gnd)2

(1)








02

04

0608 1

15

2

3

45

10


02 04 06 08 1 15 2 3 4 5 10

minus02

minus04


minus15

minus2

minus3minus4minus5

minus10

4 (3627 minus2928) ohm

(a)

02

04

0608 1

15

2

3

45

10


02 04 06 08 1 15 2 3 4 5 10

minus02

minus04


minus15

minus2

minus3minus4minus5

minus10

3 (9633 minus1621) ohm7 (1994 383) ohm

(b)


0 48

944

157

241

355

509

169

(Am)

Curr

ent (

peak

)(119891=25)

[1]

(a)

Curr

ent (

peak

)

216

649

453

308

2012612

0

(Am)

(119891=525)

[1]

(b)

















11







119863MK =ln (3119899 minus 4)ln (119899)

(2)




0

0 1 2 3 4 5 6 7

Inpu

t refl

ectio

n co

effici

ent (

dB)

Frequency (GHz)

minus25

minus20

minus15

minus10

minus5


02

04

0608 1

15

2

3

45

10


02 04 06 08 1 15 2 3 4 5 10


minus02

minus04


minus15

minus2

minus3minus4minus5

minus10

4 (3792 minus3927) ohm

(a)

02

04

0608 1

15

2

3

45

10


02 04 06 08 1 15 2 3 4 5 10

minus02

minus04


minus15

minus2

minus3minus4minus5

minus10

3 (2322 minus2507) ohm7 (1493 2443) ohm

(b)



11



11987811






0

0 1 2 3 4 5 6 7

Inpu

t refl

ectio

n co

effici

ent (

dB)

Frequency (GHz)

minus25

minus20

minus15

minus10

minus5





2le 5mm Changes






4 Discussion



02

04

0608 1

15

2

3

45

10


02 04 06 08 1 15 2 3 4 5 10


minus02

minus04


minus15

minus2

minus3minus4minus5

minus10

) ohm

(a)

02

04

0608 1

15

2

3

45

10


02 04 06 08 1 15 2 3 4 5 10

3 (1464 minus2226) ohm

minus02

minus04


minus15

minus2

minus3minus4minus5

minus10

7 (1329 3341) ohm

(b)




1 2

3


0 1 2 3 4 5 6 7

Inpu

t refl

ectio

n co

effici

ent (

dB)

Frequency (GHz)

0

minus10

minus20

minus30






BW119881(GHz) 0231 0598 0182 1000 0191 1050 0182 0950

FBW119881


119876119903(dB) +89 +78 +99 +57 +97 +54 +98 +59

119876119905(dB) +92 +86 +104 +62 +102 +59 +104 +66


02

04

0608 1

15

2

3

45

10


02 04 06 08 1 15 2 3 4 5 10


minus02

minus04


minus15

minus2

minus3minus4minus5

minus10

(a)

02

04

0608 1

15

2

3

45

10


02 04 06 08 1 15 2 3 4 5 10

3 (3304 minus314) ohm7 (1091 2279) ohm

minus02

minus04


minus15

minus2

minus3minus4minus5

minus10

(b)






(a)

1 2 3 4 5 6 7

SimulatedMeasured

0

Frequency (GHz)

minus10

minus20

minus30

minus40

Inpu

t refl

ectio

nco

effici

ent 11987811

(dB)

(b)


22192165137

11082405490275


120601

120579


119910

119909


Farfield

2197 dB

(dB)

(a)

43438

326271217163109

05430




Farfield

4344 dB

(dB)

120601

120579

119909

119911

119910

(b)



FOM = 10 + 10 log (119899total)

+ 10 log (FBW) minus 10 log (119896119886) (3)




119876119903=119876

119899rad (4)




119876119905=

119876

119899total (5)


119905in decibels


119903and 119876



30

210

60

240

90

270

120

300

150

330

180 0

SimulatedMeasured

0

1

2

minus1

minus2

minus3

(a)

30

210

60

240

90

270

120

300

150

330

180 0

SimulatedMeasured

0

5

minus5minus10

minus15

minus20

(b)


30

210

60

240

90

270

120

300

150

330

180 0

SimulatedMeasured

0246


(a)

30

210

60

240

90

270

120

300

150

330

180 0

SimulatedMeasured

0

5

minus5

minus10

minus15

minus20

(b)





119881119906(GHz) 0829 1182 1241 1132

FBW119881ℓ+ FBW

1198811199060204 0258 0269 0248







ℓ119887= 376



1198761015840
















is FBWℓ= 0090


0ℎ= 5395GHz





ℓ+ BW



ℎ= 0196









6 Conclusion



119881 The study of










Acknowledgments


References








































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0

0 1 2 3 4 5 6 7

Inpu

t refl

ectio

n co

effici

ent (

dB)

Frequency (GHz)

minus40

minus30

minus20

minus10





3GHz8






119886 =1

2

radic1198822

strip + (119882PIFA + 119871 fs + 119871gnd)2

(1)








02

04

0608 1

15

2

3

45

10


02 04 06 08 1 15 2 3 4 5 10

minus02

minus04


minus15

minus2

minus3minus4minus5

minus10

4 (3627 minus2928) ohm

(a)

02

04

0608 1

15

2

3

45

10


02 04 06 08 1 15 2 3 4 5 10

minus02

minus04


minus15

minus2

minus3minus4minus5

minus10

3 (9633 minus1621) ohm7 (1994 383) ohm

(b)


0 48

944

157

241

355

509

169

(Am)

Curr

ent (

peak

)(119891=25)

[1]

(a)

Curr

ent (

peak

)

216

649

453

308

2012612

0

(Am)

(119891=525)

[1]

(b)

















11







119863MK =ln (3119899 minus 4)ln (119899)

(2)




0

0 1 2 3 4 5 6 7

Inpu

t refl

ectio

n co

effici

ent (

dB)

Frequency (GHz)

minus25

minus20

minus15

minus10

minus5


02

04

0608 1

15

2

3

45

10


02 04 06 08 1 15 2 3 4 5 10


minus02

minus04


minus15

minus2

minus3minus4minus5

minus10

4 (3792 minus3927) ohm

(a)

02

04

0608 1

15

2

3

45

10


02 04 06 08 1 15 2 3 4 5 10

minus02

minus04


minus15

minus2

minus3minus4minus5

minus10

3 (2322 minus2507) ohm7 (1493 2443) ohm

(b)



11



11987811






0

0 1 2 3 4 5 6 7

Inpu

t refl

ectio

n co

effici

ent (

dB)

Frequency (GHz)

minus25

minus20

minus15

minus10

minus5





2le 5mm Changes






4 Discussion



02

04

0608 1

15

2

3

45

10


02 04 06 08 1 15 2 3 4 5 10


minus02

minus04


minus15

minus2

minus3minus4minus5

minus10

) ohm

(a)

02

04

0608 1

15

2

3

45

10


02 04 06 08 1 15 2 3 4 5 10

3 (1464 minus2226) ohm

minus02

minus04


minus15

minus2

minus3minus4minus5

minus10

7 (1329 3341) ohm

(b)




1 2

3


0 1 2 3 4 5 6 7

Inpu

t refl

ectio

n co

effici

ent (

dB)

Frequency (GHz)

0

minus10

minus20

minus30






BW119881(GHz) 0231 0598 0182 1000 0191 1050 0182 0950

FBW119881


119876119903(dB) +89 +78 +99 +57 +97 +54 +98 +59

119876119905(dB) +92 +86 +104 +62 +102 +59 +104 +66


02

04

0608 1

15

2

3

45

10


02 04 06 08 1 15 2 3 4 5 10


minus02

minus04


minus15

minus2

minus3minus4minus5

minus10

(a)

02

04

0608 1

15

2

3

45

10


02 04 06 08 1 15 2 3 4 5 10

3 (3304 minus314) ohm7 (1091 2279) ohm

minus02

minus04


minus15

minus2

minus3minus4minus5

minus10

(b)






(a)

1 2 3 4 5 6 7

SimulatedMeasured

0

Frequency (GHz)

minus10

minus20

minus30

minus40

Inpu

t refl

ectio

nco

effici

ent 11987811

(dB)

(b)


22192165137

11082405490275


120601

120579


119910

119909


Farfield

2197 dB

(dB)

(a)

43438

326271217163109

05430




Farfield

4344 dB

(dB)

120601

120579

119909

119911

119910

(b)



FOM = 10 + 10 log (119899total)

+ 10 log (FBW) minus 10 log (119896119886) (3)




119876119903=119876

119899rad (4)




119876119905=

119876

119899total (5)


119905in decibels


119903and 119876



30

210

60

240

90

270

120

300

150

330

180 0

SimulatedMeasured

0

1

2

minus1

minus2

minus3

(a)

30

210

60

240

90

270

120

300

150

330

180 0

SimulatedMeasured

0

5

minus5minus10

minus15

minus20

(b)


30

210

60

240

90

270

120

300

150

330

180 0

SimulatedMeasured

0246


(a)

30

210

60

240

90

270

120

300

150

330

180 0

SimulatedMeasured

0

5

minus5

minus10

minus15

minus20

(b)





119881119906(GHz) 0829 1182 1241 1132

FBW119881ℓ+ FBW

1198811199060204 0258 0269 0248







ℓ119887= 376



1198761015840
















is FBWℓ= 0090


0ℎ= 5395GHz





ℓ+ BW



ℎ= 0196









6 Conclusion



119881 The study of










Acknowledgments


References








































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











02

04

0608 1

15

2

3

45

10


02 04 06 08 1 15 2 3 4 5 10

minus02

minus04


minus15

minus2

minus3minus4minus5

minus10

4 (3627 minus2928) ohm

(a)

02

04

0608 1

15

2

3

45

10


02 04 06 08 1 15 2 3 4 5 10

minus02

minus04


minus15

minus2

minus3minus4minus5

minus10

3 (9633 minus1621) ohm7 (1994 383) ohm

(b)


0 48

944

157

241

355

509

169

(Am)

Curr

ent (

peak

)(119891=25)

[1]

(a)

Curr

ent (

peak

)

216

649

453

308

2012612

0

(Am)

(119891=525)

[1]

(b)

















11







119863MK =ln (3119899 minus 4)ln (119899)

(2)




0

0 1 2 3 4 5 6 7

Inpu

t refl

ectio

n co

effici

ent (

dB)

Frequency (GHz)

minus25

minus20

minus15

minus10

minus5


02

04

0608 1

15

2

3

45

10


02 04 06 08 1 15 2 3 4 5 10


minus02

minus04


minus15

minus2

minus3minus4minus5

minus10

4 (3792 minus3927) ohm

(a)

02

04

0608 1

15

2

3

45

10


02 04 06 08 1 15 2 3 4 5 10

minus02

minus04


minus15

minus2

minus3minus4minus5

minus10

3 (2322 minus2507) ohm7 (1493 2443) ohm

(b)



11



11987811






0

0 1 2 3 4 5 6 7

Inpu

t refl

ectio

n co

effici

ent (

dB)

Frequency (GHz)

minus25

minus20

minus15

minus10

minus5





2le 5mm Changes






4 Discussion



02

04

0608 1

15

2

3

45

10


02 04 06 08 1 15 2 3 4 5 10


minus02

minus04


minus15

minus2

minus3minus4minus5

minus10

) ohm

(a)

02

04

0608 1

15

2

3

45

10


02 04 06 08 1 15 2 3 4 5 10

3 (1464 minus2226) ohm

minus02

minus04


minus15

minus2

minus3minus4minus5

minus10

7 (1329 3341) ohm

(b)




1 2

3


0 1 2 3 4 5 6 7

Inpu

t refl

ectio

n co

effici

ent (

dB)

Frequency (GHz)

0

minus10

minus20

minus30






BW119881(GHz) 0231 0598 0182 1000 0191 1050 0182 0950

FBW119881


119876119903(dB) +89 +78 +99 +57 +97 +54 +98 +59

119876119905(dB) +92 +86 +104 +62 +102 +59 +104 +66


02

04

0608 1

15

2

3

45

10


02 04 06 08 1 15 2 3 4 5 10


minus02

minus04


minus15

minus2

minus3minus4minus5

minus10

(a)

02

04

0608 1

15

2

3

45

10


02 04 06 08 1 15 2 3 4 5 10

3 (3304 minus314) ohm7 (1091 2279) ohm

minus02

minus04


minus15

minus2

minus3minus4minus5

minus10

(b)






(a)

1 2 3 4 5 6 7

SimulatedMeasured

0

Frequency (GHz)

minus10

minus20

minus30

minus40

Inpu

t refl

ectio

nco

effici

ent 11987811

(dB)

(b)


22192165137

11082405490275


120601

120579


119910

119909


Farfield

2197 dB

(dB)

(a)

43438

326271217163109

05430




Farfield

4344 dB

(dB)

120601

120579

119909

119911

119910

(b)



FOM = 10 + 10 log (119899total)

+ 10 log (FBW) minus 10 log (119896119886) (3)




119876119903=119876

119899rad (4)




119876119905=

119876

119899total (5)


119905in decibels


119903and 119876



30

210

60

240

90

270

120

300

150

330

180 0

SimulatedMeasured

0

1

2

minus1

minus2

minus3

(a)

30

210

60

240

90

270

120

300

150

330

180 0

SimulatedMeasured

0

5

minus5minus10

minus15

minus20

(b)


30

210

60

240

90

270

120

300

150

330

180 0

SimulatedMeasured

0246


(a)

30

210

60

240

90

270

120

300

150

330

180 0

SimulatedMeasured

0

5

minus5

minus10

minus15

minus20

(b)





119881119906(GHz) 0829 1182 1241 1132

FBW119881ℓ+ FBW

1198811199060204 0258 0269 0248







ℓ119887= 376



1198761015840
















is FBWℓ= 0090


0ℎ= 5395GHz





ℓ+ BW



ℎ= 0196









6 Conclusion



119881 The study of










Acknowledgments


References








































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation
























11







119863MK =ln (3119899 minus 4)ln (119899)

(2)




0

0 1 2 3 4 5 6 7

Inpu

t refl

ectio

n co

effici

ent (

dB)

Frequency (GHz)

minus25

minus20

minus15

minus10

minus5


02

04

0608 1

15

2

3

45

10


02 04 06 08 1 15 2 3 4 5 10


minus02

minus04


minus15

minus2

minus3minus4minus5

minus10

4 (3792 minus3927) ohm

(a)

02

04

0608 1

15

2

3

45

10


02 04 06 08 1 15 2 3 4 5 10

minus02

minus04


minus15

minus2

minus3minus4minus5

minus10

3 (2322 minus2507) ohm7 (1493 2443) ohm

(b)



11



11987811






0

0 1 2 3 4 5 6 7

Inpu

t refl

ectio

n co

effici

ent (

dB)

Frequency (GHz)

minus25

minus20

minus15

minus10

minus5





2le 5mm Changes






4 Discussion



02

04

0608 1

15

2

3

45

10


02 04 06 08 1 15 2 3 4 5 10


minus02

minus04


minus15

minus2

minus3minus4minus5

minus10

) ohm

(a)

02

04

0608 1

15

2

3

45

10


02 04 06 08 1 15 2 3 4 5 10

3 (1464 minus2226) ohm

minus02

minus04


minus15

minus2

minus3minus4minus5

minus10

7 (1329 3341) ohm

(b)




1 2

3


0 1 2 3 4 5 6 7

Inpu

t refl

ectio

n co

effici

ent (

dB)

Frequency (GHz)

0

minus10

minus20

minus30






BW119881(GHz) 0231 0598 0182 1000 0191 1050 0182 0950

FBW119881


119876119903(dB) +89 +78 +99 +57 +97 +54 +98 +59

119876119905(dB) +92 +86 +104 +62 +102 +59 +104 +66


02

04

0608 1

15

2

3

45

10


02 04 06 08 1 15 2 3 4 5 10


minus02

minus04


minus15

minus2

minus3minus4minus5

minus10

(a)

02

04

0608 1

15

2

3

45

10


02 04 06 08 1 15 2 3 4 5 10

3 (3304 minus314) ohm7 (1091 2279) ohm

minus02

minus04


minus15

minus2

minus3minus4minus5

minus10

(b)






(a)

1 2 3 4 5 6 7

SimulatedMeasured

0

Frequency (GHz)

minus10

minus20

minus30

minus40

Inpu

t refl

ectio

nco

effici

ent 11987811

(dB)

(b)


22192165137

11082405490275


120601

120579


119910

119909


Farfield

2197 dB

(dB)

(a)

43438

326271217163109

05430




Farfield

4344 dB

(dB)

120601

120579

119909

119911

119910

(b)



FOM = 10 + 10 log (119899total)

+ 10 log (FBW) minus 10 log (119896119886) (3)




119876119903=119876

119899rad (4)




119876119905=

119876

119899total (5)


119905in decibels


119903and 119876



30

210

60

240

90

270

120

300

150

330

180 0

SimulatedMeasured

0

1

2

minus1

minus2

minus3

(a)

30

210

60

240

90

270

120

300

150

330

180 0

SimulatedMeasured

0

5

minus5minus10

minus15

minus20

(b)


30

210

60

240

90

270

120

300

150

330

180 0

SimulatedMeasured

0246


(a)

30

210

60

240

90

270

120

300

150

330

180 0

SimulatedMeasured

0

5

minus5

minus10

minus15

minus20

(b)





119881119906(GHz) 0829 1182 1241 1132

FBW119881ℓ+ FBW

1198811199060204 0258 0269 0248







ℓ119887= 376



1198761015840
















is FBWℓ= 0090


0ℎ= 5395GHz





ℓ+ BW



ℎ= 0196









6 Conclusion



119881 The study of










Acknowledgments


References








































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0

0 1 2 3 4 5 6 7

Inpu

t refl

ectio

n co

effici

ent (

dB)

Frequency (GHz)

minus25

minus20

minus15

minus10

minus5


02

04

0608 1

15

2

3

45

10


02 04 06 08 1 15 2 3 4 5 10


minus02

minus04


minus15

minus2

minus3minus4minus5

minus10

4 (3792 minus3927) ohm

(a)

02

04

0608 1

15

2

3

45

10


02 04 06 08 1 15 2 3 4 5 10

minus02

minus04


minus15

minus2

minus3minus4minus5

minus10

3 (2322 minus2507) ohm7 (1493 2443) ohm

(b)



11



11987811






0

0 1 2 3 4 5 6 7

Inpu

t refl

ectio

n co

effici

ent (

dB)

Frequency (GHz)

minus25

minus20

minus15

minus10

minus5





2le 5mm Changes






4 Discussion



02

04

0608 1

15

2

3

45

10


02 04 06 08 1 15 2 3 4 5 10


minus02

minus04


minus15

minus2

minus3minus4minus5

minus10

) ohm

(a)

02

04

0608 1

15

2

3

45

10


02 04 06 08 1 15 2 3 4 5 10

3 (1464 minus2226) ohm

minus02

minus04


minus15

minus2

minus3minus4minus5

minus10

7 (1329 3341) ohm

(b)




1 2

3


0 1 2 3 4 5 6 7

Inpu

t refl

ectio

n co

effici

ent (

dB)

Frequency (GHz)

0

minus10

minus20

minus30






BW119881(GHz) 0231 0598 0182 1000 0191 1050 0182 0950

FBW119881


119876119903(dB) +89 +78 +99 +57 +97 +54 +98 +59

119876119905(dB) +92 +86 +104 +62 +102 +59 +104 +66


02

04

0608 1

15

2

3

45

10


02 04 06 08 1 15 2 3 4 5 10


minus02

minus04


minus15

minus2

minus3minus4minus5

minus10

(a)

02

04

0608 1

15

2

3

45

10


02 04 06 08 1 15 2 3 4 5 10

3 (3304 minus314) ohm7 (1091 2279) ohm

minus02

minus04


minus15

minus2

minus3minus4minus5

minus10

(b)






(a)

1 2 3 4 5 6 7

SimulatedMeasured

0

Frequency (GHz)

minus10

minus20

minus30

minus40

Inpu

t refl

ectio

nco

effici

ent 11987811

(dB)

(b)


22192165137

11082405490275


120601

120579


119910

119909


Farfield

2197 dB

(dB)

(a)

43438

326271217163109

05430




Farfield

4344 dB

(dB)

120601

120579

119909

119911

119910

(b)



FOM = 10 + 10 log (119899total)

+ 10 log (FBW) minus 10 log (119896119886) (3)




119876119903=119876

119899rad (4)




119876119905=

119876

119899total (5)


119905in decibels


119903and 119876



30

210

60

240

90

270

120

300

150

330

180 0

SimulatedMeasured

0

1

2

minus1

minus2

minus3

(a)

30

210

60

240

90

270

120

300

150

330

180 0

SimulatedMeasured

0

5

minus5minus10

minus15

minus20

(b)


30

210

60

240

90

270

120

300

150

330

180 0

SimulatedMeasured

0246


(a)

30

210

60

240

90

270

120

300

150

330

180 0

SimulatedMeasured

0

5

minus5

minus10

minus15

minus20

(b)





119881119906(GHz) 0829 1182 1241 1132

FBW119881ℓ+ FBW

1198811199060204 0258 0269 0248







ℓ119887= 376



1198761015840
















is FBWℓ= 0090


0ℎ= 5395GHz





ℓ+ BW



ℎ= 0196









6 Conclusion



119881 The study of










Acknowledgments


References








































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











0

0 1 2 3 4 5 6 7

Inpu

t refl

ectio

n co

effici

ent (

dB)

Frequency (GHz)

minus25

minus20

minus15

minus10

minus5





2le 5mm Changes






4 Discussion



02

04

0608 1

15

2

3

45

10


02 04 06 08 1 15 2 3 4 5 10


minus02

minus04


minus15

minus2

minus3minus4minus5

minus10

) ohm

(a)

02

04

0608 1

15

2

3

45

10


02 04 06 08 1 15 2 3 4 5 10

3 (1464 minus2226) ohm

minus02

minus04


minus15

minus2

minus3minus4minus5

minus10

7 (1329 3341) ohm

(b)




1 2

3


0 1 2 3 4 5 6 7

Inpu

t refl

ectio

n co

effici

ent (

dB)

Frequency (GHz)

0

minus10

minus20

minus30






BW119881(GHz) 0231 0598 0182 1000 0191 1050 0182 0950

FBW119881


119876119903(dB) +89 +78 +99 +57 +97 +54 +98 +59

119876119905(dB) +92 +86 +104 +62 +102 +59 +104 +66


02

04

0608 1

15

2

3

45

10


02 04 06 08 1 15 2 3 4 5 10


minus02

minus04


minus15

minus2

minus3minus4minus5

minus10

(a)

02

04

0608 1

15

2

3

45

10


02 04 06 08 1 15 2 3 4 5 10

3 (3304 minus314) ohm7 (1091 2279) ohm

minus02

minus04


minus15

minus2

minus3minus4minus5

minus10

(b)






(a)

1 2 3 4 5 6 7

SimulatedMeasured

0

Frequency (GHz)

minus10

minus20

minus30

minus40

Inpu

t refl

ectio

nco

effici

ent 11987811

(dB)

(b)


22192165137

11082405490275


120601

120579


119910

119909


Farfield

2197 dB

(dB)

(a)

43438

326271217163109

05430




Farfield

4344 dB

(dB)

120601

120579

119909

119911

119910

(b)



FOM = 10 + 10 log (119899total)

+ 10 log (FBW) minus 10 log (119896119886) (3)




119876119903=119876

119899rad (4)




119876119905=

119876

119899total (5)


119905in decibels


119903and 119876



30

210

60

240

90

270

120

300

150

330

180 0

SimulatedMeasured

0

1

2

minus1

minus2

minus3

(a)

30

210

60

240

90

270

120

300

150

330

180 0

SimulatedMeasured

0

5

minus5minus10

minus15

minus20

(b)


30

210

60

240

90

270

120

300

150

330

180 0

SimulatedMeasured

0246


(a)

30

210

60

240

90

270

120

300

150

330

180 0

SimulatedMeasured

0

5

minus5

minus10

minus15

minus20

(b)





119881119906(GHz) 0829 1182 1241 1132

FBW119881ℓ+ FBW

1198811199060204 0258 0269 0248







ℓ119887= 376



1198761015840
















is FBWℓ= 0090


0ℎ= 5395GHz





ℓ+ BW



ℎ= 0196









6 Conclusion



119881 The study of










Acknowledgments


References








































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










02

04

0608 1

15

2

3

45

10


02 04 06 08 1 15 2 3 4 5 10


minus02

minus04


minus15

minus2

minus3minus4minus5

minus10

) ohm

(a)

02

04

0608 1

15

2

3

45

10


02 04 06 08 1 15 2 3 4 5 10

3 (1464 minus2226) ohm

minus02

minus04


minus15

minus2

minus3minus4minus5

minus10

7 (1329 3341) ohm

(b)




1 2

3


0 1 2 3 4 5 6 7

Inpu

t refl

ectio

n co

effici

ent (

dB)

Frequency (GHz)

0

minus10

minus20

minus30






BW119881(GHz) 0231 0598 0182 1000 0191 1050 0182 0950

FBW119881


119876119903(dB) +89 +78 +99 +57 +97 +54 +98 +59

119876119905(dB) +92 +86 +104 +62 +102 +59 +104 +66


02

04

0608 1

15

2

3

45

10


02 04 06 08 1 15 2 3 4 5 10


minus02

minus04


minus15

minus2

minus3minus4minus5

minus10

(a)

02

04

0608 1

15

2

3

45

10


02 04 06 08 1 15 2 3 4 5 10

3 (3304 minus314) ohm7 (1091 2279) ohm

minus02

minus04


minus15

minus2

minus3minus4minus5

minus10

(b)






(a)

1 2 3 4 5 6 7

SimulatedMeasured

0

Frequency (GHz)

minus10

minus20

minus30

minus40

Inpu

t refl

ectio

nco

effici

ent 11987811

(dB)

(b)


22192165137

11082405490275


120601

120579


119910

119909


Farfield

2197 dB

(dB)

(a)

43438

326271217163109

05430




Farfield

4344 dB

(dB)

120601

120579

119909

119911

119910

(b)



FOM = 10 + 10 log (119899total)

+ 10 log (FBW) minus 10 log (119896119886) (3)




119876119903=119876

119899rad (4)




119876119905=

119876

119899total (5)


119905in decibels


119903and 119876



30

210

60

240

90

270

120

300

150

330

180 0

SimulatedMeasured

0

1

2

minus1

minus2

minus3

(a)

30

210

60

240

90

270

120

300

150

330

180 0

SimulatedMeasured

0

5

minus5minus10

minus15

minus20

(b)


30

210

60

240

90

270

120

300

150

330

180 0

SimulatedMeasured

0246


(a)

30

210

60

240

90

270

120

300

150

330

180 0

SimulatedMeasured

0

5

minus5

minus10

minus15

minus20

(b)





119881119906(GHz) 0829 1182 1241 1132

FBW119881ℓ+ FBW

1198811199060204 0258 0269 0248







ℓ119887= 376



1198761015840
















is FBWℓ= 0090


0ℎ= 5395GHz





ℓ+ BW



ℎ= 0196









6 Conclusion



119881 The study of










Acknowledgments


References








































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










1 2

3


0 1 2 3 4 5 6 7

Inpu

t refl

ectio

n co

effici

ent (

dB)

Frequency (GHz)

0

minus10

minus20

minus30






BW119881(GHz) 0231 0598 0182 1000 0191 1050 0182 0950

FBW119881


119876119903(dB) +89 +78 +99 +57 +97 +54 +98 +59

119876119905(dB) +92 +86 +104 +62 +102 +59 +104 +66


02

04

0608 1

15

2

3

45

10


02 04 06 08 1 15 2 3 4 5 10


minus02

minus04


minus15

minus2

minus3minus4minus5

minus10

(a)

02

04

0608 1

15

2

3

45

10


02 04 06 08 1 15 2 3 4 5 10

3 (3304 minus314) ohm7 (1091 2279) ohm

minus02

minus04


minus15

minus2

minus3minus4minus5

minus10

(b)






(a)

1 2 3 4 5 6 7

SimulatedMeasured

0

Frequency (GHz)

minus10

minus20

minus30

minus40

Inpu

t refl

ectio

nco

effici

ent 11987811

(dB)

(b)


22192165137

11082405490275


120601

120579


119910

119909


Farfield

2197 dB

(dB)

(a)

43438

326271217163109

05430




Farfield

4344 dB

(dB)

120601

120579

119909

119911

119910

(b)



FOM = 10 + 10 log (119899total)

+ 10 log (FBW) minus 10 log (119896119886) (3)




119876119903=119876

119899rad (4)




119876119905=

119876

119899total (5)


119905in decibels


119903and 119876



30

210

60

240

90

270

120

300

150

330

180 0

SimulatedMeasured

0

1

2

minus1

minus2

minus3

(a)

30

210

60

240

90

270

120

300

150

330

180 0

SimulatedMeasured

0

5

minus5minus10

minus15

minus20

(b)


30

210

60

240

90

270

120

300

150

330

180 0

SimulatedMeasured

0246


(a)

30

210

60

240

90

270

120

300

150

330

180 0

SimulatedMeasured

0

5

minus5

minus10

minus15

minus20

(b)





119881119906(GHz) 0829 1182 1241 1132

FBW119881ℓ+ FBW

1198811199060204 0258 0269 0248







ℓ119887= 376



1198761015840
















is FBWℓ= 0090


0ℎ= 5395GHz





ℓ+ BW



ℎ= 0196









6 Conclusion



119881 The study of










Acknowledgments


References








































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










02

04

0608 1

15

2

3

45

10


02 04 06 08 1 15 2 3 4 5 10


minus02

minus04


minus15

minus2

minus3minus4minus5

minus10

(a)

02

04

0608 1

15

2

3

45

10


02 04 06 08 1 15 2 3 4 5 10

3 (3304 minus314) ohm7 (1091 2279) ohm

minus02

minus04


minus15

minus2

minus3minus4minus5

minus10

(b)






(a)

1 2 3 4 5 6 7

SimulatedMeasured

0

Frequency (GHz)

minus10

minus20

minus30

minus40

Inpu

t refl

ectio

nco

effici

ent 11987811

(dB)

(b)


22192165137

11082405490275


120601

120579


119910

119909


Farfield

2197 dB

(dB)

(a)

43438

326271217163109

05430




Farfield

4344 dB

(dB)

120601

120579

119909

119911

119910

(b)



FOM = 10 + 10 log (119899total)

+ 10 log (FBW) minus 10 log (119896119886) (3)




119876119903=119876

119899rad (4)




119876119905=

119876

119899total (5)


119905in decibels


119903and 119876



30

210

60

240

90

270

120

300

150

330

180 0

SimulatedMeasured

0

1

2

minus1

minus2

minus3

(a)

30

210

60

240

90

270

120

300

150

330

180 0

SimulatedMeasured

0

5

minus5minus10

minus15

minus20

(b)


30

210

60

240

90

270

120

300

150

330

180 0

SimulatedMeasured

0246


(a)

30

210

60

240

90

270

120

300

150

330

180 0

SimulatedMeasured

0

5

minus5

minus10

minus15

minus20

(b)





119881119906(GHz) 0829 1182 1241 1132

FBW119881ℓ+ FBW

1198811199060204 0258 0269 0248







ℓ119887= 376



1198761015840
















is FBWℓ= 0090


0ℎ= 5395GHz





ℓ+ BW



ℎ= 0196









6 Conclusion



119881 The study of










Acknowledgments


References








































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










(a)

1 2 3 4 5 6 7

SimulatedMeasured

0

Frequency (GHz)

minus10

minus20

minus30

minus40

Inpu

t refl

ectio

nco

effici

ent 11987811

(dB)

(b)


22192165137

11082405490275


120601

120579


119910

119909


Farfield

2197 dB

(dB)

(a)

43438

326271217163109

05430




Farfield

4344 dB

(dB)

120601

120579

119909

119911

119910

(b)



FOM = 10 + 10 log (119899total)

+ 10 log (FBW) minus 10 log (119896119886) (3)




119876119903=119876

119899rad (4)




119876119905=

119876

119899total (5)


119905in decibels


119903and 119876



30

210

60

240

90

270

120

300

150

330

180 0

SimulatedMeasured

0

1

2

minus1

minus2

minus3

(a)

30

210

60

240

90

270

120

300

150

330

180 0

SimulatedMeasured

0

5

minus5minus10

minus15

minus20

(b)


30

210

60

240

90

270

120

300

150

330

180 0

SimulatedMeasured

0246


(a)

30

210

60

240

90

270

120

300

150

330

180 0

SimulatedMeasured

0

5

minus5

minus10

minus15

minus20

(b)





119881119906(GHz) 0829 1182 1241 1132

FBW119881ℓ+ FBW

1198811199060204 0258 0269 0248







ℓ119887= 376



1198761015840
















is FBWℓ= 0090


0ℎ= 5395GHz





ℓ+ BW



ℎ= 0196









6 Conclusion



119881 The study of










Acknowledgments


References








































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










30

210

60

240

90

270

120

300

150

330

180 0

SimulatedMeasured

0

1

2

minus1

minus2

minus3

(a)

30

210

60

240

90

270

120

300

150

330

180 0

SimulatedMeasured

0

5

minus5minus10

minus15

minus20

(b)


30

210

60

240

90

270

120

300

150

330

180 0

SimulatedMeasured

0246


(a)

30

210

60

240

90

270

120

300

150

330

180 0

SimulatedMeasured

0

5

minus5

minus10

minus15

minus20

(b)





119881119906(GHz) 0829 1182 1241 1132

FBW119881ℓ+ FBW

1198811199060204 0258 0269 0248







ℓ119887= 376



1198761015840
















is FBWℓ= 0090


0ℎ= 5395GHz





ℓ+ BW



ℎ= 0196









6 Conclusion



119881 The study of










Acknowledgments


References








































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












119881119906(GHz) 0829 1182 1241 1132

FBW119881ℓ+ FBW

1198811199060204 0258 0269 0248







ℓ119887= 376



1198761015840
















is FBWℓ= 0090


0ℎ= 5395GHz





ℓ+ BW



ℎ= 0196









6 Conclusion



119881 The study of










Acknowledgments


References








































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













is FBWℓ= 0090


0ℎ= 5395GHz





ℓ+ BW



ℎ= 0196









6 Conclusion



119881 The study of










Acknowledgments


References








































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation















Acknowledgments


References








































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation


































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









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