research article design of high-gain and beam steering...

Research ArticleDesign of High-Gain and Beam Steering Antennas Using a NewPlanar Folded-Line Metamaterial Structure

Minh Thuy Le12 Quoc Cuong Nguyen12 and Tan Phu Vuong3

1 International Research Institute MICA HUST-CNRSUMI-2954-Grenoble INP Hanoi University of Science and TechnologyHanoi 10000 Vietnam

2Department of Instrumentation and Industrial Informatics School of Electrical Engineering Hanoi University ofScience and Technology Hanoi 10000 Vietnam

3 IMEP-LAHC Laboratory UMR 5130 INPG-UJF-CNRS Grenoble INP Grenoble Cedex 1 Grenoble 38400 France

Correspondence should be addressed to MinhThuy Le minh-thuylemicaeduvn

Received 21 April 2014 Revised 7 July 2014 Accepted 8 July 2014 Published 15 September 2014

Academic Editor Miguel F Bataller

Copyright copy 2014 MinhThuy Le et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

In the last few years there has been growing interest in employing metamaterials (MTMs) to enhance antenna gain In this paperwe proposed a novel structure of planar folded-line left-handed metamaterial (FL-LHM) and applied it to improve the gain ofthree 58GHz microstrip antenna types a circularly polarized patch antenna an antenna array and a beam steering antenna Theplanar FL-LHM structure was designed based on transmission line analysis Their scattering parameters were obtained using anumericalmodel the negative effective permittivity and permeabilitywere then calculated from these parameters for the assessmentof negative refraction index regionThe S

11and radiation patterns of three fabricated antennasweremeasured these resultsmatched

well with the simulation We observed that the gain was increased up to 3 dBi for all the antennas In addition we were also able tomaintain the circular polarization as well as the steering of the antenna without changing its dimensions

1 Introduction

Antenna is an important component that affects the perfor-mance of wireless communication systems Antennas withlow profile low manufacturing costs and high gain aremore desirable for the system To satisfy the requirementsmicrostrip antenna is a good candidate for the antennadesign However it is difficult to obtain a high gain usinga normal microstrip antenna To resolve this issue sometraditional technologies for enhanced-gain antenna are usedsuch as reflectors directors dielectric lenses superstrates orarray techniques In recent years electromagnetic bandgap(EBG) structures andmetamaterials have been demonstratedto enhance the antenna gainThis paperwill be focused on thehigh gain antenna using MTM technique

Metamaterials denote artificial constructedmaterials thatmay not be found in nature Metamaterials has negativepermittivity (120576 lt 0) andor negative permeability (120583 lt 0)The MTM is called double-negative material (DNM) or left-handedmaterial (LHM) when it has double-negative 120576 and 120583

With the same incident wave the reflected wave through aLHM is in opposition to the reflected wave through a positivepermittivity and permeability material LHM acts like lensesto focus wave in the same direction thus it is usually placedabove an antenna to increase its gain In general LHM usesa periodic structure and is modeled as an infinite array ofMTM unit-cells Therefore in this paper a single LHM unit-cell will be studied instead of the entire array of unit-cellsThe dimension of a LHM unit-cell is very small compared to1205820where 120582

0is the wavelength in free space at the operating

frequency In this paper we concentrate on the design of anew LHM and its applications in gain enhancement for low-profile antennas

In the context of improving the antenna gain two types ofMTM are usually found the left-handedmaterials or double-negativematerials and evanescentmaterials LHMshave bothnegative permittivity and permeability that were mentionedby Veselago in 1968 [1] His paper introduced the propagationof waves in LHMs that is opposite to the wave vector in theright-handed materials (RHMs) LHMs possess the negative

Hindawi Publishing CorporationInternational Journal of Antennas and PropagationVolume 2014 Article ID 302580 16 pageshttpdxdoiorg1011552014302580

2 International Journal of Antennas and Propagation

Table 1 Review of LHM structures

LHM structure (3D) Planar LHM structure (2D)

SSRRThin wire

xy

z

Substrate dielectric

x

y

z

z

SSRR-TMW LHM [4 5] SSRR-TMW LHM [6]119891 = 5GHz 119891 = 96GHzSize 8 times 8 times 8mm3

sim 120582075 Size 455 times 505mm2

sim 12058206

hrl

w

x

yz

a

b

rext

rintS

Ω shaped LHM [8] Ω shaped LHM [10]119891 = 835GHz 119891 = 13GHzSize 4 times 4 times 4mm3


sim 120582065

x(E)

y(H)z(k)

S shaped LHM [11]119891 = 11GHz

Size 52 times 28mm2sim 12058205 times 120582

097

x

y

z

w

g

dx

dy

Our FL-LHM119891 = 58GHz

Size 43 times 43mm2sim 120582095

refraction index (119899) and their wave vector 119896 is also calledthe ldquobackward waverdquo Evanescent materials are the other typeof MTMs with single negative 120576 lt 0 or 120583 lt 0 whichwere considered by Prendry and his colleagues thirty yearslater He found out that thin metallic wire lattices (TMWs)had effectively negative permittivity in [2] and split ringresonators (SRRs) had effectively negative permeability in[3] in specified frequency bands The first practical LHMunit-cell structure was proposed in [4 5] by Smith and hiscolleagues based on SRR of Prendry in [3] It is constituted ofTMW and SRR which have dimension in 3D of 119889 = 120582

075

(119889119909times 119889119910times 119889119911) Ziolkowski then successfully investigated and

realized some slabs of planar LHM structures that compriseda substrateDuroid 5880 (ℎsub = 08mm)with embedded stripline operating at the 119883 band [6] This one is more compactthan the first LHMstructure in 3Dand suitable for low-profileantenna application The dimension of these planar LHMunit-cells in 2D is around 119889 = 120582

06 (119889119909times119889119910timesℎsub)The other

LHM structure the ldquoΩ shapedrdquo was first suggested in 1992 by

Saadoun and Engheta [7] In 1997 Simovski et al presentedldquoΩrdquo shaped LHM unit-cell in 3D with the dimension of 119889 =

12058209 (119889119909times119889119910times119889119911) application for antenna gain enhancement

in [8] This LHM unit-cell is smaller than the LHM unit-cellof Prendry and Smith At the same time they also designedthe ldquoΩrdquo shaped LHM unit-cell in 2D in [9] then the ldquoΩrdquoshaped LHM unit-cell in 2D was fabricated in 2008 [10] withthe dimension of 119889 = 120582

065 (119889

119909times 119889119910times ℎsub) using Roger

Duroid substrate The new planar ldquoSrdquo shaped LHM unit-cellwas investigated by Chen et al in [11] with the dimension of1205825 times 12058297 times ℎsub but this LHM could not be smaller than120582065 (see Table 1)In addition the negative effective permittivity permeabil-

ity and refraction index can be extracted from average H-field and E-field of each LHM unit-cell [6 12ndash15] or fromtheir reflection and transmission coefficient parameters [16ndash18] These methods have been researched and validated bymany researchers especially matched results between thesimulation and the experimental 119878 parameters which have

International Journal of Antennas and Propagation 3

been demonstrated in [16 18ndash20] For this reason our newplanar ldquofolded-linerdquo LHM (FL-LHM) unit-cell structure willretrieve their effective 120576 and 120583 from 119878 parameters based on thenumerical LHM unit-cell model This FL-LHM unit-cell hasa smallest dimension of 120582

095 compared with the published

unit-cell structures which are listed in Table 1 In Section 2we show the methodology to design and to obtain this FL-LHM at defined operating frequency

The design of novel high gain and beam steering antennasusing FL-LHM substrate will be presented more in detailin Section 3 When a LHM substrate covers a referenceantenna it enhances the gain of that antenna and alsomaintains its performance This performance can be circularpolarization or beam steering This one is a major advantageof LHM substrate which will be presented in Section 2 Aswe have reported in our previous work [21 22] the operatingfrequency of FL-LHM as well as FL-LHM antenna wasdefined at 58GHz in order to satisfy the operation-rangerequirement for reader antenna of electronic-toll-collection(ETC) free-flow systemapplication on the highway inEuropeThe ETC free-flow system allows automatic fee payments ofvehicles without stopping on the highway It is composedof a reader and transponders (badges) where the reader isfixed on a gantry of the road and the badge is mounted ona vehicle [22 23] Each badge stores all information of eachvehicle such as the class the owner of vehicle his addressand his bank account Reader detects and then communicateswith badge to collect all vehicle information when a vehicleenters its operating zone The fee is offered and then paidbased on this collected information between reader andbadge Physical layer of the equipment (the reader and thebadge) uses the microwave communication at the spectrumof 5795GHzndash5815GHz or 5875GHzndash5905GHz accordingto European dedicated short-range communication (DSRC)standard [24 25] In this DSRC system an antenna withhigher gain gives a longer distance of communication andhence vehicles can be allowed to pass faster In addition anantenna only covers a lane if a beam steering antenna is usedit could cover multilanes therefore the price and the size ofhighway equipment in ETC free-flow system will be reducedThe high gain low profile and multibeams are always therequirements for designing of antenna at 58GHz in thissystem

2 Theory and Design of New Planar FL-LHM

FL-LHM substrate is created by periodic arrays of 119873119909times 119873119910

FL-LHM unit-cells in 119909 and 119910 directions Hence to designa LHM substrate we primarily focus on the design of a newplanar FL-LHM unit-cell

21 Transmission Line Analysis LHM substrate is createdfrom periodic LHM unit-cells Each planar unit-cell consistsof two conductor faces etched on a substrate The shapes ofthese two conductor faces are the same Thus a LHM unit-cell is described by the equivalent circuit using transmissionline method as shown in Figure 1

Mutual impedanceSelf-impedance

S

x(E)

y(H)

z(k)

A LHM unit-cell

Lself LmutualLmutual

Cmutual Cmutual

Cself

dy

dx

Figure 1 LHM substrate is created by periodic arrays of LHM unit-cells (left) and the equivalent circuit of a unit-cell (right) excitationwaves (from the reference antenna) are coming to LHM substrate in119911 direction

Unit-cell n

In Zs2Zs2 In+1

Vn Yp Vn+1

Figure 2 LHM unit-cell is described by symmetrical circuit model

According to this circuit the resonant frequency of unit-cell can be estimated using the formula 119891 = 12120587radic119871

119905119862119905

where119871119905and119862

119905denote total inductance and total capacitance

of unit-cell respectively

119871119905= 119871 self + 2119871mutual

119862119905= 119862self +

119862mutual2

(1)

The gap 119904 between two conductors of two adjacent unit-cellsdetermines their mutual coupling level The closer the unit-cells are the larger the currentmagnitude is thus the resonantfrequency will be increased refer to (1) We found thatthese components define resonant frequency like effectivepermittivity and permeability For easier understanding anddesigning each unit-cell is represented by a symmetricalcircuit model as in Figure 2 according to [14 26] where thetotal inductance 119871

119905has been split into series (119871

119904) and parallel

(119871119901) components similarly for the total capacitance 119862

119905

119871119904depends on the total length of conductor line 119897

and its value is dominant in series impedance (119885119904) On

the other hand 119862119901depends on area of parallel surface

between two conductor faces its value is dominant in shuntadmittance (119884

119901) and depends on the ldquocommonrdquo parallel

area As consequence we can change the total length of


w

x

y

z

g

dy

dx

(a)

lsquolsquoCommonrsquorsquoparallel area

(b)

x

y

z

g

Ay

Ax

(c)

z

y

x

Substratedielectric

Conductorfaces

h

120576r

(d)

Figure 3 New FL-LHM unit-cell structure for resonant frequency at 58 GHz (a) front view of FL-LHM unit-cell (b) ldquocommonrdquo parallelarea of unit-cell (c) back view (d) side view The details of parameters are summarized in Table 2

Table 2 Parameters of new FL-LHM in Figures 1 and 3

Symbol Value119908 025 (mm)119897 2825 (mm)119892 025 (mm)119904 2 (mm) (gap between two folded lines)119860119909

43 (mm)119860119910

43 (mm)119889119909

53 (mm) (dimension of a unit-cell in 119909 direction)119889119910


355 permittivity of substrate (355 + j00027)120583119903

Permeability of substrate

line (119897) or the ldquocommonrdquo parallel area to achieve desiredresonant frequencyThis means the higher the 119897 or ldquocommonrdquoparallel area is the lower the resonant frequency is The

series impedance and shunt admittance of a unit-cell can beobtained from

119885119904= minus119895120596119871

119904minus

1

119895120596119862119904

119884119875= minus119895120596119862

119901minus

1

119895120596119871119901

(2)

The effective permittivity and permeability of unit-cellin this model in Figure 2 can be calculated using the Blochtheorem We start from the relation of the current andthe voltage that passes thought a unit-cell as the followingequation

119868119899+1

= 119868119899119890119895120573

119881119899+1

= 119881119899119890119895120573

(3)


where 120573 is the phase crossing through unit-cell 119899

120573 = 119896119901 (4)

where 119896 is the wave vector in the unit-cell and 119901 is thedimension of the periodic unit-cell As in Figure 1 119901 = 119889

119909=

119889119910= 119889Involving the spatial dispersion in these effective param-

eters according to [14 26] the effective permittivity and per-meability of a unit-cell can be calculated from the followingequations

120583eff =

120596119871119904minus (1120596119862

119904)

2120596119901120573 tan (1205732)

120576eff =

2120573 tan (1205732)

(120596119871119904minus (1120596119862

119904)) 120596119901

(5)

The phase crossing through one unit-cell 120573 in (4) can benow obtained by (6) with the boundary condition in (7)

sin2 (120573

2

) =

11988511990410158401198841199011015840

4

(6)

0 le

11988511990410158401198841199011015840

4

le 1 lArrrArr 0 le 11988511990410158401198841199011015840 le 4 (7)

where 1198851199041015840 1198841199011015840 are real numbers they can be negative or

positive depending on the values of 119871119904 119862119904and 119871

119901 119862119901as

follows

1198851199041015840 = 120596119871

119904minus

1

120596119862119904

1198841199011015840 = 120596119862

119901minus

1

120596119871119901

(8)

The wave impedance of LHM unit-cell is

119885 =

119881119899

119868119899

=

1

2

1198851199041015840

tan (1205732)

(9)

From (5) we can summarize that a LHM unit-cell can beobtained by choosing suitable values of 119871

119904 119862119904and 119871

119901 119862119901

under the condition in (7) combined with (10)

120596119871119904lt

1

120596119862119904

(10)

As presented the total length of the conductor lineincreases while the resonant frequency increases This waywe can tune the FL-LHM to any operating frequency Forconvenience at the frequency of 58 GHz of LHM unit-cell58times10

9= 12120587radic119871

119905119862119905 we suppose that 119871

119905and119862

119905are defined

as 119871119904

= 3273 nH 119862119904

= 0018 pF and 119862119901

= 095 pF with120596119862119901lt 1120596119871

119901 As in Figure 3 the investigated FL-LHMunit-

cell consists of two conductor lines etched on Roger 4003substrate and has the following dimensions

(i) Each conductor face is created by a line with thewidth of 119908 = 025mm and the total length of 119897 =

2825mm (around 12058202) to satisfy conditions (7) and

(10) above to have resonant frequency at 58GHzThisline is folded in one unit-cell with dimensions of 43times43mm2 (120582

095) by using meander line structure in

119910 direction as in Figures 3(a) and 3(c) to reduce thedimension

(ii) The separation between two unit-cells is of 119904 = 2mm

(iii) Two conductor lines are maintained parallel to eachother by the substrate dielectric Roger 4003 that hasthickness of ℎsub = 08mm permittivity of 120576

119903= 35

permeability of 120583119903

= 1 and loss tangent of tan 120575 =

00027 The ldquocommonrdquo parallel area between thesetwo conductors is defined as in Figure 3(b)

The novel FL-LHM has both negative effective permittiv-ity and permeability which are denoted by 120576eff and 120583eff Theirreal parts are negative while the imaginary parts are nearlyequal to zero at the operating frequency of 58 GHz

22 Numerical FL-LHMModel A quantity of 119871 and 119862 valuescan be calculated to have a desired FL-LHM using thetransmission line analysis in Section 21 However themutualinductance and capacitance as well as fringing effect aredifficult to evaluate In addition this quantification will bemore complicatedwhen the incident wave variesTherefore anumerical model in Figure 4 is created to simplify the designof a FL-LHM unit-cell and the evaluation of their effectivepermittivity and permeability likewise

Figure 4(a) illustrates a FL-LHM antenna model the FL-LHM substrate is excited by a reference antenna (RA) whichcould be any type of antennas In this case the pattern ofRA is equivalent to an incident plane wave at the directionvarying from minus120579 to 120579 The released wave from a FL-LHMis propagating in +119911 direction These waves consist of theforward wave (solid red line) and the wave reflected at theback FL-LHM (dotted blue line) Both waves have the samephase so that antenna gain is improved

From this FL-LHM antenna model we create FL-LHMunit-cell modeling as in Figure 4(b) The FL-LHM unit-cellis excited by an incidence wave in 119911 direction To coverall the types of RA the excitation of FL-LHM unit-cellis modeled by a plane wave incident in direction of theta(minus90∘ lt 120579 lt 90

∘) The released wave from a FL-LHM ispropagating in +119911 direction Hence 119911max is set to perfect-matched layer (PML) (open boundary) Due to a geometricaland electrical symmetry of each unit-cell in Figure 2 thesidewall of each unit-cell model can be replaced by periodicboundary conditions Particularly the boundaries 119909 = 119909minand 119909 = 119909max and 119910 = 119910min and 119910 = 119910max are set to beperiodic boundaries From this model the field distributionand the reflection-transmission coefficients of a FL-LHMunit-cell under a normally incident plane wave at any angle120579 are calculated as in Figures 5 and 6 using commercialelectromagnetic software CST Microwave Studio 2012 Theeffective 120576eff 120583eff and refractive index 119899 of FL-LHM can beextracted from 119878 parameters this method has been validatedand demonstrated a good agreement between simulation


z(k)

y(H)x(E)

h

Roger 4003 substrate

Pattern of reference antenna

A unit-cell

(excitation of LHM substrate)

LHM substrate

θθminus

(a)

x(E)

y(H)

z(k)

Zmin-port 1

Zmax-port 2

Periodic

Periodic

S incident wave

PML

S 120579

(b)

Figure 4 (a) FL-LHM antenna model which improves the antenna gain by FL-LHM substrate The reference antenna makes excitation forFL-LHM substrate The solid red line represents the forward wave and the dotted blue line indicates the wave reflected at the back FL-LHM(b) Numerical FL-LHM unit-cell model for simulation

Min

Max1

0x(E)

y(H)

z(k)

E energy

(a)

Min

Max1

0

x(E)

y(H)

z(k)

H energy

(b)

Figure 5 Electric and magnetic field distribution in FL-LHM unit-cell

and measurement in [16ndash18] The retrieval of these effectiveparameters will be shown in the next section

23 Retrieval of Effective Permittivity and Permeability of theNewFL-LHM fromSParameters Considering our numericalFL-LHMmodel the wave propagation through the FL-LHMis shown as in Figure 7

As we presented in Section 22 the reflection and trans-mission coefficients (119878

11and 119878

21) of the FL-LHM unit-cell

that are created from Section 21 according to [9 16] aregiven by these equations

11987811

=

1198871

1198861

=

(1 minus 1198792) 119877

1 minus 11987721198792

11987821

=

1198862

1198861

=

(1 minus 1198772) 119879

1 minus 11987721198792

(11)

where119877 is the reflection coefficient of an incident wave on theinterface between free space and FL-LHM whereas 119879 is thetransmission term through the FL-LHM slab

119877 =

119885 minus 1198850

119885 + 1198850

=

119911 minus 1

119911 + 1

119879 = 119890minus1198951198960119899119889

(12)

where 1198850 1198960are wave impedance and wave number in free

space respectively The normalized wave impedance 119911 =

1198851198850and refractive index 119899 of the FL-LHM can be expressed

in terms of scattering parameters as

119911 = plusmnradic

(1 + 11987811)2

minus 1198782

21

(1 minus 11987811)2

minus 1198782

21

119899 = minus

1

1198960119889

[[ln (119879)]10158401015840+ 2119898120587] minus 119895[ln (119877)]

1015840

(13)


Frequency (GHz)3 4 5 6 7 8

x(E)y(H)

z(k)

Port 1

Port 2S

S incident wave

minus45

minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

S11 120579 = 45∘

S21 120579 = 45∘S11 120579 = 0∘

S21 120579 = 0∘

58GHz

Figure 6 Reflection and transmission coefficient in dB of FL-LHMunit-cell under an incident wave at angle of 0∘ and 45∘

Source

LHM

Interface between Free space and LHM

Free spaceFree space

z

a1 a2

b1 b2

Figure 7 Wave propagation of an infinite slab FL-LHM in freespace

where 119898 is an integer related to the branch index of 1198991015840

(principal value of 119898 = 0) and the transmission term as afunction of scattering parameters is given by [14]

119879 =

1 minus 1198782

11+ 1198782

21

211987821

plusmn 119895radic1 minus (

1 minus 1198782

11+ 1198782

21

211987821

)

2

(14)

The effective permittivity and permeability of the FL-LHM are directly calculated from the refractive index 119899 andnormalized impedance 119911

120576eff =

119899

119911

120583eff = 119899119911 (15)

Frequency (GHz)

(dB)

3 4 5 6 7 8

minus45minus50

minus40minus35minus30minus25minus20minus15minus10

minus50

S11mdashtheta 0∘

S21mdashtheta 0∘

S11mdashtheta 15∘

S21mdashtheta 15∘

S11mdashtheta 30∘

S21mdashtheta 30∘

S11mdashtheta 45∘

S21mdashtheta 45∘

S11mdashtheta 60∘

S21mdashtheta 60∘

Figure 8 Reflection and transmission coefficients of FL-LHMunit-cell under incident wave at any direction from 0∘ to 90∘

The retrieval of effective permittivity and permeability ofany metamaterial from the scattering parameters is a suffi-ciently accurate method which allows characterizing a FL-LHM Since the FL-LHM is not homogeneous the improve-ment based on the determination of two effective boundaries[19] needs to be determined to increase the accuracy Besidesthe measurementsimulation noise of 119878 parameters influenton the effective impedance is also considered This methodgives us a theoretical validation of the effective permittivityand permeability of the FL-LHM substrate and its dimensionfrom the 119878 parameters results Because of the periodicstructure we only consider the varying incident angle from0∘ to 90∘ the results are repeated with minus90

∘lt 120579 lt 0

∘ 119878parameters at any angle are shown in Figure 8 We found that119878 parameters are nearly stable when theta squints from 0∘to less than 30∘ only one resonant frequency at 58 GHz isobtained Varying theta in the range from 30∘ to 50∘ these 119878

values are changed the resonant frequency is increased above58GHz and the second resonant frequency at 38 GHz hasbeen added The resonant frequency is shifted as the thetaincreases This gives limited condition for RA pattern in FL-LHM antenna especially in the case of a steering RA

From the 119878 parameters obtained based on numerical FL-LHM model combined with the retrieval method accordingto (11)ndash(15) the effective parameters of our new FL-LHMare presented in Figures 9ndash12 Both desired negative 120576effand 120583eff are obtained in the range of 55ndash62GHz (LHMbandwidth) according to Figures 10 and 11 while the effectiverefraction index is negative in the range of 51ndash62GHz (MTMbandwidth) At this LHM bandwidth their real parts (solidlines) are negative while imaginary parts (dotted lines) arenearly equal to zero which shows that this FL-LHM workswell with the low loss at this range especially in the range ofminus45∘le 120579 le 45

∘ as in Figures 9 and 10


Peakminus61

0

Re(120576)Im(120576)

minus400

minus200

0

200

400

3 4 5Frequency (GHz)

minus1056 58 6 62

minus5

0

5

Frequency (GHz)

minus063

minus366

58

(a)

minus356

068

583 4 5minus10

0

10

20

30

6 7 8

Frequency (GHz)

Re(120583)Im(120583)

(b)

Figure 9 Effective permittivity (a) and permeability (b) of FL-LHM unit-cell under an incident wave of 45∘ extracted from 119878 parameterscorrespondent


Re(n)Im(n)

minus30

minus20

minus10

0

10

20

30

40

Re(n) lt 0

019

minus361

(a)

3 4 5 6 7 8Frequency (GHz)

Re(Z)Im(Z)

minus1

minus05

0

05

1

(b)

Figure 10 Effective refraction index (a) and normalized impedance (b) of FL-LHM unit-cell under an incident wave of 45∘ extractedcorrespondent

3 FL-LHM in Enhanced-Gain for 58 Patchand Beam Steering Antenna

In general the gain of a microstrip patch antenna is around6-7 dBi The gain can be increased by using antenna arrays(adding dimensions in 119909 119910 directions) metamaterial tech-nology (only changing dimension in 119911 direction) or both ofthemTheLHMantenna structure is presented in Figure 4(a)

it consists of a RA and a FL-LHM substrate to increase theoverall gain Interestingly this increasing gain is in goodagreement with any type of RA such as the circular polar-ization antenna or beam steering antenna For experimentalverification of the enhanced-gain effect of FL-LHM substratewe have realized three types of RA the patch antenna theantenna arrays of four patches and the beam steering patchantenna The Vector Network Analyzer 8510C is used for 119878

11


55minus20minus400

minus200

0

200

400

600

minus10

0

10

56 58 6 62

Re(120576) lt 0

Re(120576) lt0

3 4 5 6 7 8

Frequency (GHz) Frequency (GHz)

Re(120576)mdashTheta 45Im(120576)mdashTheta 45Re(120576)mdashTheta 30

Im(120576)mdashTheta 30Re(120576)mdashTheta 60

Re(120576)mdashTheta 60

Im(120576)mdashTheta 60

∘

Figure 11 Effective permittivity values are obtained with varying incident wave

55 62

Re(120583) lt 0

minus20

minus10

0

10

40

20

30

3 4 5 6 7 8

Frequency (GHz)


Im(120583)mdashTheta 30Re(120583)mdashTheta 60Im(120583)mdashTheta 60

(a)

Re(n) lt 0

3 4 5 6 7 8

Frequency (GHz)

minus60

minus40

minus20

0

20

40

Re(n)mdashTheta 45Im(n)mdashTheta 45Re(n)mdashTheta 30

Im(n)mdashTheta 30Re(n)mdashTheta 60Im(n)mdashTheta 60

(b)

Figure 12 Effective permeability (a) and refraction index (b) values are obtained with varying incident wave

measurementThemeasurement of radiation pattern antennais performed using the anechoic chamber in our laboratory

The size of FL-LHM substrate is an important parameterthat needs to be defined According to analysis in Section 2especially in Figure 4(a) when a RA is covered by a suitableFL-LHM substrate at the height ℎ = 120582

02 the RA gain will

be improved and the LHM antenna is always well matchedat operating frequency In general dimensions of FL-LHMsubstrate (119871

119909 119871119910) are proportional to the angular width of

RA and the air-gap height of ℎ between RA and FL-LHMsubstrate In addition suitable FL-LHMsubstrate dimensionsare optimized depending on the dimension of RA as well asthe application systems

31 Circularly Polarized Patch Antenna Gain EnhancementA circularly polarized rectangular patch antennawith dimen-sions of 46 times 46 times 08mm has been created This RA uses


Excitation point

W

L

(a)

h

(b)

Figure 13 Prototype of FL-LHM antenna (a) circularly polarized patch reference antenna (b) prototype of FL-LHM antenna

minus30

minus25

minus20

minus15

minus10

minus5

0

5 55 6 65Frequency (GHz)

|S|(

dB)

11

Reference antennaLHM antenna h = 28mmLHM antenna h = 29mm

LHM antenna h = 30

LHM antenna h = 31

Figure 14 Reflection coefficients of antenna with varying air-gapheight

96

965

97

975

98

985

27 28 29 30 31 32Air-gap height (mm)

Gai

n (a

bs) (

dB)

Figure 15 Gain versus air-gap height at 58 GHz

the Roger 4003 substrate with the thickness of 08mmThe circular polarization is obtained by trimming oppositecorners of a square patch [27] and exciting at the feed pointas in Figure 13(a) A common measure for the quality ofthe achieved circular polarization is the axial ratio ARRA =

119864max119864min = minus008 dB This antenna gain is 65 dBi andreflection coefficient 119878

11at 58GHz is minus20 dB and minus15 dB in

simulation and measurement respectively

minus25

minus20

minus15

minus10

minus5

0

5 525 55 575 6 625 65Frequency (GHz)

LHM antenna measurementLHM antenna simulation

|S|(

dB)

11

Figure 16 Reflection coefficients of FL-LHM antenna with ℎ =

30mm in simulation and measurement

Axial ratio

Axi

al ra

tio (d

B)

0

minus2

minus4

minus6

minus85 52 54 56 58 6

Frequency (GHz)

LHM antenna measurementLHM antenna simulationPatch antenna simulationPatch antenna measurement

Figure 17 Axial ratio of reference antenna and FL-LHM antenna


minus20minus15minus10minus5

05

1015

minus18

0

minus15

0

minus12

0

minus90

minus60

minus30 0 30 60 90 12

0

150

180

(dB)

Patch antennaLHM antenna measurementLHM antenna simulation

120579 (deg)

Far-field gain dB (phi = 0)

Figure 18 Radiation pattern of fabricated FL-LHM antenna insimulation and measurement


Ground plane

h

Excitation by 1ndash4-feed

LHM substrate

1ndash4-feed structure

Antenna arraysz

y

Figure 19 Structure of FL-LHM antenna arrays using 1ndash4-feedstructure

Our study shows that FL-LHM antenna is well matchedwith air-gap heights from28 to 31mm(Figure 14) In this casedimensions of fabricated FL-LHM substrate are defined by119871119909= 119871119910= 46mm Figure 15 illustrates the FL-LHM antenna

gain versus air-gap height at the frequency of 58GHz Thechosen air-gap height of 30mm gives the good circularpolarization with ARLHMminus119860 = minus012 dB and highest gain(Figure 15) while 119878

11lt minus20 dB at 58GHzThe simulated gain

is increased from 66 dBi to 98 dBi by using this FL-LHMlayer the measured gain is 95 dBi (Figure 16) The reflectioncoefficients axial ratios and radiation pattern of FL-LHMantenna are shown in Figures 17 and 18

32 Antenna Arrays Gain Enhancement From the patchantenna designed in Section 31 an array of 2times2 patch anten-nas is created using the 1ndash4-feed structure as in Figure 19Theantenna arrays gain is 127 dBi and 121 dBi in simulation andmeasurement respectively (see Figure 20)

When this antenna is covered by FL-LHM substrate withthe air-gap height ℎ = 30mm the 119878

11is minus12 dB and minus14 dB

h

Back view Front view

Figure 20 Prototype of FL-LHM antenna arrays with dimensionsof 90 times 90 times 30mm3

minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

5 525 55 575 6 625 65Frequency (GHz)

measurementsimulation

|S|(

dB)

11

S11S11

Figure 21 Reflection coefficients of FL-LHM antenna arrays withℎ = 30mm in simulation and measurement

(Figure 21) while the gain is improved to 153 dBi and 154 dBi(Figure 22) in simulation and measurement respectively

33 Beam Steering Antenna Gain Enhancement The refer-ence antenna is used as a beam steering antenna using twopassive patches at the right side and the left side of theactive patch (driven element) in 119909 direction (Figure 23(a))according to [28] The active patch is excited by RF sourcetwo patches passive at the right side (patch 2) and at the leftside (patch 3) are loaded by the reactive elements 1198622 and1198623 respectivelyThemutual couplings between three patchesare proportional to the distance ds between them [29] Thecurrent magnitude on the passive radiator is larger when dsis smaller so that the gain will be increased

The phases shifted between antenna elements are turnedby changing the reactive loadWe denote by 119868

1the current on

the active patch 1198682and 1198683are the induced currents on passive

patches 1198752 and 1198753 respectively The array factor is given by[28]

AF =

3

sum

119894=1

10038161003816100381610038161003816100381610038161003816

119868119894

1198681

10038161003816100381610038161003816100381610038161003816

119890119895(119896lowast119889

119909lowastsin 120579+ang(119868

1198941198681)) (16)


minus180

minus150

minus120 minus9

0

minus60

minus30 0 30 60 90 120

150

180

LHM antenna arrays measurementLHM antenna arrays simulationAntenna arrays

120579 (deg)


minus505

101520

(dB)


Figure 22 Radiation pattern of fabricated FL-LHM antenna arrays in simulation and measurement

xsub

ds

Port 2 Port 1 Port 3

W1

L1

C3W2C2

l

ysub xfye y

zx

(a)

h

(b)

Figure 23 Structure of FL-LHM beam steering antenna (a) beam steering reference antenna (b) FL-LHM beam steering antenna withℎ = 30mm

Table 3 Parameters of LHM beam steering antenna at 58 GHz asin Figure 23

Symbol Value1198821= 1198711

14 (mm)ds 3 (mm) (gap between two patches)119910119890

5 (mm)119909119891

05 (mm)1198822

17 (mm)119897 2 (mm)ℎ 30 (mm)119909sub 30 (mm) (substrate Roger 4003)119910sub 90 (mm)

The steering of reference antenna is described in thefollowing three cases (Figures 24 and 25)

(i) Case 1 1198622 = 1198623 = 02 pF the AF is maximum themain lobe is located at theta of 0∘ Case 1 is noted inred color in all figures

(ii) Case 2 1198622 = 2 pF and 1198623 = 02 pF the main lobeis steered at theta of 20∘ Case 2 is presented in greencolor

(iii) Case 3 inversely if 1198622 = 02 pF and 1198623 = 2 pFthe main lobe is steered at theta of minus20∘ Case 3 isrepresented in blue color

Figures 24 and 25 represent the 11987811and radiation pattern

of beam steering reference antenna in simulation and mea-surement respectively

Our study found that the beam steering reference antennais always adaptive in three cases at 58GHz (119878

11simulation =

minus15 dB 11987811measurement = minus20 dB) the peak of 119878

11is shifted at

the higher frequency in case 2 and case 3 The gain of RA isaround 82 dBi83 dBi in measurement and simulations forcase 1 The gain reduces to 77 dBi in simulation and to 75 dBiin measurement for cases 2 and 3 (Table 3)

The enhancement gain will be obtained when beamsteering antenna is covered by the FL-LHM substrate as inFigure 23(b) The FL-LHM beam steering antenna is wellmatched at the range of 575ndash587GHz (Figure 26) that coversthe DSRC standard However the steering angles are reduced


Simulation (case 1)Simulation (case 2)Simulation (case 3)

Frequency (GHz)5 52 54 56 58 6 62 64 65

0

minus2

minus4

minus6

minus8

minus10

minus12

minus14

minus16

minus18

|S|(

dB)

11

(a)

minus25

minus20

minus15

minus10

minus5

0

5 525 55 575 6 625 65Frequency (GHz)

Measurement (case 1)Measurement (case 2)Measurement (case 3)

|S|(

dB)

11

(b)

Figure 24 (a) Reflection coefficients of beam steering reference antenna in simulation (b) Reflection coefficients of beam steering referenceantenna in measurement

Gai

n (d

B)

Case 1 (main lobe at 0∘)Case 2 (main lobe at 20∘)Case 3 (main lobe at minus20∘)

120579 (deg)

10

5

0

minus5

minus10

minus15

minus20

minus25

minus180

minus150

minus120

minus90

minus60

minus30 0

30

60

90

120

150

180

Radiation pattern in horizontally 0∘)(phi =

(a)

Gai

n (d

B)

minus40

minus30

minus20

minus10

0

10


120579 (deg)

minus180

minus150

minus120

minus90

minus60

minus30 0

30

60

90

120

150

180


(b)

Figure 25 (a) Radiation pattern of beam steering RA in simulation Beam steering horizontally steering angles minus20∘ (case 2) 0∘ (case 1)and 20∘ (case 3) (b) Radiation pattern of beam steering RA in measurement Beam steering horizontally steering angles minus20∘ (case 2) 0∘(case 1) and 20∘ (case 3)

to plusmn10∘ instead of plusmn20∘ because of FL-LHM effect accordingto Snellrsquos law when the waves propagate through FL-LHMsubstrate

The reflection coefficient 11987811and radiation pattern of FL-

LHM beam steering antenna in three cases are shown inFigures 26 and 27 This FL-LHM antenna has dimensions of30 times 90 times 30mm3

In simulation the gain of beam steering antenna isimproved from 82 dBi to 12 dBi for case 1 and from 77 dBito 11 dBi for cases 2 and 3 (Figure 27(a))

In measurement the gain obtained is 116 dBi for case 1and 10 dBi for cases 2 and 3 (Figure 27(b)) The differenceof FL-LHM antenna gain between case 1 and case 2case 3is caused by the limited condition of the FL-LHM substrate



Frequency (GHz)5 52 54 56 58 6 62 64 65

minus45

minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

|S|(

dB)

11

(a)

minus30

minus25

minus20

minus15

minus10

minus5

0

5 525 55 575 6 625 65Frequency (GHz)


|S|(

dB)

11

(b)

Figure 26 (a) Reflection coefficients of FL-LHMbeam steering antennawith ℎ = 30mm in simulation (b) Reflection coefficients of FL-LHMbeam steering antenna with ℎ = 30mm in measurement


Gai

n (d

B)

15

10

5

0

minus5

minus10

minus15

minus20

minus25

minus180

minus150

minus120

minus90

minus60

minus30 0

30

60

90

120

150

180

120579 (deg)


(a)


Gai

n (d

B)

minus180

minus150

minus120

minus90

minus60

minus30 0

30

60

90

120

150

180

120579 (deg)

10

0

minus10

minus20

minus30

minus40


(b)

Figure 27 (a) Radiation pattern of FL-LHM beam steering antenna with ℎ = 30mm in simulation Beam steering horizontally steeringangles minus10∘ (case 2) 0∘ (case 1) and 10∘ (case 3) (b) Radiation pattern of FL-LHM beam steering antenna with ℎ = 30mm in measurementBeam steering horizontally steering angles minus10∘ (case 2) 0∘ (case 1) and 10∘ (case 3)

that is analyzed in Section 22 as well as the effect of capacitorloaded in passive patches

Table 4 resumes the simulation and measurement resultsof FL-LHM beam steering antenna in three cases

4 Conclusion

In this paper a new planar FL-LHM structure is pre-sented An equivalent circuit is useful for understanding and

designing a FL-LHM substrate for an arbitrary operatingfrequency In addition the FL-LHM modeling is createdfor easy simulation using electromagnetic software and forenhancement antenna gain In consequence the new FL-LHM substrate is used to increase the gain of three typesof low-profile antennas which are the circularly polarizedrectangular patch antenna the antenna arrays and the beamsteering antenna These three low-profile FL-LHM antennasoperate at the frequency according to the DSRC standard for


Table 4 Simulation and measurement results of LHM beamsteering antenna

119891 = 58GHzLHM beam steering antenna (30 times 90 times 30mm3)

Case 1 Case 2 Case 3Sim Meas Sim Meas Sim Meas

11987811(dB) minus20 minus15 minus11 minus27 minus10 minus24

BW(MHz) 277 250 179 120 194 140Peak gain (dBi) 12 116 111 10 11 98ΔG (dBi) 38 33 34 25 32 23Sim simulationMeas measurementBW bandwidthΔG increased gain by using FL-LHM substrate (compared with RA)

ETC free-flow system application The gains measured are95 dBi 153 dBi and 11 dBi in measurement The gain of anyRA is increased up to around 25ndash3 dBi by using this planarFL-LHM substrate The 119878

11and radiation pattern results in

measurement of three FL-LHM antennas are well fit withsimulation results

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors wish to thank A Gachon (IMEP-LAHC) for hishelp in fabrication and K Belmkaddem (CEA-LETI) for herhelp in the measurement of the prototypes A and B

References

[1] V G Veselago ldquoThe electrodynamics of substances with simul-taneously negative values of 120576 and 120583rdquo Soviet Physics Uspekhi vol10 no 4 pp 509ndash514 1968

[2] J B Prendry ldquoExtremely low frequency plasmons in metallicmesostructuresrdquo Physical Review Letters vol 76 p 4773 1996

[3] J B Prendry A J Holden D J Robbins and W J Stew-art ldquoMagnetism from conductors and enhanced nonlinearphenomenardquo IEEE Transactions on Microwave Theory andTechniques vol 47 no 11 pp 2075ndash2084 1999

[4] D R Smith D C Vier N Kroll and S Schultz ldquoDirectcalculation of permeability and permittivity for a left-handedmetamaterialrdquo Applied Physics Letters vol 77 article 2246 no14 2000

[5] D R Smith W J Padilla D C Vier S C Nemat-Nasser andS Schultz ldquoComposite mediu m with simultaneously negativepermeability and permittivityrdquo Physical Review Letters vol 84no 18 pp 4184ndash4187 2000

[6] R W Ziolkowski ldquoDesign fabrication and testing of doublenegative metamaterialsrdquo IEEE Transactions on Antennas andPropagation vol 51 no 7 pp 1516ndash1529 2003

[7] M M I Saadoun and N Engheta ldquoA reciprocal phase shifterusing novel pseudochiral or120596mediumrdquoMicrowave and OpticalTechnology Letters vol 5 no 4 pp 184ndash188 1992

[8] C R Simovski S A Tretyakov A A Sochava B Sauviac FMariotte and T G Kharina ldquoAntenna model for conductiveomega particlesrdquo Journal of Electromagnetic Waves and Appli-cations vol 11 no 11 pp 1509ndash1530 1997

[9] C R Simovski ldquoPlane-wave reflection and transmission bygrids of conducting Ω-particles and dispersion of Ω electro-magnetic crystalsrdquoAEU-International Journal of Electronics andCommunications vol 57 no 5 pp 358ndash364 2003

[10] E Lheurette G Houzet J Carbonell F Zhang O Vanbesienand D Lippens ldquoOmega-type balanced composite negativerefractive index materialsrdquo IEEE Transactions on Antennas andPropagation vol 56 no 11 pp 3462ndash3469 2008

[11] H Chen L Ran J Huangfu et al ldquoLeft-handed materialscomposed of only S-shaped resonatorsrdquo Physical Review E vol70 Article ID 057605 2004

[12] D R Smith and J B Pendry ldquoHomogenization ofmetamaterialsby field averagingrdquo Journal of the Optical Society of America Bvol 23 no 3 pp 391ndash403 2006

[13] A Ramakrishna and J Pendry ldquoNon-linear effects in negativemagnetive mata-materialsrdquo Physical Review vol 4 2006

[14] R Liu T J Cui D Huang B Zhao and D R Smith ldquoDescrip-tion and explanation of electromagnetic behaviors in artificialmetamaterials based on effective medium theoryrdquo PhysicalReview EmdashStatistical Nonlinear and SoftMatter Physics vol 76Article ID 026606 2007

[15] D R Smith J Gollub J J Mock W J Padilla and D SchurigldquoCalculation and measurement of bianisotropy in a split ringresonator metamaterialrdquo Journal of Applied Physics vol 100 no2 Article ID 024507 2006

[16] X Chen T M Grzegorczyk B-I Wu J Pacheco Jr and JA Kong ldquoRobust method to retrieve the constitutive effectiveparameters of metamaterialsrdquo Physical Review EmdashStatisticalNonlinear and Soft Matter Physics vol 70 Article ID 0166082004

[17] Y H Liu and X P Zhao ldquoInvestigation of anisotropic neg-ative permeability medium cover for patch antennardquo IETMicrowaves Antennas and Propagation vol 2 no 7 pp 737ndash744 2008

[18] T Zwick A Chandrasekhar C W Baks U R Pfeiffer SBrebels and B P Gaucher ldquoDetermination of the complexpermittivity of packagingmaterials atmillimeter-wave frequen-ciesrdquo IEEE Transactions on Microwave Theory and Techniquesvol 54 no 3 pp 1001ndash1009 2006

[19] P Markos and C M Soukoulis ldquoLeft-handed materialsrdquo Physi-cal Review B vol 65 Article ID 033401 2002

[20] D McGinnis ldquoPBAR NOTE 585 Measurement of Ralativepermittivity and Permeability using Two Port S-parametertechniquerdquo April 1998 httplssfnalgovarchivepbarnotefermilab-pbar-note-585pdf

[21] M T Le Q C Nguyen T P Vuong and C Defay ldquoNewmetamaterial structure for the design of a high gain antenna at58 GHzrdquo in Proceedings of the IEEE International Conference onWireless Information Technology and Systems (ICWITS 12) pp1ndash4 Maui Hawaii USA November 2012

[22] M T Le Q C Nguyen T T T Vu and T P Vuong ldquoDesignof an directive antenna for ldquofree-flowrdquo system applicationrdquo inProceedings of the IEEE Conference of Advanced Technologies forCommunication August 2011

[23] K Thales Global Specification for Short Range CommunicationKapsch Thales 2003

[24] CEN ldquoDIN EN12253rdquo 2002


[25] CEN ldquoNF EN ISO 14906rdquo AFNOR 2005[26] T J Cui ldquoA symmetrical circuit model describing all kinds of

circuit metamaterialsrdquo Progress in Electromagnetics Research Bvol 5 pp 63ndash76 2008

[27] A Balanis Antenna Theory Analysis and Design John Wiley ampSons 3rd edition 2005

[28] Y Yusuf and X Gong ldquoA low-cost patch antenna phased arraywith analog beam steering using mutual coupling and reactiveloadingrdquo IEEE Antennas and Wireless Propagation Letters vol7 pp 81ndash84 2008

[29] N G Alexopoulos and I E Rana ldquoMutual impedance compu-tation between printed dipolesrdquo IEEE Transactions on Antennasand Propagation vol 29 no 1 pp 106ndash111 1981

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Control Scienceand Engineering

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Hindawi Publishing Corporation httpwwwhindawicom

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Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

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Advances inOptoElectronics


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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



Table 1 Review of LHM structures

LHM structure (3D) Planar LHM structure (2D)

SSRRThin wire

xy

z

Substrate dielectric

x

y

z

z

SSRR-TMW LHM [4 5] SSRR-TMW LHM [6]119891 = 5GHz 119891 = 96GHzSize 8 times 8 times 8mm3


sim 12058206

hrl

w

x

yz

a

b

rext

rintS

Ω shaped LHM [8] Ω shaped LHM [10]119891 = 835GHz 119891 = 13GHzSize 4 times 4 times 4mm3


sim 120582065

x(E)

y(H)z(k)

S shaped LHM [11]119891 = 11GHz

Size 52 times 28mm2sim 12058205 times 120582

097

x

y

z

w

g

dx

dy

Our FL-LHM119891 = 58GHz

Size 43 times 43mm2sim 120582095

refraction index (119899) and their wave vector 119896 is also calledthe ldquobackward waverdquo Evanescent materials are the other typeof MTMs with single negative 120576 lt 0 or 120583 lt 0 whichwere considered by Prendry and his colleagues thirty yearslater He found out that thin metallic wire lattices (TMWs)had effectively negative permittivity in [2] and split ringresonators (SRRs) had effectively negative permeability in[3] in specified frequency bands The first practical LHMunit-cell structure was proposed in [4 5] by Smith and hiscolleagues based on SRR of Prendry in [3] It is constituted ofTMW and SRR which have dimension in 3D of 119889 = 120582

075

(119889119909times 119889119910times 119889119911) Ziolkowski then successfully investigated and

realized some slabs of planar LHM structures that compriseda substrateDuroid 5880 (ℎsub = 08mm)with embedded stripline operating at the 119883 band [6] This one is more compactthan the first LHMstructure in 3Dand suitable for low-profileantenna application The dimension of these planar LHMunit-cells in 2D is around 119889 = 120582

06 (119889119909times119889119910timesℎsub)The other

LHM structure the ldquoΩ shapedrdquo was first suggested in 1992 by

Saadoun and Engheta [7] In 1997 Simovski et al presentedldquoΩrdquo shaped LHM unit-cell in 3D with the dimension of 119889 =

12058209 (119889119909times119889119910times119889119911) application for antenna gain enhancement

in [8] This LHM unit-cell is smaller than the LHM unit-cellof Prendry and Smith At the same time they also designedthe ldquoΩrdquo shaped LHM unit-cell in 2D in [9] then the ldquoΩrdquoshaped LHM unit-cell in 2D was fabricated in 2008 [10] withthe dimension of 119889 = 120582

065 (119889

119909times 119889119910times ℎsub) using Roger

Duroid substrate The new planar ldquoSrdquo shaped LHM unit-cellwas investigated by Chen et al in [11] with the dimension of1205825 times 12058297 times ℎsub but this LHM could not be smaller than120582065 (see Table 1)In addition the negative effective permittivity permeabil-

ity and refraction index can be extracted from average H-field and E-field of each LHM unit-cell [6 12ndash15] or fromtheir reflection and transmission coefficient parameters [16ndash18] These methods have been researched and validated bymany researchers especially matched results between thesimulation and the experimental 119878 parameters which have











S

x(E)

y(H)

z(k)

A LHM unit-cell


Cmutual Cmutual

Cself

dy

dx


Unit-cell n

In Zs2Zs2 In+1

Vn Yp Vn+1



119905119862119905

where119871119905and119862



119871119905= 119871 self + 2119871mutual

119862119905= 119862self +

119862mutual2

(1)





119905








w

x

y

z

g

dy

dx

(a)


(b)

x

y

z

g

Ay

Ax

(c)

z

y

x

Substratedielectric

Conductorfaces

h

120576r

(d)




43 (mm)119860119910

43 (mm)119889119909







119885119904= minus119895120596119871

119904minus

1

119895120596119862119904

119884119875= minus119895120596119862

119901minus

1

119895120596119871119901

(2)


119868119899+1

= 119868119899119890119895120573

119881119899+1

= 119881119899119890119895120573

(3)



120573 = 119896119901 (4)


119909=



120583eff =

120596119871119904minus (1120596119862

119904)

2120596119901120573 tan (1205732)

120576eff =

2120573 tan (1205732)

(120596119871119904minus (1120596119862

119904)) 120596119901

(5)


sin2 (120573

2

) =

11988511990410158401198841199011015840

4

(6)

0 le

11988511990410158401198841199011015840

4

le 1 lArrrArr 0 le 11988511990410158401198841199011015840 le 4 (7)



119901 119862119901as

follows

1198851199041015840 = 120596119871

119904minus

1

120596119862119904

1198841199011015840 = 120596119862

119901minus

1

120596119871119901

(8)


119885 =

119881119899

119868119899

=

1

2

1198851199041015840

tan (1205732)

(9)


119904 119862119904and 119871

119901 119862119901


120596119871119904lt

1

120596119862119904

(10)


9= 12120587radic119871

119905119862119905 we suppose that 119871

119905and119862

119905are defined

as 119871119904

= 3273 nH 119862119904

= 0018 pF and 119862119901

= 095 pF with120596119862119901lt 1120596119871










119903= 35










z(k)

y(H)x(E)

h



A unit-cell


LHM substrate

θθminus

(a)

x(E)

y(H)

z(k)

Zmin-port 1

Zmax-port 2

Periodic

Periodic

S incident wave

PML

S 120579

(b)


Min

Max1

0x(E)

y(H)

z(k)

E energy

(a)

Min

Max1

0

x(E)

y(H)

z(k)

H energy

(b)





11and 119878



11987811

=

1198871

1198861

=

(1 minus 1198792) 119877

1 minus 11987721198792

11987821

=

1198862

1198861

=

(1 minus 1198772) 119879

1 minus 11987721198792

(11)


119877 =

119885 minus 1198850

119885 + 1198850

=

119911 minus 1

119911 + 1

119879 = 119890minus1198951198960119899119889

(12)






(1 + 11987811)2

minus 1198782

21

(1 minus 11987811)2

minus 1198782

21

119899 = minus

1

1198960119889

[[ln (119879)]10158401015840+ 2119898120587] minus 119895[ln (119877)]

1015840

(13)



x(E)y(H)

z(k)

Port 1

Port 2S

S incident wave

minus45

minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

S11 120579 = 45∘

S21 120579 = 45∘S11 120579 = 0∘

S21 120579 = 0∘

58GHz


Source

LHM



z

a1 a2

b1 b2




119879 =

1 minus 1198782

11+ 1198782

21

211987821


1 minus 1198782

11+ 1198782

21

211987821

)

2

(14)


120576eff =

119899

119911

120583eff = 119899119911 (15)

Frequency (GHz)

(dB)

3 4 5 6 7 8

minus45minus50


minus50

S11mdashtheta 0∘

S21mdashtheta 0∘

S11mdashtheta 15∘

S21mdashtheta 15∘

S11mdashtheta 30∘

S21mdashtheta 30∘

S11mdashtheta 45∘

S21mdashtheta 45∘

S11mdashtheta 60∘

S21mdashtheta 60∘



∘lt 120579 lt 0






Peakminus61

0

Re(120576)Im(120576)

minus400

minus200

0

200

400


minus1056 58 6 62

minus5

0

5

Frequency (GHz)

minus063

minus366

58

(a)

minus356

068

583 4 5minus10

0

10

20

30

6 7 8

Frequency (GHz)

Re(120583)Im(120583)

(b)



Re(n)Im(n)

minus30

minus20

minus10

0

10

20

30

40

Re(n) lt 0

019

minus361

(a)


Re(Z)Im(Z)

minus1

minus05

0

05

1

(b)





11


55minus20minus400

minus200

0

200

400

600

minus10

0

10

56 58 6 62

Re(120576) lt 0

Re(120576) lt0

3 4 5 6 7 8






∘


55 62

Re(120583) lt 0

minus20

minus10

0

10

40

20

30

3 4 5 6 7 8

Frequency (GHz)



(a)

Re(n) lt 0

3 4 5 6 7 8

Frequency (GHz)

minus60

minus40

minus20

0

20

40



(b)




02 the RA gain will






Excitation point

W

L

(a)

h

(b)


minus30

minus25

minus20

minus15

minus10

minus5

0


|S|(

dB)

11


LHM antenna h = 30

LHM antenna h = 31


96

965

97

975

98

985

27 28 29 30 31 32Air-gap height (mm)

Gai

n (a

bs) (

dB)






minus25

minus20

minus15

minus10

minus5

0

5 525 55 575 6 625 65Frequency (GHz)


|S|(

dB)

11



Axial ratio

Axi

al ra

tio (d

B)

0

minus2

minus4

minus6

minus85 52 54 56 58 6

Frequency (GHz)





05

1015

minus18

0

minus15

0

minus12

0

minus90

minus60

minus30 0 30 60 90 12

0

150

180

(dB)


120579 (deg)




Ground plane

h


LHM substrate


Antenna arraysz

y









h



minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

5 525 55 575 6 625 65Frequency (GHz)


|S|(

dB)

11

S11S11





1the current on



AF =

3

sum

119894=1

10038161003816100381610038161003816100381610038161003816

119868119894

1198681

10038161003816100381610038161003816100381610038161003816

119890119895(119896lowast119889

119909lowastsin 120579+ang(119868

1198941198681)) (16)


minus180

minus150

minus120 minus9

0

minus60

minus30 0 30 60 90 120

150

180


120579 (deg)


minus505

101520

(dB)



xsub

ds


W1

L1

C3W2C2

l

ysub xfye y

zx

(a)

h

(b)



Symbol Value1198821= 1198711


5 (mm)119909119891

05 (mm)1198822









11simulation =


11is shifted at





Frequency (GHz)5 52 54 56 58 6 62 64 65

0

minus2

minus4

minus6

minus8

minus10

minus12

minus14

minus16

minus18

|S|(

dB)

11

(a)

minus25

minus20

minus15

minus10

minus5

0

5 525 55 575 6 625 65Frequency (GHz)


|S|(

dB)

11

(b)


Gai

n (d

B)


120579 (deg)

10

5

0

minus5

minus10

minus15

minus20

minus25

minus180

minus150

minus120

minus90

minus60

minus30 0

30

60

90

120

150

180


(a)

Gai

n (d

B)

minus40

minus30

minus20

minus10

0

10


120579 (deg)

minus180

minus150

minus120

minus90

minus60

minus30 0

30

60

90

120

150

180


(b)









Frequency (GHz)5 52 54 56 58 6 62 64 65

minus45

minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

|S|(

dB)

11

(a)

minus30

minus25

minus20

minus15

minus10

minus5

0

5 525 55 575 6 625 65Frequency (GHz)


|S|(

dB)

11

(b)



Gai

n (d

B)

15

10

5

0

minus5

minus10

minus15

minus20

minus25

minus180

minus150

minus120

minus90

minus60

minus30 0

30

60

90

120

150

180

120579 (deg)


(a)


Gai

n (d

B)

minus180

minus150

minus120

minus90

minus60

minus30 0

30

60

90

120

150

180

120579 (deg)

10

0

minus10

minus20

minus30

minus40


(b)




4 Conclusion














Acknowledgments


References

































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation



















S

x(E)

y(H)

z(k)

A LHM unit-cell


Cmutual Cmutual

Cself

dy

dx


Unit-cell n

In Zs2Zs2 In+1

Vn Yp Vn+1



119905119862119905

where119871119905and119862



119871119905= 119871 self + 2119871mutual

119862119905= 119862self +

119862mutual2

(1)





119905








w

x

y

z

g

dy

dx

(a)


(b)

x

y

z

g

Ay

Ax

(c)

z

y

x

Substratedielectric

Conductorfaces

h

120576r

(d)




43 (mm)119860119910

43 (mm)119889119909







119885119904= minus119895120596119871

119904minus

1

119895120596119862119904

119884119875= minus119895120596119862

119901minus

1

119895120596119871119901

(2)


119868119899+1

= 119868119899119890119895120573

119881119899+1

= 119881119899119890119895120573

(3)



120573 = 119896119901 (4)


119909=



120583eff =

120596119871119904minus (1120596119862

119904)

2120596119901120573 tan (1205732)

120576eff =

2120573 tan (1205732)

(120596119871119904minus (1120596119862

119904)) 120596119901

(5)


sin2 (120573

2

) =

11988511990410158401198841199011015840

4

(6)

0 le

11988511990410158401198841199011015840

4

le 1 lArrrArr 0 le 11988511990410158401198841199011015840 le 4 (7)



119901 119862119901as

follows

1198851199041015840 = 120596119871

119904minus

1

120596119862119904

1198841199011015840 = 120596119862

119901minus

1

120596119871119901

(8)


119885 =

119881119899

119868119899

=

1

2

1198851199041015840

tan (1205732)

(9)


119904 119862119904and 119871

119901 119862119901


120596119871119904lt

1

120596119862119904

(10)


9= 12120587radic119871

119905119862119905 we suppose that 119871

119905and119862

119905are defined

as 119871119904

= 3273 nH 119862119904

= 0018 pF and 119862119901

= 095 pF with120596119862119901lt 1120596119871










119903= 35










z(k)

y(H)x(E)

h



A unit-cell


LHM substrate

θθminus

(a)

x(E)

y(H)

z(k)

Zmin-port 1

Zmax-port 2

Periodic

Periodic

S incident wave

PML

S 120579

(b)


Min

Max1

0x(E)

y(H)

z(k)

E energy

(a)

Min

Max1

0

x(E)

y(H)

z(k)

H energy

(b)





11and 119878



11987811

=

1198871

1198861

=

(1 minus 1198792) 119877

1 minus 11987721198792

11987821

=

1198862

1198861

=

(1 minus 1198772) 119879

1 minus 11987721198792

(11)


119877 =

119885 minus 1198850

119885 + 1198850

=

119911 minus 1

119911 + 1

119879 = 119890minus1198951198960119899119889

(12)






(1 + 11987811)2

minus 1198782

21

(1 minus 11987811)2

minus 1198782

21

119899 = minus

1

1198960119889

[[ln (119879)]10158401015840+ 2119898120587] minus 119895[ln (119877)]

1015840

(13)



x(E)y(H)

z(k)

Port 1

Port 2S

S incident wave

minus45

minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

S11 120579 = 45∘

S21 120579 = 45∘S11 120579 = 0∘

S21 120579 = 0∘

58GHz


Source

LHM



z

a1 a2

b1 b2




119879 =

1 minus 1198782

11+ 1198782

21

211987821


1 minus 1198782

11+ 1198782

21

211987821

)

2

(14)


120576eff =

119899

119911

120583eff = 119899119911 (15)

Frequency (GHz)

(dB)

3 4 5 6 7 8

minus45minus50


minus50

S11mdashtheta 0∘

S21mdashtheta 0∘

S11mdashtheta 15∘

S21mdashtheta 15∘

S11mdashtheta 30∘

S21mdashtheta 30∘

S11mdashtheta 45∘

S21mdashtheta 45∘

S11mdashtheta 60∘

S21mdashtheta 60∘



∘lt 120579 lt 0






Peakminus61

0

Re(120576)Im(120576)

minus400

minus200

0

200

400


minus1056 58 6 62

minus5

0

5

Frequency (GHz)

minus063

minus366

58

(a)

minus356

068

583 4 5minus10

0

10

20

30

6 7 8

Frequency (GHz)

Re(120583)Im(120583)

(b)



Re(n)Im(n)

minus30

minus20

minus10

0

10

20

30

40

Re(n) lt 0

019

minus361

(a)


Re(Z)Im(Z)

minus1

minus05

0

05

1

(b)





11


55minus20minus400

minus200

0

200

400

600

minus10

0

10

56 58 6 62

Re(120576) lt 0

Re(120576) lt0

3 4 5 6 7 8






∘


55 62

Re(120583) lt 0

minus20

minus10

0

10

40

20

30

3 4 5 6 7 8

Frequency (GHz)



(a)

Re(n) lt 0

3 4 5 6 7 8

Frequency (GHz)

minus60

minus40

minus20

0

20

40



(b)




02 the RA gain will






Excitation point

W

L

(a)

h

(b)


minus30

minus25

minus20

minus15

minus10

minus5

0


|S|(

dB)

11


LHM antenna h = 30

LHM antenna h = 31


96

965

97

975

98

985

27 28 29 30 31 32Air-gap height (mm)

Gai

n (a

bs) (

dB)






minus25

minus20

minus15

minus10

minus5

0

5 525 55 575 6 625 65Frequency (GHz)


|S|(

dB)

11



Axial ratio

Axi

al ra

tio (d

B)

0

minus2

minus4

minus6

minus85 52 54 56 58 6

Frequency (GHz)





05

1015

minus18

0

minus15

0

minus12

0

minus90

minus60

minus30 0 30 60 90 12

0

150

180

(dB)


120579 (deg)




Ground plane

h


LHM substrate


Antenna arraysz

y









h



minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

5 525 55 575 6 625 65Frequency (GHz)


|S|(

dB)

11

S11S11





1the current on



AF =

3

sum

119894=1

10038161003816100381610038161003816100381610038161003816

119868119894

1198681

10038161003816100381610038161003816100381610038161003816

119890119895(119896lowast119889

119909lowastsin 120579+ang(119868

1198941198681)) (16)


minus180

minus150

minus120 minus9

0

minus60

minus30 0 30 60 90 120

150

180


120579 (deg)


minus505

101520

(dB)



xsub

ds


W1

L1

C3W2C2

l

ysub xfye y

zx

(a)

h

(b)



Symbol Value1198821= 1198711


5 (mm)119909119891

05 (mm)1198822









11simulation =


11is shifted at





Frequency (GHz)5 52 54 56 58 6 62 64 65

0

minus2

minus4

minus6

minus8

minus10

minus12

minus14

minus16

minus18

|S|(

dB)

11

(a)

minus25

minus20

minus15

minus10

minus5

0

5 525 55 575 6 625 65Frequency (GHz)


|S|(

dB)

11

(b)


Gai

n (d

B)


120579 (deg)

10

5

0

minus5

minus10

minus15

minus20

minus25

minus180

minus150

minus120

minus90

minus60

minus30 0

30

60

90

120

150

180


(a)

Gai

n (d

B)

minus40

minus30

minus20

minus10

0

10


120579 (deg)

minus180

minus150

minus120

minus90

minus60

minus30 0

30

60

90

120

150

180


(b)









Frequency (GHz)5 52 54 56 58 6 62 64 65

minus45

minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

|S|(

dB)

11

(a)

minus30

minus25

minus20

minus15

minus10

minus5

0

5 525 55 575 6 625 65Frequency (GHz)


|S|(

dB)

11

(b)



Gai

n (d

B)

15

10

5

0

minus5

minus10

minus15

minus20

minus25

minus180

minus150

minus120

minus90

minus60

minus30 0

30

60

90

120

150

180

120579 (deg)


(a)


Gai

n (d

B)

minus180

minus150

minus120

minus90

minus60

minus30 0

30

60

90

120

150

180

120579 (deg)

10

0

minus10

minus20

minus30

minus40


(b)




4 Conclusion














Acknowledgments


References

































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










w

x

y

z

g

dy

dx

(a)


(b)

x

y

z

g

Ay

Ax

(c)

z

y

x

Substratedielectric

Conductorfaces

h

120576r

(d)




43 (mm)119860119910

43 (mm)119889119909







119885119904= minus119895120596119871

119904minus

1

119895120596119862119904

119884119875= minus119895120596119862

119901minus

1

119895120596119871119901

(2)


119868119899+1

= 119868119899119890119895120573

119881119899+1

= 119881119899119890119895120573

(3)



120573 = 119896119901 (4)


119909=



120583eff =

120596119871119904minus (1120596119862

119904)

2120596119901120573 tan (1205732)

120576eff =

2120573 tan (1205732)

(120596119871119904minus (1120596119862

119904)) 120596119901

(5)


sin2 (120573

2

) =

11988511990410158401198841199011015840

4

(6)

0 le

11988511990410158401198841199011015840

4

le 1 lArrrArr 0 le 11988511990410158401198841199011015840 le 4 (7)



119901 119862119901as

follows

1198851199041015840 = 120596119871

119904minus

1

120596119862119904

1198841199011015840 = 120596119862

119901minus

1

120596119871119901

(8)


119885 =

119881119899

119868119899

=

1

2

1198851199041015840

tan (1205732)

(9)


119904 119862119904and 119871

119901 119862119901


120596119871119904lt

1

120596119862119904

(10)


9= 12120587radic119871

119905119862119905 we suppose that 119871

119905and119862

119905are defined

as 119871119904

= 3273 nH 119862119904

= 0018 pF and 119862119901

= 095 pF with120596119862119901lt 1120596119871










119903= 35










z(k)

y(H)x(E)

h



A unit-cell


LHM substrate

θθminus

(a)

x(E)

y(H)

z(k)

Zmin-port 1

Zmax-port 2

Periodic

Periodic

S incident wave

PML

S 120579

(b)


Min

Max1

0x(E)

y(H)

z(k)

E energy

(a)

Min

Max1

0

x(E)

y(H)

z(k)

H energy

(b)





11and 119878



11987811

=

1198871

1198861

=

(1 minus 1198792) 119877

1 minus 11987721198792

11987821

=

1198862

1198861

=

(1 minus 1198772) 119879

1 minus 11987721198792

(11)


119877 =

119885 minus 1198850

119885 + 1198850

=

119911 minus 1

119911 + 1

119879 = 119890minus1198951198960119899119889

(12)






(1 + 11987811)2

minus 1198782

21

(1 minus 11987811)2

minus 1198782

21

119899 = minus

1

1198960119889

[[ln (119879)]10158401015840+ 2119898120587] minus 119895[ln (119877)]

1015840

(13)



x(E)y(H)

z(k)

Port 1

Port 2S

S incident wave

minus45

minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

S11 120579 = 45∘

S21 120579 = 45∘S11 120579 = 0∘

S21 120579 = 0∘

58GHz


Source

LHM



z

a1 a2

b1 b2




119879 =

1 minus 1198782

11+ 1198782

21

211987821


1 minus 1198782

11+ 1198782

21

211987821

)

2

(14)


120576eff =

119899

119911

120583eff = 119899119911 (15)

Frequency (GHz)

(dB)

3 4 5 6 7 8

minus45minus50


minus50

S11mdashtheta 0∘

S21mdashtheta 0∘

S11mdashtheta 15∘

S21mdashtheta 15∘

S11mdashtheta 30∘

S21mdashtheta 30∘

S11mdashtheta 45∘

S21mdashtheta 45∘

S11mdashtheta 60∘

S21mdashtheta 60∘



∘lt 120579 lt 0






Peakminus61

0

Re(120576)Im(120576)

minus400

minus200

0

200

400


minus1056 58 6 62

minus5

0

5

Frequency (GHz)

minus063

minus366

58

(a)

minus356

068

583 4 5minus10

0

10

20

30

6 7 8

Frequency (GHz)

Re(120583)Im(120583)

(b)



Re(n)Im(n)

minus30

minus20

minus10

0

10

20

30

40

Re(n) lt 0

019

minus361

(a)


Re(Z)Im(Z)

minus1

minus05

0

05

1

(b)





11


55minus20minus400

minus200

0

200

400

600

minus10

0

10

56 58 6 62

Re(120576) lt 0

Re(120576) lt0

3 4 5 6 7 8






∘


55 62

Re(120583) lt 0

minus20

minus10

0

10

40

20

30

3 4 5 6 7 8

Frequency (GHz)



(a)

Re(n) lt 0

3 4 5 6 7 8

Frequency (GHz)

minus60

minus40

minus20

0

20

40



(b)




02 the RA gain will






Excitation point

W

L

(a)

h

(b)


minus30

minus25

minus20

minus15

minus10

minus5

0


|S|(

dB)

11


LHM antenna h = 30

LHM antenna h = 31


96

965

97

975

98

985

27 28 29 30 31 32Air-gap height (mm)

Gai

n (a

bs) (

dB)






minus25

minus20

minus15

minus10

minus5

0

5 525 55 575 6 625 65Frequency (GHz)


|S|(

dB)

11



Axial ratio

Axi

al ra

tio (d

B)

0

minus2

minus4

minus6

minus85 52 54 56 58 6

Frequency (GHz)





05

1015

minus18

0

minus15

0

minus12

0

minus90

minus60

minus30 0 30 60 90 12

0

150

180

(dB)


120579 (deg)




Ground plane

h


LHM substrate


Antenna arraysz

y









h



minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

5 525 55 575 6 625 65Frequency (GHz)


|S|(

dB)

11

S11S11





1the current on



AF =

3

sum

119894=1

10038161003816100381610038161003816100381610038161003816

119868119894

1198681

10038161003816100381610038161003816100381610038161003816

119890119895(119896lowast119889

119909lowastsin 120579+ang(119868

1198941198681)) (16)


minus180

minus150

minus120 minus9

0

minus60

minus30 0 30 60 90 120

150

180


120579 (deg)


minus505

101520

(dB)



xsub

ds


W1

L1

C3W2C2

l

ysub xfye y

zx

(a)

h

(b)



Symbol Value1198821= 1198711


5 (mm)119909119891

05 (mm)1198822









11simulation =


11is shifted at





Frequency (GHz)5 52 54 56 58 6 62 64 65

0

minus2

minus4

minus6

minus8

minus10

minus12

minus14

minus16

minus18

|S|(

dB)

11

(a)

minus25

minus20

minus15

minus10

minus5

0

5 525 55 575 6 625 65Frequency (GHz)


|S|(

dB)

11

(b)


Gai

n (d

B)


120579 (deg)

10

5

0

minus5

minus10

minus15

minus20

minus25

minus180

minus150

minus120

minus90

minus60

minus30 0

30

60

90

120

150

180


(a)

Gai

n (d

B)

minus40

minus30

minus20

minus10

0

10


120579 (deg)

minus180

minus150

minus120

minus90

minus60

minus30 0

30

60

90

120

150

180


(b)









Frequency (GHz)5 52 54 56 58 6 62 64 65

minus45

minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

|S|(

dB)

11

(a)

minus30

minus25

minus20

minus15

minus10

minus5

0

5 525 55 575 6 625 65Frequency (GHz)


|S|(

dB)

11

(b)



Gai

n (d

B)

15

10

5

0

minus5

minus10

minus15

minus20

minus25

minus180

minus150

minus120

minus90

minus60

minus30 0

30

60

90

120

150

180

120579 (deg)


(a)


Gai

n (d

B)

minus180

minus150

minus120

minus90

minus60

minus30 0

30

60

90

120

150

180

120579 (deg)

10

0

minus10

minus20

minus30

minus40


(b)




4 Conclusion














Acknowledgments


References

































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











120573 = 119896119901 (4)


119909=



120583eff =

120596119871119904minus (1120596119862

119904)

2120596119901120573 tan (1205732)

120576eff =

2120573 tan (1205732)

(120596119871119904minus (1120596119862

119904)) 120596119901

(5)


sin2 (120573

2

) =

11988511990410158401198841199011015840

4

(6)

0 le

11988511990410158401198841199011015840

4

le 1 lArrrArr 0 le 11988511990410158401198841199011015840 le 4 (7)



119901 119862119901as

follows

1198851199041015840 = 120596119871

119904minus

1

120596119862119904

1198841199011015840 = 120596119862

119901minus

1

120596119871119901

(8)


119885 =

119881119899

119868119899

=

1

2

1198851199041015840

tan (1205732)

(9)


119904 119862119904and 119871

119901 119862119901


120596119871119904lt

1

120596119862119904

(10)


9= 12120587radic119871

119905119862119905 we suppose that 119871

119905and119862

119905are defined

as 119871119904

= 3273 nH 119862119904

= 0018 pF and 119862119901

= 095 pF with120596119862119901lt 1120596119871










119903= 35










z(k)

y(H)x(E)

h



A unit-cell


LHM substrate

θθminus

(a)

x(E)

y(H)

z(k)

Zmin-port 1

Zmax-port 2

Periodic

Periodic

S incident wave

PML

S 120579

(b)


Min

Max1

0x(E)

y(H)

z(k)

E energy

(a)

Min

Max1

0

x(E)

y(H)

z(k)

H energy

(b)





11and 119878



11987811

=

1198871

1198861

=

(1 minus 1198792) 119877

1 minus 11987721198792

11987821

=

1198862

1198861

=

(1 minus 1198772) 119879

1 minus 11987721198792

(11)


119877 =

119885 minus 1198850

119885 + 1198850

=

119911 minus 1

119911 + 1

119879 = 119890minus1198951198960119899119889

(12)






(1 + 11987811)2

minus 1198782

21

(1 minus 11987811)2

minus 1198782

21

119899 = minus

1

1198960119889

[[ln (119879)]10158401015840+ 2119898120587] minus 119895[ln (119877)]

1015840

(13)



x(E)y(H)

z(k)

Port 1

Port 2S

S incident wave

minus45

minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

S11 120579 = 45∘

S21 120579 = 45∘S11 120579 = 0∘

S21 120579 = 0∘

58GHz


Source

LHM



z

a1 a2

b1 b2




119879 =

1 minus 1198782

11+ 1198782

21

211987821


1 minus 1198782

11+ 1198782

21

211987821

)

2

(14)


120576eff =

119899

119911

120583eff = 119899119911 (15)

Frequency (GHz)

(dB)

3 4 5 6 7 8

minus45minus50


minus50

S11mdashtheta 0∘

S21mdashtheta 0∘

S11mdashtheta 15∘

S21mdashtheta 15∘

S11mdashtheta 30∘

S21mdashtheta 30∘

S11mdashtheta 45∘

S21mdashtheta 45∘

S11mdashtheta 60∘

S21mdashtheta 60∘



∘lt 120579 lt 0






Peakminus61

0

Re(120576)Im(120576)

minus400

minus200

0

200

400


minus1056 58 6 62

minus5

0

5

Frequency (GHz)

minus063

minus366

58

(a)

minus356

068

583 4 5minus10

0

10

20

30

6 7 8

Frequency (GHz)

Re(120583)Im(120583)

(b)



Re(n)Im(n)

minus30

minus20

minus10

0

10

20

30

40

Re(n) lt 0

019

minus361

(a)


Re(Z)Im(Z)

minus1

minus05

0

05

1

(b)





11


55minus20minus400

minus200

0

200

400

600

minus10

0

10

56 58 6 62

Re(120576) lt 0

Re(120576) lt0

3 4 5 6 7 8






∘


55 62

Re(120583) lt 0

minus20

minus10

0

10

40

20

30

3 4 5 6 7 8

Frequency (GHz)



(a)

Re(n) lt 0

3 4 5 6 7 8

Frequency (GHz)

minus60

minus40

minus20

0

20

40



(b)




02 the RA gain will






Excitation point

W

L

(a)

h

(b)


minus30

minus25

minus20

minus15

minus10

minus5

0


|S|(

dB)

11


LHM antenna h = 30

LHM antenna h = 31


96

965

97

975

98

985

27 28 29 30 31 32Air-gap height (mm)

Gai

n (a

bs) (

dB)






minus25

minus20

minus15

minus10

minus5

0

5 525 55 575 6 625 65Frequency (GHz)


|S|(

dB)

11



Axial ratio

Axi

al ra

tio (d

B)

0

minus2

minus4

minus6

minus85 52 54 56 58 6

Frequency (GHz)





05

1015

minus18

0

minus15

0

minus12

0

minus90

minus60

minus30 0 30 60 90 12

0

150

180

(dB)


120579 (deg)




Ground plane

h


LHM substrate


Antenna arraysz

y









h



minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

5 525 55 575 6 625 65Frequency (GHz)


|S|(

dB)

11

S11S11





1the current on



AF =

3

sum

119894=1

10038161003816100381610038161003816100381610038161003816

119868119894

1198681

10038161003816100381610038161003816100381610038161003816

119890119895(119896lowast119889

119909lowastsin 120579+ang(119868

1198941198681)) (16)


minus180

minus150

minus120 minus9

0

minus60

minus30 0 30 60 90 120

150

180


120579 (deg)


minus505

101520

(dB)



xsub

ds


W1

L1

C3W2C2

l

ysub xfye y

zx

(a)

h

(b)



Symbol Value1198821= 1198711


5 (mm)119909119891

05 (mm)1198822









11simulation =


11is shifted at





Frequency (GHz)5 52 54 56 58 6 62 64 65

0

minus2

minus4

minus6

minus8

minus10

minus12

minus14

minus16

minus18

|S|(

dB)

11

(a)

minus25

minus20

minus15

minus10

minus5

0

5 525 55 575 6 625 65Frequency (GHz)


|S|(

dB)

11

(b)


Gai

n (d

B)


120579 (deg)

10

5

0

minus5

minus10

minus15

minus20

minus25

minus180

minus150

minus120

minus90

minus60

minus30 0

30

60

90

120

150

180


(a)

Gai

n (d

B)

minus40

minus30

minus20

minus10

0

10


120579 (deg)

minus180

minus150

minus120

minus90

minus60

minus30 0

30

60

90

120

150

180


(b)









Frequency (GHz)5 52 54 56 58 6 62 64 65

minus45

minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

|S|(

dB)

11

(a)

minus30

minus25

minus20

minus15

minus10

minus5

0

5 525 55 575 6 625 65Frequency (GHz)


|S|(

dB)

11

(b)



Gai

n (d

B)

15

10

5

0

minus5

minus10

minus15

minus20

minus25

minus180

minus150

minus120

minus90

minus60

minus30 0

30

60

90

120

150

180

120579 (deg)


(a)


Gai

n (d

B)

minus180

minus150

minus120

minus90

minus60

minus30 0

30

60

90

120

150

180

120579 (deg)

10

0

minus10

minus20

minus30

minus40


(b)




4 Conclusion














Acknowledgments


References

































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










z(k)

y(H)x(E)

h



A unit-cell


LHM substrate

θθminus

(a)

x(E)

y(H)

z(k)

Zmin-port 1

Zmax-port 2

Periodic

Periodic

S incident wave

PML

S 120579

(b)


Min

Max1

0x(E)

y(H)

z(k)

E energy

(a)

Min

Max1

0

x(E)

y(H)

z(k)

H energy

(b)





11and 119878



11987811

=

1198871

1198861

=

(1 minus 1198792) 119877

1 minus 11987721198792

11987821

=

1198862

1198861

=

(1 minus 1198772) 119879

1 minus 11987721198792

(11)


119877 =

119885 minus 1198850

119885 + 1198850

=

119911 minus 1

119911 + 1

119879 = 119890minus1198951198960119899119889

(12)






(1 + 11987811)2

minus 1198782

21

(1 minus 11987811)2

minus 1198782

21

119899 = minus

1

1198960119889

[[ln (119879)]10158401015840+ 2119898120587] minus 119895[ln (119877)]

1015840

(13)



x(E)y(H)

z(k)

Port 1

Port 2S

S incident wave

minus45

minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

S11 120579 = 45∘

S21 120579 = 45∘S11 120579 = 0∘

S21 120579 = 0∘

58GHz


Source

LHM



z

a1 a2

b1 b2




119879 =

1 minus 1198782

11+ 1198782

21

211987821


1 minus 1198782

11+ 1198782

21

211987821

)

2

(14)


120576eff =

119899

119911

120583eff = 119899119911 (15)

Frequency (GHz)

(dB)

3 4 5 6 7 8

minus45minus50


minus50

S11mdashtheta 0∘

S21mdashtheta 0∘

S11mdashtheta 15∘

S21mdashtheta 15∘

S11mdashtheta 30∘

S21mdashtheta 30∘

S11mdashtheta 45∘

S21mdashtheta 45∘

S11mdashtheta 60∘

S21mdashtheta 60∘



∘lt 120579 lt 0






Peakminus61

0

Re(120576)Im(120576)

minus400

minus200

0

200

400


minus1056 58 6 62

minus5

0

5

Frequency (GHz)

minus063

minus366

58

(a)

minus356

068

583 4 5minus10

0

10

20

30

6 7 8

Frequency (GHz)

Re(120583)Im(120583)

(b)



Re(n)Im(n)

minus30

minus20

minus10

0

10

20

30

40

Re(n) lt 0

019

minus361

(a)


Re(Z)Im(Z)

minus1

minus05

0

05

1

(b)





11


55minus20minus400

minus200

0

200

400

600

minus10

0

10

56 58 6 62

Re(120576) lt 0

Re(120576) lt0

3 4 5 6 7 8






∘


55 62

Re(120583) lt 0

minus20

minus10

0

10

40

20

30

3 4 5 6 7 8

Frequency (GHz)



(a)

Re(n) lt 0

3 4 5 6 7 8

Frequency (GHz)

minus60

minus40

minus20

0

20

40



(b)




02 the RA gain will






Excitation point

W

L

(a)

h

(b)


minus30

minus25

minus20

minus15

minus10

minus5

0


|S|(

dB)

11


LHM antenna h = 30

LHM antenna h = 31


96

965

97

975

98

985

27 28 29 30 31 32Air-gap height (mm)

Gai

n (a

bs) (

dB)






minus25

minus20

minus15

minus10

minus5

0

5 525 55 575 6 625 65Frequency (GHz)


|S|(

dB)

11



Axial ratio

Axi

al ra

tio (d

B)

0

minus2

minus4

minus6

minus85 52 54 56 58 6

Frequency (GHz)





05

1015

minus18

0

minus15

0

minus12

0

minus90

minus60

minus30 0 30 60 90 12

0

150

180

(dB)


120579 (deg)




Ground plane

h


LHM substrate


Antenna arraysz

y









h



minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

5 525 55 575 6 625 65Frequency (GHz)


|S|(

dB)

11

S11S11





1the current on



AF =

3

sum

119894=1

10038161003816100381610038161003816100381610038161003816

119868119894

1198681

10038161003816100381610038161003816100381610038161003816

119890119895(119896lowast119889

119909lowastsin 120579+ang(119868

1198941198681)) (16)


minus180

minus150

minus120 minus9

0

minus60

minus30 0 30 60 90 120

150

180


120579 (deg)


minus505

101520

(dB)



xsub

ds


W1

L1

C3W2C2

l

ysub xfye y

zx

(a)

h

(b)



Symbol Value1198821= 1198711


5 (mm)119909119891

05 (mm)1198822









11simulation =


11is shifted at





Frequency (GHz)5 52 54 56 58 6 62 64 65

0

minus2

minus4

minus6

minus8

minus10

minus12

minus14

minus16

minus18

|S|(

dB)

11

(a)

minus25

minus20

minus15

minus10

minus5

0

5 525 55 575 6 625 65Frequency (GHz)


|S|(

dB)

11

(b)


Gai

n (d

B)


120579 (deg)

10

5

0

minus5

minus10

minus15

minus20

minus25

minus180

minus150

minus120

minus90

minus60

minus30 0

30

60

90

120

150

180


(a)

Gai

n (d

B)

minus40

minus30

minus20

minus10

0

10


120579 (deg)

minus180

minus150

minus120

minus90

minus60

minus30 0

30

60

90

120

150

180


(b)









Frequency (GHz)5 52 54 56 58 6 62 64 65

minus45

minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

|S|(

dB)

11

(a)

minus30

minus25

minus20

minus15

minus10

minus5

0

5 525 55 575 6 625 65Frequency (GHz)


|S|(

dB)

11

(b)



Gai

n (d

B)

15

10

5

0

minus5

minus10

minus15

minus20

minus25

minus180

minus150

minus120

minus90

minus60

minus30 0

30

60

90

120

150

180

120579 (deg)


(a)


Gai

n (d

B)

minus180

minus150

minus120

minus90

minus60

minus30 0

30

60

90

120

150

180

120579 (deg)

10

0

minus10

minus20

minus30

minus40


(b)




4 Conclusion














Acknowledgments


References

































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











x(E)y(H)

z(k)

Port 1

Port 2S

S incident wave

minus45

minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

S11 120579 = 45∘

S21 120579 = 45∘S11 120579 = 0∘

S21 120579 = 0∘

58GHz


Source

LHM



z

a1 a2

b1 b2




119879 =

1 minus 1198782

11+ 1198782

21

211987821


1 minus 1198782

11+ 1198782

21

211987821

)

2

(14)


120576eff =

119899

119911

120583eff = 119899119911 (15)

Frequency (GHz)

(dB)

3 4 5 6 7 8

minus45minus50


minus50

S11mdashtheta 0∘

S21mdashtheta 0∘

S11mdashtheta 15∘

S21mdashtheta 15∘

S11mdashtheta 30∘

S21mdashtheta 30∘

S11mdashtheta 45∘

S21mdashtheta 45∘

S11mdashtheta 60∘

S21mdashtheta 60∘



∘lt 120579 lt 0






Peakminus61

0

Re(120576)Im(120576)

minus400

minus200

0

200

400


minus1056 58 6 62

minus5

0

5

Frequency (GHz)

minus063

minus366

58

(a)

minus356

068

583 4 5minus10

0

10

20

30

6 7 8

Frequency (GHz)

Re(120583)Im(120583)

(b)



Re(n)Im(n)

minus30

minus20

minus10

0

10

20

30

40

Re(n) lt 0

019

minus361

(a)


Re(Z)Im(Z)

minus1

minus05

0

05

1

(b)





11


55minus20minus400

minus200

0

200

400

600

minus10

0

10

56 58 6 62

Re(120576) lt 0

Re(120576) lt0

3 4 5 6 7 8






∘


55 62

Re(120583) lt 0

minus20

minus10

0

10

40

20

30

3 4 5 6 7 8

Frequency (GHz)



(a)

Re(n) lt 0

3 4 5 6 7 8

Frequency (GHz)

minus60

minus40

minus20

0

20

40



(b)




02 the RA gain will






Excitation point

W

L

(a)

h

(b)


minus30

minus25

minus20

minus15

minus10

minus5

0


|S|(

dB)

11


LHM antenna h = 30

LHM antenna h = 31


96

965

97

975

98

985

27 28 29 30 31 32Air-gap height (mm)

Gai

n (a

bs) (

dB)






minus25

minus20

minus15

minus10

minus5

0

5 525 55 575 6 625 65Frequency (GHz)


|S|(

dB)

11



Axial ratio

Axi

al ra

tio (d

B)

0

minus2

minus4

minus6

minus85 52 54 56 58 6

Frequency (GHz)





05

1015

minus18

0

minus15

0

minus12

0

minus90

minus60

minus30 0 30 60 90 12

0

150

180

(dB)


120579 (deg)




Ground plane

h


LHM substrate


Antenna arraysz

y









h



minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

5 525 55 575 6 625 65Frequency (GHz)


|S|(

dB)

11

S11S11





1the current on



AF =

3

sum

119894=1

10038161003816100381610038161003816100381610038161003816

119868119894

1198681

10038161003816100381610038161003816100381610038161003816

119890119895(119896lowast119889

119909lowastsin 120579+ang(119868

1198941198681)) (16)


minus180

minus150

minus120 minus9

0

minus60

minus30 0 30 60 90 120

150

180


120579 (deg)


minus505

101520

(dB)



xsub

ds


W1

L1

C3W2C2

l

ysub xfye y

zx

(a)

h

(b)



Symbol Value1198821= 1198711


5 (mm)119909119891

05 (mm)1198822









11simulation =


11is shifted at





Frequency (GHz)5 52 54 56 58 6 62 64 65

0

minus2

minus4

minus6

minus8

minus10

minus12

minus14

minus16

minus18

|S|(

dB)

11

(a)

minus25

minus20

minus15

minus10

minus5

0

5 525 55 575 6 625 65Frequency (GHz)


|S|(

dB)

11

(b)


Gai

n (d

B)


120579 (deg)

10

5

0

minus5

minus10

minus15

minus20

minus25

minus180

minus150

minus120

minus90

minus60

minus30 0

30

60

90

120

150

180


(a)

Gai

n (d

B)

minus40

minus30

minus20

minus10

0

10


120579 (deg)

minus180

minus150

minus120

minus90

minus60

minus30 0

30

60

90

120

150

180


(b)









Frequency (GHz)5 52 54 56 58 6 62 64 65

minus45

minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

|S|(

dB)

11

(a)

minus30

minus25

minus20

minus15

minus10

minus5

0

5 525 55 575 6 625 65Frequency (GHz)


|S|(

dB)

11

(b)



Gai

n (d

B)

15

10

5

0

minus5

minus10

minus15

minus20

minus25

minus180

minus150

minus120

minus90

minus60

minus30 0

30

60

90

120

150

180

120579 (deg)


(a)


Gai

n (d

B)

minus180

minus150

minus120

minus90

minus60

minus30 0

30

60

90

120

150

180

120579 (deg)

10

0

minus10

minus20

minus30

minus40


(b)




4 Conclusion














Acknowledgments


References

































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Peakminus61

0

Re(120576)Im(120576)

minus400

minus200

0

200

400


minus1056 58 6 62

minus5

0

5

Frequency (GHz)

minus063

minus366

58

(a)

minus356

068

583 4 5minus10

0

10

20

30

6 7 8

Frequency (GHz)

Re(120583)Im(120583)

(b)



Re(n)Im(n)

minus30

minus20

minus10

0

10

20

30

40

Re(n) lt 0

019

minus361

(a)


Re(Z)Im(Z)

minus1

minus05

0

05

1

(b)





11


55minus20minus400

minus200

0

200

400

600

minus10

0

10

56 58 6 62

Re(120576) lt 0

Re(120576) lt0

3 4 5 6 7 8






∘


55 62

Re(120583) lt 0

minus20

minus10

0

10

40

20

30

3 4 5 6 7 8

Frequency (GHz)



(a)

Re(n) lt 0

3 4 5 6 7 8

Frequency (GHz)

minus60

minus40

minus20

0

20

40



(b)




02 the RA gain will






Excitation point

W

L

(a)

h

(b)


minus30

minus25

minus20

minus15

minus10

minus5

0


|S|(

dB)

11


LHM antenna h = 30

LHM antenna h = 31


96

965

97

975

98

985

27 28 29 30 31 32Air-gap height (mm)

Gai

n (a

bs) (

dB)






minus25

minus20

minus15

minus10

minus5

0

5 525 55 575 6 625 65Frequency (GHz)


|S|(

dB)

11



Axial ratio

Axi

al ra

tio (d

B)

0

minus2

minus4

minus6

minus85 52 54 56 58 6

Frequency (GHz)





05

1015

minus18

0

minus15

0

minus12

0

minus90

minus60

minus30 0 30 60 90 12

0

150

180

(dB)


120579 (deg)




Ground plane

h


LHM substrate


Antenna arraysz

y









h



minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

5 525 55 575 6 625 65Frequency (GHz)


|S|(

dB)

11

S11S11





1the current on



AF =

3

sum

119894=1

10038161003816100381610038161003816100381610038161003816

119868119894

1198681

10038161003816100381610038161003816100381610038161003816

119890119895(119896lowast119889

119909lowastsin 120579+ang(119868

1198941198681)) (16)


minus180

minus150

minus120 minus9

0

minus60

minus30 0 30 60 90 120

150

180


120579 (deg)


minus505

101520

(dB)



xsub

ds


W1

L1

C3W2C2

l

ysub xfye y

zx

(a)

h

(b)



Symbol Value1198821= 1198711


5 (mm)119909119891

05 (mm)1198822









11simulation =


11is shifted at





Frequency (GHz)5 52 54 56 58 6 62 64 65

0

minus2

minus4

minus6

minus8

minus10

minus12

minus14

minus16

minus18

|S|(

dB)

11

(a)

minus25

minus20

minus15

minus10

minus5

0

5 525 55 575 6 625 65Frequency (GHz)


|S|(

dB)

11

(b)


Gai

n (d

B)


120579 (deg)

10

5

0

minus5

minus10

minus15

minus20

minus25

minus180

minus150

minus120

minus90

minus60

minus30 0

30

60

90

120

150

180


(a)

Gai

n (d

B)

minus40

minus30

minus20

minus10

0

10


120579 (deg)

minus180

minus150

minus120

minus90

minus60

minus30 0

30

60

90

120

150

180


(b)









Frequency (GHz)5 52 54 56 58 6 62 64 65

minus45

minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

|S|(

dB)

11

(a)

minus30

minus25

minus20

minus15

minus10

minus5

0

5 525 55 575 6 625 65Frequency (GHz)


|S|(

dB)

11

(b)



Gai

n (d

B)

15

10

5

0

minus5

minus10

minus15

minus20

minus25

minus180

minus150

minus120

minus90

minus60

minus30 0

30

60

90

120

150

180

120579 (deg)


(a)


Gai

n (d

B)

minus180

minus150

minus120

minus90

minus60

minus30 0

30

60

90

120

150

180

120579 (deg)

10

0

minus10

minus20

minus30

minus40


(b)




4 Conclusion














Acknowledgments


References

































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










55minus20minus400

minus200

0

200

400

600

minus10

0

10

56 58 6 62

Re(120576) lt 0

Re(120576) lt0

3 4 5 6 7 8






∘


55 62

Re(120583) lt 0

minus20

minus10

0

10

40

20

30

3 4 5 6 7 8

Frequency (GHz)



(a)

Re(n) lt 0

3 4 5 6 7 8

Frequency (GHz)

minus60

minus40

minus20

0

20

40



(b)




02 the RA gain will






Excitation point

W

L

(a)

h

(b)


minus30

minus25

minus20

minus15

minus10

minus5

0


|S|(

dB)

11


LHM antenna h = 30

LHM antenna h = 31


96

965

97

975

98

985

27 28 29 30 31 32Air-gap height (mm)

Gai

n (a

bs) (

dB)






minus25

minus20

minus15

minus10

minus5

0

5 525 55 575 6 625 65Frequency (GHz)


|S|(

dB)

11



Axial ratio

Axi

al ra

tio (d

B)

0

minus2

minus4

minus6

minus85 52 54 56 58 6

Frequency (GHz)





05

1015

minus18

0

minus15

0

minus12

0

minus90

minus60

minus30 0 30 60 90 12

0

150

180

(dB)


120579 (deg)




Ground plane

h


LHM substrate


Antenna arraysz

y









h



minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

5 525 55 575 6 625 65Frequency (GHz)


|S|(

dB)

11

S11S11





1the current on



AF =

3

sum

119894=1

10038161003816100381610038161003816100381610038161003816

119868119894

1198681

10038161003816100381610038161003816100381610038161003816

119890119895(119896lowast119889

119909lowastsin 120579+ang(119868

1198941198681)) (16)


minus180

minus150

minus120 minus9

0

minus60

minus30 0 30 60 90 120

150

180


120579 (deg)


minus505

101520

(dB)



xsub

ds


W1

L1

C3W2C2

l

ysub xfye y

zx

(a)

h

(b)



Symbol Value1198821= 1198711


5 (mm)119909119891

05 (mm)1198822









11simulation =


11is shifted at





Frequency (GHz)5 52 54 56 58 6 62 64 65

0

minus2

minus4

minus6

minus8

minus10

minus12

minus14

minus16

minus18

|S|(

dB)

11

(a)

minus25

minus20

minus15

minus10

minus5

0

5 525 55 575 6 625 65Frequency (GHz)


|S|(

dB)

11

(b)


Gai

n (d

B)


120579 (deg)

10

5

0

minus5

minus10

minus15

minus20

minus25

minus180

minus150

minus120

minus90

minus60

minus30 0

30

60

90

120

150

180


(a)

Gai

n (d

B)

minus40

minus30

minus20

minus10

0

10


120579 (deg)

minus180

minus150

minus120

minus90

minus60

minus30 0

30

60

90

120

150

180


(b)









Frequency (GHz)5 52 54 56 58 6 62 64 65

minus45

minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

|S|(

dB)

11

(a)

minus30

minus25

minus20

minus15

minus10

minus5

0

5 525 55 575 6 625 65Frequency (GHz)


|S|(

dB)

11

(b)



Gai

n (d

B)

15

10

5

0

minus5

minus10

minus15

minus20

minus25

minus180

minus150

minus120

minus90

minus60

minus30 0

30

60

90

120

150

180

120579 (deg)


(a)


Gai

n (d

B)

minus180

minus150

minus120

minus90

minus60

minus30 0

30

60

90

120

150

180

120579 (deg)

10

0

minus10

minus20

minus30

minus40


(b)




4 Conclusion














Acknowledgments


References

































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Excitation point

W

L

(a)

h

(b)


minus30

minus25

minus20

minus15

minus10

minus5

0


|S|(

dB)

11


LHM antenna h = 30

LHM antenna h = 31


96

965

97

975

98

985

27 28 29 30 31 32Air-gap height (mm)

Gai

n (a

bs) (

dB)






minus25

minus20

minus15

minus10

minus5

0

5 525 55 575 6 625 65Frequency (GHz)


|S|(

dB)

11



Axial ratio

Axi

al ra

tio (d

B)

0

minus2

minus4

minus6

minus85 52 54 56 58 6

Frequency (GHz)





05

1015

minus18

0

minus15

0

minus12

0

minus90

minus60

minus30 0 30 60 90 12

0

150

180

(dB)


120579 (deg)




Ground plane

h


LHM substrate


Antenna arraysz

y









h



minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

5 525 55 575 6 625 65Frequency (GHz)


|S|(

dB)

11

S11S11





1the current on



AF =

3

sum

119894=1

10038161003816100381610038161003816100381610038161003816

119868119894

1198681

10038161003816100381610038161003816100381610038161003816

119890119895(119896lowast119889

119909lowastsin 120579+ang(119868

1198941198681)) (16)


minus180

minus150

minus120 minus9

0

minus60

minus30 0 30 60 90 120

150

180


120579 (deg)


minus505

101520

(dB)



xsub

ds


W1

L1

C3W2C2

l

ysub xfye y

zx

(a)

h

(b)



Symbol Value1198821= 1198711


5 (mm)119909119891

05 (mm)1198822









11simulation =


11is shifted at





Frequency (GHz)5 52 54 56 58 6 62 64 65

0

minus2

minus4

minus6

minus8

minus10

minus12

minus14

minus16

minus18

|S|(

dB)

11

(a)

minus25

minus20

minus15

minus10

minus5

0

5 525 55 575 6 625 65Frequency (GHz)


|S|(

dB)

11

(b)


Gai

n (d

B)


120579 (deg)

10

5

0

minus5

minus10

minus15

minus20

minus25

minus180

minus150

minus120

minus90

minus60

minus30 0

30

60

90

120

150

180


(a)

Gai

n (d

B)

minus40

minus30

minus20

minus10

0

10


120579 (deg)

minus180

minus150

minus120

minus90

minus60

minus30 0

30

60

90

120

150

180


(b)









Frequency (GHz)5 52 54 56 58 6 62 64 65

minus45

minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

|S|(

dB)

11

(a)

minus30

minus25

minus20

minus15

minus10

minus5

0

5 525 55 575 6 625 65Frequency (GHz)


|S|(

dB)

11

(b)



Gai

n (d

B)

15

10

5

0

minus5

minus10

minus15

minus20

minus25

minus180

minus150

minus120

minus90

minus60

minus30 0

30

60

90

120

150

180

120579 (deg)


(a)


Gai

n (d

B)

minus180

minus150

minus120

minus90

minus60

minus30 0

30

60

90

120

150

180

120579 (deg)

10

0

minus10

minus20

minus30

minus40


(b)




4 Conclusion














Acknowledgments


References

































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











05

1015

minus18

0

minus15

0

minus12

0

minus90

minus60

minus30 0 30 60 90 12

0

150

180

(dB)


120579 (deg)




Ground plane

h


LHM substrate


Antenna arraysz

y









h



minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

5 525 55 575 6 625 65Frequency (GHz)


|S|(

dB)

11

S11S11





1the current on



AF =

3

sum

119894=1

10038161003816100381610038161003816100381610038161003816

119868119894

1198681

10038161003816100381610038161003816100381610038161003816

119890119895(119896lowast119889

119909lowastsin 120579+ang(119868

1198941198681)) (16)


minus180

minus150

minus120 minus9

0

minus60

minus30 0 30 60 90 120

150

180


120579 (deg)


minus505

101520

(dB)



xsub

ds


W1

L1

C3W2C2

l

ysub xfye y

zx

(a)

h

(b)



Symbol Value1198821= 1198711


5 (mm)119909119891

05 (mm)1198822









11simulation =


11is shifted at





Frequency (GHz)5 52 54 56 58 6 62 64 65

0

minus2

minus4

minus6

minus8

minus10

minus12

minus14

minus16

minus18

|S|(

dB)

11

(a)

minus25

minus20

minus15

minus10

minus5

0

5 525 55 575 6 625 65Frequency (GHz)


|S|(

dB)

11

(b)


Gai

n (d

B)


120579 (deg)

10

5

0

minus5

minus10

minus15

minus20

minus25

minus180

minus150

minus120

minus90

minus60

minus30 0

30

60

90

120

150

180


(a)

Gai

n (d

B)

minus40

minus30

minus20

minus10

0

10


120579 (deg)

minus180

minus150

minus120

minus90

minus60

minus30 0

30

60

90

120

150

180


(b)









Frequency (GHz)5 52 54 56 58 6 62 64 65

minus45

minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

|S|(

dB)

11

(a)

minus30

minus25

minus20

minus15

minus10

minus5

0

5 525 55 575 6 625 65Frequency (GHz)


|S|(

dB)

11

(b)



Gai

n (d

B)

15

10

5

0

minus5

minus10

minus15

minus20

minus25

minus180

minus150

minus120

minus90

minus60

minus30 0

30

60

90

120

150

180

120579 (deg)


(a)


Gai

n (d

B)

minus180

minus150

minus120

minus90

minus60

minus30 0

30

60

90

120

150

180

120579 (deg)

10

0

minus10

minus20

minus30

minus40


(b)




4 Conclusion














Acknowledgments


References

































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










minus180

minus150

minus120 minus9

0

minus60

minus30 0 30 60 90 120

150

180


120579 (deg)


minus505

101520

(dB)



xsub

ds


W1

L1

C3W2C2

l

ysub xfye y

zx

(a)

h

(b)



Symbol Value1198821= 1198711


5 (mm)119909119891

05 (mm)1198822









11simulation =


11is shifted at





Frequency (GHz)5 52 54 56 58 6 62 64 65

0

minus2

minus4

minus6

minus8

minus10

minus12

minus14

minus16

minus18

|S|(

dB)

11

(a)

minus25

minus20

minus15

minus10

minus5

0

5 525 55 575 6 625 65Frequency (GHz)


|S|(

dB)

11

(b)


Gai

n (d

B)


120579 (deg)

10

5

0

minus5

minus10

minus15

minus20

minus25

minus180

minus150

minus120

minus90

minus60

minus30 0

30

60

90

120

150

180


(a)

Gai

n (d

B)

minus40

minus30

minus20

minus10

0

10


120579 (deg)

minus180

minus150

minus120

minus90

minus60

minus30 0

30

60

90

120

150

180


(b)









Frequency (GHz)5 52 54 56 58 6 62 64 65

minus45

minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

|S|(

dB)

11

(a)

minus30

minus25

minus20

minus15

minus10

minus5

0

5 525 55 575 6 625 65Frequency (GHz)


|S|(

dB)

11

(b)



Gai

n (d

B)

15

10

5

0

minus5

minus10

minus15

minus20

minus25

minus180

minus150

minus120

minus90

minus60

minus30 0

30

60

90

120

150

180

120579 (deg)


(a)


Gai

n (d

B)

minus180

minus150

minus120

minus90

minus60

minus30 0

30

60

90

120

150

180

120579 (deg)

10

0

minus10

minus20

minus30

minus40


(b)




4 Conclusion














Acknowledgments


References

































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











Frequency (GHz)5 52 54 56 58 6 62 64 65

0

minus2

minus4

minus6

minus8

minus10

minus12

minus14

minus16

minus18

|S|(

dB)

11

(a)

minus25

minus20

minus15

minus10

minus5

0

5 525 55 575 6 625 65Frequency (GHz)


|S|(

dB)

11

(b)


Gai

n (d

B)


120579 (deg)

10

5

0

minus5

minus10

minus15

minus20

minus25

minus180

minus150

minus120

minus90

minus60

minus30 0

30

60

90

120

150

180


(a)

Gai

n (d

B)

minus40

minus30

minus20

minus10

0

10


120579 (deg)

minus180

minus150

minus120

minus90

minus60

minus30 0

30

60

90

120

150

180


(b)









Frequency (GHz)5 52 54 56 58 6 62 64 65

minus45

minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

|S|(

dB)

11

(a)

minus30

minus25

minus20

minus15

minus10

minus5

0

5 525 55 575 6 625 65Frequency (GHz)


|S|(

dB)

11

(b)



Gai

n (d

B)

15

10

5

0

minus5

minus10

minus15

minus20

minus25

minus180

minus150

minus120

minus90

minus60

minus30 0

30

60

90

120

150

180

120579 (deg)


(a)


Gai

n (d

B)

minus180

minus150

minus120

minus90

minus60

minus30 0

30

60

90

120

150

180

120579 (deg)

10

0

minus10

minus20

minus30

minus40


(b)




4 Conclusion














Acknowledgments


References

































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











Frequency (GHz)5 52 54 56 58 6 62 64 65

minus45

minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

|S|(

dB)

11

(a)

minus30

minus25

minus20

minus15

minus10

minus5

0

5 525 55 575 6 625 65Frequency (GHz)


|S|(

dB)

11

(b)



Gai

n (d

B)

15

10

5

0

minus5

minus10

minus15

minus20

minus25

minus180

minus150

minus120

minus90

minus60

minus30 0

30

60

90

120

150

180

120579 (deg)


(a)


Gai

n (d

B)

minus180

minus150

minus120

minus90

minus60

minus30 0

30

60

90

120

150

180

120579 (deg)

10

0

minus10

minus20

minus30

minus40


(b)




4 Conclusion














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









research article design of high-gain and beam steering...

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