Dual Band Microstrip Circular Patch

Research ArticleNovel Dual Band Microstrip Circular Patch AntennasLoaded with ENG and MNG Metamaterials

Md Ababil Hossain1 Md Saimoom Ferdous2

Shah Mahmud Hasan Chowdhury1 and Md Abdul Matin1

1 Department of Electrical and Electronic Engineering BUET Dhaka 1000 Bangladesh2Department of ECE University of British Columbia Okanagan BC Canada

Correspondence should be addressed to Md Ababil Hossain ababilhgmailcom

Received 13 September 2013 Accepted 20 November 2013 Published 11 February 2014

Academic Editor Guo Qing Luo

Copyright copy 2014 Md Ababil Hossain et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

Novel design of a dual band microstrip circular patch antenna loaded with ENG (120576 negative) metamaterial has been shown inthe first section Using ENG metamaterial instead of the conventional dielectric unconventional TM12057510 (1 lt 120575 lt 2) mode wasproduced to yield a dual band performance Optimized parameters such as permittivity (1205761) and filling ratio (120578) of metamaterialswere selected with the aid of a MATLAB based parameter optimization algorithm developed for all these sort of patch antennasIn the second section a dual band circular patch antenna loaded with MNG (120583 negative) metamaterial has been reported Anunconventional modified TM12057510 (0 lt 120575 lt 1) mode has been produced along with conventional TM110 mode due to using MNGmetamaterial Here also the optimum values of permeability (1205831) and filling ratio (120578) for these sorts of patch antennas have beencalculated from a MATLAB based parameter optimization algorithm Both the proposed antennas provide good and resonanceand satisfactory radiation performances (directivity radiation efficiency and gain) with a dual band performance

1 Introduction

Satellite communications wireless communications surveil-lance weather radar and so forth require highly directive andmultiband antennas In fact in recent times highly directivemultiband antennas have become a prime concern in satellitecommunication

The use of multiband antenna has brought about revo-lutionary change and dynamism in the trends of commu-nication over the last few decades However antenna sizeminiaturization is also an important factor as far as antennasize is concernedTherefore a unique radiating element suchas patch antenna which incorporates multiband performancewith size miniaturization can further open up a new horizonin telecommunication sector In [1] a generalized MATLABbased parameter optimization algorithm for designing cir-cular patch antenna loaded with metamaterials has been

developedOn the basis of that design algorithm in this paperwe have presented the design model for dual band antennasloaded with both ENG and MNG metamaterials without theuse of any symmetrical slotting which was done in [1 2]

Wong andHsieh [2] constructed dual band circular patchantenna by using conventional dielectrics as substrate andby using symmetrical slots where conventional TM210 modewas modified to yield dual band performance In that casethe first order mode (TM110 mode frequency) and secondordermode (TM210mode frequency) were determined by theantenna geometry structure (ie radius of the patch) Oncethe one mode has been selected the other mode frequencyautomatically becomes fixed In that case the designer couldonly tune any one mode frequency according to his willhe had no control over choosing the other mode frequencyas the other mode frequency is determined by antennaradius In that particular case the degree of freedom was

Hindawi Publishing CorporationInternational Journal of Antennas and PropagationVolume 2014 Article ID 904374 9 pageshttpdxdoiorg1011552014904374

2 International Journal of Antennas and Propagation

only one that is radius of the patch So with one degree offreedom designers could choose only one resonant frequencyindependently but not both at the same time

In the first section of this paper a novel design ofdual band ENG metamaterial loaded circular patch antennahas been shown Its main feature is in the flexibility ofchoosing both resonant frequencies according to userrsquos willand apart from conventional TM110 mode newly producedunconventional TM12057510 (1 lt 120575 lt 2) mode provides highdirectivity Our designed antenna has two degrees of freedom(radius of the patch and filling ratio of the metamaterial) Inour case the first band that is first ordermode is determinedby the patch geometry only Using ENGmetamaterial insteadof conventional dielectrics causes resonance in between firstand second ordermode frequency For this reason the biggestadvantage here is that the designer can tune the secondband almost anywhere in between conventional first andsecond order mode by just changing the filling ratio of themetamaterial That is why this design provides a great deal offlexibility in choosing resonant frequency in comparison toother dual band circular patch antennas reported so far

Alu et al proposed design method to obtain electricallysmall rectangular patch antennas usingDPS (double positive)ENGmetamaterial juxtaposed layer [3] But such rectangularpatches give broadside null radiation pattern at subwave-length regime as illustrated in Figure 2 of [4] Finally it waspredicted that all these electrically small rectangular antennasloaded with metamaterial can only be good resonators butmay not be good radiators But if the shape is circular[4 5] or elliptical [6] theoretically it is possible to achieveelectrically small size without deterioration of radiationperformance With this concept we developed a properalgorithm in [1] where achieving additional unconventionalmode in metamaterial loaded circular patch antenna hasbeen possible By using the same algorithm here a dualband ENG metamaterial loaded patch antenna has beendesigned Highly directive performance and flexibility intuning frequency are the two prime criteria of this dual bandpatch antenna

In the second section of this paper by using MNG (120583negative) metamaterial in the inner core as substrate insteadof natural dielectric in circular microstrip patch antennadual band performance has been achieved with a reducedsize antenna Apart from conventional TM110 mode hereunconventional TM12057510 (0 lt 120575 lt 1) mode has beenproduced Applying our proposed design algorithm [1] wecan achieve broadside radiation at TM12057510 (0 lt 120575 lt 1) modeand hence achieve a dual band performance with a reducedsize antenna In this sort of metamaterial loaded patchantennas the resonant frequency can be tuned accordingto designerrsquos will But it has been shown that electricallysmall size patch antenna having metamaterial loading is notpracticable without degradation of radiation performance[7 8] In fact the gain performances of such electrically smallantennas degrade rapidly due to the size reduction Howevernearly 35 size reductionmay be possiblewhere gain remainsabove 0 dB [8] In our proposed designed antenna based onour developed algorithm we have obtained around 30 sizereduction with a gain of 22 dB Flexibility in tuning resonant

frequency along with size miniaturization has certainly madethis dual band patch antenna unique from other dual bandantennas reported in current literature

MNGmetamaterial can be fabricated in the laboratory atmicrowave frequencies by using Split Ring Resonators (SRR)and helices whereas thin wired structure placed at a periodicdistance works as negative Epsilon material when the dis-tance between consecutive wires becomes comparable to thewavelength of the propagating electromagnetic wave Overthe years a lot of research has been carried out in ENG loadedpatch antenna but ironically the practical implementation ofENGmetamaterial atmicrowave regime using Lorentzmodelis a tough task [9] However recent advancement of ENGmedium applications in microwave regime urges its practicalimplementation Although the practical application of ENGmedium using Lorentz model in microwave regime is reallya tough one the directivity and gain performance of suchantennas are attractive with conventional size

2 Mathematical Modeling of MetamaterialLoaded Circular Microstrip Patch Antenna

The basic magnetization vector equation for a circular patchantenna can be written as

119860119899

119911(120588 120601 119911) = [119860119898119899119869119898 (119896120588119899120588) + 119861119898119899119884119898 (119896120588119899120588)]

times [119862119899 cos (119898120601) + 119863119899 sin (119898120601)]

times [1198623 cos (119896119911119899119911) + 1198633 sin (119896119911119899119911)]

(1)

But radial component of the electric field can be derived as

119864119899

120588= minus119895

1

120596120576119899120583119899

1205972

120597120588120597119911

(119860119899

119911) (2)

Here 119899 = 1 for region 1 (metamaterial region) and 119899 = 2 forregion 2 (conventional dielectric region)

From boundary conditions (perfect electric wall assump-tion of cavity model)

at 119911 = ℎ 119864120588 = 0 we get 1198633 = 0

and at 119911 = 0 119864120588 = 0 then we get 1198623 = 1

Therefore

119860119899

119911(120588 120601 119911) = [119860119898119899119869119898 (119896120588119899120588) + 119861119898119899119884119898 (119896120588119899120588)]

times [119862119899 cos (119898120601) + 119863119899 sin (119898120601)]

times cos (119896119911119899119911)

(3)

119864119899

120588(120588 120601 119911) = minus119895

119896120588119899119896119911119899

120596120576119899120583119899

times [1198601198981198991198691015840

119898(119896120588119899120588) + 119861119898119899119884

1015840

119898(119896120588119899120588)]

times [119862119899 cos (119898120601) + 119863119899 sin (119898120601)] sin (119896119911119899119911) (4)

International Journal of Antennas and Propagation 3

Generalized equation for the phi component of the electricfield is as follows

119864119899

120601= minus119895

1

120596120576119899120583119899

1

120588

1205972

120597120601120597119911

(119860119899

119911) (5)

By calculation from the equation of 119860119899119911we get

119864119899

120601(120588 120601 119911) = 119895

119896119911119899119898

120588 120596120576119899120583119899

times [119860119898119899119869119898 (119896120588119899120588) + 119861119898119899119884119898 (119896120588119899120588)]

times [minus119862119899 sin (119898120601) + 119863119899 cos (119898120601)] sin (119896119911119899119911) (6)

Finally 119911-component of electric field becomes

119864119899

119911= minus

119895

120596120576119899120583119899

(

1205972

1205971199112+ 1198962

119899)119860119899

119911 (7)

Again calculation from the equation of 119860119899119911yields

119864119899

119911(120588 120601 119911) =minus119895

1198962

120588119899

120596120576119899120583119899

[119860119898119899119869119898 (119896120588119899120588)+119861119898119899119884119898 (119896120588119899120588)]

times [119862119899 cos (119898120601) + 119863119899 sin (119898120601)] cos (119896119911119899119911) (8)

For the magnetic fields component of the cavity 119911-compo-nent of the magnetic field is 0 everywhere

So

119867119899

119911= 0 (9)

Again radial component of the magnetic field is formulatedas

119867119899

120588=

1

120588120583119899

120597119860119899

119911

120597120601

=

119898

120588120583119899

[119860119898119899119869119898 (119896120588119899120588) + 119861119898119899119884119898 (119896120588119899120588)]

times [minus119862119899 sin (119898120601) + 119863119899 cos (119898120601)] cos (119896119911119899119911)

(10)

Finally

119867119899

120601= minus

1

120583119899

120597119860119899

119911

120597120588

(11)

which gives

119867119899

120601= minus

119896120588119899

120583119899

[1198601198981198991198691015840

119898(119896120588119899120588) + 119861119898119899119884

1015840

119898(119896120588119899120588)]

times [119862119899 cos (119898120601) + 119863119899 sin (119898120601)] cos (119896119911119899119911)

(12)

For all the above equations 119869119898 and 1198691015840119898are Bessel functions

of first kind and its derivative denoted by prime order of

119898 119884119898 and 1198841015840119898are Bessel functions of second kind and its

derivative denoted by prime order of119898Now applying boundary condition at the interface that is

at 120588 = 119887 1198641119885= 1198642

119885we get from electric field equations

[

1198962

1205881

12058311205981

119869119898 (1198961205881119887)]1198601198981 minus [

1198962

1205882

12058321205982

119869119898 (1198961205882119887)]1198601198982

minus [

1198962

1205882

12058321205982

119884119898 (1198961205882119887)]1198611198982 = 0

(13)

Again at 120588 = 119887 1198671

120601= 1198672

120601 we get from magnetic field

equations that

[

1198961205881

1205831

1198691015840

119898(1198961205881119887)]1198601198981 minus [

1198961205882

1205832

1198691015840

119898(1198961205882119887)]1198601198982

minus

1198961205882

1205832

1198841015840

119898(1198961205882119887) 1198611198982 = 0

(14)

Finally at 120588 = 119886 1198672120601= 0 and then we get similarly

[

1198961205882

1205832

1198691015840

119898(1198961205882119886)]1198601198982 + [

1198961205882

1205832

1198841015840

119898(1198961205882119886)]1198611198982 = 0 (15)

From the previous three equations that is (13) (14)and (15) we see that the right side is zero So in order tohave solutions the determinant formed by the correspondingmatrix must be equal to 010038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1198962

1205881

12058311205981

119869119898 (1198961205881119887) minus

1198962

1205882

12058321205982

119869119898 (1198961205882119887) minus

1198962

1205882

12058321205982

119884119898 (1198961205882119887)

1198961205881

1205831

1198691015840

119898(1198961205881119887) minus

1198961205882

1205832

1198691015840

119898(1198961205882119887) minus

1198961205882

1205832

1198841015840

119898(1198961205882119887)

0

1198961205882

1205832

1198691015840

119898(1198961205882119886)

1198961205882

1205832

1198841015840

119898(1198961205882119886)

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

= 0

(16)

Solving the above determinant we get

1198961205881

1205981

119869119898 (1198961205881119887)

1198691015840119898(1198961205881119887)

=

1198961205882

1205982

[

119869119898 (1198961205882119886)1198841015840

119898(1198961205882119886) minus 119869

1015840

119898(1198961205882119886)119884119898 (1198961205882119887)

1198691015840119898(1198961205882119887) 119884

1015840119898(1198961205882119886) minus 119869

1015840119898(1198961205882119886)119884

1015840119898(1198961205882119887)

]

(17)

Now for ENG metamaterial

1198961205881 asymp 1198961= 119895120596radic1205831

10038161003816100381610038161205981

1003816100381610038161003816 (18)

And for MNGmetamaterial

1198961205881 asymp 1198961= 119895120596radic1205981

10038161003816100381610038161205831

1003816100381610038161003816 (19)


ENG1205761

h

tg y

z

x120578a

DPS1205762

Dg

Region 1Region 2

a

Figure 1 Geometry of a circular microstrip patch antenna partiallyloaded with metamaterial (ENG) substrate and ground plane withparameters 120578119886 = (56) (20mm) = 112mm 119886 = 20mm ℎ =

43mm 119905119892= 2mm 119863

119892= 40mm 120576

2= 133 120576

1= minus19 (at

42686GHz) 1205832 = 1 1205831 = 1 and feed position from the centre119891119901 = 15mm

Table 1 Selected permittivity and filling ratio for ENG-metamate-rial loading in antenna

Chosen resonantfrequency 119891119903 (GHz) 1205761 (at 119891119903) Filling ratio (120578)

42686 minus190 056

Putting the above relation the dispersion relation forENG metamaterial loaded patch antenna becomes

2radic

12058311205982

1205832

10038161003816100381610038161205981

1003816100381610038161003816

119868119898 (

100381610038161003816100381610038161198961205881119887

10038161003816100381610038161003816)

119868119898minus1 (

100381610038161003816100381610038161198961205881

10038161003816100381610038161003816119887) + 119868119898+1 (

100381610038161003816100381610038161198961205881

10038161003816100381610038161003816119887)

=

119869119898 (1198961205881119887) 1198841015840

119898(1198961205881119886) minus 119869

1015840

119898(1198961205881119886)119884

1015840

119898(1198961205881119887)

1198691015840119898(1198961205882119887) 119884

1015840119898(1198961205882119886) minus 119869

1015840119898(1198961205882119886)119884

1015840119898(1198961205882119887)

(20)

And for MNGmetamaterial the dispersion relation is

minus 2radic

10038161003816100381610038161205831

10038161003816100381610038161205982

12058321205981

119868119898 (

100381610038161003816100381610038161198961205881119887

10038161003816100381610038161003816)

119868119898minus1 (

100381610038161003816100381610038161198961205881

10038161003816100381610038161003816119887) + 119868119898+1 (

100381610038161003816100381610038161198961205881

10038161003816100381610038161003816119887)

=

119869119898 (1198961205881119887) 1198841015840

119898(1198961205881119886) minus 119869

1015840

119898(1198961205881119886)119884

1015840

119898(1198961205881119887)

1198691015840119898(1198961205882119887) 119884

1015840119898(1198961205882119886) minus 119869

1015840119898(1198961205882119886)119884

1015840119898(1198961205882119887)

(21)

By using the above two dispersion relations a MATLABbased parameter optimization algorithm has been developedin [1] In that algorithm the optimized value of metamaterialparameter such as filling ratio permittivity and permeabilityhas been calculated for metamaterial loaded circular patchantennas

30

20

10

0

minus10

minus20

35 4 45 5

Frequency (GHz)

Lorentz model of ENG

Re[120583]Im[120583]

Figure 2 Lorentz dispersive model of ENG for proposed antenna

0

minus5

minus10

minus15

minus20

Frequency (GHz)2 3 4 5

S11 parameter (dB)

Figure 3 11987811 parameter for 20mm circular patch antenna usingENG as core material

3 ENG Metamaterial Loaded Dual BandCircular Patch Antenna

31 Antenna Design Structure and Specifications In circularmicrostrip patch antenna by using ENGas a substrate insteadof regular dielectric we can achieve dual band performanceApart from conventional TM110mode unconventional TM12057510(1 lt 120575 lt 2) mode can be modified

In designing our proposed antenna geometry of a cir-cular patch with metamaterial block as shown in Figure 1has been used With proper choice of filling ratio (120578)ENG metamaterial (1205761) is loaded concentrically with regulardielectric (1205762) In Figure 1 ENG metamaterial is denoted byregion 1 (green) and regular dielectric is denoted by region 2(yellow)The antenna consists of ametallic patch of thickness(119905119901 = 1mm) and radius (119886 = 20mm) at the top A metallicplate placed at the bottom with radius (2 times 119886 = 40mm) and


(a) (b)

Figure 4 3D view of (a) conventional TM110 mode at 36665GHz and (b) unconventional TM12057510 (1 lt 120575 lt 2) modersquos radiation pattern at42686GHz

(a) (b)

Figure 5 Electric field distribution on the 119910 = 0 plane at (a)119891110 = 36665GHz and (b) 11989112057510 (1 lt 120575 lt 2) = 42686GHz

thickness (119905119892 = 2mm) acts as ground This chosen optimumradius and thickness of the ground plate causes maximumreflection from the ground that enhances the directivityConductivity of the metal is selected as 058Meg120590 As a feedwe have used coaxial cable designed to have 119885119901 = 50Ω

characteristic impedance with inner radius of coaxial cable(119903in = 04mm) and outer radius of coaxial cable (119903out =

10456mm) and its position is set at 119891119901 = 15mm from thecenter for achieving goodmatching properties over operatingfrequency range The underneath substrate is filled withconcentric dielectrics with ENG metamaterial as the innercore and DPS material as outer core Dielectric substrateheight is ℎ = 43mm Of all the dielectric parameters 1205762 =131205760 1205832 = 101205830 and 1205831 = 101205830 are chosen as the optimumvalues for these parameters However the rest two controllingparameters that is ENGmetamaterialrsquos permittivity (1205761) andfilling ratio (120578) have been calculated by a MATLAB basedparameter optimization algorithm [1] and with the aid ofdispersive equation (20) developed for ENGmetamaterial InTable 1 those optimum parameters are shown at our desiredresonant frequency of 426GHz

Actually SNG or DNG metamaterials are inherentlydispersive and lossy [10 11] So without using dispersivelossy model the simulated results cannot give proper realisticresults Here we have used Lorentz model for ENG metama-terial dispersive relation

120576 (120596) = 120576infin +

(120576119904 minus 120576infin) 1205962

0

1205962

0minus 1205962minus 119895120596120575

(22)

where 120576infin = 101205760 120576119904 = 1231205760 1205960 = 266Gradsec 119891119903 =426GHz and damping frequency 120575 = 1MHz

Plugging these parameters into (22) dispersive relation ofour desired ENG material should be as in Figure 2

Using all the above stated material and geometric param-eters CSTmicrowave studio [12] simulation gives the follow-ing results 119878-parameter 3D radiation patterns and electricand current distribution (Figures 3ndash6)

32 Resonance and Radiation Characteristics of the AntennaFrom the S11 parameter curve of we see that correspondingreturn losses at 366GHz and 42686GHz frequencies fallwell below minus10 dB that ensures satisfactory resonance forthe antenna structure But satisfactory resonance does notalways guarantee good radiation So in order to ensuregood radiation and thus call it a good radiator we need tolook into its radiation patterns at those particular resonantfrequencies also The radiation patterns obtained at theresonant frequencies indicated at the 11987811 parameter curve ofFigure 3 are shown in Figure 4

From the 3D radiation patterns of the ENG loaded patchantenna (see Figure 4) we see that conventional TM110modeas well as the modified TM12057510 mode (1 lt 120575 lt 2) showssatisfactory 119911-directed radiation (Figures 4(a) and 4(b)) Theconventional TM110 mode has the gain of 945 dB whereasthe gain of the modified mode TM12057510 (1 lt 120575 lt 2) atfrequency 42686GHz is 955 dB which is even higher thanthe conventional mode


(a) (b)

Figure 6 Current distribution on the patch at (a) 119891110 = 36665GHz and (b) 11989112057510 (1 lt 120575 lt 2) = 42686GHz

MNG1205831 DPS1205832

h

tg y

z

x120578a

Dg

Region 1Region 2

a

Figure 7 Geometry of a circular microstrip patch antenna partiallyloaded with metamaterial (MNG) substrate and ground plane withparameters 120578119886 = (56mm) (20mm) = 112mm 119886 = 20mm ℎ =5mm 119905119892 = 2mm 119863119892 = 40mm 1205762 = 133 1205761 = 133 1205832 = 11205831 = minus283 (at 256GHz) and feed position 119891119901 = 15mm

33 Electric Field and Current Distribution From the electricfield distribution at the plane 119910 = 0 it is apparent that incase of conventional TM110 mode electric field flips its signpassing from one side to the other side of the patch thussatisfying the condition for broadside radiation (Figure 5(a))But in case of modified TM12057510 (1 lt 120575 lt 2) mode due to usingmetamaterial phase change of electric field at the ENG-DPSinterface occurs in such a way that the electric field flips fromone side to the other side of the patch as a result of which theelectric field distribution of TM12057510 (1 lt 120575 lt 2) mode lookslike that of TM110mode thus also satisfying the condition forbroadside radiation (Figure 5(b))

Microstrip circular patch antenna theory says that if themetallic patch induced current remains in the same phasepassing from one side to the other side of the patch thatis current distribution remains symmetric around 119910-axis itmust show broadside radiation At (119909 = 0 119910 = 0 119911 = 0) pointmagnetic field distribution from the two opposite current

Lorentz model of MNG

Frequency (GHz)

20

10

0

minus10

minus20

1 15 2 25 3 35 4

Re[120583]Im[120583]

Figure 8 Lorentz dispersive model for proposed MNG loadedantenna

elements reinforce in 119911 direction That is why TM110 modeshows 119911-directed radiation (Figure 6(a)) But any other modedoes not normally show this property What metamaterialdoes is that in our desired frequency at interface of DPS-ENG it causes phase change in such a way that the currentdistribution at that frequency resembles with TM110 modersquoscurrent distribution Figure 6(b) shows current distributionof the patch for TM12057510 (1 lt 120575 lt 2) mode that resembles withTM110 modersquos pattern It is noticeable that despite the smalldimension of the patch the current distribution is closed inelectrically small resonant loops and it resembles the currentdistribution of TM110 mode

4 MNG Metamaterial Loaded Dual BandCircular Patch Antenna

41 AntennaDesign Structure and Specifications In designingour proposed antenna geometry of a circular patch withmetamaterial block as shown in Figure 7 has been used It


0 1 2 3 4 5

0

10

minus30

minus20

minus10

Frequency (GHz)

S11 parameter (dB)

Figure 9 11987811-parameter for 20mm radius circular patch antennausing MNG as core material

is almost similar to the ENG loaded patch structure It alsoconsists of a metallic patch of thickness (119905119901 = 1mm) andradius (119886 = 20mm) at the top A metallic plate placed atthe bottom with radius (2 times 119886 = 40mm) and thickness(119905119892 = 1mm) acts as ground This chosen optimum radiusand thickness of the ground plate causes maximum reflectionfrom the ground that enhances the directivity The metalhas a conductivity of 058Meg120590 As a feed we have usedcoaxial cable designed to have 119885119901 = 50Ω characteristicimpedance with inner radius of coaxial cable (119903in = 04mm)and outer radius of coaxial cable (119903out = 10351mm) and itsposition is set at 119891119901 = 12mm from the center for achievinggood matching properties over operating frequency rangeThe underneath substrate is filled with concentric dielectricswith MNG metamaterial as the inner core and DPS materialas outer core Dielectric substrate height (ℎ = 5mm) isspacious enough so as to allow realistic hosting of split ringresonator (SRR) to construct MNG material [13] Of all thedielectric parameters 1205762 = 131205760 1205832 = 101205830 and 1205761 =

131205760 are chosen as the optimum values for these parametersHowever MNG metamaterialrsquos permeability (1205831) and fillingratio (120578) have been calculated by aMATLAB based parameteroptimization algorithm [1] and with the aid of our deriveddispersive equation (21) for MNG metamaterial Calculatedoptimum permeability and filling ratio are shown in Table 2

We have used Lorentz model for MNG metamaterialdispersive relation

120583 (120596) = 120583infin +

(120583119904 minus 120583infin) 1205962

0

1205962

0minus 1205962minus 119895120596120575

(23)

where 120583infin = 101205830 120583119904 = 151205830 and 1205960 = 1476Gradseccauses resonance at 119891119903 = 256GHz and damping frequency(120575 = 10MHz) Putting these values in (3) we get the disper-sion curve for MNG as shown in Figure 8

42 Resonance and Radiation Characteristics Using allthe above stated material and geometric parameters CSTmicrowave studio [12] simulation gives the following results119878-parameter (Figure 9) 3D radiation patterns and electricfield distribution (Figures 10 and 11)

Table 2 Selected permeability (1205831) and filling ratio (120578) for MNGloading


256 minus283 035

11987811 parameter curve in Figure 9 shows that at frequen-cies 11989112057510 (0 lt 120575 lt 1) = 256GHz 119891110 = 38 GHz resonanceoccurs which causes the corresponding return losses at thesefrequencies to fall well below minus10 dB that ensures satisfactoryresonance Again from Figure 9 it is also evident that whenantenna size is reduced resonant frequency has tomove awayfrom the TM110 frequency which eventually causes to loseits 119911-directed radiation characteristics So it is not alwaysproductive to reduce patch antenna size whimsically But inour study we have found that around 70 size reductionprovides us with nearly minus9 dB gain whereas size reductionthat is

(119891110 minus 11989112057510 (0 lt 120575 lt 1))

119891110

times 100

=

(366GHz minus 256GHz)366GHz

times 100 asymp 30

(24)

provides us 22 dB gainwhich is quite satisfactory for practicalantenna operation This is the maximum allowable limit ofsize reduction with realizable gain performance that we havefound in our study In fact antenna size reduction can beextended up to nearly 35 to get gain over 0 dB

From the 3D radiation patterns of MNG loaded antenna(see Figure 10) we see that conventional TM110 mode as wellas the modified TM12057510 mode (0 lt 120575 lt 1) shows satisfactory119911-directed radiation The conventional mode TM110 has thegain 92 dB (Figure 10(b)) at frequency 38GHz whereas thegain of the modified mode TM12057510 (0 lt 120575 lt 1) at frequency256GHz is 183 dB (Figure 10(a)) which is much lower thanthe conventionalmode So this sort of dual band antenna canbe a suitable choice where low gain and less directive dualband performance is a prior requirement

43 Electric Field Distribution From the electric field distri-bution at the plane 119910 = 0 it is apparent that for conventionalTM110 mode electric field flips its sign passing from one sideto the other side of the patch thus satisfying the conditionfor broadside radiation (Figure 11(b)) But in case of modifiedTM12057510 (0 lt 120575 lt 1) mode due to using metamaterial phasechange of electric field at the MNG-DPS interface occurs insuch a way that the electric field flips from one side to theother side of the patch as a result of which the electric fielddistribution of TM12057510 (0 lt 120575 lt 1) mode looks like that ofTM110 mode thus also satisfying the condition for broadsideradiation (Figure 11(a))

5 Conclusions

In the first section of this paper a novel dual band cir-cular patch antenna with high directivity performance in


(a) (b)

Figure 10 3D view of (a) unconventional TM12057510 (0 lt 120575 lt 1) modersquos radiation pattern at 256GHz and (b) conventional TM110 modersquosradiation pattern at 38 GHz

(a) (b)

Figure 11 Electric field distribution on the 119910 = 0 plane on the metallic patch for the antenna of Figure 7 at (a) 256GHz for unconventionalTM12057510

(0 lt 120575 lt 1) mode and (b) 38GHz for conventional TM110

mode

both bands has been shown Inserting ENG metamaterialprovides us with an additional modified mode with highgain By controlling ENGmetamaterialrsquos filling ratio differentfrequency can be tuned in So this novel antenna designcan be a suitable choice where highly directive gain alongwith userrsquos flexibility in choosing resonant frequencies fordual band antenna purpose is required In the second sectionof this paper a miniaturized size dual band antenna loadedwith MNG metamaterial has been designed In this sort ofantenna since the unconventional mode yields a much lowergain than the conventionalmode one of its dual bands can beused as a substitute for low-gain antenna Actually this sortof antenna can be very effective where the use of less directiveand low-gain small antennas is a prime concern The use ofthis MNG loaded patch antenna is expected to be conducivefor reasonably well signal propagation in some other specialareas such as high multipath interference regions regionshaving frequent obstacles between transmitters and receivershighly dense populated areas and in spacecraft as a backup tothe high-gain antenna

Conflict of Interests

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

References

[1] S Ferdous A Hossain S M H Chowdhury M R CMahdy and M Abdul ldquoReduced and conventional size multi-band circular patch antennas loaded with metamaterialsrdquo IETMicrowaves Antennas amp Propagation vol 7 no 9 pp 768ndash7762013

[2] K-L Wong and G-B Hsieh ldquoDual-frequency circularmicrostrip antenna with a pair of arc-shaped slotsrdquo Microwaveand Optical Technology Letters vol 19 no 6 pp 410ndash412 1998

[3] A Alu F Bilotti N Engheta and L Vegni ldquoSubwavelengthcompact resonant patch antennas loaded with metamaterialsrdquoIEEE Transactions on Antennas and Propagation vol 55 no 1pp 13ndash25 2007

[4] K S ZhengW Y Tam andD B Ge ldquoBroadside subwavelengthmicrostrip antennas partially loaded with metamaterialsrdquo inProceedings of the International Workshop on Metamaterials(META rsquo08) pp 39ndash42 Nanjing China November 2008

[5] F Bilotti A Alu and L Vegni ldquoDesign of miniaturizedmetamaterial patch antennas with 120583-negative loadingrdquo IEEETransactions on Antennas and Propagation vol 56 no 6 pp1640ndash1647 2008

[6] P Y Chen and A Alu ldquoSub-wavelength elliptical patch antennaloaded with 120583-negative metamaterialsrdquo IEEE Transactions onAntennas and Propagation vol 58 no 9 pp 2909ndash2919 2010

[7] J Pruitt and D Strickland ldquoExperimental exploration of meta-material substrate design for an electrically small patch-like


antennardquo inProceedings of the Antennas and Propagation SocietyInternational Symposium (APSURSI rsquo10) IEEE July 2010

[8] S Jahani J Rashed-Mohassel and M Shahabadi ldquoMiniatur-ization of circular patch antennas using MNG metamaterialsrdquoIEEEAntennas andWireless Propagation Letters vol 9 pp 1194ndash1196 2010

[9] J Xiong H Li B Z Wang Y Jin and S He ldquoTheoreticalinvestigation of rectangular patch antenna miniaturizationbased on the DPS-ENG bi-layer super-slow TM waverdquo Progressin Electromagnetics Research vol 118 pp 379ndash396 2011

[10] M R C Mahdy M R A Zuboraj A A N Ovi and M AMatin ldquoAn idea of additional modified modes in rectangularpatch antennas loaded with metamaterialrdquo IEEE Antennas andWireless Propagation Letters vol 10 pp 869ndash872 2011

[11] M Hassan M R C Mahdy G M Hasan and L AkterldquoA novelminiaturized triple-band antennardquo in Proceedings ofthe 7th International Conference on Electrical and ComputerEngineering (ICECE rsquo12) pp 702ndash705 Dhaka BangladeshDecember 2012

[12] CST Microwave Studio CST of America httpwwwcstcom[13] S M H Chowdhury M A Hossain M S Ferdous M R

Chowdhury Mahdy and M A Matin ldquoConceptual and prac-tical realizationof reduced size multi-band circular microstrippatch antenna loaded with MNGmetamaterialrdquo in Proceedingsof the 7th International Conference on Electrical and ComputerEngineering (ICECE rsquo12) pp 834ndash837 Dhaka BangladeshDecember 2012

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014


Shock and Vibration


Mechanical Engineering

Advances in


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of


Distributed Sensor Networks


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Advances inOptoElectronics


Volume 2014

RoboticsJournal of


Chemical EngineeringInternational Journal of


Control Scienceand Engineering

Journal of


Antennas andPropagation




Navigation and Observation



only one that is radius of the patch So with one degree offreedom designers could choose only one resonant frequencyindependently but not both at the same time

In the first section of this paper a novel design ofdual band ENG metamaterial loaded circular patch antennahas been shown Its main feature is in the flexibility ofchoosing both resonant frequencies according to userrsquos willand apart from conventional TM110 mode newly producedunconventional TM12057510 (1 lt 120575 lt 2) mode provides highdirectivity Our designed antenna has two degrees of freedom(radius of the patch and filling ratio of the metamaterial) Inour case the first band that is first ordermode is determinedby the patch geometry only Using ENGmetamaterial insteadof conventional dielectrics causes resonance in between firstand second ordermode frequency For this reason the biggestadvantage here is that the designer can tune the secondband almost anywhere in between conventional first andsecond order mode by just changing the filling ratio of themetamaterial That is why this design provides a great deal offlexibility in choosing resonant frequency in comparison toother dual band circular patch antennas reported so far

Alu et al proposed design method to obtain electricallysmall rectangular patch antennas usingDPS (double positive)ENGmetamaterial juxtaposed layer [3] But such rectangularpatches give broadside null radiation pattern at subwave-length regime as illustrated in Figure 2 of [4] Finally it waspredicted that all these electrically small rectangular antennasloaded with metamaterial can only be good resonators butmay not be good radiators But if the shape is circular[4 5] or elliptical [6] theoretically it is possible to achieveelectrically small size without deterioration of radiationperformance With this concept we developed a properalgorithm in [1] where achieving additional unconventionalmode in metamaterial loaded circular patch antenna hasbeen possible By using the same algorithm here a dualband ENG metamaterial loaded patch antenna has beendesigned Highly directive performance and flexibility intuning frequency are the two prime criteria of this dual bandpatch antenna

In the second section of this paper by using MNG (120583negative) metamaterial in the inner core as substrate insteadof natural dielectric in circular microstrip patch antennadual band performance has been achieved with a reducedsize antenna Apart from conventional TM110 mode hereunconventional TM12057510 (0 lt 120575 lt 1) mode has beenproduced Applying our proposed design algorithm [1] wecan achieve broadside radiation at TM12057510 (0 lt 120575 lt 1) modeand hence achieve a dual band performance with a reducedsize antenna In this sort of metamaterial loaded patchantennas the resonant frequency can be tuned accordingto designerrsquos will But it has been shown that electricallysmall size patch antenna having metamaterial loading is notpracticable without degradation of radiation performance[7 8] In fact the gain performances of such electrically smallantennas degrade rapidly due to the size reduction Howevernearly 35 size reductionmay be possiblewhere gain remainsabove 0 dB [8] In our proposed designed antenna based onour developed algorithm we have obtained around 30 sizereduction with a gain of 22 dB Flexibility in tuning resonant

frequency along with size miniaturization has certainly madethis dual band patch antenna unique from other dual bandantennas reported in current literature

MNGmetamaterial can be fabricated in the laboratory atmicrowave frequencies by using Split Ring Resonators (SRR)and helices whereas thin wired structure placed at a periodicdistance works as negative Epsilon material when the dis-tance between consecutive wires becomes comparable to thewavelength of the propagating electromagnetic wave Overthe years a lot of research has been carried out in ENG loadedpatch antenna but ironically the practical implementation ofENGmetamaterial atmicrowave regime using Lorentzmodelis a tough task [9] However recent advancement of ENGmedium applications in microwave regime urges its practicalimplementation Although the practical application of ENGmedium using Lorentz model in microwave regime is reallya tough one the directivity and gain performance of suchantennas are attractive with conventional size

2 Mathematical Modeling of MetamaterialLoaded Circular Microstrip Patch Antenna

The basic magnetization vector equation for a circular patchantenna can be written as

119860119899

119911(120588 120601 119911) = [119860119898119899119869119898 (119896120588119899120588) + 119861119898119899119884119898 (119896120588119899120588)]

times [119862119899 cos (119898120601) + 119863119899 sin (119898120601)]

times [1198623 cos (119896119911119899119911) + 1198633 sin (119896119911119899119911)]

(1)

But radial component of the electric field can be derived as

119864119899

120588= minus119895

1

120596120576119899120583119899

1205972

120597120588120597119911

(119860119899

119911) (2)

Here 119899 = 1 for region 1 (metamaterial region) and 119899 = 2 forregion 2 (conventional dielectric region)

From boundary conditions (perfect electric wall assump-tion of cavity model)

at 119911 = ℎ 119864120588 = 0 we get 1198633 = 0

and at 119911 = 0 119864120588 = 0 then we get 1198623 = 1

Therefore

119860119899

119911(120588 120601 119911) = [119860119898119899119869119898 (119896120588119899120588) + 119861119898119899119884119898 (119896120588119899120588)]

times [119862119899 cos (119898120601) + 119863119899 sin (119898120601)]

times cos (119896119911119899119911)

(3)

119864119899

120588(120588 120601 119911) = minus119895

119896120588119899119896119911119899

120596120576119899120583119899

times [1198601198981198991198691015840

119898(119896120588119899120588) + 119861119898119899119884

1015840

119898(119896120588119899120588)]

times [119862119899 cos (119898120601) + 119863119899 sin (119898120601)] sin (119896119911119899119911) (4)



119864119899

120601= minus119895

1

120596120576119899120583119899

1

120588

1205972

120597120601120597119911

(119860119899

119911) (5)


119864119899

120601(120588 120601 119911) = 119895

119896119911119899119898

120588 120596120576119899120583119899

times [119860119898119899119869119898 (119896120588119899120588) + 119861119898119899119884119898 (119896120588119899120588)]



119864119899

119911= minus

119895

120596120576119899120583119899

(

1205972

1205971199112+ 1198962

119899)119860119899

119911 (7)


119864119899

119911(120588 120601 119911) =minus119895

1198962

120588119899

120596120576119899120583119899

[119860119898119899119869119898 (119896120588119899120588)+119861119898119899119884119898 (119896120588119899120588)]

times [119862119899 cos (119898120601) + 119863119899 sin (119898120601)] cos (119896119911119899119911) (8)


So

119867119899

119911= 0 (9)


119867119899

120588=

1

120588120583119899

120597119860119899

119911

120597120601

=

119898

120588120583119899

[119860119898119899119869119898 (119896120588119899120588) + 119861119898119899119884119898 (119896120588119899120588)]


(10)

Finally

119867119899

120601= minus

1

120583119899

120597119860119899

119911

120597120588

(11)

which gives

119867119899

120601= minus

119896120588119899

120583119899

[1198601198981198991198691015840

119898(119896120588119899120588) + 119861119898119899119884

1015840

119898(119896120588119899120588)]

times [119862119899 cos (119898120601) + 119863119899 sin (119898120601)] cos (119896119911119899119911)

(12)





at 120588 = 119887 1198641119885= 1198642


[

1198962

1205881

12058311205981

119869119898 (1198961205881119887)]1198601198981 minus [

1198962

1205882

12058321205982

119869119898 (1198961205882119887)]1198601198982

minus [

1198962

1205882

12058321205982

119884119898 (1198961205882119887)]1198611198982 = 0

(13)

Again at 120588 = 119887 1198671

120601= 1198672


equations that

[

1198961205881

1205831

1198691015840

119898(1198961205881119887)]1198601198981 minus [

1198961205882

1205832

1198691015840

119898(1198961205882119887)]1198601198982

minus

1198961205882

1205832

1198841015840

119898(1198961205882119887) 1198611198982 = 0

(14)


[

1198961205882

1205832

1198691015840

119898(1198961205882119886)]1198601198982 + [

1198961205882

1205832

1198841015840

119898(1198961205882119886)]1198611198982 = 0 (15)


1198962

1205881

12058311205981

119869119898 (1198961205881119887) minus

1198962

1205882

12058321205982

119869119898 (1198961205882119887) minus

1198962

1205882

12058321205982

119884119898 (1198961205882119887)

1198961205881

1205831

1198691015840

119898(1198961205881119887) minus

1198961205882

1205832

1198691015840

119898(1198961205882119887) minus

1198961205882

1205832

1198841015840

119898(1198961205882119887)

0

1198961205882

1205832

1198691015840

119898(1198961205882119886)

1198961205882

1205832

1198841015840

119898(1198961205882119886)

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

= 0

(16)


1198961205881

1205981

119869119898 (1198961205881119887)

1198691015840119898(1198961205881119887)

=

1198961205882

1205982

[

119869119898 (1198961205882119886)1198841015840

119898(1198961205882119886) minus 119869

1015840

119898(1198961205882119886)119884119898 (1198961205882119887)

1198691015840119898(1198961205882119887) 119884

1015840119898(1198961205882119886) minus 119869

1015840119898(1198961205882119886)119884

1015840119898(1198961205882119887)

]

(17)


1198961205881 asymp 1198961= 119895120596radic1205831

10038161003816100381610038161205981

1003816100381610038161003816 (18)


1198961205881 asymp 1198961= 119895120596radic1205981

10038161003816100381610038161205831

1003816100381610038161003816 (19)


ENG1205761

h

tg y

z

x120578a

DPS1205762

Dg

Region 1Region 2

a


43mm 119905119892= 2mm 119863

119892= 40mm 120576

2= 133 120576

1= minus19 (at




42686 minus190 056


2radic

12058311205982

1205832

10038161003816100381610038161205981

1003816100381610038161003816

119868119898 (

100381610038161003816100381610038161198961205881119887

10038161003816100381610038161003816)

119868119898minus1 (

100381610038161003816100381610038161198961205881

10038161003816100381610038161003816119887) + 119868119898+1 (

100381610038161003816100381610038161198961205881

10038161003816100381610038161003816119887)

=

119869119898 (1198961205881119887) 1198841015840

119898(1198961205881119886) minus 119869

1015840

119898(1198961205881119886)119884

1015840

119898(1198961205881119887)

1198691015840119898(1198961205882119887) 119884

1015840119898(1198961205882119886) minus 119869

1015840119898(1198961205882119886)119884

1015840119898(1198961205882119887)

(20)


minus 2radic

10038161003816100381610038161205831

10038161003816100381610038161205982

12058321205981

119868119898 (

100381610038161003816100381610038161198961205881119887

10038161003816100381610038161003816)

119868119898minus1 (

100381610038161003816100381610038161198961205881

10038161003816100381610038161003816119887) + 119868119898+1 (

100381610038161003816100381610038161198961205881

10038161003816100381610038161003816119887)

=

119869119898 (1198961205881119887) 1198841015840

119898(1198961205881119886) minus 119869

1015840

119898(1198961205881119886)119884

1015840

119898(1198961205881119887)

1198691015840119898(1198961205882119887) 119884

1015840119898(1198961205882119886) minus 119869

1015840119898(1198961205882119886)119884

1015840119898(1198961205882119887)

(21)


30

20

10

0

minus10

minus20

35 4 45 5

Frequency (GHz)


Re[120583]Im[120583]


0

minus5

minus10

minus15

minus20


S11 parameter (dB)






(a) (b)


(a) (b)






120576 (120596) = 120576infin +

(120576119904 minus 120576infin) 1205962

0

1205962

0minus 1205962minus 119895120596120575

(22)







(a) (b)


MNG1205831 DPS1205832

h

tg y

z

x120578a

Dg

Region 1Region 2

a





Frequency (GHz)

20

10

0

minus10

minus20

1 15 2 25 3 35 4

Re[120583]Im[120583]






0 1 2 3 4 5

0

10

minus30

minus20

minus10

Frequency (GHz)

S11 parameter (dB)





120583 (120596) = 120583infin +

(120583119904 minus 120583infin) 1205962

0

1205962

0minus 1205962minus 119895120596120575

(23)





256 minus283 035


(119891110 minus 11989112057510 (0 lt 120575 lt 1))

119891110

times 100

=


times 100 asymp 30

(24)




5 Conclusions



(a) (b)


(a) (b)



mode




References

















VLSI Design



RotatingMachinery





Shock and Vibration



Advances in







Journal of





SensorsJournal of







Volume 2014

RoboticsJournal of





Journal of










119864119899

120601= minus119895

1

120596120576119899120583119899

1

120588

1205972

120597120601120597119911

(119860119899

119911) (5)


119864119899

120601(120588 120601 119911) = 119895

119896119911119899119898

120588 120596120576119899120583119899

times [119860119898119899119869119898 (119896120588119899120588) + 119861119898119899119884119898 (119896120588119899120588)]



119864119899

119911= minus

119895

120596120576119899120583119899

(

1205972

1205971199112+ 1198962

119899)119860119899

119911 (7)


119864119899

119911(120588 120601 119911) =minus119895

1198962

120588119899

120596120576119899120583119899

[119860119898119899119869119898 (119896120588119899120588)+119861119898119899119884119898 (119896120588119899120588)]

times [119862119899 cos (119898120601) + 119863119899 sin (119898120601)] cos (119896119911119899119911) (8)


So

119867119899

119911= 0 (9)


119867119899

120588=

1

120588120583119899

120597119860119899

119911

120597120601

=

119898

120588120583119899

[119860119898119899119869119898 (119896120588119899120588) + 119861119898119899119884119898 (119896120588119899120588)]


(10)

Finally

119867119899

120601= minus

1

120583119899

120597119860119899

119911

120597120588

(11)

which gives

119867119899

120601= minus

119896120588119899

120583119899

[1198601198981198991198691015840

119898(119896120588119899120588) + 119861119898119899119884

1015840

119898(119896120588119899120588)]

times [119862119899 cos (119898120601) + 119863119899 sin (119898120601)] cos (119896119911119899119911)

(12)





at 120588 = 119887 1198641119885= 1198642


[

1198962

1205881

12058311205981

119869119898 (1198961205881119887)]1198601198981 minus [

1198962

1205882

12058321205982

119869119898 (1198961205882119887)]1198601198982

minus [

1198962

1205882

12058321205982

119884119898 (1198961205882119887)]1198611198982 = 0

(13)

Again at 120588 = 119887 1198671

120601= 1198672


equations that

[

1198961205881

1205831

1198691015840

119898(1198961205881119887)]1198601198981 minus [

1198961205882

1205832

1198691015840

119898(1198961205882119887)]1198601198982

minus

1198961205882

1205832

1198841015840

119898(1198961205882119887) 1198611198982 = 0

(14)


[

1198961205882

1205832

1198691015840

119898(1198961205882119886)]1198601198982 + [

1198961205882

1205832

1198841015840

119898(1198961205882119886)]1198611198982 = 0 (15)


1198962

1205881

12058311205981

119869119898 (1198961205881119887) minus

1198962

1205882

12058321205982

119869119898 (1198961205882119887) minus

1198962

1205882

12058321205982

119884119898 (1198961205882119887)

1198961205881

1205831

1198691015840

119898(1198961205881119887) minus

1198961205882

1205832

1198691015840

119898(1198961205882119887) minus

1198961205882

1205832

1198841015840

119898(1198961205882119887)

0

1198961205882

1205832

1198691015840

119898(1198961205882119886)

1198961205882

1205832

1198841015840

119898(1198961205882119886)

10038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

= 0

(16)


1198961205881

1205981

119869119898 (1198961205881119887)

1198691015840119898(1198961205881119887)

=

1198961205882

1205982

[

119869119898 (1198961205882119886)1198841015840

119898(1198961205882119886) minus 119869

1015840

119898(1198961205882119886)119884119898 (1198961205882119887)

1198691015840119898(1198961205882119887) 119884

1015840119898(1198961205882119886) minus 119869

1015840119898(1198961205882119886)119884

1015840119898(1198961205882119887)

]

(17)


1198961205881 asymp 1198961= 119895120596radic1205831

10038161003816100381610038161205981

1003816100381610038161003816 (18)


1198961205881 asymp 1198961= 119895120596radic1205981

10038161003816100381610038161205831

1003816100381610038161003816 (19)


ENG1205761

h

tg y

z

x120578a

DPS1205762

Dg

Region 1Region 2

a


43mm 119905119892= 2mm 119863

119892= 40mm 120576

2= 133 120576

1= minus19 (at




42686 minus190 056


2radic

12058311205982

1205832

10038161003816100381610038161205981

1003816100381610038161003816

119868119898 (

100381610038161003816100381610038161198961205881119887

10038161003816100381610038161003816)

119868119898minus1 (

100381610038161003816100381610038161198961205881

10038161003816100381610038161003816119887) + 119868119898+1 (

100381610038161003816100381610038161198961205881

10038161003816100381610038161003816119887)

=

119869119898 (1198961205881119887) 1198841015840

119898(1198961205881119886) minus 119869

1015840

119898(1198961205881119886)119884

1015840

119898(1198961205881119887)

1198691015840119898(1198961205882119887) 119884

1015840119898(1198961205882119886) minus 119869

1015840119898(1198961205882119886)119884

1015840119898(1198961205882119887)

(20)


minus 2radic

10038161003816100381610038161205831

10038161003816100381610038161205982

12058321205981

119868119898 (

100381610038161003816100381610038161198961205881119887

10038161003816100381610038161003816)

119868119898minus1 (

100381610038161003816100381610038161198961205881

10038161003816100381610038161003816119887) + 119868119898+1 (

100381610038161003816100381610038161198961205881

10038161003816100381610038161003816119887)

=

119869119898 (1198961205881119887) 1198841015840

119898(1198961205881119886) minus 119869

1015840

119898(1198961205881119886)119884

1015840

119898(1198961205881119887)

1198691015840119898(1198961205882119887) 119884

1015840119898(1198961205882119886) minus 119869

1015840119898(1198961205882119886)119884

1015840119898(1198961205882119887)

(21)


30

20

10

0

minus10

minus20

35 4 45 5

Frequency (GHz)


Re[120583]Im[120583]


0

minus5

minus10

minus15

minus20


S11 parameter (dB)






(a) (b)


(a) (b)






120576 (120596) = 120576infin +

(120576119904 minus 120576infin) 1205962

0

1205962

0minus 1205962minus 119895120596120575

(22)







(a) (b)


MNG1205831 DPS1205832

h

tg y

z

x120578a

Dg

Region 1Region 2

a





Frequency (GHz)

20

10

0

minus10

minus20

1 15 2 25 3 35 4

Re[120583]Im[120583]






0 1 2 3 4 5

0

10

minus30

minus20

minus10

Frequency (GHz)

S11 parameter (dB)





120583 (120596) = 120583infin +

(120583119904 minus 120583infin) 1205962

0

1205962

0minus 1205962minus 119895120596120575

(23)





256 minus283 035


(119891110 minus 11989112057510 (0 lt 120575 lt 1))

119891110

times 100

=


times 100 asymp 30

(24)




5 Conclusions



(a) (b)


(a) (b)



mode




References

















VLSI Design



RotatingMachinery





Shock and Vibration



Advances in







Journal of





SensorsJournal of







Volume 2014

RoboticsJournal of





Journal of









ENG1205761

h

tg y

z

x120578a

DPS1205762

Dg

Region 1Region 2

a


43mm 119905119892= 2mm 119863

119892= 40mm 120576

2= 133 120576

1= minus19 (at




42686 minus190 056


2radic

12058311205982

1205832

10038161003816100381610038161205981

1003816100381610038161003816

119868119898 (

100381610038161003816100381610038161198961205881119887

10038161003816100381610038161003816)

119868119898minus1 (

100381610038161003816100381610038161198961205881

10038161003816100381610038161003816119887) + 119868119898+1 (

100381610038161003816100381610038161198961205881

10038161003816100381610038161003816119887)

=

119869119898 (1198961205881119887) 1198841015840

119898(1198961205881119886) minus 119869

1015840

119898(1198961205881119886)119884

1015840

119898(1198961205881119887)

1198691015840119898(1198961205882119887) 119884

1015840119898(1198961205882119886) minus 119869

1015840119898(1198961205882119886)119884

1015840119898(1198961205882119887)

(20)


minus 2radic

10038161003816100381610038161205831

10038161003816100381610038161205982

12058321205981

119868119898 (

100381610038161003816100381610038161198961205881119887

10038161003816100381610038161003816)

119868119898minus1 (

100381610038161003816100381610038161198961205881

10038161003816100381610038161003816119887) + 119868119898+1 (

100381610038161003816100381610038161198961205881

10038161003816100381610038161003816119887)

=

119869119898 (1198961205881119887) 1198841015840

119898(1198961205881119886) minus 119869

1015840

119898(1198961205881119886)119884

1015840

119898(1198961205881119887)

1198691015840119898(1198961205882119887) 119884

1015840119898(1198961205882119886) minus 119869

1015840119898(1198961205882119886)119884

1015840119898(1198961205882119887)

(21)


30

20

10

0

minus10

minus20

35 4 45 5

Frequency (GHz)


Re[120583]Im[120583]


0

minus5

minus10

minus15

minus20


S11 parameter (dB)






(a) (b)


(a) (b)






120576 (120596) = 120576infin +

(120576119904 minus 120576infin) 1205962

0

1205962

0minus 1205962minus 119895120596120575

(22)







(a) (b)


MNG1205831 DPS1205832

h

tg y

z

x120578a

Dg

Region 1Region 2

a





Frequency (GHz)

20

10

0

minus10

minus20

1 15 2 25 3 35 4

Re[120583]Im[120583]






0 1 2 3 4 5

0

10

minus30

minus20

minus10

Frequency (GHz)

S11 parameter (dB)





120583 (120596) = 120583infin +

(120583119904 minus 120583infin) 1205962

0

1205962

0minus 1205962minus 119895120596120575

(23)





256 minus283 035


(119891110 minus 11989112057510 (0 lt 120575 lt 1))

119891110

times 100

=


times 100 asymp 30

(24)




5 Conclusions



(a) (b)


(a) (b)



mode




References

















VLSI Design



RotatingMachinery





Shock and Vibration



Advances in







Journal of





SensorsJournal of







Volume 2014

RoboticsJournal of





Journal of









(a) (b)


(a) (b)






120576 (120596) = 120576infin +

(120576119904 minus 120576infin) 1205962

0

1205962

0minus 1205962minus 119895120596120575

(22)







(a) (b)


MNG1205831 DPS1205832

h

tg y

z

x120578a

Dg

Region 1Region 2

a





Frequency (GHz)

20

10

0

minus10

minus20

1 15 2 25 3 35 4

Re[120583]Im[120583]






0 1 2 3 4 5

0

10

minus30

minus20

minus10

Frequency (GHz)

S11 parameter (dB)





120583 (120596) = 120583infin +

(120583119904 minus 120583infin) 1205962

0

1205962

0minus 1205962minus 119895120596120575

(23)





256 minus283 035


(119891110 minus 11989112057510 (0 lt 120575 lt 1))

119891110

times 100

=


times 100 asymp 30

(24)




5 Conclusions



(a) (b)


(a) (b)



mode




References

















VLSI Design



RotatingMachinery





Shock and Vibration



Advances in







Journal of





SensorsJournal of







Volume 2014

RoboticsJournal of





Journal of









(a) (b)


MNG1205831 DPS1205832

h

tg y

z

x120578a

Dg

Region 1Region 2

a





Frequency (GHz)

20

10

0

minus10

minus20

1 15 2 25 3 35 4

Re[120583]Im[120583]






0 1 2 3 4 5

0

10

minus30

minus20

minus10

Frequency (GHz)

S11 parameter (dB)





120583 (120596) = 120583infin +

(120583119904 minus 120583infin) 1205962

0

1205962

0minus 1205962minus 119895120596120575

(23)





256 minus283 035


(119891110 minus 11989112057510 (0 lt 120575 lt 1))

119891110

times 100

=


times 100 asymp 30

(24)




5 Conclusions



(a) (b)


(a) (b)



mode




References

















VLSI Design



RotatingMachinery





Shock and Vibration



Advances in







Journal of





SensorsJournal of







Volume 2014

RoboticsJournal of





Journal of









0 1 2 3 4 5

0

10

minus30

minus20

minus10

Frequency (GHz)

S11 parameter (dB)





120583 (120596) = 120583infin +

(120583119904 minus 120583infin) 1205962

0

1205962

0minus 1205962minus 119895120596120575

(23)





256 minus283 035


(119891110 minus 11989112057510 (0 lt 120575 lt 1))

119891110

times 100

=


times 100 asymp 30

(24)




5 Conclusions



(a) (b)


(a) (b)



mode




References

















VLSI Design



RotatingMachinery





Shock and Vibration



Advances in







Journal of





SensorsJournal of







Volume 2014

RoboticsJournal of





Journal of









(a) (b)


(a) (b)



mode




References

















VLSI Design



RotatingMachinery





Shock and Vibration



Advances in







Journal of





SensorsJournal of







Volume 2014

RoboticsJournal of





Journal of

















VLSI Design



RotatingMachinery





Shock and Vibration



Advances in







Journal of





SensorsJournal of







Volume 2014

RoboticsJournal of





Journal of








Dual Band Microstrip Circular Patch

Documents

Transcript of Dual Band Microstrip Circular Patch