research article a modified vivaldi antenna for improved angular...

Hindawi Publishing CorporationInternational Journal of Antennas and PropagationVolume 2013 Article ID 270845 7 pageshttpdxdoiorg1011552013270845

Research ArticleA Modified Vivaldi Antenna for Improved Angular-DependentFidelity Property

Zhi Zeng1 Ke Xu2 Zhaohui Song3 and Qinyu Zhang1

1 Shenzhen Graduate School Harbin Institute of Technology Shenzhen 518055 China2 Graduate School Harbin Institute of Technology Harbin 150001 China3Harbin Institute of Technology Harbin 150001 China

Correspondence should be addressed to Qinyu Zhang zqyhiteducn

Received 23 December 2012 Revised 10 April 2013 Accepted 4 May 2013

Academic Editor Renato Cicchetti

Copyright copy 2013 Zhi Zeng et alThis is an open access article distributed under the Creative CommonsAttribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The analysis design and realization of a modified Vivaldi antenna optimized for time domain fidelity factor in the half-spacelocated in the direction of the antennamain beam are presentedThe proposed antenna shows improved angular-dependent fidelityproperty with respect to the signal transmitted in the main beam direction A substantial increase in the fidelity factor is achievedby utilizing spatial filter effect introduced by adding two dielectric slabs parallel to the antenna substrate By choosing optimaldimensions and location of the slabs the signal waveforms in thementioned half-space are equalized so as to improve the quality ofthe radiated signal waveform in the main beam direction As a result the fidelity property in the half-space is improved greatlyThesimulated andmeasured fidelity factor in the angular operational region is studied and comparedwith experimentalmeasurementsThe ranges with the fidelity factor better than the value of 09 are improved by 95 in H-plane and by 14 in E-plane respectively

1 Introduction

Since Federal Communication Commission (FCC) of USAopened up the frequency range 31ndash106GHz for ultrawide-band (UWB) communication in 2002 UWB has attracteda lot of attention in the wireless communications field fromboth academia and industries [1] UWB system has manyadvantages such as high data rate high spatial resolutionlow-cost transceiver low transmit power and low inter-ference which are quite suited to short-range high-ratecommunication real-time localization and see-through-the-wall and ground penetrating radar [2 3] There have beenlots of investigations about these UWB applications some ofthem have already been commercially used

UWB antenna is one of the key parts in UWB system Awell-designed UWB antenna should have a wide bandwidtha stable gain pattern that ensures a flat magnitude of thetransfer function and a linear phase response characteristicsuseful to minimize the distortion of the transmittedreceivedpulses [4] In [5] a nondirective UWB printed antenna forwireless applications characterized by a low group delay

excellent integration capability with the activepassive com-ponents forming the receivertransmitter front end and goodradiative performances when arranged in arrays has beenpresented In [6] an UWB antenna that rejects extremelysharply the two narrow and closely spaced USWLAN 80211abands is presented while in [7] a compact low dispersiveUWB antenna with sectorial radiation pattern and high frontto back ratio has been proposed

Vivaldi antenna is a kind of tapered slot UWB antennaThe first tapered slot antenna was presented by Lewis et alin 1974 [8] and named Vivaldi antenna by Gibson in 1979[9] Vivaldi antennas are widely used in UWB system forits wide bandwidth high directivity low cross-polarizationand easy fabrication During the past decades many inves-tigators studied Vivaldi antennas The miniaturization andthe bandwidth performances are key requirements in thedesign of modern wideband antennas In this context Hoodpresented a compact Vivaldi antenna fabricated with a394times 346mm substrate which operates in the frequencyband 33ndash106GHz [10] In [11] a slot loaded Vivaldi antennawith bandwidth over 25 1 is presented In addition the pulse

2 International Journal of Antennas and Propagation

W

L

x

z

0

119862119886

1198711

1198771

(a)

0

z

x

119882119891120572

1198712

1198772

(b)

W

L

x

z

0

119862119886

1198711

1198771

(c)

Figure 1 Geometry of the original Vivaldi antenna (a) top view (b)central layer (feed) and (c) bottom view

120593

120579

x

y

z

Antenna0

Figure 2 Vivaldi antenna (the reference frame is indicated in thefigure)

radiation characteristics are quite important for antennasused in the impulse UWB system In [12] the authors studiedthe transient distortion reflection coefficient and cross-polarization level of Vivaldi antenna Vivaldi antenna is quitefitting for UWB antenna array due to its wide bandwidthhigh directivity low cross-polarization and low profileIn the past decades especially after the computer is gettingpowerful enough to analyze antenna arrays many inves-tigations were carried out to improve the performance ofVivaldi antenna arrays As of this time no competing arraytechnology canmatch thewide bandwidth andwide scanning

0 05 1

minus1

minus05

0

05

1

Sign

al st

reng

th (V

)

Time (ns)

Figure 3 Excitation signal

375 4 425 45 475

minus05

0

05

1

Time (ns)

120579 = 0120579 = 30

120579 = 60120579 = 90

minus1

Figure 4 Normalized radiation signal waveform in E-plane (120593 =0∘)

375 4 425 45 475

minus05

0

05

1

Time (ns)

120579 = 0120579 = 30

120579 = 60120579 = 90

minus1

Figure 5 Normalized radiation signal waveform in H-plane (120593 =90∘)

International Journal of Antennas and Propagation 3

impedance performance of Vivaldi antenna arrays which arewidely used in modern electronic warfare system and radarsystem [13 14]

It is quite important for an antenna array element tokeep good performance in a wide spatial region whilethe main beam is scanning In practice all the antennasradiate different signals in different spatial directions Soit is quite important to study the correlation between thesignal radiated and spatial directions both in frequencyand in time domains In [15] the angular distortion of thesignal radiated with respect to that emitted in the mainbeam direction of UWB antennas has been investigated Thecorrelation properties of the pulse signals are determinedby the so-called fidelity factor It can be quantified throughthe analysis of the correlation between the signal in anarbitrary angular direction and the signal in the main beamdirection Usually a fidelity factor which is greater than thevalue of 09 could be considered to be acceptable In [16]Quintero et al introduced system fidelity factor (SFF) tocompare UWB antennas In [3] the half-spherical fidelityfactor pattern measurement results of Bowtie and Vivaldiantenna are presented The fidelity factor pattern describeshow does the signal vary in the different angular directionswith respect to the signal in the main beam direction In [17]Pancera and Wiesbeck introduced an optimization methodbased on the fidelity factor criterion to improve the radiationproperties of Bowtie antennas for medical applications

In this paper a method to improve the fidelity factor ofVivaldi antenna in spatial range is presented The originalVivaldi antenna operates in the frequency band 31ndash106GHzThemodified antenna has two dielectric slabs that are parallelto the antenna substrate These dielectric slabs are located ata distance 119889 from the upper and bottom faces of the antennaThe dielectric slabs act as a spatial filter to reform the signalwaveform Using the GA algorithm the parameters of thedielectric slabs have been optimized producing an incrementof the fidelity factor in a larger angular range The simu-lations of both original antenna and improved antenna areperformed using the commercial electromagnetic simulationsoftware CST MWS The available ranges with the fidelityfactor greater than the value of 09 in H-plane and in E-planeare improved by 95 and 14 respectivelyThe prototypes ofboth original antenna and improved antenna were fabricatedandmeasuredThe numerical results concerning the antennaparameters are found to be in good agreement with theexperimental measurements

2 Improvement of the Vivaldi AntennaFidelity Factor

21 Original Vivaldi Antenna Vivaldi antenna is one kindof classic end-fired directive travelling wave antennas whichhas a tapered slot characterized by a bell-shaped exponentialon it The slot curve on the substrate board becomes widergradually from the narrow end to thewide end and it radiatesthe electromagnetic waves using the corresponding part ofthe slot as constant electric size at the relevant frequency Sotheoretically Vivaldi antenna has an infinite wide frequency

Ws

x

y

0

Dielectric slab

119882119904

1198713

119871119904

(a)

0

y

x

d

t

Ant

enna

Die

lect

ric sl

ab(b)

Figure 6 Geometry of the improved Vivaldi antenna (a) top viewand (b) lateral view

band [5] In practice Vivaldi antenna has a band width betterthan 10 1 and has the features of low cross-polarization andhighly directive radiation patterns over the whole frequencyband In this paper a Vivaldi antenna operating in thefrequency band 31ndash106GHz is investigated The antenna isfabricated on a two-layer substrate with dielectric constantof 35 size of 85mmlowast70mm and each layer thickness of08mm The geometry of the original Vivaldi antenna isshown in Figure 1 with the xz-plane and yz-plane referred toas the E-plane and H-plane respectivelyThe reference frameadopted to express the field quantities is shown in Figure 2The tapers of the antennas are defined as

119909 = plusmn 119888119886sdot exp [119888

119887(119910 minus 10)] (1)

The values of the antenna geometrical parameters are shownin Table 1

A commercial Finite IntegrationTechnique (FIT) electro-magnetic simulation software CST MWS is used to analyzethe radiative performances of the Vivaldi antenna Theantenna is excited by aUWB signal in the frequency band 31ndash106GHz which is a Gaussian pulse in the frequency band 0ndash375GHzmodulated by a cosine wave carrier at the frequency


minus90 minus70 minus50 minus30 3010minus10 50 70 900

010203040506070809

1

Improved antennaOriginal antenna

Fide

lity

fact

or in

H-p

lane

120579 (deg)

(a)

0010203040506070809

1

Fide

lity

fact

or in

E-p

lane

120579 (deg)



(b)

Figure 7 (a) Simulation results of fidelity factor in H-plane (120593 =90∘) and (b) simulation results of fidelity factor in E-plane (120593 = 0∘)

685GHz The waveform of excitation signal is shown inFigure 3 A set of probes have been placed at a distance of1000mm from the antenna on a plane around the antennaand spaced by 5 degrees to detect the time-domain signalradiated by the antenna Since the Vivaldi antenna has quitegood cross-polar property only the copolar radiation signalsare consideredThe normalized signal waveforms at themainbeam direction and other directions computed in the E- andH-planes are shown in Figures 4 and 5 respectively

The fidelity factor between the signal at the main beamdirection 119878

1(119905) and the signal in an arbitrary angular direction

1198782(119905) is defined as the normalized cross-correlation between

them and can be calculated by [3]

fidelity = max120591

int

+infin

minusinfin

1198781(119905 minus 120591) 119878

2(119905) 119889119905

radicint

+infin

minusinfin

10038171003817100381710038171198781(119905)1003817100381710038171003817

2

119889119905 int

+infin

minusinfin

10038171003817100381710038171198781(119905)1003817100381710038171003817

2

119889119905

(2)

(a)

(b)

Figure 8 (a) Picture of the original antenna and (b) picture of theimproved antenna

0 1 2 3 4 5 6 7 8 9 10 11 12 13minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

MeasurementSimulation

|11987811|

(dB)

Frequency (GHz)

Figure 9 |11987811

| of improved antenna

The fidelity factor results computed in E- and H-planes arelisted in Table 2

From Table 2 it appears that the fidelity factor in H-planedegrades quickly as the angle between the antennarsquos mainbeam and the observation point is larger than 35 degrees


Table 1 Geometrical parameters of the original Vivaldi antenna

Parameter Value Unit119882 70 mm119871 85 mm1198711

10 mm1198712

1225 mm119882119891

085 mm1198771

207 mm1198772

33 mm120572 46 ∘

119862119886

04440119862119887

00559

Table 2 Computed fidelity factor of the original antenna inH-planeand E-plane

H-plane (120593 = 90) E-plane (120593 = 0)120579 (degree) Fidelity factor 120579 (degree) Fidelity factor0 1 0 15 099998 5 09918210 099157 10 09915415 099012 15 09904020 098533 20 09875825 097260 25 09826330 094303 30 09762635 088816 35 09732040 077987 40 09700445 062700 45 09731850 046141 50 09755855 053453 55 09728860 053101 60 09615465 044638 65 09322670 034619 70 08661575 033003 75 07383080 035294 80 05776685 035444 85 063184

And this distortion will cause poor performance degradationwhile the beam is scanning out of this range

To improve the signal fidelity factor in a larger angularregion two dielectric slabs with relative dielectric constant120576119903and thickness 119905 which parallel the antenna substrate are

added to the original Vivaldi antenna The distance betweenthe slabs and antenna substrate is 119889 The structure of theproposed antenna is shown in Figure 6

The dielectric slabs play a role as a spatial filter whichhave the angular-dependant effect on the incident wave Soby proper tuning of 120576

119903 119905 and 119889 the quality of the radiated

wave can be restored This effect can be used to optimizethe antenna fidelity factor in the angular operational regionBesides the parameters above the length of the slabs 119871

119904and

the position of the slabs along the 119910-axis 1198713also can be

considered as optimization parameters because they decidethe angular range covered by the slabs

minus80 minus60 minus40 minus20 0 20 40 60 80

minus80

minus60

minus40

minus20

0

20

40

60

80

Azimuth angle (deg)

Elev

atio

n an

gle (

deg)

05

06

07

08

09

092

094

096

098

(a)

05

06

07

08

09

092

094

096

098


minus80

minus60

minus40

minus20

0

20

40

60

80

Azimuth (deg)

Elev

atio

n (d

eg)

(b)

Figure 10 (a) Fidelity factor test results of the original antenna and(b) fidelity factor test results of the improved antenna

3 Antenna Simulation and Measurement

The polyformaldehyde having a relative dielectric constant120576119903= 38 is chosen for the realization of the two dielectric

slabs thanks to its intrinsic characteristics consisting in theeasy machining and good temperature characteristics Thestructure of the Vivaldi antenna is optimized with the goalof the better fidelity factor in H-plane and in E-plane usingGenetic Algorithms optimizer in CSTMWSThe criterion ofthe fidelity factor is set to 09 The optimal parameters of thedielectric slabs are listed in Table 3

The fidelity factor of improved antenna computed in E-plane and H-plane is listed in Table 4 and compared with theresults of the original antenna as shown in Figure 7

The fidelity factor in H-plane has been improved signifi-cantly The available range of the original antenna in H-planeis 70 degrees and the improved antenna has an availablerange wider than 135 degrees which has been improved byabout 97 Besides that the available range in E-plane hasbeen improved from 136 degrees to 156 degrees which is notsuch remarkable as that in H-plane


0010203040506070809

1


Fide

lity

fact

or in

H-p

lane

minus90 minus70 minus50 minus30 3010minus10 50 70 90120579 (deg)

(a)

0

010203040506070809

1

Fide

lity

fact

or in

E-p

lane

120579 (deg)



(b)

Figure 11 (a) Measurement results of fidelity factor in H-plane and(b) measurement results of fidelity factor in E-plane

Table 3 The geometrical parameters of the dielectric slabs

Parameter Value Unit119905 44 mm119882119904

40 mm1198713

43 mm119889 915 mm119871119904

70 mm

The prototypes of the two considered antennas are shownin Figure 8 while the numerical and measurement resultsconcerning the frequency behavior of the parameter |119878

11| of

the new antenna are reported in Figure 9The measurement of fidelity factor was carried out in

an enclosed anechoic chamber The measured antenna isinstalled on a rotating platform A wideband probe is used

Table 4 Fidelity factor of the improved antenna computed in E-plane and H-plane


to receive the transient signal radiated by the antenna undertest when changing the azimuth and the elevation angle ofthe antennaThe fidelity factors calculated in the upper half-plane are plotted in Figure 10Themeasurement results of thefidelity factor in E-plane and H-plane are shown in Figure 11

The original Vivaldi antenna shows its good fidelity factorcharacteristics in a side-ways H-shape area with azimuthangle scanning less than 35 degrees in H-plane and elevationangle less than 65 degrees in E-plane respectively Theimproved Vivaldi antenna shows its good fidelity factorcharacteristics in a cross-shape area with azimuth anglescanning better than 65 degrees in H-plane and elevationangle better than 70 degrees in E-plane respectively whichis extended in horizontal direction significantly

4 Conclusion

In this paper a new method to improve the fidelity factorof a planar Vivaldi UWB antenna has been proposed Twodielectric slabs which play the role of a spatial filter suitableto restore the signal waveform in time domain are added tothe original Vivaldi antenna By tuning the dimensions andthe relative position of the dielectric slabs the fidelity factorin the half space is optimized The angular available range inH-plane with the fidelity factor greater than the value of 09has been improved by 95 and the available angular range inE-plane has been improved by 14

Acknowledgments

The authors would like to express their sincere gratitude toCSTLtd Germany for providing a free package of CSTMWS


softwareThis workwas supported in part by the key programof the National Natural Science Foundation of China underGrant 61032003 and the National Basic Research Program ofChina under Grant 2009CB320402

References

[1] Y Q Zhang Y X Guo and M S Leong ldquoA novel multilayerUWB antenna on LTCCrdquo IEEE Transactions on Antennas andPropagation vol 58 no 9 pp 3013ndash3019 2010

[2] T A Vu M Z Dooghabadi S Sudalaiyandi et al ldquoUWBVivaldi antenna for impulse radio beamformingrdquo inProceedingsof the 27th Norchip Conference pp 1ndash5 Trondeim NorwayNovember 2009

[3] E Pancera T Zwick and W Wiesbeck ldquoSpherical fidelitypatterns of UWB antennasrdquo IEEE Transactions on Antennas andPropagation vol 59 no 6 pp 2111ndash2119 2011

[4] F Gross Frontiers in Antennas Next Generation Design ampEngineering McGraw-Hill 2011

[5] G Cappelletti D Caratelli R Cicchetti and M SimeonildquoA low profile printed drop-shaped dipole antenna for wide-band wireless applicationsrdquo IEEE Transactions on Antennas andPropagation vol 59 no 10 pp 3526ndash3535 2011

[6] A A Gheethan and D E Anagnostou ldquoDual band-reject UWBantenna with sharp rejection of narrow and closely-spacedbandsrdquo IEEETransactions onAntennas and Propagation vol 60no 4 pp 2071ndash2076 2012

[7] L Desrumaux A Godard M Lalande V Bertrand J Andrieuand B Jecko ldquoAn original antenna for transient high powerUWB arrays the Shark antennardquo IEEE Transactions on Anten-nas and Propagation vol 58 no 8 pp 2515ndash2522 2010

[8] L R LewisM Fassett and J Hunt ldquoA broadband stripline arrayelementrdquo in Proceedings of the IEEE Antennas and PropagationSymposium Digest pp 335ndash337 Atlanta Ga USA 1974

[9] Y Li and A Chen ldquoDesign and application of Vivaldi antennaarrayrdquo in Proceedings of the 8th International Symposium onAntennas Propagation andEMTheory (ISAPE rsquo08) pp 267ndash270Kunming China November 2008

[10] A Z Hood T Karacolak and E Topsakal ldquoA small antipodalvivaldi antenna for ultrawide-band applicationsrdquo IEEE Anten-nas and Wireless Propagation Letters vol 7 pp 656ndash660 2008

[11] J Bai S Shi and D W Prather ldquoUltra-wideband slot-loaded antipodal Vivaldi antenna arrayrdquo in Proceedings of theIEEE International Symposium on Antennas and Propagation(APSURSI rsquo11) pp 79ndash81 Spokane Wash USA 2011

[12] J Zhang J Wang and W Hu ldquoAnalysis of UWB signal distor-tion in transmittingreceiving antenna systemsrdquo in Proceedingsof the 9th International Symposium on Antennas Propagationand EM Theory (ISAPE rsquo10) pp 163ndash166 Guangzhou ChinaDecember 2010

[13] K Trott B Cummings R Cavener M Deluca J Biondi andT Sikina ldquoWideband phased array radiatorrdquo in Proceedings ofthe IEEE International Symposium on Phased Array Systems ampTechnology pp 383ndash386 Boston Mass USA October 2003

[14] D Carsenat and C Decroze ldquoUWB antennas beamformingusing passive time-reversal devicerdquo IEEE Antennas andWirelessPropagation Letters vol 11 pp 779ndash782 2012

[15] M A Elmansouri andD S Filipovic ldquoPulse distortion andmit-igation thereof in spiral antenna-based UWB communicationsystemsrdquo IEEE Antennas and Wireless Propagation Letters vol59 no 10 pp 3863ndash3871 2011

[16] G Quintero J F Zurcher and A K Skrivervik ldquoSystem fidelityfactor a new method for comparing UWB antennasrdquo IEEETransactions on Antennas and Propagation vol 59 no 7 pp2502ndash2512 2011

[17] E Pancera and W Wiesbeck ldquoFidelity based optimization ofUWB antenna-radiation for medical applicationsrdquo in Proceed-ings of the IEEE International Symposium on Antennas andPropagation (APSURSI rsquo11) p 2411 Spokane Wash USA July2011

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Control Scienceand Engineering

Journal of



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Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

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Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



W

L

x

z

0

119862119886

1198711

1198771

(a)

0

z

x

119882119891120572

1198712

1198772

(b)

W

L

x

z

0

119862119886

1198711

1198771

(c)

Figure 1 Geometry of the original Vivaldi antenna (a) top view (b)central layer (feed) and (c) bottom view

120593

120579

x

y

z

Antenna0

Figure 2 Vivaldi antenna (the reference frame is indicated in thefigure)

radiation characteristics are quite important for antennasused in the impulse UWB system In [12] the authors studiedthe transient distortion reflection coefficient and cross-polarization level of Vivaldi antenna Vivaldi antenna is quitefitting for UWB antenna array due to its wide bandwidthhigh directivity low cross-polarization and low profileIn the past decades especially after the computer is gettingpowerful enough to analyze antenna arrays many inves-tigations were carried out to improve the performance ofVivaldi antenna arrays As of this time no competing arraytechnology canmatch thewide bandwidth andwide scanning

0 05 1

minus1

minus05

0

05

1

Sign

al st

reng

th (V

)

Time (ns)

Figure 3 Excitation signal

375 4 425 45 475

minus05

0

05

1

Time (ns)

120579 = 0120579 = 30

120579 = 60120579 = 90

minus1

Figure 4 Normalized radiation signal waveform in E-plane (120593 =0∘)

375 4 425 45 475

minus05

0

05

1

Time (ns)

120579 = 0120579 = 30

120579 = 60120579 = 90

minus1

Figure 5 Normalized radiation signal waveform in H-plane (120593 =90∘)







Ws

x

y

0

Dielectric slab

119882119904

1198713

119871119904

(a)

0

y

x

d

t

Ant

enna

Die

lect

ric sl

ab(b)



119909 = plusmn 119888119886sdot exp [119888

119887(119910 minus 10)] (1)





010203040506070809

1


Fide

lity

fact

or in

H-p

lane

120579 (deg)

(a)

0010203040506070809

1

Fide

lity

fact

or in

E-p

lane

120579 (deg)



(b)








int

+infin

minusinfin

1198781(119905 minus 120591) 119878

2(119905) 119889119905

radicint

+infin

minusinfin

10038171003817100381710038171198781(119905)1003817100381710038171003817

2

119889119905 int

+infin

minusinfin

10038171003817100381710038171198781(119905)1003817100381710038171003817

2

119889119905

(2)

(a)

(b)


0 1 2 3 4 5 6 7 8 9 10 11 12 13minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0


|11987811|

(dB)

Frequency (GHz)

Figure 9 |11987811







10 mm1198712

1225 mm119882119891

085 mm1198771

207 mm1198772

33 mm120572 46 ∘

119862119886

04440119862119887

00559









119904and




minus80

minus60

minus40

minus20

0

20

40

60

80

Azimuth angle (deg)

Elev

atio

n an

gle (

deg)

05

06

07

08

09

092

094

096

098

(a)

05

06

07

08

09

092

094

096

098


minus80

minus60

minus40

minus20

0

20

40

60

80

Azimuth (deg)

Elev

atio

n (d

eg)

(b)








0010203040506070809

1


Fide

lity

fact

or in

H-p

lane


(a)

0

010203040506070809

1

Fide

lity

fact

or in

E-p

lane

120579 (deg)



(b)




40 mm1198713

43 mm119889 915 mm119871119904

70 mm


11| of







4 Conclusion


Acknowledgments




References




















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation















Ws

x

y

0

Dielectric slab

119882119904

1198713

119871119904

(a)

0

y

x

d

t

Ant

enna

Die

lect

ric sl

ab(b)



119909 = plusmn 119888119886sdot exp [119888

119887(119910 minus 10)] (1)





010203040506070809

1


Fide

lity

fact

or in

H-p

lane

120579 (deg)

(a)

0010203040506070809

1

Fide

lity

fact

or in

E-p

lane

120579 (deg)



(b)








int

+infin

minusinfin

1198781(119905 minus 120591) 119878

2(119905) 119889119905

radicint

+infin

minusinfin

10038171003817100381710038171198781(119905)1003817100381710038171003817

2

119889119905 int

+infin

minusinfin

10038171003817100381710038171198781(119905)1003817100381710038171003817

2

119889119905

(2)

(a)

(b)


0 1 2 3 4 5 6 7 8 9 10 11 12 13minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0


|11987811|

(dB)

Frequency (GHz)

Figure 9 |11987811







10 mm1198712

1225 mm119882119891

085 mm1198771

207 mm1198772

33 mm120572 46 ∘

119862119886

04440119862119887

00559









119904and




minus80

minus60

minus40

minus20

0

20

40

60

80

Azimuth angle (deg)

Elev

atio

n an

gle (

deg)

05

06

07

08

09

092

094

096

098

(a)

05

06

07

08

09

092

094

096

098


minus80

minus60

minus40

minus20

0

20

40

60

80

Azimuth (deg)

Elev

atio

n (d

eg)

(b)








0010203040506070809

1


Fide

lity

fact

or in

H-p

lane


(a)

0

010203040506070809

1

Fide

lity

fact

or in

E-p

lane

120579 (deg)



(b)




40 mm1198713

43 mm119889 915 mm119871119904

70 mm


11| of







4 Conclusion


Acknowledgments




References




















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











010203040506070809

1


Fide

lity

fact

or in

H-p

lane

120579 (deg)

(a)

0010203040506070809

1

Fide

lity

fact

or in

E-p

lane

120579 (deg)



(b)








int

+infin

minusinfin

1198781(119905 minus 120591) 119878

2(119905) 119889119905

radicint

+infin

minusinfin

10038171003817100381710038171198781(119905)1003817100381710038171003817

2

119889119905 int

+infin

minusinfin

10038171003817100381710038171198781(119905)1003817100381710038171003817

2

119889119905

(2)

(a)

(b)


0 1 2 3 4 5 6 7 8 9 10 11 12 13minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0


|11987811|

(dB)

Frequency (GHz)

Figure 9 |11987811







10 mm1198712

1225 mm119882119891

085 mm1198771

207 mm1198772

33 mm120572 46 ∘

119862119886

04440119862119887

00559









119904and




minus80

minus60

minus40

minus20

0

20

40

60

80

Azimuth angle (deg)

Elev

atio

n an

gle (

deg)

05

06

07

08

09

092

094

096

098

(a)

05

06

07

08

09

092

094

096

098


minus80

minus60

minus40

minus20

0

20

40

60

80

Azimuth (deg)

Elev

atio

n (d

eg)

(b)








0010203040506070809

1


Fide

lity

fact

or in

H-p

lane


(a)

0

010203040506070809

1

Fide

lity

fact

or in

E-p

lane

120579 (deg)



(b)




40 mm1198713

43 mm119889 915 mm119871119904

70 mm


11| of







4 Conclusion


Acknowledgments




References




















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












10 mm1198712

1225 mm119882119891

085 mm1198771

207 mm1198772

33 mm120572 46 ∘

119862119886

04440119862119887

00559









119904and




minus80

minus60

minus40

minus20

0

20

40

60

80

Azimuth angle (deg)

Elev

atio

n an

gle (

deg)

05

06

07

08

09

092

094

096

098

(a)

05

06

07

08

09

092

094

096

098


minus80

minus60

minus40

minus20

0

20

40

60

80

Azimuth (deg)

Elev

atio

n (d

eg)

(b)








0010203040506070809

1


Fide

lity

fact

or in

H-p

lane


(a)

0

010203040506070809

1

Fide

lity

fact

or in

E-p

lane

120579 (deg)



(b)




40 mm1198713

43 mm119889 915 mm119871119904

70 mm


11| of







4 Conclusion


Acknowledgments




References




















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0010203040506070809

1


Fide

lity

fact

or in

H-p

lane


(a)

0

010203040506070809

1

Fide

lity

fact

or in

E-p

lane

120579 (deg)



(b)




40 mm1198713

43 mm119889 915 mm119871119904

70 mm


11| of







4 Conclusion


Acknowledgments




References




















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











References




















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









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