research article broadband circular polarizer based on...

Research ArticleBroadband Circular Polarizer Based on Multilayer GradualFrequency Selective Surfaces

Wei Zhang Jian-ying Li and Ling Wang

School of Electronics and Information Northwestern Polytechnical University Xirsquoan 710072 China

Correspondence should be addressed to Wei Zhang zhangwei19900410163com

Received 17 June 2016 Revised 8 August 2016 Accepted 21 August 2016

Academic Editor Giuseppe Mazzarella

Copyright copy 2016 Wei Zhang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

This paper presents a broadband circular polarizer based on multilayer gradual frequency selective surfaces The unit cell includestwo identical circles and a bar whose dimensions decrease layer by layer with a reduction factor This design can provide a goodphase difference that is close to 90∘ The bandwidth of the polarizer reaches 667 from 79 to 158 GHz which can convert theincident linear polarization waves into circular polarization waves A sample polarizer is fabricated andmeasuredThe results showthat the operation frequency ranges from 775 to 152GHz coinciding with the simulation Meanwhile the working frequency bandcovers the range of 82ndash145 GHz when the incident angle increases to 25∘

1 Introduction

Circular polarizers which converts linear polarization waves(LPWs) to circular polarization waves (CPWs) are of greatimportance in many applications where the diversity ofpolarization is desired [1] For example circular polarizers areapplied in minimizing the effectiveness of Faraday rotationincurred by the ionosphere of the satellite systems [2]Also they can be utilized to mitigate echoes from rain orsuppressing interference in communicational systems [3 4]A variety of polarization converters have already been provennowadays [5] for instance alternate medium plate of var-ious materials [6] four-arm structure [7] lattice structuresutilizing rods or strips [8] and rectangular slot antenna[9] However most of these polarizers are limited by theiroperational bandwidth

It is quite a goodway to get CPWby employing frequencyselective surfaces (FSS) which has been successfully prac-ticed in former circular polarizers Because of the low profileand the sample fabrication FSS is more attractive amongperiodic structures

As discussed in [10] a single layer polarizer is proposedfor remote environmental monitoring which can be conve-niently implemented in the submillimeter wave range The3 dB axial ratios (AR) bandwidth of this polarizer is nearly1175 In [11] the bandwidth increases to 21 based on the

same unit cell geometry The polarizer in [12] is made upof Jerusalem-cross which provides nearly 99 polarizationpurity at the operation frequency yet the bandwidth is only43With a similar high purity [13] offers a dual-band polar-ization convertor based on two concentric rings The totalbandwidth is up to 99 while the insertion loss increasesto 51 dB In [14] the authors found that the insertion losscould be significantly reduced by adding one FSS layer Table 1shows the comparison of these circular polarizers

In this paper a broadband circular polarizer is presentedbased on multilayer gradual frequency selective surfaces(MG-FSS) The AR lower than 3 dB are over the frequencyrange from79GHz to 158GHzMeanwhile the polarizer canobtain the working frequency band over the range of 82ndash145 GHz when the incident angle increases to 25∘

2 Principle of Operation

Polarization of a plane wave is the direction of its electricfield vector which may be in a fixed orientation or mightalter over time CPW is featured by electric field in which thetwo orthogonal parts have the same amplitude and a phasedifference of 90∘ A LPW passes through a polarizer whichoffers such feature between two orthogonal parts In this waya CPW is obtained

Hindawi Publishing CorporationInternational Journal of Antennas and PropagationVolume 2016 Article ID 4928109 5 pageshttpdxdoiorg10115520164928109

2 International Journal of Antennas and Propagation

Table 1 Comparison of circular polarizers

Ref Size of unit cell(times1205823mm3)

Frequency(GHz)

AR lt 3 dBBandwidth ()

[10] 051 times 059 times 001 325 1175[11] 051 times 059 times 001 325 21[12] 033 times 033 times 009 178 43

[13] 056 times 056 times 008 2721 563955 43

[14] 060 times 052 times 003 10 68This paper 03 times 06 times 024 12 667

Ey

Ex

kt

(a)

a

rnc

ln

wn b

(b)

Figure 1 (a) The unit cell of the MG-FSS (b) Geometry of eachlayer

The proposed circular polarizer is shown in Figure 1(a)Each layer consists of two identical circles and a bar in themiddle of the unit We superimpose a four-layer architecturewhich can achieve not only the desired phase differencebut also a good transmission coefficient It should be notedthat the size of the FSS strip in each layer varies graduallyFigure 1(b) presents the front view of the metal strip where119899 denotes the 119899th layer The first is the biggest one and theother three are diminishing according to the reduction factor120578

Consider an incident LPW traveling along the minus119911 direc-tion whose electric field

119894

is slant at 120595 = 45∘ to the 119909-axisThe incident LPW can be decomposed into two even parts inhorizontal and vertical directions accordingly

119894

=

119894

119909

+

119894

119910

= 1198640( + ) 119890

119895119896119911

(1)

where the unit vectors and are parallel and perpendicularto the metal bar respectively Generally the incident LPWcan be decomposed into

119894

119909

and 119894

119910

which are in the samephase andmagnitude Ideally the two parts will be completelytransmitted without reflection and insertion loss One stepfurther the FSS provides an inductive behavior for

119894

119909

mainlybecause of the metal bar in 119909-direction while the FSSbecomes capacitive for

119894

119910

due to the nonmetal in119910-directionThe transmitted wave can also be presented as a sum of

Figure 2 The fabricated polarizer and the four layers of the unitThe size is diminished from the top down

two orthogonal linearly polarized components with equalmagnitudes

119905

=

119905

119909

+

119905

119910

= 1198640(119879119909 + 119879119910) 119890119895119896119911

(2)

where 119879119909= |119879119909|119890119895120593119909 and 119879

119910= |119879119910|119890119895120593119910 are the transmission

coefficients of 119894

119909

and 119894

119910

respectively The metal bar in 119909-direction and the nonmetal in 119910-direction provide differenttransmission characteristics for the two orthogonal electricfield vectors The phase of the 119909-direction part is delayed by120593119909 while that of the 119910-direction part is advanced by 120593

119910Thus

a phase difference Δ120593 = |120593119909minus 120593119910| appears between the two

components at the output of the polarizer If the parameters ofthe polarizer are adjusted to satisfy |119879

119909| = |119879119910| and Δ120593 = 90∘

then CPW can be produced

3 Optimization Design and Manufacturing

The proposed polarizer operates in X-band In the followingexperiments a four-layer polarizer with each layer consistingof 18 times 36 elements is fabricated and tested The metalliclayers are modeled as a 005mm copper film with an electricconductivity 120590 = 58 times 107 Sm The substrate is selectedas Arlon Diclad 880 with a relative permittivity of 22 and adielectric loss tangent of 0009 whose thickness is 119905 = 2mmFigure 2 shows the sample polarizer As shown in Figure 1 thedimensions of the biggest layer are 119886 = 75mm 119887 = 15mm1198971= 25mm 119908

1= 3mm and 119903

1= 24mm The reduction

factor 120578 = 09 which means that the size of the metal stripin one layer reduces to 90 compared to that of the previouslayer while the location is a constant

A vector network analyzer (VNA) is applied to measurethe polarizer which is in connection with the two standardLP horn antennas which radiate electromagnetic waves in abroadband of 7ndash16GHz The horn antennas are aligned formaximumreception and the transmitting one is set to providea LPW whose electric field is oriented 45∘ to the 119909-axis Theprototype has been put in the middle between two antennasBesides all the helpful information of transmission forvarious polarizations can be obtained through transformingthe directions of the two LP horn antennas

International Journal of Antennas and Propagation 3

Δ120593 (sim) Δ120593 (mea)

40

60

80

Δ120593

(deg

)

100

120

10 12 14 168

Frequency (GHz)

minus10

minus8

minus6

minus4

minus2

0

Tran

smiss

ion

coeffi

cien

t (dB

)

Tx (sim)Ty (sim)

Tx (mea)Ty (mea)

Figure 3The simulated andmeasured magnitudes of the transmis-sion coefficients 119879

119909

and 119879119910

and the phase difference Δ120593

In order to better illustrate the polarized conversion of theMG-FSS discussed in the paper the axial ratio is calculated as

AR = [(1119886) cos2120591 + sin 2120591 cosΔ120593 + 119886 sin2120591(1119886) sin2120591 minus sin 2120591 cosΔ120593 + 119886 cos2120591

] (3)

119886 =

100381610038161003816100381610038161003816

119905

119909

100381610038161003816100381610038161003816

100381610038161003816100381610038161003816

119905

119910

100381610038161003816100381610038161003816

(4)

tan 2120591 = 21198861 minus 119886

cosΔ120593 (5)

where |119905

119909

| and |119905

119910

| refer to the maximummagnitudes of thehorizontal and vertical transmission parts in the electric fieldThe inclination angle 120591 of the ellipse can be generated by (5)

The magnitudes of the transmission coefficients 119879119909and

119879119910are shown in Figure 3 as well as the phase difference Δ120593

Due to the measured conclusion for finite units instead ofan infinite periodic structure in simulation there is a littlebit of deflection between the simulated andmeasured resultsFigure 4 shows the simulated and measured AR of the trans-mitted wave A rational agreement between the simulatedand measured results is detected The operation bandwidthof the proposed structure will reach 667 ranging from79GHz to 158GHzThe actual measurement results indicatethat the fabricated device can work as a circular polarizerover the frequency range from 775GHz to 152GHz Thedifferences between numerical simulations and experimentalresults can be explained by the fact that the measured resultsare for the finite elements while the simulation results arefor infinite periodic units Moreover machining toleranceborder effects and slight ellipticity of the incident LPW mayalso deteriorate the measured results

For better illustration polarization ellipses are plottedon the basis of the measure results Eight uniformly spacedfrequency points along the working band are plotted to

AR (sim)AR (mea)

0

1

2

3

4

5

AR

(dB)

8 12 14 1610

Frequency (GHz)

Figure 4 The simulated and measured AR

observe the polarization Figure 5 shows the ellipses of theCPW obtained at 8ndash15GHz with a step of 1 GHz

4 Discussion

41 Oblique Incidence The transmission features of any peri-odic structure would vary according to the change of inci-dence angle 120579inc Different angles of oblique incidence areassessed It can be seen fromFigure 6 that as 120579inc increases thebandwidth varies slightly while the AR changes remarkablyIt is notable that such deterioration proves to be morepronounced for higher frequencies In addition the AR closeto the center frequency is stable The experimental resultsshow that the proposed circular polarizer can make the ARunder 3 dB over the range of 82ndash145 GHz when the incidentangle increases to 25∘

42 Reduction Factor One of themost important parametersin the designed polarizer is the reduction factor 120578 Figure 7displays the simulated variation as 120578 changes from 07 to 1It is clear to see that the reduction factor has a large impacton the performance Circular polarization characteristicsgradually get better with the increase of 120578 However the ARbecomes unsatisfactory when the reduction factor reaches1 It means that the structure could no longer be used as acircular polarizer if the four layers are the same Extensiveexperiments show that themain reason is the phase differenceof the two orthogonal components of the transmitted wavesIn the second section we discuss the relationship betweenthe circular polarization and the phase difference For thisstructure the electromagnetic waves will produce certainphase difference Δ120593

119899through each layer and different size

generates different phase difference When the waves passthrough the entire polarizer the difference between the twoorthogonal components of the transmitted waves Δ120593 is thesuperposition of all Δ120593

119899 It should be noted that Δ120593

119899are not


8GHz 9GHz 10 GHz 11 GHz

12 GHz 13 GHz 14 GHz 15 GHz

Figure 5 Polarization ellipses of the proposed polarizer based on the measure results

120579inc = 0∘

120579inc = 5∘

120579inc = 10∘

120579inc = 15∘

120579inc = 20∘

120579inc = 25∘

10 12 14 168

Frequency (GHz)

0

2

4

6

8

Mea

sure

d A

R (d

B)


identical to each other because of the coupling of layers andtheir different dimensions

According to the simulation results the waveforms ofthe two orthogonal waves through each layer are presentedFigure 8 shows the waveforms at 12GHz when 120578 = 09 and120578 = 1 respectively 119864119894

119909

is the incident wave 119864119899119909

and 119864119899119910

(119899 =1 2 3) denote the electric fields through the 119899th layer inthe 119909 direction and 119910 direction respectively 119864119905

119909

representsthe electric field through the fourth layer which is also thetransmittedwave Figure 8 displays that periodic units of eachlayer produce discrepant effect on the two parts When thewaves pass through the fourth layer Δ120593 approximates 90∘ if

120578 = 07

120578 = 08

120578 = 09

120578 = 10

0

2

4

6

8

10

Sim

ulat

ed A

R (d

B)

8 12 14 1610

Frequency (GHz)

Figure 7 The simulated variation as the reduction factor

120578 = 09 In this way a LPW can be successfully convertedinto a CPW If all the layers are the sameΔ120593 is only about 55∘Therefore the structure cannot be used as a circular polarizerany more

It is worth noting that in the process of the experimentwe also found that the proposed polarizer does not existpositively or negatively That is whether the propagation ofelectromagnetic waves is +119911 or minus119911 the results are the same

5 Conclusion

A broadband circular polarizer based on multilayer gradualfrequency selective surfaces has been presented in this paper


Eix

E1x

E2x

E3x

0 180 270 36090

Etx

Eiy

E1y

E2y

E3y

270 36090 1800

Ety

(a)

Eix

E1x

E2x

E3x

90 180 270 3600

Etx

Eiy

E1y

E2y

E3y

270 36090 1800

Ety

(b)

Figure 8 The waveforms at 12GHz (a) reduction factor is 09 (b) reduction factor is 1

The investigated results show that the 3 dB AR bandwidth forthe proposed polarizer reaches 667 at normal incidencefrom79 to 158GHzAlso a sample polarizer is fabricated andtestedThemeasured results show that the sample can operatefrom 775 to 152 GHz which is in a reasonable agreementwith simulation resultsMeanwhile the polarizer can obtain aworking frequency band over the range of 82ndash145GHzwhenthe incident angle is as high as 25∘

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

This work was supported in part by the National NaturalScience Foundation of China (nos 61271416 and 61301093)the Fundamental Research Funds for the Central Universities(no 3102014KYJD027) andNPU Foundation for Fundamen-tal Research (no JCY20130132) The authors would like tothank Wei Kun and Xu Rui for their kind assistance with thetest

References

[1] K S Min J Hirokawa K Sakurai and M Ando ldquoSingle-layerdipole array for linear-to-circular polarisation conversion ofslotted waveguide arrayrdquo Microwaves Antennas and Propaga-tion vol 143 no 13 pp 211ndash216 1996

[2] G Maral and M Bousquet Satellite Communications Systems-SystemsTechniques and Technology JohnWiley amp Sons SussexUK 5th edition 2009

[3] G Liu L Xu and Y Wang ldquoModified dual-band stacked cir-cularly polarized microstrip antennardquo International Journal ofAntennas and Propagation vol 2013 Article ID 382958 5 pages2013

[4] C Liu A Yan C Yu and T Xu ldquoImprovement on a 2times 2 ele-ments high-gain circularly polarized antenna arrayrdquo Interna-tional Journal of Antennas and Propagation vol 2015 Article ID252717 8 pages 2015

[5] C Dietlein A Luukanen Z Popovic and E Grossman ldquoA W-band polarization converter and isolatorrdquo IEEE Transactions onAntennas and Propagation vol 55 no 6 pp 1804ndash1809 2007

[6] J Bornemann ldquoComputer-aided design of multilayered dielec-tric frequency-selective surfaces for circularly polarized mil-limeter-wave applicationsrdquo IEEE Transactions on Antennas andPropagation vol 41 no 11 pp 1588ndash1591 1993

[7] S X Ta and I Park ldquoDual-band operation of a circularly polar-ized four-arm curl antenna with asymmetric arm lengthrdquo Inter-national Journal of Antennas and Propagation vol 2016 ArticleID 3531089 10 pages 2016

[8] D S Lerner ldquoA wave polarization converter for circular polar-izationrdquo IEEE Transactions on Antennas and Propagation vol13 no 1 pp 3ndash7 1965

[9] B Li Y Ding and Y-Z Yin ldquoA novel dual-band circularlypolarized rectangular slot antennardquo International Journal ofAntennas and Propagation vol 2016 Article ID 9071610 8pages 2016

[10] M Euler V Fusco R Cahill and R Dickie ldquo325GHz singlelayer sub-millimeter wave FSS based split slot ring linear tocircular polarization convertorrdquo IEEE Transactions on Antennasand Propagation vol 58 no 7 pp 2457ndash2459 2010

[11] M Euler V Fusco R Dickie R Cahill and J Verheggen ldquoSub-mm wet etched linear to circular polarization FSS based polar-ization convertersrdquo IEEE Transactions on Antennas and Propa-gation vol 59 no 8 pp 3103ndash3106 2011

[12] I Sohail Y Ranga K P Esselle and S G Hay ldquoA linear tocircular polarization converter based on Jerusalem-Cross fre-quency selective surfacerdquo in Proceedings of the 7th EuropeanConference on Antennas and Propagation (EuCAP rsquo13) pp 2141ndash2143 Gothenburg Sweden April 2013

[13] Y Ranga L Matekovits S G Hay and T S Bird ldquoAn ani-sotropic impedance surface for dual-band linear-to-circulartransmission polarization convertorrdquo in Proceedings of theInternational Workshop on Antenna Technology (iWAT rsquo13) pp47ndash50 Karlsruhe Germany March 2013

[14] M Euler V Fusco R Cahill and R Dickie ldquoComparison offrequency-selective screen-based linear to circular split-ringpolarisation convertorsrdquo IET Microwaves Antennas and Prop-agation vol 4 no 11 pp 1764ndash1772 2010

International Journal of

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RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

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



Table 1 Comparison of circular polarizers

Ref Size of unit cell(times1205823mm3)

Frequency(GHz)

AR lt 3 dBBandwidth ()

[10] 051 times 059 times 001 325 1175[11] 051 times 059 times 001 325 21[12] 033 times 033 times 009 178 43

[13] 056 times 056 times 008 2721 563955 43

[14] 060 times 052 times 003 10 68This paper 03 times 06 times 024 12 667

Ey

Ex

kt

(a)

a

rnc

ln

wn b

(b)

Figure 1 (a) The unit cell of the MG-FSS (b) Geometry of eachlayer

The proposed circular polarizer is shown in Figure 1(a)Each layer consists of two identical circles and a bar in themiddle of the unit We superimpose a four-layer architecturewhich can achieve not only the desired phase differencebut also a good transmission coefficient It should be notedthat the size of the FSS strip in each layer varies graduallyFigure 1(b) presents the front view of the metal strip where119899 denotes the 119899th layer The first is the biggest one and theother three are diminishing according to the reduction factor120578

Consider an incident LPW traveling along the minus119911 direc-tion whose electric field

119894

is slant at 120595 = 45∘ to the 119909-axisThe incident LPW can be decomposed into two even parts inhorizontal and vertical directions accordingly

119894

=

119894

119909

+

119894

119910

= 1198640( + ) 119890

119895119896119911

(1)

where the unit vectors and are parallel and perpendicularto the metal bar respectively Generally the incident LPWcan be decomposed into

119894

119909

and 119894

119910

which are in the samephase andmagnitude Ideally the two parts will be completelytransmitted without reflection and insertion loss One stepfurther the FSS provides an inductive behavior for

119894

119909

mainlybecause of the metal bar in 119909-direction while the FSSbecomes capacitive for

119894

119910

due to the nonmetal in119910-directionThe transmitted wave can also be presented as a sum of

Figure 2 The fabricated polarizer and the four layers of the unitThe size is diminished from the top down

two orthogonal linearly polarized components with equalmagnitudes

119905

=

119905

119909

+

119905

119910

= 1198640(119879119909 + 119879119910) 119890119895119896119911

(2)

where 119879119909= |119879119909|119890119895120593119909 and 119879

119910= |119879119910|119890119895120593119910 are the transmission

coefficients of 119894

119909

and 119894

119910

respectively The metal bar in 119909-direction and the nonmetal in 119910-direction provide differenttransmission characteristics for the two orthogonal electricfield vectors The phase of the 119909-direction part is delayed by120593119909 while that of the 119910-direction part is advanced by 120593

119910Thus

a phase difference Δ120593 = |120593119909minus 120593119910| appears between the two

components at the output of the polarizer If the parameters ofthe polarizer are adjusted to satisfy |119879

119909| = |119879119910| and Δ120593 = 90∘

then CPW can be produced

3 Optimization Design and Manufacturing

The proposed polarizer operates in X-band In the followingexperiments a four-layer polarizer with each layer consistingof 18 times 36 elements is fabricated and tested The metalliclayers are modeled as a 005mm copper film with an electricconductivity 120590 = 58 times 107 Sm The substrate is selectedas Arlon Diclad 880 with a relative permittivity of 22 and adielectric loss tangent of 0009 whose thickness is 119905 = 2mmFigure 2 shows the sample polarizer As shown in Figure 1 thedimensions of the biggest layer are 119886 = 75mm 119887 = 15mm1198971= 25mm 119908

1= 3mm and 119903

1= 24mm The reduction

factor 120578 = 09 which means that the size of the metal stripin one layer reduces to 90 compared to that of the previouslayer while the location is a constant

A vector network analyzer (VNA) is applied to measurethe polarizer which is in connection with the two standardLP horn antennas which radiate electromagnetic waves in abroadband of 7ndash16GHz The horn antennas are aligned formaximumreception and the transmitting one is set to providea LPW whose electric field is oriented 45∘ to the 119909-axis Theprototype has been put in the middle between two antennasBesides all the helpful information of transmission forvarious polarizations can be obtained through transformingthe directions of the two LP horn antennas


Δ120593 (sim) Δ120593 (mea)

40

60

80

Δ120593

(deg

)

100

120

10 12 14 168

Frequency (GHz)

minus10

minus8

minus6

minus4

minus2

0

Tran

smiss

ion

coeffi

cien

t (dB

)

Tx (sim)Ty (sim)

Tx (mea)Ty (mea)


119909

and 119879119910




] (3)

119886 =

100381610038161003816100381610038161003816

119905

119909

100381610038161003816100381610038161003816

100381610038161003816100381610038161003816

119905

119910

100381610038161003816100381610038161003816

(4)

tan 2120591 = 21198861 minus 119886

cosΔ120593 (5)

where |119905

119909

| and |119905

119910






AR (sim)AR (mea)

0

1

2

3

4

5

AR

(dB)

8 12 14 1610

Frequency (GHz)



4 Discussion






119899are not





120579inc = 0∘

120579inc = 5∘

120579inc = 10∘

120579inc = 15∘

120579inc = 20∘

120579inc = 25∘

10 12 14 168

Frequency (GHz)

0

2

4

6

8

Mea

sure

d A

R (d

B)




119909


and 119864119899119910


119909


120578 = 07

120578 = 08

120578 = 09

120578 = 10

0

2

4

6

8

10

Sim

ulat

ed A

R (d

B)

8 12 14 1610

Frequency (GHz)




5 Conclusion



Eix

E1x

E2x

E3x

0 180 270 36090

Etx

Eiy

E1y

E2y

E3y

270 36090 1800

Ety

(a)

Eix

E1x

E2x

E3x

90 180 270 3600

Etx

Eiy

E1y

E2y

E3y

270 36090 1800

Ety

(b)



Competing Interests


Acknowledgments


References

















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Δ120593 (sim) Δ120593 (mea)

40

60

80

Δ120593

(deg

)

100

120

10 12 14 168

Frequency (GHz)

minus10

minus8

minus6

minus4

minus2

0

Tran

smiss

ion

coeffi

cien

t (dB

)

Tx (sim)Ty (sim)

Tx (mea)Ty (mea)


119909

and 119879119910




] (3)

119886 =

100381610038161003816100381610038161003816

119905

119909

100381610038161003816100381610038161003816

100381610038161003816100381610038161003816

119905

119910

100381610038161003816100381610038161003816

(4)

tan 2120591 = 21198861 minus 119886

cosΔ120593 (5)

where |119905

119909

| and |119905

119910






AR (sim)AR (mea)

0

1

2

3

4

5

AR

(dB)

8 12 14 1610

Frequency (GHz)



4 Discussion






119899are not





120579inc = 0∘

120579inc = 5∘

120579inc = 10∘

120579inc = 15∘

120579inc = 20∘

120579inc = 25∘

10 12 14 168

Frequency (GHz)

0

2

4

6

8

Mea

sure

d A

R (d

B)




119909


and 119864119899119910


119909


120578 = 07

120578 = 08

120578 = 09

120578 = 10

0

2

4

6

8

10

Sim

ulat

ed A

R (d

B)

8 12 14 1610

Frequency (GHz)




5 Conclusion



Eix

E1x

E2x

E3x

0 180 270 36090

Etx

Eiy

E1y

E2y

E3y

270 36090 1800

Ety

(a)

Eix

E1x

E2x

E3x

90 180 270 3600

Etx

Eiy

E1y

E2y

E3y

270 36090 1800

Ety

(b)



Competing Interests


Acknowledgments


References

















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













120579inc = 0∘

120579inc = 5∘

120579inc = 10∘

120579inc = 15∘

120579inc = 20∘

120579inc = 25∘

10 12 14 168

Frequency (GHz)

0

2

4

6

8

Mea

sure

d A

R (d

B)




119909


and 119864119899119910


119909


120578 = 07

120578 = 08

120578 = 09

120578 = 10

0

2

4

6

8

10

Sim

ulat

ed A

R (d

B)

8 12 14 1610

Frequency (GHz)




5 Conclusion



Eix

E1x

E2x

E3x

0 180 270 36090

Etx

Eiy

E1y

E2y

E3y

270 36090 1800

Ety

(a)

Eix

E1x

E2x

E3x

90 180 270 3600

Etx

Eiy

E1y

E2y

E3y

270 36090 1800

Ety

(b)



Competing Interests


Acknowledgments


References

















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Eix

E1x

E2x

E3x

0 180 270 36090

Etx

Eiy

E1y

E2y

E3y

270 36090 1800

Ety

(a)

Eix

E1x

E2x

E3x

90 180 270 3600

Etx

Eiy

E1y

E2y

E3y

270 36090 1800

Ety

(b)



Competing Interests


Acknowledgments


References

















RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









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