Electrically small planar antenna for circular polarization

Johan Herman Huysamen

Thesis presented in partial fullment of the requirements for

the degree of Master of S ien e in Engineering (Ele troni

Engineering with Computer S ien e) at the University of

Stellenbos h

Departmentof Ele tri and Ele troni Engineering

University of Stellenbos h

Private Bag X1,7602 Matieland, SouthAfri a

De laration

I, the undersigned, hereby de larethatthe work ontainedinthis thesisis myown

originalwork and that I havenot previously inits entirety or inpart submitted it

at any university for a degree.

Signature: ...

J.H. Huysamen

Abstra t

Ele tri ally Small Planar Antenna for Cir ular Polarization

J.H. Huysamen

Department of Ele tri and Ele troni Engineering

University of Stellenbos h

Private Bag X1, 7602 Matieland,South Afri a

Thesis: MS Eng (Ele troni Eng with CS)

De ember 2006

The designofanele tri allysmallplanarantennafor ompa t ir ularpolarization

ispresented. Afteranin-depthstudy ofthe performan e limitationsonele tri ally

smallantennasandaninvestigationintotheworkingofvariousexistingele tri ally

small antennas, the design, simulation and measurement of the proposed antenna

Uittreksel

Elektries Klein Platvlak Antenna vir Sirkulêr e Polarisasie

(Ele tri ally Small PlanarAntennafor Cir ular Polarization)

J.H. Huysamen

Departement Elektries en Elektroniese Ingenieurswese

Universiteitvan Stellenbos h

PrivaatsakX1, 7602 Matieland,Suid Afrika

Tesis: MS Ing (Elektroniese Ing met RW)

Desember 2006

Die ontwerp van 'n elektries klein platvlak antenna vir kompakte sirkulêre

polar-isasie word voorgestel. Na 'n studie van die beperkte werkve rrigting van elektries

kleinantennasen'nondersoeknadiewerkingvanverske iebestaandeelektriesklein

antennas, word die ontwerp, simulasie en meting van die voorgestelde antenna in

A knowledgements

I would like to express my sin ere gratitude to the following people and

organisa-tions

Prof. Palmer forhisinsightand support and forour informativedis ussions,

Omnipless for their nan ialsupport,

Wessel Croukamp from SED for the onstru tionof all antennas,

My parents fortheir support throughout my a ademi areer and

Dedi ations

Contents De laration i Abstra t ii Uittreksel iii A knowledgements iv Dedi ations v Contents vi

List of Figures viii

List of Tables xi

1 Introdu tion 1

2 Fundamental limitations in small antennas 3

2.1 Introdu tion . . . 3

2.2 Relative size . . . 4

2.3 Bandwidth and radiationQ . . . 4

2.4 Gain . . . 17

2.5 E ien y . . . 20

3 Ele tri ally small antennas 26 3.1 Introdu tion . . . 26

3.4 Diele tri ally loadedpat h antenna . . . 35

3.5 Shorted probe fed mi rostripantenna . . . 37

3.6 Planar inverted-F antenna . . . 38

4 Design of a sequentially rotated PIFA for ir ular polarization 41 4.1 Introdu tion . . . 41

4.2 Spe i ations . . . 41

4.3 Proposed design . . . 41

4.4 Ee t of the shortingpin as ompared toa shortingplate . . . 42

4.5 Ee t of foldingthe antenna body . . . 44

4.6 Sequential rotationfor ir ularpolarization. . . 45

4.7 Design of the feednetwork . . . 46

5 Simulated and measured results of the sequentially rotated PIFA 50 5.1 Introdu tion . . . 50

5.2 Simulation . . . 50

5.3 Constru tion . . . 54

5.4 Measurement . . . 56

5.5 Results . . . 58

5.6 Q of the single folded PIFA . . . 63

5.7 Arraying the antenna element . . . 66

List of Figures

2.1 S hemati diagramof a verti ally polarized omni-dire tionalantenna. 5

2.2 Equivalent ir uit of a verti ally polarized omni-dire tionalantenna. . 6

2.3 Equivalent ir uit of ele tri dipole.

a

is the radius of the sphereand

c

isthe speed of light. . . 8

2.4 Equivalent ir uit of

T M

n

spheri al wave.

a

is the radius of the sphere and

c

is the speed of light. . . 8

2.5 Qfor ele tri allysmall antennas as dened by Chu. . . 10

2.6 Qfor ele tri allysmall antennas as dened by M Lean. . . 14

2.7 Normal gain for ele tri ally small antennas. . . 19

2.8 Per entage e ien yforaluminiumand opperantennasversusrelative size. The approximationbe omes invalidfor

kr > 1

.. . . 22

2.9 S hemati of antenna with mat hing network. . . 23

3.1 Quarter-wave monopole antenna. . . 27

3.2 Folded monopoleantenna . . . 27

3.3 Simulated

s

11

of the quarter-wave and folded monopole antennas . . . 28

3.4 Simulated

s

11

for the folded monopole and top-loadedfolded monopole antennas. . . 28

3.5 Goubau's broad-band multi-element monopoleantenna. . . 29

3.6 Dimensionsof the simulated Goubau antennain m. . . 30

3.7 Simulated

s

11

of the Goubauantenna. . . 31

3.8 Design of the ele tri ally small planarwire antenna. . . 32

3.9 Dimensionsof antenna A in mm. . . 32

3.10 Simulated

s

11

for antennaA of gure 3.9 . . . 33

3.13 Cir ularpat hsize against

ǫ

r

for

f

r

= 1.6GHz

and

h = 1.588mm

. . . . 36

3.14 Simulated

s

11

for ir ular pat h antennas with various values of

ǫ

r

and

f

r

= 1.6GHz

and

h = 1.588mm

.. . . 36

3.15 S hemati of probe-fedpat hwith shorting post. . . 37

3.16 Simulated

s

11

of the probe-fedpat hwith shorting post. . . 38

3.17 E-eld patternfor half-wavemi rostrippat h antenna. . . 39

3.18 Simulated

s

11

for the

λ

2

pat h and the

λ

4

PIFA . . . 40

4.1 Finaldesign. . . 42

4.2 Simulated

s

11

of the pin-shortened and plate-shortened PIFA showing the redu tion in resonantfrequen y. . . 43

4.3 Unfolded and folded versions of the PIFA. . . 44

(a) Unfolded . . . 44

(b) Folded . . . 44

4.4 Simulated

s

11

for the unfolded and folded PIFA's. . . 45

4.5 Sequential rotationof the four elements. . . 46

4.6 Rotatingeld ve tor. . . 46

4.7 Layout of the feed network. . . 47

4.8 Simulated relative gain from input to ea h of the four arms of the feed network. . . 48

4.9 Simulated relativephase frominput toea hof thefourarms ofthe feed network. . . 49

5.1 FEKOmodel of the antenna. Dimensions inm. . . 51

5.2 Simulated Right-hand (RHP)and Left-hand (LHP)polarized gain ver-sus radiationangle.. . . 52

5.3 Simulated

s

11

for singlePIFA element. . . 52

5.4 Simulated

s

11

of the antenna onne ted tothe feed network. . . 53

5.5 Final onstru ted antenna. . . 54

5.6 Antenna with ondu tive groundplane. . . 55

5.7 Measured

s

11

of the antenna input versus frequen y. . . 57 5.8 MeasuredRight-hand(RHP)andLeft-hand(LHP)polarizedgainversus

5.9 Measured and simulated right-hand and left-hand ir ularly polarized

gain againsttheta at the enter frequen y of

1.541GHz

. . . 59 5.10 Measuredandsimulatedright-handandleft-handpolarizedgainagainst

theta atthe upper limitof the frequen y band at

1.562GHz

. . . 60 5.11 Measured and simulated

s

11

forthe antenna. . . 61 5.12 Simulated

s

11

forthe antenna with aninnite and anite groundplane. 62 5.13 Equivalent ir uit for the single folded PIFA. . . 63

5.14 Simulated impedan e and impedan e of the equivalent ir uit for the

single folded PIFA. . . 64

5.15 Q versus relative size for the folded PIFA and other ele tri ally small

antennas againstthe limitsproposed by Chu and M lean. . . 65

5.16 Simulationmodel of 9-element re tangulararray. . . 66

5.17 Right-handpolarizedgainforthesingleelementand the9-element

re t-angulararray phase steered to

θ = 45

◦

. . . 67

5.18 Right-handpolarizedgainforthesingleelementand the9-element

re t-angulararray phase steered to

θ = 85

◦

List of Tables

Chapter 1

Introdu tion

The obje tiveis to design anele tri allysmall ir ularly polarized pat h-type

ele-ment tobe used in aphase-steered array antenna.

Pat h antennas are onsidered as physi ally onstrained be ause of their limited

height. It is this limitation in height that makes these antennas ideal for use on

air raft as their low prole redu es the aerodynami drag they produ e. In the

defen e industry this low prole has the added advantage of redu ing the radar

signature of the air raft.

Thisredu tioninheightmakesthepat hantennaaninherentlynarrow-band

stru -ture. Further redu tion in the overall size of the pat h will have a signi antly

detrimental ee t on the bandwidth and this, along with the redu ed e ien y, is

one of the main on erns inthe designof ele tri ally small pat h antennas.

An intensive study of the theoreti al ee ts of antenna size on the performan e

of ele tri ally small antennas is presented. The ee t of antenna size on gain,

bandwidth and e ien y is onsidered and the on ept of fundamental limits on

these three performan e indi esis presented.

Next various ele tri ally small planar and pat h-type geometries are onsidered.

(PIFA's) isproposed to meet the design goals. The PIFA is hosen asthis

geome-try halvesthe size of aresonant pat h by the simpleadditionofa shorteningpost.

Cir ularpolarizationisa hieved by usingfourrotatedandsequentiallyfedPIFA's.

To ensure that the whole stru ture is ele tri ally small ea h of these PIFA's has

to be folded to halve their size on e more. This results in an antenna onsisting

of four sequentially rotated, folded PIFA's, ea h approximately an eighth of the

free-spa e wavelengthinsize. Thusthe wholeantenna isaquarter-wave stru ture,

whi h qualies itas ele tri ally small.

The design and onstru tion of this antenna is related along with simulated and

Chapter 2

Fundamental limitations in small

antennas

2.1 Introdu tion

In allareasof engineeringitisthe responsibilityof theengineer tostrikea balan e

between performan e and the ost asso iated with that performan e. In general

performan eisdire tly proportionalto ost andthe relationisquiteintuitive. But

in some ases a small in rease in performan e omes at a largely in reased ost.

It was stated by Hansen (1) that when a mu h higher performan e is needed the

ost may in rease exponentially. In su h a ase the performan e is said to have a

fundamentallimit.

The purpose of an antenna is to ouple to a free spa e wave. As su h there is

a limit on the size redu tion of antennas. The performan e indi es of bandwidth,

gain and e ien y are losely relatedto the ost fa tor of size.

Size redu tion has long been the normin many areasof ele troni engineering.

In the area of onsumer ele troni s size redu tion has be ome a very su essful

marketingstrategyand the onsumer has ometoexpe t newele troni devi esto

besmallerthantheirprede essors. Assu htheantennason ellularphones, GPS's

and satellitephoneshavebe omesmallerandsmaller,but atwhat ost intermsof

performan e?

In the aeronauti al and spa e industries small antennas are valued highly for

ing and gain stages whi h would, in themselves, require more spa e.

Withthis inmindthe antenna designer must strikeabalan ebetween size and

performan e. In the past mu hhas been writtenon the ee t of anantenna's size

onits performan e by the likesof Wheeler (2),Chu (3), Harrington(4)and others

(5;6)and morere ently byM Lean (7),Grimesand Grimes(8)andThiele(9). In

this hapter quantitive relationshipsbetween the ost fa tor of size and the three

performan e indi es of bandwidth,gain and e ien y are investigated.

2.2 Relative size

The on ept of relativesize is used torelate the physi alsize of an antennato the

size relativeto itsoperating frequen y. The relative size is dene as

kr

, where the free-spa e wave number

k

is given by

k =

2π

λ

(2.2.1)

and

r

is the radius of the smallest spherethat in ludes the whole antenna.

Tobe dened as ele tri ally small anantenna must have arelative size of

kr ≤ 1

. This relatesinto aradius of

r ≤

λ

2π

2.3 Bandwidth and radiation Q

RF devi es aremostly usedtotransmitdatainastandardizedformat andinthese

asesthetransmissionbandwidthispredetermined. Redu ingthesizeofanantenna

redu es the bandwidthand, for thegiven bandwidth, thereis afundamentallower

limitonthe sizeof theantenna. Mu hworkhasbeendoneontherelationbetween

antenna size and Q-fa tor. The Q-fa toris the relationbetween the stored energy

and radiated power of the antenna. In general the Q-fa tor is taken to be the

For that reason two popular derivations of the fundamental limit on radiation

Q-fa tor, and indire tly bandwidth,are given here. The rst isthe equivalent ir uit

derivation proposed by Chu (3) and the se ond is the dire t derivation proposed

by M Lean (7). Next a more a urate relationof Q-fa tor tobandwidth proposed

by Fante(6) isexamined.

2.3.1 Derivation of radiation Q from equivalent ir uit of

the spheri al waves

As stated by Harrington (4) radiationQ isgenerally dened as

Q =











2ωW

e

P

rad

W

e

> W

m

2ωW

m

P

rad

W

m

> W

e

,

(2.3.1)

with

W

e

thetime-average,nonpropagating,storedele tri energy,

W

m

the time-average, non propagating,stored magneti energy,

ω

the frequen y in radians and with

P

rad

the radiatedpower.

ANTENNA

INPUT

STRUCTURE

Figure 2.1: S hemati diagramof a verti ally polarized omni-dire t ional antenna.

Chu(3) onsideredaverti allypolarized,omni-dire tionalantennalyingwithin

a spheri al surfa e of radius

r = a

as shown in gure 2.1. The eld outside the sphere isexpressed intermsofa omplete set oforthogonal,spheri al waves,

prop-agating radially outward. The ir ularly symmetri al eld an be des ribed using

As the energy is not linear in the eld omponents, Chu had di ulty separating

the energy asso iated with the lo al eld from the radiated energy. To over ome

this, the eld problem was redu ed to a ir uit problem with the radiation loss

repla ed by a ondu tionloss.

As a result of the orthogonal properties of the spheri al wave fun tions, the

to-tal energy stored outside the sphere is equal tothe sum of the energies asso iated

with ea h spheri al wave and the omplex powertransmitted a ross the surfa e of

the sphereisequaltothesum ofthe omplexpowersof ea hspheri al wave. There

is no oupling between the spheri al waves outside the sphere. This enabled Chu

to repla e the spa e outside the sphere with a number of independent equivalent

ir uits. The number of equivalent ir uits is equal to the number of spheri al

wavesneeded todes ribe the eld outside the sphere.

INPUT

COUPLING

REPRESENTING

ANTENNA

NETWORK

STRUCTURE

Z

N

Z

Z

Z

1

3

5

I

I

I

I

N

3

5

1

The antenna stru ture is represente d by a oupling network that ouples the

input terminal of the antenna to the independent equivalent ir uits as shown in

gure 2.2.

The voltage, urrent and impedan e of the equivalent ir uit of the

T M

n

wave is dened as

V

n

=

µ

_ǫ

(

1

4

)

A

n

k



4πn(n+1)

2n+1



1

2

j (kah

n

(ka))

′

I

n

=

µ

_ǫ

(

1

4

)

A

n

k



4πn(n+1)

2n+1



1

2

kah

n

(ka)

Z

n

=

j(kah

n

(ka))

′

kah

n

(ka)

,

(2.3.2)

where

h

n

(ka)

is the spheri al Hankel fun tionof the se ondkind.

Thevoltageisproportionalto

E

θ

andthe urrentto

H

φ

. Thenormalizedimpedan e isequaltotheradialwaveimpedan eonthesurfa eofthesphere. Withthevoltage

and urrent dened asin(2.3.2),the omplex power fedintothe equivalent ir uit

isequal tothe omplexpowerasso iatedwiththe

T M

n

wave. It analsobeshown that the instantaneous powers are equal. The impedan e of the equivalent ir uit

is physi ally realizable and (2.3.2)is validat allfrequen ies.

The impedan e an be written as a ontinued fra tion by using the re urren e

formulas of the spheri al Bessel fun tions.

Z

n

=

_jka

n

+

2n−1

1

jka

+

1

1

2n−3

jka

+

· · ·

+

1

3

jka

+

1

1

jka

+1

,

(2.3.3)

This an be interpreted as a ladder network of series apa itan es and shunt

generated by ainnitesimally small dipole.

Z

₁

C=

L=

1

I

₁

a

c

_

a

c

_

Figure 2.3: Equivalent ir uit of ele tri dipole.

a

is the radius of the sphere and

c

is the speed of light.

Z

_n

C=

L=

1

I

_n

a

nc

___

a

(2n-1)c

_______

a

_______

(2n-3)c

a

_______

(2n-5)c

Figure 2.4: Equivalent ir uitof

T M

n

spheri alwave.

a

is theradius ofthe sphere and

c

isthe speed of light.

The equivalent ir uit for

Z

n

is shown in gure 2.4. The dissipation in the resistan e is equal to the radiation loss of the antenna. The apa itan es and

indu tan esare proportionaltotheratio oftheradiusof thespheretothespeed of

light. As itwould be tediousto al ulate the total ele tri energy stored inall the

apa itan es of the equivalent ir uit, Chu approximated the ir uit by a simple

series

RLC

ir uitwithsimilarfrequen y behavior losetotheoperatingfrequen y.

R

n

,

C

n

and

L

n

of the simplied equivalent ir uit are al ulated by equating the

resistan e, rea tan e and the frequen y derivativeof the rea tan e to those of the

R

n

= |kah

n

(ka)|

−2

C

n

=

_ω

2

2



_dX

_n

dω

−

X

n

ω



₋₁

L

n

=

1

₂



_dX

_n

dω

+

X

n

ω



,

(2.3.4) where

X

n

=



kaj

n

(kaj

n

)

′

+ kan

n

(kan

n

)

′



|kah

n

(ka)|

−2

, and

j

n

and

n

n

are the

spheri al Bessel fun tions of the rst and se ond kind. From the simplied

equiv-alent ir uitthe average power dissipation in

Z

n

is

P

n

=

µ

ǫ



1

2

2πn (n + 1)

2n + 1



A

n

k



2

.

(2.3.5)

Theaverageele tri energystored in

Z

n

isgiven inequation(2.3.6). Itislarger that the average storedmagneti energy.

W

n

=

µ

ǫ



1

2

πn (n + 1)

2 (2n + 1)



A

n

k



2

|kah

n

(ka)|

2



dX

n

dω

−

X

n

ω



.

(2.3.6)

Next

Q

n

for the

T M

n

wave is al ulatedas

Q

n

=

2ωW

n

P

n

=

1

2

|kah

n

(ka)|

2



ka

dX

n

d (ka)

− X

n



.

(2.3.7)

Hansen (1) stated that when multiplemodes are supported, the overall

Q

is

Q

=

P

N

n=1

a

n

a

∗

n

Q

n

(2n+1)

P

N

n=1

a

n

a

∗

n

(2n+1)

.

(2.3.8)

with

a

n

the ex itation oe ient of the nthmode. As the higherorder modes be omeevanes ent with

ka < 1

,it an be shown that the

Q

be omes:

Q

=

1 + 3k

2

_a

2

k

3

_a

3

_{(1 + k}

2

_a

2

₎

.

(2.3.9)

In gure2.5,

Q

isplottedagainst

ka

overthe range that onstitutes an ele tri- ally smallantenna. It is lear that asthe relative size of the antennais de reased

there is an exponential in rease in the Q-fa tor. This translates into a sharp

de- rease in the a hievable bandwidth.

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0

10

20

30

40

50

60

70

80

90

100

ka

Q

2.3.2 Exa t derivation of radiation Q from non propagating

energy

M Lean (7)proposed anexa t methodfor al ulatingthe radiationQof ageneral

antenna from the non propagatingenergy. M Lean obtains the elds of the

T M

01

spheri al mode from the r-dire ted magneti ve tor potential,

A

r

as taken from Harrington (10).

A

r

= − cos θe

−jkr



1 −

j

kr



(2.3.10)

H

φ

= sin θe

−jkr



j

kr

2

−

1

r



(2.3.11)

E

θ

=

1

jωǫ

sin θe

−jkr



−

1

r

2

−

jk

r

+

j

kr

3



(2.3.12)

E

r

=

1

ωǫ

2 cos θe

−jkr



1

kr

3

+

j

r

2



(2.3.13)

Theeld omponentsaretakenasRMSandfromthemtheele tri -and

magneti -energy densities,

ω

e

and

ω

m

, are al ulated.

ω

e

=

1

₂

ǫ ~

E • ~

E

∗

=

1

₂

ǫ |E

θ

|

2

+ |E

r

|

2

=

_ω

1

η

1

₂



sin

2

θ

_k

3

1

_r

6

−

1

kr

4

+

k

r

2

+ 4 cos

2

_θ

1

k

3

_r

6

+

1

kr

4



(2.3.14)

ω

m

=

1

₂

µ ~

H • ~

H

∗

=

1

₂

µ |H

φ

|

2

=

1

2

µ sin

2

_θ

1

k

2

_r

4

+

1

r

2

(2.3.15) with

η =

p

µ/ǫ

.

The ele tri -energy density asso iated with the traveling wave,

ω

rad

e

, is al ulated from the radiatingeld omponents.

H

rad

φ

= − sin θ

e

−jkr

r

(2.3.16)

E

rad

θ

= −η sin θ

e

−jkr

r

(2.3.17)

ω

rad

e

=

1

2

ǫ



E

rad

θ





2

=

η

2

r

2

sin

2

_θ

(2.3.18)

The non propagating ele tri -energy density,

ω

′

e

, is the dieren e between the total and the propagatingele tri -energy densities.

ω

e

′

= ω

e

− ω

rad

e

=

η

2ω



sin

2

θ



1

k

3

_r

6

−

1

kr

4



+ 4 cos

2

θ



1

k

3

_r

6

+

1

kr

4



(2.3.19)

Thetotalnon propagatingele tri energy,

W

′

e

, isobtainedby integrating2.3.19 over the volume outsidethe sphere with radius

a

ontainingthe antenna.

W

′

e

=

R

2π

0

R

π

0

R

_∞

a

ω

e

′

r

2

sin θdrdθdφ

=

4πη

_3ω



_k

3

1

_a

3

+

1

ka



(2.3.20)

ThetotalradiatedpowerisobtainedbyintegratingtherealpartofthePoynting

ve tor over aspheri al surfa e.

P

rad

=

R

2π

0

R

π

0

Re (E × H

∗

) • b

a

r

r

2

_{sin θdθdφ}

=

8π

₃

η

(2.3.21)

From thesethe quality fa tor isobtained. As an been seen fromgure 2.6 the

relationbetweenQ-fa torandrelativesizeissimilartothatofthe previousse tion.

Q =

2ωW

e

′

P

rad

=

1

k

3

_a

3

+

1

ka

(2.3.22)

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0

10

20

30

40

50

60

70

80

90

ka

Q

Figure 2.6: Qfor ele tri allysmall antennasasdened byM Lean.

2.3.3 Relation between Bandwidth and Q-fa tor

In general the radiation Q-fa tor of an antenna is taken to be the re ipro al of

its half-power bandwidth. This assumption is not a urate for ele tri ally small

antennas.

Fante(6)dened the relationbetween Q-fa torand fra tionalbandwidth. The

input impedan eofanantennasystem, astaken fromHarrington(10),was

onsid-ered.

Z = R + jX =

1

|I|

2

[P

rad

+ j2ω (W

m

− W

e

)]

(2.3.23)

Basedon ir uittheoryFanteassumedthat,forahigh-Qsystemwithresonan e

at

ω

0

,

dR

dω

ω

0

≈ 0

and

X (ω

0

) = 0

. Just o resonan e

Z

an be writtenas

Z ≈ R + j (ω − ω

0

)



dX

dω



ω

0

+ ...

(2.3.24)

At the half-power points





(ω − ω

0

)

dX

_dω

ω

0





 = R

and the fra tional bandwidth

B

an then be writtenas

B ≈

2R

ω

0

dX

dω

ω

0

=

2P

rad

ω

0

|I|

2

dX

dω

ω

0

(2.3.25)

Byextendingthe treatmentofthe frequen yderivativesofMaxwell'sequations

by Harrington(4,pp 394-396)Fanteevaluates

dX

dω

as

δX

δω

=

2W

|I|

2

−

2

η |I|

2

Im

Z

S

∞

~

E

_∞

•

δ ~

E

∞

∗

δω

!

dΩ

(2.3.26) Using2.3.26 in2.3.25 we obtain

B ≈



ω

0

W

P

rad

+ F (ω

0

)



−1

(2.3.27) where

F (ω

0

) = −

_ηP

ω

_rad

0

Im

R

S

∞



~

E

_∞

•

δ ~

E

∞

∗

δω



dΩ

The totalnon propagating, storedenergy,

W

, an bedened as the sum of the energy stored within the sphere of radius

a

that surrounds the antenna,

W

in

, and the nonpropagatingenergy outsidethis sphere,

W

out

. TheQ-fa toristhendened as

Q =

ω

0

W

out

P

rad

. 2.3.27 then be omes

B ≈



Q +

ω

0

W

in

P

rad

+ F (ω

0

)



₋₁

(2.3.28)

Fante goes on to show that for high-Q antennas the

F (ω

0

)

term is negligible. Inverselyforlow-Qantennasthe

F (ω

0

)

termalongwiththe

ω

0

W

in

P

rad

termrelatingthe

stored energy within the sphere has an ee t on the a hievable bandwidth. This

showsthat,whiletherelation

B =

1

2.4 Gain

From Harrington (4) the dire tive gain at a distan e

r

from the antenna is the ratio of themaximum density of outwarddire ted poweruxtothe average power

density.

G (r) =

4πr

2

_{Re (S}

r

)

_max

Re (P )

(2.4.1)

Here

S

r

is the radial omponent of the omplex Poynting ve tor at distan e

r

and

P

isthetotaloutward-dire ted omplexpower. Byexpandingtheeldexternal to asphere ontainingall sour esin termsof spheri al wave fun tions, Harrington

derives the gain as

G =

Re [(

P

n

a

n

F

n

+ jb

n

F

n

′

) (

P

n

b

n

F

n

+ ja

n

F

n

′

)

∗

]

4

P

_m,n

_ǫ

n(n+1)(n+m)!

m

(2n+1)(n−m)1

|A

mn

|

2

+ |ηB

mn

|

2

(2.4.2) where

F

n

(kr) = krh

(2)

n

(kr)

,

a

n

= n (n + 1) A

1n

,

b

n

= ηn (n + 1) B

1n

and

A

mn

and

B

mn

are the oe ients of the solutions to the Helmholtz equation. There is no limit tothe gain if allorders of spheri al wave fun tions are ex ited. A limitis

reated by restri tingthe orders to

n ≤ N

. As only

A

1n

and

B

1n

ontributeto the numerator of 2.4.2, the gain isin reased by setting

A

mn

= B

mn

= 0

m 6= 1.

(2.4.3)

As 2.4.2 issymmetri alin

a

n

and

b

n

, the maximum gain is a hieved when

G =

Re

hP

N

n=1

a

n

u

n

 P

N

_n=1

a

n

u

n



∗

i

a

P

N

_n=1

|a

n

|

2

_2n+1

1

(2.4.5) with

u

n

(kr) = F

n

(kr) + jF

n

′

(kr) .

(2.4.6)

Next 2.4.5 isin reased by setting

∠a

n

= −∠u

n

whi h leads to

G =

P

N

n=1

|a

n

| |u

n

|



2

4

P

N

_n=1

|a

n

|

2

_2n+1

1

.

(2.4.7) Byrequiring

∂G

∂

_|a

i

|

= 0

for all

|a

i

|

the

|a

n

|

are adjusted for maximum gain. This yields

G (kr)

_max

=

1

4

N

X

n=1

(2n + 1) |u

n

(kr)|

2

.

(2.4.8)

This is the maximum gain a hievable with wave fun tions of order

n ≤ N

. In the farzone, where

kr → ∞

,

|u

n

|

2

→ 4

and 2.4.8 redu es to

G (∞)

_max

=

N

X

n=1

(2n + 1) = N

2

+ 2N.

(2.4.9)

The normal gain of an antenna is dened as as the maximum gain obtainable

by using only wave fun tions of order

n ≤ N = kr

. Thus the normal gain of an antenna with radius

R

is given by

This normal gain is shown in gure 2.7 over the range that onstitutes an

ele tri ally small antenna.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0

0.5

1

1.5

2

2.5

3

kr

G

norm

Figure 2.7: Normal gainfor ele tri allysmall antennas.

A supergain antenna is one that a hieves more gain than the normal gain by

using more wave fun tions. As an be seen from 2.3.8 adding modes signi antly

in reases the Q of an antenna and for that reason supergain antennas are very

The radiatione ien y of anantenna isdened asthe ratio of the radiatedpower

to the average powersupplied tothe antenna.

To dene the fundamental limiton the radiation e ien y of anantenna

Har-rington(4) onsiders aspheri al ondu torofradius

R

ex ited bymagneti sour es on its surfa e. The hara teristi impedan es for the various modes inside the

sphere ,

r < R

,are

Z

T E

mn

=

η

c

η



F

n

(kr)

jF

′

n

(kr)



_∗

≈

η

c

η

(2.5.1)

Z

T E

mn

=

η

c

η



jF

′

n

(kr)

F

n

(kr)



_∗

≈

η

c

η

(2.5.2)

with

k

the wavenumberand

η

c

the intrinsi impedan e inthe ondu tor,

k ≈ (1 − j)

p

ωµσ

₂

η

c

≈ (1 + j)

p

ωµ

2σ

(2.5.3)

Harringtondenes the ratio of dissipated toradiated power as

P

diss

P

rad

=

|I

mn

|

2

Re (Z

−

mn

)

|I

mn

|

2

Re (Z

mn

+

)

=

Re (η

c

)

ηRe (Z

+

mn

)

(2.5.4) where

Z

−

mn

referstothe hara teristi impedan ewithinthespheri al ondu tor and

Z

+

mn

to the hara teristi impedan e outside the sphere. For equal

T E

mn

and

T M

mn

ex itationHarringtondenes the dissipation fa tors as

D

n

=

P

T E

diss

+P

diss

T M

P

T E

rad

+P

rad

T M

=

P

T E

diss

2P

T E

rad

+

P

T M

diss

2P

T M

rad

=

Re(η

c

)

2η

h

1

Re(Z

T E

mn

)

+

1

Re(Z

T M

mn

)

i

(2.5.5)

Z

T E

mn

=

F

n

(βr)

jF

′

n

(βr)

Z

T E

mn

=

jF

′

n

(βr)

F

n

(βr)

(2.5.6)

where

F

n

(βr)

is dened in 2.4.2. Using 2.5.6 in2.5.5 the result is

D

n

(βR) =

Re(η

_2η

n

)



|F

′

n

(βR)|

2

+ |F

n

(βR)|

2



=

Re(η

n

)

2η



|µ

n

|

2

− 2



(2.5.7)

where

µ

n

(βR)

is dened in 2.4.6. Harrington denes the total dissipation for an antenna with equal

T E

and

T M

ex itation as

D =

P

diss

P

rad

=

P

m,n

Re (P

mn

) D

n

P

m,n

Re (P

mn

)

(2.5.8)

where

P

mn

is the power inboth the

T E

and

T M

modes. As

|µ

n+1

|

2

> |µ

n

|

2

it

an be seen from 2.5.7 that

D

n+1

> D

n

. Using this and 2.5.8 it is lear that the lowest dissipation o urs when only the lowest order mode is ex ited. Thus the

minimum dissipation is equal to

D

1

. The per entage e ien y is given by

ef f =

100

1 + D

1

(2.5.9)

The maximum per entage e ien y versus antenna size is shown in gure 2.8

for lossyantennas onstru tedof aluminiumandof opper. Asthe approximations

in this derivation are only valid for ele tri ally small antennas, the values be ome

unrealisti for

kr > 1

.

From gure 2.8 it an be seen that as the antenna size is redu ed there is a

signi ant de rease in the a hievable radiatione ien y.

As many ele tri ally small antennas are not resonant in themselves, they need

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0

10

20

30

40

50

60

70

80

kr

Efficiency [%]

Aluminium

Copper

Figure 2.8: Per entage e ien y for aluminium and opper antennas versus relative

size. Theapproximation be omesinvalid for

kr > 1

.

mat hing network. When an antenna is ombined with a mat hing network to

optimizethe transfer of energyfromthe antenna tothe re eiverorfromthe

trans-mitter to the antenna the system e ien y is a ombination of the antenna and

mat hing network's e ien y. Fora transmittingantenna

η

s

=

P

r

P

in

= η

m

η

a

(2.5.10)

where

P

in

is the averagepowersuppliedto the system,

P

r

is the average power radiated,

η

m

isthee ien y ofthe mat hingnetwork and

η

a

isthe e ien yof the

antenna.

Matching

network

Antenna

Z

_g

= R

_g

+ jX

_g

Figure 2.9: S hemati of antenna with mat hing network.

Figure2.9 shows ansystem onsisting ofamat hing network onne tingan

an-tennatoageneratorwithasour eimpedan e of

R

g

+ jX

g

. Theradiatione ien y and Qof the antenna are given by

η

a

=

P

_P

r

_a

,

Q

a

=

2ωU

_P

_a

a

.

(2.5.11)

Ea helementinthemat hingnetwork,justliketheantennaitself,eitherstores

an average ele tri or average magneti energy at a given frequen y. Elements

storing the same type of energy as the antenna are des ribed by

Q

i

and elements storing the opposite form by

Q

′

i

. This yields

Q

i

=

2ωU

_P

_i

i

Q

′

i

=

2ωU

′

i

P

′

i

.

(2.5.12)

Theinputofthe mat hingnetworkis onjugatemat hedtothesour etoassure

maximum power

P

in

istransferedfromthe sour etothemat hingnetwork. Under a onjugatemat hthepowerdissipatedin

R

g

isequal to

P

in

. The Qfor thesour e impedan e isthen

Q

g

=

|X

g

|

R

g

=

2ωU

g

P

in

(2.5.13)

applying onservation of energy the followingequationsfor the ir uit isprodu ed

P

in

= P

a

+

n

X

i=1

P

i

+

m

X

i=1

P

_i

′

(2.5.14)

m

X

i=1

U

i

′

= U

a

+

n

X

i=1

U

i

± U

g

(2.5.15)

with

n

and

m

the numbers of ea h element of the mat hing network. If the rea tiveenergy stored in

Z

g

isof the same formasthat of the antenna,the sign of the lastterm in2.5.15 is

+

else it is

−

. Ifall the elements of the same typein the mat hing network havethe same

Q

then 2.5.14 and 2.5.15 be ome

P

in

= P

a

+

2ω

Q

n

X

i=1

U

i

+

m

X

i=1

P

′

i

(2.5.16)

Q

′

m

X

i=1

P

_i

′

= Q

a

P

a

+ 2ω

n

X

i=1

U

i

± Q

g

P

in

.

(2.5.17)

By ombining 2.5.16and 2.5.17the e ien y of the mat hing network is

η

m

=

P

a

P

in

=

1 ∓

Q

g

Q

′

−



1

Q

+

1

Q

′

 

2ω

P

n

_i=1

U

i

P

in



1 +

Q

a

Q

′

.

(2.5.18)

Asthe sour e impedan e ismostly resistive

Q

g

willbe mu h less thanthe

Q

of the elementsinthemat hingnetwork. This meansthat

Q

g

Q

′

≈ 0

. Withthisinmind it is lear from2.5.18that a maximume ien y isa hieved when allthe elements

of themat hingnetworkonlystoreenergy intheoppositeformasthe antennaand

U

i

= 0

. This is be ause there is no ex hange of energy between elements of the

η

s

= η

a

η

m

=

η

a

1 +

Q

a

Q

′

.

(2.5.19)

AstheQofanele tri allysmallantennasisoftheorderoftheQofthemat hing

network, it an be seen from2.5.19 that the mat hing networkhas asubstantially

detrimental ee t on the e ien y of an ele tri ally small antenna ombined with

a mat hing network. As su h, self-resonant stru tures should be preferred above

Chapter 3

Ele tri ally small antennas

3.1 Introdu tion

In the eld of antennas, as in all other areas of engineering, miniaturization is a

great area of interest. Mu h work has been done in this regard and many varying

te hniques for size redu tion have been proposed. In this hapter various planar

ele tri ally small antennas that are ommonly used and that have been proposed

willbe onsidered. Withthetheory developedin hapter2inmindtheseantennas

are riti ally examined. Their operation with regards to their input impedan e

and their bandwidth performan e are onsidered. In an attempt to gain better

understandingintotheworkingofele tri allysmallantennas,alltheseantennawere

simulatedinFEKOwhi hisafullwave,methodofmomentsbasedele tromagneti

solver.

3.2 Multi-element monopole antenna

The quarter-wavemonopoleisone ofthethe mostsimpleantennas. It onsistsofa

quarter wavelengthlong verti al wire fed above a groundplane as shown ingure

3.1. Be ause of itssimple onstru tionthe monopoleisone of the most ommonly

used antennasfor mobile equipment.

Be ause ofitssimpli ityand relativelysmall size the quarter-wavemonopoleis

very widely used for television and radio transmissions. Until re ently it was also

Figure 3.1: Quarter-wave monopoleantenna

Byfoldingahalf-wavemonopoleasshowningure3.2anquarter-waveantenna

that more ee tively utilizes the availablespa e is reated.

Figure 3.2: Folded monopoleantenna

As su h this folded monopole antenna has a mu h improved bandwidth as is

shown ingure 3.3.

A very popular ele tri ally small antenna is the top-loaded monopole antenna

(13;14). Atop-loadedmonopoleis onstru tedby addinga apa itivetopplateto

the foldedmonopoleantenna. Ita hievesresonan einaele tri allysmallstru ture

by balan ing the ele tri eld between the apa itivetop-plate with the magneti

eld around the monopole.

Theadditionofthe apa itiveplatesigni antlyredu es theresonantfrequen y

of the folded monopole antenna by in reasing its ee tive length. As an be seen

from gure 3.4 the resonant frequen y for two antennas of equal height is nearly

redu ed byafa tor ofthree. Whilethefoldedmonopoleantennahasarelativesize

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

−35

−30

−25

−20

−15

−10

−5

Frequency [GHz]

s

11

[dB]

Monopole

Folded monopole

Figure 3.3: Simulated

s

11

ofthe quarter-wave andfolded monopoleantennas

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

−25

−20

−15

−10

−5

0

Frequency [GHz]

s

11

Top−loaded folded monopole

Folded monopole

Figure 3.5: Goubau'sbroad-band multi-element monopole antenna.

The antenna proposed by Goubau (12) has long been seen as the ben hmark

against whi h all other ele tri ally small antennas are measured. It onsists of

four top-loaded inter onne ted monopoles. In (12) Goubau relates the in reased

input impedan e of a multi-element monopole antenna over a single monopoleto

the number of monopoles in the antenna. It is shown that, when only one of the

multiplemonopoles are fed the input urrent isgiven by

I =

V Y

N

2

(3.2.1)

It an bee seen from 3.2.1 that the ee tive radiation resistan e is in reased

by a fa tor

N

2

. A simple example is the folded monopole whi h has a radiation

resistan eofapproximatelyfourtimesthatofasinglemonopoleofthesameheight.

Goubau then goes on to state that a broad-band multi-element antenna an

be built by using a pair of thi k monopoles with small apa itive plates along

Figure 3.6: Dimensionsof the simulated Goubauantennain m.

In(12)Goubauonlystatestheheightoftheantennaalongwiththeradiusofthe

apa itive plate. After various simulations in FEKO with varying monopole radii

a frequen y response similar to the one reported by Goubau was obtained. This

antennaisshowningure3.6. Figure3.7showsthesimulated

s

11

. Theantennahas a half-powerbandwidth of morethan

75%

. As

ka = 1.123

atthe enter frequen y, this antennais only ele tri ally small inthe lowerend of itsfrequen y range.

In (12) Goubau does not attempt to explain the wide-band response of the

antenna. Asthetotal urrentpathismu hshorterthanawavelength, the urrents

on adja ent wires are relatively in-phase, but inopposite dire tions and thus their

apparent urrent is less. Further, as the urrent is divided between four wires,

the urrent density is mu h less. The lower apparent urrent and urrent density

auses the magneti energy stored in the antenna near-eld to be mu h less. As

wasshown in hapter 2,less storedenergy leads to lower

Q

and wider bandwidth. As the Goubau antenna is a omplex stru ture, it has not be ome widely used,

Figure 3.7: Simulated

s

11

of the Goubauantenna.

3.3 Loop fed spiral wire antenna

Physi allyfoldingorspiralingwire antennasisa simplewayof redu ing their size.

ChooandLing(15)proposedtheele tri allysmallplanarwireantennaofgure3.8.

This antennaisplanarinaplaneperpendi ulartothegroundplane. Theradiating

stru ture is a re tangular spiraled wire while the feed is a re tangular wire loop

that ouples indu tively to the radiatingstru ture. The spiraling of the radiating

stru ture de reases its size while the indu tive oupling at the feed in reases the

input resistan e of the antenna.

Choo and Lingusedthe Paretogeneti algorithm(16)tooptimize the antenna

for best bandwidth, highest e ien y and smallest size. An antenna with the

dimensionsofgure3.9hasarelativesizeof

kr = 0.36

. Thisantennawassimulated and its

s

11

isshown ingure 3.10. It shows a half-power bandwidthof 1.5%.

r

Figure 3.8: Designof the ele tri allysmall planar wireantenna.

44

36.3

11

6.3

8.3

27

9.8

Figure 3.9: Dimensionsof antennaAin mm.

printed antenna by using 2mm wide mi rostrip lines on 0.8 mm FR-4 substrate.

This antenna is truly planar in the sense that the whole antenna is in one plane:

the groundplane. This produ edafrequen y shiftfrom400 MHzto355MHz, but

also a broader bandwidth. The e ien y also dropped substantially. Be ause of

the high diele tri onstant (

e

r

= 4.2

) the antenna is mu h smallerthan the wire antenna whi his in free-spa e.

Choo and Lingproposed alumped element ir uitmodel to explain the

opera-tion of the indu tively oupled feed. This ir uitmodel isshown in gure 3.11

390

393

396

399

402

405

−10

−9

−8

−7

−6

−5

−4

−3

−2

−1

0

Frequency [MHz]

s11 [dB]

Figure 3.10: Simulated

s

11

for antennaAof gure3.9.

M

Z

_in

L

₁

L

₂

R

₁

C

₂

R

₂

2.65e-8

1.40e-7

1.06e-8

Z

in

= Z

f eed

+

ω

2

_M

2

Z

body

(3.3.1)

This learlyshowsthattheindu tively oupledfeedservestoinvertandamplify

the small input resistan e of the antenna body. Figure 3.12 shows that the input

rea tan eoftheantennaisequaltozeroattwopointsneartheoperatingfrequen y.

This doubleresonan e in reases the bandwidthof the antenna.

390

393

396

399

402

405

−100

−50

0

50

100

150

200

250

300

350

Frequency [MHz]

Input impedance, Z

in

Simulation

Model

Figure3.12: Inputimpedan eofthelumpedelementmodelandthesimulatedresponse.

By ombining the size redu tion of the spiralingof the radiatingwire with the

3.4 Diele tri ally loaded pat h antenna

The wavelength in a diele tri medium is dependent on the diele tri onstant of

the medium. In reasing the diele tri loadingof the substrate of a pat h antenna

redu es the resonant size of the pat h. As su h diele tri loadingis a simple way

of minimizinganpat h antenna.

From Balanis(17)the resonant radius

a

ofa ir ularpat h antennafor agiven resonant frequen y

f

r

and agiven substrate with diele tri onstant

ǫ

r

and height

h

is given by

a =

_n

F

1 +

_πǫ

2h

r

F



ln

πF

2h

+ 1.7726

o

1

2

(3.4.1) where

F =

8.791×10

9

f

r

√

ǫ

r

and

h

is in entimeters. Figure 3.13 shows how diele tri- ally loading the substrate redu es the size of the pat h antenna. But this

redu -tion omes at the ost of bandwidth. As shown in gure 3.14 diele tri loading

to de rease the size of a pat h antenna redu es the bandwidth. This is be ause

the higher diele tri onstant leads to more stored energy relative to the radiated

power. ThisresultsinahigherQ-fa torand alowerbandwidth. Whilethe ir ular

pat hantenna wastaken as anexample herethe same appliestoalltypesof pat h

antennas. It is lear that, when the required bandwidth for pat h antenna is

rela-tivelysmall,diele tri loadingis aworthwhile onsideration,but, whenbandwidth

1

2

3

4

5

0

1

2

3

4

5

6

Dielectric constant [

ε

r

]

radius [cm]

Figure 3.13: Cir ularpat h size against

ǫ

r

for

f

r

= 1

.6GHz

and

h = 1.588mm

.

1.56

1.58

1.6

1.62

1.64

1.66

1.68

1.7

−45

−40

−35

−30

−25

−20

−15

−10

−5

0

Frequency [GHz]

s

11

ε

r

=5

ε

r

=3

ε

r

=1

Figure 3.14: Simulated

s

11

for ir ular pat h antennas with various values of

ǫ

r

and

3.5 Shorted probe fed mi rostrip antenna

Re entlyWaterhouse(18;19;20;21)proposedanotherele tri allysmallmi rostrip

pat h antenna. The antenna onsists of a mi rostrippat h that ispin-fed and has

one ormore shortingposts. The largestredu tionin sizeis obtainedwhen asingle

shorting post is used. Figure3.15 shows the layout of su h anantenna.

e

_r

R

x

y

feed

short

d

z

Figure 3.15: S hemati ofprobe-fed pat hwith shortingpost.

Waterhouseexplainstheoperationofthistypeofantennathroughsimple ir uit

theoryin(20). Theee toftheshortingpostisrepresente d byaLC ir uitparallel

tothe RLC ir uitusedtodes ribethe working ofaprobefedpat hantenna. The

loser the shorting post is pla ed to the feed probe, the greater the ee t of the

apa itan e between them. The parallel ombination of this apa itive ee t and

the indu tive ee t of the probe fed pat h below resonan e results in a resonant

antenna withasigni ant redu tioninoverall size. Theantenna ofgure 3.15was

simulated with

R = 10.65mm

and

d = 10mm

. At the simulated enter frequen y of

1.9GHz

this isequal toanee tivesize of

kr = 0.58

. The simulated

s

11

for this

Figure 3.16: Simulated

s

11

ofthe probe-fed pat hwith shorting post.

3.6 Planar inverted-F antenna

The Planar Inverted-F Antenna (PIFA) is widely used in appli ations where an

ele tri ally small planar antenna isneeded. In re ent years it has ome tosurpass

the monopole antenna as the antenna of hoi e for mobile ommuni ations

equip-mentsu has ellularand ordlesstelephones. Be auseofits ompa tplanardesign

the antenna an be in orporated within the devi e unlike the monopole antenna

whi h needs tobe pla edexternal to the devi e.

Figure3.17 (from James (22)) shows a open- ir uit half-wave mi rostrip pat h

antenna operating in the dominant mode. The pat h antenna has a zero-voltage

lineatits enter. Ifthislineisshort- ir uited togroundandhalfofthestru tureis

removed, the eld patterninthe resultingquarter-wave pat h remainsun hanged.

W

L

h

Figure 3.17: E-eldpattern for half-wave mi rostrip pat h antenna.

is a resonantplanar stru ture that is only aquarter-wavelength insize.

Simulationsshow that the input impedan e of the PIFA at resonan e is in the

order oftwi ethat ofthe pat hantenna. This resultsinthe powerradiatedby the

PIFA for the same edge voltage being half that of the pat h. As the PIFA is half

the size of the pat hantenna, itsstoredenergy is alsohalved. This resultsinboth

antennashavingsimilarQ-fa torsandbandwidths. Figure3.18showsthesimulated

s

11

for a

λ

2

pat h and its orresponding

λ

4

PIFA. Its is lear that the bandwidths are very similar. This size redu tion without ex es sive loss of bandwidth makes

the planar inverted-F a very popular antenna. As su h mu h work has been done

on this geometry. Many variationson the standard PIFA have been proposed and

implemented. Salonen (23) proposed a PIFA with a U-shaped slot for dual-band

operation. Hwang (24) proposed further size redu tion by loading the PIFA with

high permittivity material. Li (25) proposed a broadband triangular PIFA, while

Row(26)in orporatedaV-shapedslottorealizeadual-frequen ytriangularPIFA.

1.58

1.59

1.6

1.61

1.62

−30

−25

−20

−15

−10

−5

0

Frequency [GHz]

s

11

[dB]

PIFA

PATCH

Figure 3.18: Simulated

s

11

for the

λ

2

pat hand the

λ

Chapter 4

Design of a sequentially rotated

PIFA for ir ular polarization

4.1 Introdu tion

This hapter details the on eptional design of the antenna element, highlighting

all aspe ts of the design pro ess. Every design hoi e is learly investigated and

motivated.

4.2 Spe i ations

The goal was todesign an ele tri ally small pat h-type stru ture to be used as an

elementinabeamsteeringarray. Theintended useisina ir ularlypolarizedarray

whi hisrequiredtos anaslowaspossible inelevation. Therequiredre eiveband

is1525-1559MHzandthe transmitband1626-1661MHz. Asthereisabandwidth

limitation on ele tri ally small antennas, separate re eive and transmit elements

are onsidered toredu e the bandwidth requirement from 8.5% to2.2%.

4.3 Proposed design

A set of four sequentially rotated, sequentially fed, folded Planar Inverted-F

An-tennas (PIFA's)in a ross formation,as shown in gure4.1 is proposed. The four

Spe i ation Symbol Value

Re eive band RX 1525-1559 MHz

Transmit band TX 1626-1661 MHz

Re eive enter frequen y

f

RX

0

1542 MHz

Transmit enter frequen y

f

T X

0

1643 MHz

Figure 4.1: Finaldesign.

are pla ed in a ross formation and all share the same shorting pin, to minimize

the spa e used. As a PIFA is a quarter-wave stru ture, ea h of the antennas has

to befolded forthe whole rossstru ture tobe smallerthana quarterwavelength.

4.4 Ee t of the shorti ng pin as ompared to a

shorting plate

As stated by Sanad (28) it is mu h easier to manufa ture a shorting pin between

the pat hand groundthan shortingthe edge of the PIFA with a plate to ground,

ex ept inthe spe ial ase ofthe pat hbeing ontheend ofthe substrate. As thisis

needforseparateshortsisremoved. Simulationsshowed thatthe ee tofrepla ing

the shorting plate with a shorting pin does not negatively ee t the performan e

of the antenna.

1.4

1.45

1.5

1.55

1.6

1.65

1.7

−30

−25

−20

−15

−10

−5

0

Frequency [GHz]

s

11

Pin

Plate

Figure 4.2: Simulated

s

11

of the pin-shortened and plate-shortened PIFA showing the redu tion in resonant frequen y.

As there is only one pin, it adds very little shunt apa itan e and thus has a

mostly indu tive ee t aused by the series indu tan e of the pin to ground. As

an beenseenfromgure4.2, thisindu tiveee tde reasesthe resonantfrequen y

of ea h PIFA. This further redu es the size withoutee ting the performan e.

Astheshortattheedgeofea hofthefourPIFA'sterminatesitssurfa e urrent

Figure 4.3: Unfolded andfolded versionsof the PIFA

The planarinverted-F antenna a hieves resonan e ina quarter-wave stru ture.

To in orporate the four PIFA's in a ross stru ture within a quarter-wavelength

it was ne essary to fold ea h individual PIFA to halve its size in the horizontal

plane. Folding the PIFA in reased its resonant frequen y and the body had to

be lengthened slightly to ompensate for this hange. As was shown in Chapter

2 redu ing the size of an antenna redu es the a hievable bandwidth and as su h

folding the body has a detrimental ee t on the bandwidth of a single PIFA as

shown in gure 4.4. Simulationsin FEKO showed that folding the PIFA redu es

the

s

11

< −15dB

bandwidth from 2.83% for the unfolded PIFA to 1.75% for the folded ase.

1.54

1.56

1.58

1.6

1.62

1.64

1.66

−50

−45

−40

−35

−30

−25

−20

−15

−10

−5

0

Frequency [GHz]

s

11

Unfolded

Folded

Figure 4.4: Simulated

s

11

for the unfolded andfolded PIFA's.

4.6 Sequential rotation for ir ular polarization

Cir ular polarization is a hieved by the arraying of the four PIFA's. The four

elements are rotated around their ommon shorting pin and pla ed

90

◦

apart as

shown s hemati ally ingure 4.5.

Ea hPIFAelementisthe fedwith aphaselaggingitsprede essorby

90

◦

. Ifthe

amplitude of all four ex itations are equal and the phasing is perfe t, the ve tor

additionofthesefourelementyieldsarotatingve torwithamaximumsizeoftwi e

thatofasingleelement. Thisrotatingeldve torpropagatesa ir ularlypolarized

waveas is shown ingure 4.6.

X

1

2

3

4

Figure 4.5: Sequential rotation ofthe four elements.

x

y

z

Figure 4.6: Rotating eldve tor.

4.7 Design of the feed network

The feed network is needed to:

feed allfour arms of the antenna with equal power,

reate the

90

◦

transform theinput impedan e of theantenna to

50Ω

overthe desired band-width.

The mi rostripfeednetworkwasdesigned on

0.508mm

Rogers RO4003Csubstrate with a relativepermittivity of

ǫ

r

= 3.38

.

As anbeseenfromgure4.7thenetwork onsistsofaquarter-wavetransformer

and a four way rea tive power divider feeding four arms onne ted to ea h of the

four PIFA's. The nal feeding arms are

85Ω

-lines to mat h to the inputs of the PIFA's. Thismeansthattheinputtothefourwaypowerdividerhasanimpedan e

of

21.25Ω

. To transform this to

50Ω

a quarter-wave transformer onsisting of a quarter-wavelength long

32.6Ω

-line, is used.

Figure 4.7: Layout of the feed network.

The

90

◦

phaseshiftbetweensequentialarmswasobtainedbymakingtheele tri

length ofea harm aquarter-wavelengthlonger thanitsprede essor. Thisresulted

in the fourth and longest arm being three quarters of a wavelength long. As the

whole antennahad tobesmallerthan aquarterof afree-spa ewave-lengtha ross,

the arms of the feed network were bent to t under the radiating stru ture. Care

wastaken topla e themi rostriplinesasfaraspossiblefromea hother,toensure

a urately simulate mi rostrip networks. Figure 4.8 shows the relative gain from

the input to the four feed arms. It an been seen learly that the longer the arm,

the greater the losses. This results in an unequal power division between the four

radiating elements. This unequal power division diminishes the a hievable axial

ratio.

1.5

1.52

1.54

1.56

1.58

1.6

1.62

1.64

1.66

1.68

1.7

−6.3

−6.25

−6.2

−6.15

−6.1

−6.05

Frequency [GHz]

Gain [dB]

Figure 4.8: Simulated relative gain from input to ea h of the four arms of the feed

network.

As shown by 4.7.1 the relative phase of ea h arm is dependent on the ele tri

length of the arm and the ele tri length is proportional to the frequen y. The

longer the arm, the greater the hange in phase over frequen y. Figure 4.9 shows

thattherelativephaseofthelongerarms hangesmorerapidlywithfrequen ythan

the shorter ones. As the axial ratio is dependent on the

90

◦

phase shift between

the sequential arms, this pla es abandwidth limitonthe axialratio.

phase = β l =

2πl

λ

=

2πf l

1.5

1.52

1.54

1.56

1.58

1.6

1.62

1.64

1.66

1.68

1.7

−150

−100

−50

0

50

100

150

200

Frequency [GHz]

Phase [Degrees]

Figure 4.9: Simulated relative phase from input to ea h of the four arms of the feed

network.

From theaboveitis learthat the feednetwork isnot idealand has a negative

inuen e onthe working of the antenna, resulting inredu ed axialratio and axial