74 Ad ances in Elec ical and Elec onic Enginee ing
DIRECTIONAL PATTERN ANALYSIS OF A LINEAR PHASED ANTENNA
ARRAYS
J. Ha ing
1)
, N. Maje
2)
, R. H onec
3)
Dep . o Telecommunica ions and Mul imedia, Facul y o Elec ical Enginee ing,
Uni e si y o Žilina, Uni e zi ná 1, 010 26 Žilina, Slo ak Republic
mail:
1)
ha ing@ el.uniza.sk,
2)
maje @ el.uniza.sk,
3)
h onec@ el.u c.sk
Summa y: An an enna a ay is a sys em compound om simply adia o s (dipoles, mic os ip an ennas), ha oge he o m
desi ed adia ion pa e n. Phased a ay an ennas consis o mul iple s a iona y an enna elemen s, ha a e ed cohe en ly and
use a iable phase o ime-delay con ol a each elemen o scan a beam o gi en angles in space. Va iable ampli ude con ol
is some imes also p o ided o an enna pa e n shaping.
1. INTRODUCTION
An an enna a ay is a sys em compound om
simply adia o s (dipoles, mic os ip an ennas),
which oge he o m desi ed adia ion pa e n. The
main emphasis is on he wid h, con ou and di ec ion
o o ien a ion du ing o m a adia ion pa e n o
an enna sys em.
By he assis ance his way o c ea ed pa e ns i
is possible o ou a adia ion ene gy o an enna
sys em in o deside a i e di ec ion, educe
in e e ence and inc ease e iciency en i e
ansmission.
In p ac ice a e known se e al echniques ha can
o m adia ion pa e n o an enna sys em. The a icle
deals wi h desc ip ion o echnique based on eeding
pa icula elemen s an enna sys em by di e en
phase signals. [1]
2. LINEAR ANTENNA ARRAY
An an enna a ay is a con igu a ion o indi idual
adia ing elemen s ha a e a anged in space and can
be used o p oduce a di ec ional adia ion pa e n.
Single-elemen an ennas ha e adia ion pa e ns
ha a e b oad and hence ha e a low di ec i i y ha
is no sui able o long dis ance communica ions.
A high di ec i i y can be s ill achie ed wi h
single elemen an ennas by inc easing he elec ical
dimensions (in e ms o wa eleng h) and hence he
physical size o he an enna.
An enna a ays come in a ious geome ical
con igu a ions, he mos common being; linea
a ays (1D).
A ays usually employ iden ical an enna
elemen s. The adia ing pa e n o he a ay depends
on he con igu a ion, he dis ance be ween he
elemen s, he ampli ude and phase exci a ion o he
elemen s, and also on he adia ion pa e n o
indi idual elemen s.
A uni o m linea a ay consis s o equispaced
elemen s, ha a e ed wi h cu en o equal
magni ude (i.e. wi h uni o m weigh ing) and can
ha e p og essi e phase-shi along he a ay. [2], [3]
The e is displayed schema ic diag am o linea
an enna a ay in he Fig. 1. [4]
Fig. 1. Schema ic diag am o linea an enna a ay
The uni o m linea a ay shown in he Figu e 1
consis s o N elemen s equally spaced a dis ance d.
The A ay ac o o a linea a ay o N pa allel
elemen s is gi en by he ela ion (1).
πθ
ϕθ
ϕθ
≤≤





+





+
=0,
cos.
2
1
sin
cos.
2
sin
1
kd
kd
N
N
AF
, (1)
whe e:
- N is he numbe o elemen s
- d is he in e elemen space
-  is he angle om he a ay axis
-  is he phase shi
Symbol k ep esen s wa ele numbe . The
wa ele numbe is gi en by he ela ion (2).
λ
π
2
=k
, (2)
Whe e  is he wa eleng h.
Di ec ional pa e n analysis o a end- i e an enna a ays 75
3. LINEAR PHASED ANTENNA ARRAY
STEERING
Phased a ay an ennas consis o mul iple
s a iona y an enna elemen s ha a e ed cohe en ly
and use a iable phase o ime - delay con ol a
each elemen o scan a beam o gi en angles in
space.
Va iable ampli ude con ol is some imes also
p o ided o pa e n shaping. A ays a e some imes
used in place o ixed ape u e an ennas ( e lec o s,
lenses), because he mul iplici y o elemen s allows
mo e p ecise con ol o he adia ion pa e n, hus
esul ing in lowe sidelobes o ca e ul pa e n
shaping.
Howe e , he p ima y eason o using a ays is
o p oduce a di ec i e beam ha can be eposi ioned
(scanned) elec onically. Al hough a ays wi h ixed
(s a iona y) beams and mul iple s a iona y beams
will be discussed in his ex , he p ima y emphasis
will be on hose a ays ha a e scanned
elec onically. [4]
The e is displayed schema ic diag am o linea
phased an enna a ay beam - s ee ing in he Figu e 2.
Fig. 2. Schema ic diag am o phased linea an enna a ay
beam - s ee ing
The phase shi  be ween wo successi e
elemen s is cons an and is called phase-inc emen .
We can de i e hese o mulas om Figu e 2:
,cos.dx
θ
=
==
=
(3)
,
x
λ
ϕ
π
=
==
=
2
(4)
,cos.d
θ
λ
π
ϕ
2
=
==
=
(5)
Fo mula 3 desc ibes he phase shi dependence
on angle o main lobe o ien a ion. [5]
4. LINEAR PHASED ANTENNA ARRAY
SIMULATIONS
Phased an enna a ay simula ions a e c ea ed by
he help o p og am Linea An enna A ays
Simula o . This p og am was c ea ed in Bo land
Delphi 7.
The a ay ac o plo in he Figu e 3 shows
dependency on he elemen spacing. As we can see
om he Figu e 3 he an enna pa e n is changed by
he a ay elemen spacing inc easing.
d = 1/4 
d = 1/2 
Fig. 3. Se o a ay ac o plo s o in luence o mu ual
elemen ’s dis ance simula ion
Pa ame e s o simula ions we e N =16, = 2
GHz,  = 0°. Dis ance o elemen s d was changed
om 1/4  o 1/2 .
Figu e 4 shows ha he an enna pa e n wid h is
no only dependen on he elemen spacing bu also
on he numbe o elemen s. I can be seen om
Figu e 4. he beam wid h inc eases as he numbe o
elemen s in he a ay inc eases. Please no e ha he
elemen spacing is kep cons an in bo h he cases.
76 Ad ances in Elec ical and Elec onic Enginee ing
N = 2
N = 8
N = 32
Fig. 4. Se o a ay ac o plo s o in luence o elemen s
numbe inc ease simula ion
Pa ame e s o simula ions we e d = 1/2 , = 2
GHz,  = 0°. Numbe o elemen s N was changed (N
= 2, 8, 16).
The e is shown dependency be ween an enna
pa e n o ien a ion and phase shi in Figu e 5.
 = 60°
 = 120°
 = 180°
Fig. 5. Se o a ay ac o plo s o phase shi change
simula ion
Pa ame e s o simula ions we e d = 1/2 , = 2
GHz, N = 16. Phase shi  was changed ( = 60°,
120°, 180°).
As shown in Figu es 6 and 7, an enna pa e n
wid h is he same i numbe o elemen s inc eases
and elemen spacing is dec eases.
Di ec ional pa e n analysis o a end- i e an enna a ays 77
A he same ime numbe o elemen s inc eases
om 10 o 20 elemen s and elemen spacing is
dec eases om d = 1/2 o d = 1/4 and beam wid h
does no change.
Fig.6 . Rela ionship be ween numbe o elemen s and he
elemen spacing, d = 1/4, N=20
Fig.7. Rela ionship be ween numbe o elemen s and he
elemen spacing, d=1/2, N=10
Pa ame e s o simula ions we e = 2 GHz, =0°.
5. CONCLUSION
In his pape we desc ibe linea phased an enna
a ay heo y, simula e his sys em and desc ibe a ay
ac o .
Phased an enna a ay simula ions a e c ea ed by
he help o p og am Linea An enna A ays
Simula o . This p og am was c ea ed in Bo land
Delphi 7.
The inal esul s a e desc ibed in Figu es 3, 4, 5,
6, 7.
As we can see om he Figu es 3, 4, 5, 6, 7 he
an enna pa e n wid h is no only dependen on he
elemen spacing and on equency bu also on he
numbe o an enna a ay elemen s.
We can change an enna pa e n o ien a ion by
phase shi a ia ion.
Acknowledgemen
The wo k on his pape was suppo ed by he
g an VEGA 1/4067/07 o Scien i ic G an Agency
o he Slo ak Republic.
REFERENCES
[1] HARING, J., MAJER, N., POLOHA, P.,
HRONEC, R.: A Mic os ip Phase Shi e as
an D i en Elemen o Dynamic Phased A ay.
Science & Mili a y No.2, Vol.2/2007, pp.68-
71.
[2] ORFANIDIS, J.: Elec omagne ic Wa es and
An ennas. USA, 2008.
[3] Flo ida S a e Uni e si y.: Elec onic Theses
and Disse a ions. USA, 2008,
www.e d.lib. su.edu
[4] MAILLOUX, R.: Phased A ay An enna
Handbook. A ech House, No wood, 2005.
[5] WOLFF, CH.: Rada g undlagen. Be lin, 2008,
www. ada u o ial.eu