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349
COhlNUh‘ICbTIONS
Resonant Quadrafilar Helix
/EXPERIMENTALPOINT
THEORETICAL PATTERN
Abstract-Theradiation of theresonant,
fractional-turn, quadrafilar helix is shown t o
be cardioid shaped and circularly polarized
regardless of axial length anddiameter.
Measured and calculated data relate the
radiation pattern characteristics and geometrical parameters.
INTRODUCTION
-ioL
Fig. 3.
.ARIZATIION
An earlier paper [l] hasshown t h a t
the resonant (element lengt,h = X/2), 1/2turn, antiphase-fed, bifilar helix radiates a
sine-shaped, circularly polarized radiat.ion
patternwhenthediameter
=0.18X and
the axial length
=0.27X; and that two such
bifilar helices, concentric with orthogonal
radials (a quadraflar helix), radiate a
cardioid-shaped, circularly polarized pattern when fed in phase quadrature.
New experimental data indicates that
resonant1/4-turn,l/f-turn,and1-turn
quadraflar helices radiate a cardioidshaped, circularly polarized patt.ern forall
axial
lengths
and
diameters.
Pattern
shapeand axial ratioaredegradedfor
verylarge or verysmallaxiallength/
diameter and forhelices with more than 1
turn. Graphs of the measured beamwidth,
axialratio,and
front-to-back ratioare
included, as shown in Fig. 3.
1nt.egral formulas for the radiation of
t h e multielement helix have been derived.
The radiation patt.erns of several helices
have been computed by numerical integration and found to agree with the measured
data.
.4KaLrsIs
Fig. 4.
ceived directly from the t.ransmitter can
be brought. down t o bet,ter than -13 dB
The method of exciting the array disin theregion around the main beamof t,he
cussed previously raises theproblem of
transmitter and beyond -20 dB in other
separatingtheincidentwavefromthe
regions.
scattered wave because only the scatt,ered
A block diagram of this experiment.al
wave (reradiat.ion from array elements) is
setup is shown in Fig. 2, andatypical
of int.erest,. I n our experiment n e used a
experimental radiation pat.tern compared
planewaveto
excitet.he
array whose
with t.he theoretical pattern at designed
polarization is such that the electric field
frequency is shown in Fig. 3.
is spat,ially orient.ed a t 45 degrees with
respect to the dipoles on the array. The
COXCLUSION
reradiatedelectric
field is detectedby
We haveinvestigatedtheradiation
the receiving antenna whichis
rotat,ed pat.tern of a spherical array by means of
such that its polarization is at 90 degrees
the scattered plane resulting froma wave
spat,ially w-it.hrespect t o t.hat of the transpropagatingalongthepolar
axis of the
mit.tedwave.
Thk will allow the scat.- sphere.Thetechnique
of det,ectingthe
tered wave to be received while the inciscattered field from the sum of the scatdent wave is rejected. This method gives
t.ered field and incident field is discussed,
approximately 10 dB decoupling between
and some experimental results are shown.
the incident signalpower and thereceived
ASDREWI(. CHAN
one (Fig. 4).
RURENS
A. SIGELMASN
Themethod is furtherimprovedby
Dept. of Elec. Engrg.
d
using microwave
a
bridge
circuit.
University of Washington
signal is derivedfromthe
plane-wave
Seattle, Wash. 98105
source in the absence of the array to cancel anysignal received by the receiving
I~EFEREKCES
antenna.Thenthearray
is placedin
(11 A. Chan, A. Ishimam,
and
R. Sige+V,
position t o measure t.he scattered field.
’Equallyspacedspherical
arrays,” Radw Sa.,
revol. 3, pp. 4 0 1 4 W , May 1968.
With t.his arrangement
the
signal
METHODOF DETECTION
T h e variables and parameters used are
defined in Fig. 1. The fields of t,he radials
and t.he fields of the helical portions d l
be
evaluat.ed
independently
and
t.hen
summed.Theassumedcurrentdistribution is sinusoidal wit,h maxima a t t h efeed
andthedistalend.Utilizingtheusual
approximations[a],the
4 component of
the t.otal field of element 1 is
Field of the Helical Portions
Let 01 betheintegrationvariable.
From Fig. 1
and the general formula is
-j w p ~ o e - j l x
E’H
=
4flCOS6
2xz
. Ja=o
i+(+,or)ej~r’
+de.
For each element of the helix 6he current
magnitudes are
O1
id(.)
=
l o c o s (kso) cos -cos 8.
2N
Manuscript received
August
1. 1968;
revised
December 2, 1968. This work was supported by the
U S . Department of the Navy under Cont.ract NOW
62-0604-C-CFBhl).
350
IEEE TRANSACTIONS ON ANTENNAS ANDPROPAGATION,
MAT
1969
1
AXIAL LENGTH = PN
P-PITCH LENGTH FOR ONE
ELEMENT
N=NUMEER OFTURNS FORONE
ELEMENT
7
Fig. 1.
MB
EEAMWIDTH
(DEGREES1
60
OT
0
I
I
I
.I
.2
.3
3
AXIAL LENGTH (WAVELENGTHS]
I
!
.5
.6
(a)
I/Z TURN
Odb
6)
0
(b)
Fig. 2. (a) Q u a d r a k helix 1 turn. $=O, P=O.IG, ro=O.OGX. (b) Quadrhelix 1/4 turn. +=O, P=1.36h, ro=O.OSL
AXIAL LENGTH (WAVELENGTHS)
(C)
Fig. 3 Quadrafilar h@x. experimental data. Solid lines % (e) indicate p e k &a1
ratio over t h e henuwhere rn front of helix; dashed lines n d x a t e peak a s dL ratio
over 3-dB beamwidth of helix.
351
COMMUNICATIONS
Impedance
Limited data indicates a variation in
at resonancefrom
theinputimpedance
70 ohms for the 1/4-turn helix t o 15 ohms
for the I-turn helix.
For elements 1 and 2:
&(+,a) = &(a) cos
(4 -
a).
For e1ement.s 3 and 4:
- a).
&(+,a) = i9(a)sin (+
-ro cos CY sin e sin
Pff
+cos e)]
2r
The phase term for element 1 is
7 r ’ r
T’ cos $ = r
=
+ ro
Pa:
.sin a sin e sin + + 2a
1/4-turn helix
e.
C. C. IGLGUS
Appl. Phys. Lab.
The Johns Hopkins University
Silver Spring, Md.
da.
Field of the Radials
If thecurrentontheradials
is apa uniformdistribution,
proximatedby
the following simplified solutions result:
r0 cos a sir1 e cos +
.COS
+
REFERENCES
[I] C.
C. DKilgus, ‘Multielement., fractionalturn
helices, I E E E T r a m Antennas and Propagation (Communieafions).vol. AP-16, pp. 499-500,
July 1968.
[ 2 ] S. A . SchelkunoE. “ A general radiation formula,”
Proc. I R E , vol. 27, pp. 660-666. October 1939.
Define
uplor0
K =
cos (kro)e-ikr
4irr
Then E+ for the helical portion of element
1 is given by
1/2-turn helix
Equatorial Plane Pattern of an
Axial-TEM Slot on a Finite Size
Ground Plane
. sin e cos 4
+ro sin a sin e sin 4
1-turn helix
Similarly, the field of element 2 is
.cos + (1 + eikP
sin 0 cos + -ro sin a sin 0 sin 4
Pol
+cos e)]
2r
da.
Elements 3 and 4 (thesecond
bifilar
t.0
helix) arefedinphasequadrature,
e1ement.s 1 and 2, respectively. T h e fields
are
- exp [ik ( - r o sin a sin e cos 4
+ ro cos
(Y
sin e sin
+cos 91
2r
COS
8).
Computation
Numerical
integrat,ion
of t.hese expropressions with a digitalcomputer
vided the t.heoretica1 patterns of Fig. 2.
The measured patterns plotted for
comparison were taken under the conditions
outlinedinthe
following section. T h e
experimental patterns are circularly
polarized for all e and +, indicating that EO
has the same shape asE+.
EXPERINENTAL
DATA
+
Radiation Patterns
These details are common in the data
of Fig. 3:
Pff
The c0ncept.s of edge diffraction have
been used to compute the scattered and
radiated fields of waveguidegeometries
[1]-[2]. They can also be used to predict
theperturbat.ions in the patterns introduced by such features as the edges of a
ground plane. Lopez [3] hasobtained a
rather inaccurate result for the case of a
monopoleover a circularground plane.
Ryan and Peters [4] have introduccd an
equivalent
current
concept
to
demonstrate that good accuracy can be obtained
for this case.
This communication considers a TEMmodeaxiallyslottedgroundplane
of
finite width and lengt,h, as shown i n Fig.
1. T h e diffractions from the edges of the
ground plane and their contributions to
t h e overall pattern are shown in thecomputed results. The radiation-pattern
calculation will consist of the superposition
of raysemanatingfromtheaperture
the
additional
(wedges 1 and 2) and
diffractedraysfrom
wedges 3-6 when
added in proper relative phase. T o check
t h e va1idit.y of thetechnique,
experimentalresultsareusedforcomparison
since rigorous solut.ions do not exist.
The total diffracted field from wedges
1 and 2 includingsecond-andhigher
order diffractions [l], [2] is given by
e--j(kro+z/4)
ED(TO,+O)
= -=-
measurementfrequency
400 MHz
element
diameter
0.1 inch
element
length
16.0 inches
feed
orthogonal folded baluns; power division and phase
quadrature obtained with a directional coupler
v‘2rkro
mechanical
support
0.625-inch diameter
aluminum
tube
provides
shieldand a shortingpoint for thedistalends
elements
geometry
L, =
~
N+/-
RD(+o)
(1)
where
a balun
of t h e
1 (16.0“ - 2r0)? - 4r2r02.
N!
Manuscript received September 4, 1968; revised
January 13, 1969.
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