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7/23/2019 The Archimedean Two-wire Spiral Antenna-EFc
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312 I R ER A M S A C T I O N S
Oh: A X T E X N A S A N D
PR.0Pz4GATION
ods, especially in the V H F region. Moreover, the great
variations of the constants with frequency , contrary to
the commonlyaccepted fact that they should be practi-
cally constant, justify the somewhat extensive discus-
sion of the results obta ined. In this discussion it is seen
that,although heconstantsvarygreatlywith fre-
quency, the general behaviorof soil as a reflecting layer
for radiopropaga tion compares qualitatively well with
the other methods cited.
Though local variations of the soil may be of less im-
portance n adiopropagation,where heaverage soil
condition over a large area should be taken, the present
method may prove useful
as
a means for investigating
generalphysicalproperties of soil and geological sur-
face phenomena through their relation to themeasured
electric characteristics, and, in this sense, the knowledge
of local variations of soil ca n be of importance.
APPENDIX
Demonstration of Formula ( 5 )
Fromelementaryelectromagnetic heory we have
u e
Hence,
EG G 8.85 Gmho
Demonstration
of Formulas (8 )
and
( 9 )
We have from ordinary transmission line theory
z Z&)
tanh
yl
zo
tanh
2yl
zz Z,,(21)
Z 2 tanh
V I
1
Z1
tanh
2
(1 tanh2y l ) ,
which results in
andsubsequently
Za Z1.tanh yE d Z 1 ( 2 2 2 Z,).
ACKXOWLEDGMENT
The auth or wishes
to
thank he authori ties of the
LaboratoriodeElectronicaydeCommunicaciones
(ArgentineArmedForcesResearchLaboratory)or
their encouragement in the present work. He also wi
to acknowledge the stimulus and helpful suggestions of
Luis P.
Poli.
The Archimedean Two-Wire Spiral Antenna*
JULIUS A. KAISER?
Summary-A pair of equally xcited but oppositely sen sed
Archimedean two-wire spirals situated close to one another in the
same plane-a doublet-is used
to
generate a linearly olarized field
in which the direction of polarization and phase are controlled or
varied independentlyof each
other
by rotationof the spiral radiators.
An array of these double ts can be made to scan by rotation of the
several spiral elements; an eight-doublet array which was made
scan over an 83O sector with small amplitude variation is discussed.
A doublet fed from
a
ring network can be employed a s a polarization
diversity circuit.
A
virtual doublet
is
achieved by placing a single
spiral in a right angle trough. A preliminary scanning array com-
prising four spirals in a trough was made to scan +36. The possi-
bility of using a parasitic spiral in conjunction with a driven spiral
for obtaining linear polarization of variable direction and phase
is
indicated. Also,
a
briefsimplified analysis of the two-wire Archi-
medean spiral
is
presented, which leads to the concept of higher-
order modesof radiation.
Manuscript received
by
thePGAP,June
1959;
evised
t
Diamond Ordnance
Fuze Labs.,
Washington,
D.
C.
manuscript received, October 1959.
INTRODUCTION
HE two-wireArchimedeanspiralconfigurations
shown in Fig.
1,
when properly excited, have bee
shown to becircularlypolarizedradiatorswith
broadband characteristic-broadband with respect not
only to input impedance but also to radiation pattern
Inpractice,eitherconfiguration senergized rom
a
transmiss ion line connected to the center terminals of
th e configuration.
So energized, the configuration radiates
a
broad cir-
cularly polarized beam t o each side
of
the spiral. Each
radiated beam is normal to the plane of th e spira l, and
the sense
of
circularity of polarization of t he beam on
one side corresponds to the winding sense
of
the spiral
Ohio, Tech. Note WCLR-55-8 WADC; June,
1955.
E.
M . Turner, Spiral Slot Antenna, Wright-Patterson AFB
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Kaiser :
Th.e Archimedean
Tzoo-FVi.re
Sp i r a l An.tenna
as viewedrom theppositeide . AAccordingly, hewo
THEORETICALONSIDERATIONS
radiated beams are identical except that the rotational
sense of polarization of t he radiated field on one side
is
theoppos ite of th at
on
theother.Forexample, he
spira l of Fig. l ( a j would radiate ight ircularlJ-
polarized beam away from a viewer of t he figure, and a
left circularly polarized beam toward him. In most ap-
plications
i t
is desirable that the spiral radiate to one
side 01111-; his is readily accomplished by appropriately
backing hespiral
on
oneside b,r agroundplaneor
cavits-.
The spiral antennaescribed above has eceived much
attention
i n
recent .ears-principally because
its
broad-
band characteristics render
it
admirably adaptable to
the equirementsof adar ountermea~ures. ~-~This
paper presen ts a simplified analysis of t he -Archimedean
spiral antenna and points out some of the mportant
properties of its radiation field. Earlier work has been
reported previously.0 A few applications utilizing some
of the hitherto unexplored properties of the spira l are
presented. spiral doublet array is treated in somewhat
greater detail, since, o date, most effort has been di-
rected toward it.
a ) (b)
Fig. 1-Circular and rectangular Archimedean spirals.
.Abstracts of the Fifth .Annual Svmuosium on USAF Antenna
lies.
and Del-.,
publisher, hlonticello, fll.,University of Illinois Press,
Urbana; October, 1955.
Massachusett s Inst. of Tech., Cambridge Res. Lab.
of
Electronics.
B.
H. Burdineand R . M . McElvery,TheSpiralAntenna,
Rept. Nos. 1 and 2 .
J. C. Pullara and H. H. Hibbs, The Study
on
Flush-Mounted
Circularlv Polarized Antennas
and
Polarization Modulation. hlel-
par, Inc.: Falls Church, Va., P.O. 569838, Prime Con tra cto rkp erv
Gyroscope Co.,
XF
33(6001- 35177; March, 1955.
1.
C. Pullara. H. H., Hibbs, and H.
T.
\5:ard, S-Band Trans-
mittiing and Receiving Antennas. Melpar, Inc., Falls Church, Va.,
P.O. 5201 l7C, Prime Contr actor- Speq Gyroscope Co., A F 33(038)-
14524; February, 1958.
An Experimental Invest igation and .Application of the Spiral
Antenna,
Temco
Aircraft Corp., Dallas,
Tes.,
inal Engrg. Rept.;
ResearchStudies on
Problems
Related t o EC M Antennas,
310; October, 1957.
University of Illinois, Urbana, Rept .
Kos.
1-3,8-11, A F 33(616)-
John
Dyson, -An
Experimental nvestigation of theSpiral
Antenna. University of Illinois Press, Vrbana, Ill. ; May, 1957.
9
Bibliography
of
Spiral -Antenna Reports and Papers, Melpar,
Inc.,
Falls
Church, \:a.
J.
A. Kalser, Scanning * h a y sUsing the Fla t Spiral -Antenna,
Na\:al Res. Lab., \Yashington,
D.
C . ,
N R L
Rept. KO. 5103; March,
1958.
Electronic Scanning Symposium, AFCRC and RXDC, Cambridge,
J.
-4. aiser, Spiral -Antennas .\pplied
to
Scanning .Arrays,
Mass.
April, 1958.
ulv,
1957.
313
There has not een an y rigorous theory to explain the
spiral ntenna.However , he followingheuristic x-
planation of the radia tin g mechanism of the two-wir
Archimedean spiral is offered since it is in accord with
experimentalobservationsand is of genuinehelp i
unders tanding the design possibilities of this relatively
new antenna.
The po int of view taken
is
th at the two-wire spiral
antenna behaves
as
though
i t
were
a
two-wire trans
mission inewhich gradually,byvir tue of itsspiral
geometry, transforms tself into
a
radiating structure o
antenna. I t is well
knon-n
that a two-wire transmission
line, of narrow spacing relative to wavelength andf an
length, yields
a
negligible amount of radiation when ex
cited at its terminals. This
is
due to the fact that the
currents in the twowires of the line a t an>-normal cros
section are always 180 out-of-phase
so
that radiation
from one ine
is
effectively cancelled by the rad iat ion
from the other.
Suppose now that
a
two-wire ransmission line i
formed into the spi ral configuration of Fig. Le t
P
be a point
on
one wire of the transmission line at
a
dis
tance measured along the wire from the input terminal
4.
hen the point
Q
on the other wire at the sam e dis
tance from he n put erminal
B
is situated diametri-
callyopposite hepoint
P
with respect o he center
0
and both P and
Q
lie
on
the same circle centered
a
0.
Thi s implies that he point P and ts neighborin
point P (on the othe r wire directly alongside
P )
lie a
such arc distances from -1 and
B ,
respectively, that th
di-fference
of these distances is precisely the arc length
QP along the spiral. f the spacing between wires,
much smaller than
I,
he arc lengthQP is approximatel
equal to
7rr.
Th is difference i n wire lengths does not d
pend on the number of turns within r
i f
the spac ing be
tween wires
is
uniform.
X
similar situation holds for he square spiral con-
figuration of Fig . 2(b) . Here, for
a
cross-sectional poin
P P
n th e two-wire line, the pat h difference in the tw
wire lengths is given very closely by where d is th
perpendicular distance from the center
0
to the side
o
thesquarespiral urnon which
P-P
lies. Also th
circumference of the tu rn on which
P-P
lies
is
approx
a)
( b )
Fig. 2-Construction of the circular
and
rectangular
Archimedean
spirals.
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314 I R E TRA:\ SACTIO;VS O S B K T E L Y X A S AiYD PROPAGA TIOjV
mate ly Th is difference of 4d in wire lengths of the
transmission line
is
independent of th e numb er of tu rns
appearing on the spiral, provided only that the spacing
d
between elements on the spiral s cons tant and small
compared to
There are two items of inte rest t hat att ach to a par-
ticular point on the two-wire spiral line: the total dif-
ference in wire lengths of the two-wire line to t he po int
an d the ircumference orpath lengthof the particu-
ar turn on which the point lies. For he rectangular
difference in wire lengths
4d
circumference
d is X/8, where
X
is the current wavelength
n
the
phase hangeor otaldifference in wire
is X/2,
while the tota l circumferentia l path length
X
or a quarter wavelength on each side
f
the square.
f the radia ted field from opposite sides of the
re is such as to add in a direction normal to the
containing hespiral.Rloreover,radiationfrom
adjacent sides
is
equal n ntensitybutwitha
90 electrical degrees, so that
radia ted field no rmal to the plane of the spir al
is
For hecircular piralwhereagain hewiresare
at
a
point whose radial distance from
is
r , we have
difference in line lengths
r
circumference
2nr.
r
is
X/27r,
the phase change
s h 2
and the circum-
is
X.
Assuming tha t eac h wire supp orts a pro-
essive wave of curre nt and that thes e curren t waves
at
the input terminals and
B ,
i t
is
clear
difference in phase of the two current elements
tanypoint
PP'
on he two-wire ine,measured n
7r (the nputphase difference)
+27rjX(nr) .
us neighboring current elements star t anti- phas e
at
points
A
and
B,
and gradually come into phase
one proceeds outward along the spiral two-mire line.
r
is
X,f27r,
these currents are recisely in phase and
a
maximum.Moreover, hecondition for
currentsoccurs a t twopointsdia-
0.
Appendix I for typica l plots of phases along each
and forprogressivephasechangesbetween
Radiation from the spiral then is centeredn an annu-
ing of turns of one wavelength mean circumference.
devic e, he basic equirementbeingonly
radiu s be large enough to allow a half wave-
of phase shift. -Also, ina smu ch as the radia ting
is
a
wavelength in circumference for all frequencies
over which the spiral operates, a constant beamwidth
should be maintained.
The input imped ance f spiral antennas
as
a
function
of filament geometry is not known a t this time.
How-
ever, the impedancef a few spirals with relatively lose
filament spacings has been found to be on the orde r of
100 ohms near their centers.
HIGHER-ORDER MODES
F
RADIATION
Radiation from the one-wavelength ring
s
described
above has been termed the first modef radiation, since
this represents the first occasionor which conditions re
correct for ra diation . It can be reasoned that curre nts
existing beyond the one-wave length ring will continue
experiencingphasechangeas heyprogressoutward.
Assuming that the spira l s truct ures large enough, these
curr ents will be out-of-phase again a t a radius where the
circumference is two wavelengths and in-phase at the
three-wavelength ircumference.
N o
radiationoccurs
from the two-wavelength ring because the currents on
adjacent filaments are anti-phase. At he hree-wave-
length ring radiation can occur if curr ents exist, giving
rise to the third mod e of r adi ati on. It follows tha t cur-
rents which are anti-phase at the inpu t term ina ls can
excite only the odd modes of radiation.
If, on the other hand, the two center terminals are
tied together and excited in some manner, currents s
in-phase at the centerof th e spi ral . In progressing out-
ward, these currents experience phase change. When t
one-wavelength circumference is reached, they are anti-
phase and no radiation occurs. At the two-wave lengt h
circumference, which
is
defined
as
th e locus of t he second
radiation mode, the currents are once again in phase,
and radiation is once again strong. Currents around the
two-wavelength circumference of a circular spiral, and
possibly
a
rectangular spiral, are n such phase as o
cause
a
rad iat ion p att ern of minimu m field on-axis and
maximum field, which is omnidirectiona l, in the plane
of
the spiral. Since he second mode diameter for he
circular spirals approximately (2X:/n), a very broad pat
tern in the plane of the spiral axis is obtained. Thus,
evenmodesonlyareproducedwhencurrentsare n-
phase at the input terminals.
One method of exci ting the second mode
is
shown in
Fig.
3 .
The inpu t s treated
as
a microstrip line with two
branching circuits, connected to the center conductorf
a coaxial line, above a ground plane which
is
connected
to the outer conduct or of t he coaxial line. Th e p ar t of
the spiral immediate ly above the ground plane can be
considered as a microstr ip transmission ine feeding th e
second mode radiator with two terminals
at
the edge of
the ground plane. The ground plane is continued only
far enough to establish the currents in the microstrip
mode. Th e impe dance of the two microstrip line termi-
n'als at the edgeof the groun d plane should matc h that
of the two terminals of the spiral for maximum power
transfer.
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315
Fig. &Second mode excitation method.
PHASINGROPERTIES
F THE
SINGLE
SPIRALNTENNA
pro per ty of the spiral which has not been fully ex-
ploited s th at of circularsymmetrgabout he axis,
which llows otation bouthe xisoproduce a
change i n phase of the adiated field everywhere n
spacewithoutvaria tions n he far-field ampl itude .
Onedegree of mechanical otationproducesacorre-
sponding change in phase of one electrical degree."
To see, i n a simple way, why this phasing property
is so,
first epresent hecircularspiralantennaasa
circularconductor,onewavelength ncircumference,
which support s a uniform progressive current wave . Re-
ferring to Fig. 4 he arrows on the circular conductor
indicate hedirection nwhichcurrentphase ronts
move. Consider now two points in the far field of this
circularcurrentdistribution,
Pl(O, 41
and
P, O,
whose spherical coordinates differ only in the azimuth
coordinate I t is clear that these two points see the
same cur rent distribution except or
a
shi ft of phase in
the cur ren t sources along the circle; th at
is,
the sources
for the rad iat ion ield at Pzare identical with the sources
for the radiation ield at P1 except for
a
phase lag n the
sources forPr over those forP1,of A 4 electrical degfees.
Accordingly, the adiation field of the ircularone-
wavelength current loop depends only with respect to
phase on the azimuth coordinate and this dependence
is given by the facto r I t follows immediatel y that a
rotation of thecircularcurrent oop, which doesnot
disturb the intrinsic current phasing, changes the phase
of the ad iatio n field of th e loopeverywhere byan
amount which in electrical degrees
is
precisely equal to
the number of degrees of mechanical rotation.
Similarly, rotation of t he second-mode spiral changes
thephase of the adiati on field everywhereby n
amoun t which in electrical degrees is twice the number
of degrees of mechanical rotation.
PHASINGND POLARIZATION PROPERTIES
F THE
SPIRALOUBLET
Two spirals of opposite sense, placed side by side in
the same plane and xcited equally (Fig. will radia te
t o the
first
mode of radiation.
12
Unless specifically excepted, further discussions pertain only
Fig. A-Phase properties of
a
single spiral radiator.
Fig. 5-Spiral doublet schematic.
a combined field which will be linearly polarized every-
where. This is true because both left- and right-hand
spiralscontr ibute ellipses of po larization of the same
amplitude and orientation, but oppositely sensed, e
where i n space. Xlthough linearly polarized, the direc-
tion
of
polarization of the far field a t a particular point
will be a function of the rela tive electrical phasing be-
tween he wo spirals and he relative space phasing.
Consider, irst,anon-axis fixed position and et he
phase of one spiral be varied with respect to the other
by rotation as illustrated inFig.6. Thi s figure shows
three possible instantaneous orient ations for th e field
vectors radiated from the spiral doublet and the result-
an t on-axis fields. Fig.6(a) howshat when both
vector fields a re imultaneou slyvertical nd i n the
same direction, the resultant instantaneousield
is
verti-
cal. Ninety degrees later in time the left vecto r will be
pointing to the left and the right vectorill be pointing
to the right, produc ing no ne t field on-axis. It ma y be
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concluded tha t the time average field radiated from the
doublet
as
shown in Fig. 6(a) will be linear and verti-
callypolarized.Similarly, as shown nFig.6(c) he
instantaneous vectors as oriented produce
no
net verti-
cal field on-axis. Kinety degrees later in time, however,
both vectors will be pointing in the same direction, pro-
ducing
a
horizontallypolarized field. Fig.6(b) llus-
trateshe onditionwhereheadiated fields are
phasedorthogonally.Thesum of the adiat ed fields
then from the two equally excited spirals remains linear
Fig.
7--A
spiral doublet array.
(a )
(b)
C)
Fig.
6-On-axis
phasing
possibilities
of the
doublet.
when the phase f one element ( the element on the right
in Fig. 6) is changed relativ e to that of the other, but
the direction of pol.arization rotates hrough an angle
when the relative phases changed If the relat ive
input phasing to the spirals
is
constant with change in
frequency, hen hedirection of polar ization or he
doublet a t a given point will also be independent of fre-
quency.
Looking again
at
the spiral doublet schematic shown
in Fig. 5 , i t is clear that symme try exists in the YY'
plane,whichbisects hespiraldoublet,since n o dif-
ferential pacephasingbetween heelementsexists.
Direction of polar ization in theX X plane, which bisects
the spiral axes, however, will be
a
function not only of
the elativephasingbetween hespiralelementsbut
also of the differential space phasing between them.
O n
the other hand , if one spiral is rotated in either
direction through an angle 8, while the other spiral
is
simultaneously rotated in the opposite direction through
the same angle 8, the polar izat ion of the radiat ion field
remains unchanged n direction but he phase of this
field a t all points changes by precisely
8
electrical de-
grees. In his change of phase here snochange n
amplitude provided each spiral has perfect axial sym-
metry. Since the spirals an inherently broad-band radi-
ator, the above propertieshold over a wide band of fre-
quencies.
APPLICATIONS
F THE
SPIRALOUBLET
A Spiral
Doublet A r r a y
A spiral doublet,
as
discussed above, is a linear radi-
ator, the direction
of
polarization
of
which
is
varied by
rotation of either spiral element and phase
s
independ-
ently varied by rotating simultaneously both spiral ele-
ments. An arrayof such doublets leads o an antennaof
any arbitrary linear polarization which can be made to
scan by changing the relative phase between the spiral
doublets. Fig. 7 is a photograph of an array consi sting
of eight spiral doublets arranged so that each vertical
pair of spirals
is
a doublet. The bottomview is a photo-
graph of the back of the array showing eed harness and
dials that ndicatephase ettings.Spacingbetween
doublets is a half-wavelength for the test frequency of
1430
mc, and the polarization selected here is vertical.
Fig.
8
shows patterns at 1430 mc of a typica l spiral
elementmakingup hisarray.Thebeamwidthfora
total varia tion of
2
d b is approximately The spac-
ing of the spira l above the ground plane is 23 inches,
which a t this frequency is correct to give approxima te
a 1-db dimple in the center of the pattern for vertic al
polarization. This spacingf the spiral above the grou
plane was selected because it results in small amplitude
variations over
a
broad beam, which in turn
~ I I O W S
broadscan.Like hedipolebehaviorover
a
ground
plane, closer spacing of the spira l to the ground plane
would result in less amplitude variation over a smaller
angle, while a greater spacing would produce a deeper
dimplewith orrespondinglywiderbeamwidths nd
larger amplitude variations. With a linearly polarized
antenna-a dipole-used for transmitting, this particu-
lar spiral showed
a
maximum variation in response for
recep tion over the useful por tion of the pat ter n of ap -
proximately 1 d b for the various angular positions or
cuts shown. The maximum variation with rotation for
any individual spiral was approximately
1$
db.
Fig.
9
shows patterns of one of the spira l double ts
used in the array. The upper groupf four curves repre-
sents patterns of the vertical doublet set for vertical
polarization but for four different phasings. One spiral
of thedoublet was nitially djusted ormaximum
responsewithverticalpolarization ndhepattern
labelled 0" was taken; the phase was changed
90"
by
rotating one spiral of the doublet
90"
in
a
clockwise
direction while simultaneously rotating the other spiral
counterclockwise 90" and the pat tern labelled
90 mas
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Fig. 8-Single spiral
over
a groundlane. Fig. 10-Eight doubletrrayatterns.
Fig. 9-Spiral doublet patterns.
recorded; s imilarly, pa tterns were recorded for relative
phasings of and 250 in order to see the variat ion
in doublet response with changes in phasing. The par-
ticular doublet shown producesa variation in amplitude
with change in phase of as much as 2 d b in some places.
Xlso
to be noticed from these patterns is
a
squint or a
pointing of the beam of?
to
the right which did not ap-
pear in the individual spiral patterns. This is
a
condi-
tion which conceivably can be eliminated.
The lower group of four patterns in Fig. 9 represents
the cross-polarized components. For these patterns the
transmitting antenna was rotated
0" so
that
i t was
radi-
atingwithhorizontalpolarizationandpatternswere
take n of th e doub let for the phas ings shown while i t
was
still adiusted for vertical Dolarization. The cross-
able improvement in doublet performance is clearly in-
dicated.
I n Fig. 10 are the patterns taken or the eight double
array hown in Fig. 7. Patterns considered areonly
those n thehorizontalplane.
A
Tchebycheficurrent
distr ibution for a 25-db sidelobe level was obtained us-
ing a printedmicrostrip feed harness.Eachpattern
shown is for the ndica tedphase difference between
adjacentdoubletsmeasured in mechanicaldegrees.
The direction and widthf each main beam
is
in very
close agreement \vith the heore ticallyderivedarray-
factor patterns. The scan demonstrated here, ignoring
the extreme right pattern,
is
from 53" to the left of th e
on-axis direction to 30" to the right, with a total varia-
tion
i n
amp litude of the main beam of less tha n
1;
db.
Patter ns taken of the individual doublets mounted in
the arr ay, and n the presence of all other doublets, indi
cate that the sca n could have been made from 30" to
the right of the on-axis direction to approxim ately 65"
on the left for
a
total useful scan
of
greater than k.5'.
The scanwould be symmet rical about the n-axis direc-
tion
i f
thespiraldoubletpatterns were symmetrical
about their axes.
T he sidelobe levels in Fig. are down approximatel
15 db or better, which
is
considerably above those the-
oretically predicted-namely,
25
db . Th e sidelobe level
would be more nearlqr that predicted by the theory if
individualdoubletperformanceswereuniformly he
same.I3
Because of the squint asso ciated with the indivi dua
doublets
i t
was necessary to employ spiralsof one sense
along the op row n the ar ray and of opposite sense
along the bottom ow. With this arrangement symme
polarized components are
Seen to
be
doWn
Only
l 3 d b
ElectromechanicalScanningArray:"NavalRes.Lab., K;ashington,
For later results,see J .
R.
Donnellan, "Xn Eight Spiral Doubl
in some portions
of
the pattern. recessity for consider- D. C . , N R L Rept. KO. 283; April, 1959.
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318 IRE TRANSACTIONS ALt TELYA AS
A N D
PROPAGATIOll M a y
is maintained in the plane of scan so t hat , for a given
polarization on-axis, he same polarization will obtain
throughout heplane of scan.However, in theother
principalplane hedirection of polarization will tilt
from th a t of the on-axis direction due to the differential
space phasing betw een the two elements f the doublet.
If symmetry about the on-axis direction of the doublet
can be obtained, an alternating arrangementf doublets
canbeemployed to give symmetry n both principal
planes.
Spiral in
a
Trough
A
broad-band linearly polarized radiator of variable
phase can be obtained by combining a single spiral with
acornerreflector,orright-angled roughopen at the
ends. Thearrangementshown nFig.
11,
where he
spiral lies in the plane bisecting the corner reflector, re-
sults navirtualdoubletbecause hespiralradiates
right-handcircularlypolarizedenergy nonedirection
and left-hand circularly polarized energy n the opposite
direction. Th e sides of the trough then reflect two spiral
images of opposite sense which are equallp energized.
Rotat ion of the single piral esults in simultaneous
phase advance or retardation
of
both images. Constant
direction of polarization is there foremaintainedand
only the phase is changed by spiral rotation. -411exam-
ination
of
Fig.
11
(a) shows that in the bisecting plane
through hevertex hoseradiatedcomponentswhich
appear vertical from the endview cancel in the far field
while the orizontal omponents dd.Direction of
polarization in the bisecting plane for such an arrange-
ment will always be along the axisof the trough.
There
is, i n
addition,radiation n heplane of the
spiralwhich is down
less
than 3 db from heon-axis
radiation.Furthermore,he irectadiationnhe
plane
of
the spiral varies in phase with change
f
angu-
lar position in the bisecting plane of the trough, while
the phase of the reflected magesdescribedabovere-
mainsconstant.
A
permanentbeamcock is therefore
imparted to the radiation field; that is, in the bisecting
plane of the trough, the beam, representing the sum
of
the constant phase fields reflected from the trough sides
and he variable phase fields radiated
i n
the plane of
thespiral, s n a directionother han hatalong a
normal bisecting the trough vertex. If the beam cock
is
to one side of this normal for a given spiral, then for a
spiral of opposite sense he beam cock will be to th e
opposite sideof the normal.
Spirals of the same sense placed longitudinally along
the trough constitute an array with linear polarization
whichcanbemade toscan.Phasechange is simpler
than in a spiral doublet array since rotation f only one
spiral accomplishes the same end as rotating both spirals
in a doublet. .Also there are ewer initial adjustments re-
quired the direct ion of polarization
is
predetermined
so
it does not have to be set initially, nor will it change
during the coursef adjustments.
( a ) ( b )
Fig. 11-Spiral
in
a trough.
Fig.
12-Spiral in a trough-a variation.
Another arrangement of a spiral in a trough is shown
in Fig. 12. Here a spiral is mounted with its axis coinci-
dent with a normal bisecting the trough vertex. This ar
rangement also produces linear polarization, the phase
of which can be varied by rotation of the single spiral
antenn a. I n thi s case, however, the r adiatio n pat tern in
the bisecting plane of the vertex is symmetrical about
the axis
of
the spira l, and the direc tion of polarization
in a plane normal
to
the spiral axis is dependent upon
the spacing of the spiral above he vertex. Using he
plane bisecting the vertex
as a
reference, the direction
of polarization rotates for an increase in the spiral to
vertexspacing in a counterclockwisemannerwhena
right circular spiral is used, and rotates in a clockwise
manner when
a
left circular spiral
s
used. The direction
of polar ization was found to rotat e
f20"
for
a
change
in pacing of to
1.
The adiatedbeamhadaxial
ratios of approximately 25 db, while the beamwidths in
the bisecting plane ranged from
0
to 70 .
An arr ay of spirals in
a
trough, where each spiral ax
lies in the bisecting plane f the trough, rad iate s beam
which is linearly polarized an d which can be made to
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Scan sJ?mmetrically in a plane bisecting he trough axis.
Such an array (Fig.
13 ,
consisting of four equal ly ex-
cited spirals with a half-wavelength separation between
centers, was made to scan 5 3 6 in the plane bisecting
the vertex with less than 1-db variat ion i n the main-
beamamplitude.Themajor-lobebeamwidthwasap-
proximately
27
and the sidelobes were down a t least 9
db. Spacin gs of the spiral s above the vertex were ad-
jus ted to give a direction of polarization
along
the ver-
tex
i n
order that alternating-sense spirals ould be used.
A
broad-band scanning array would require spirals all
of one sense in order to have identical change in direc-
tion of polarization with change in frequency.
The Para s i t i c Sp i ra l
X parasitic spiral placed along the same axis as, and
relatively close to, a driven spiral (Fig. 14) radiates cir-
cular polarization of opposite sense from tha t radia ted
from the dr iven spiral. Theolarization of the combined
field varies from near linear to circular, depending upon
the degree of coupling between the parasite and driven
spira ls. The behavior of the pa rasit ic spiral differs from
the driven spiral in that the phas e of th e re radiate d en-
ergy from the parasitic spiral changes by twice the angle
of rotation (ro tat ion signifies here rotation of the para-
sitic element about its axis or change
i n
phase of the
field incident on the paras ite). This implies that rotation
of t he parasi te rotates only the major axis of t he com-
bined field ellipse; furthermore, the polarization which
is assumed along the maj or axis of the ellipse rotat es
linear117 wi th ro tationof the parasite.
B y
the same token,
rotation of the dr iven e lement results only inchange of
phase of the combined fields, since the phases of both
direc t and reradia ted fields will be affected.
The parasitic spiral can presumably bef either sense,
regardless of the sense of the driven element, and yete-
radiate circular polarizationof opposite sense from th a t
of the driven element. This
is
true because a circularly
polarized field incident on a given spiral will cause cur-
ren ts to flow either
i n
toward the center or out toward
th e edge of the spiral, s ince the di rectionof the current
flow
is a function f the sense of the inci den t ield as well
as the sense of the parasitic spiral. Currents reaching
either unterminated end would be reflected and trave l
back out to be reradiated in a sense opposite to th at
which
was
eceived. This means, that linear polarization
incident
on
aparasitic piral will be eradiated s
linear, since a linear field incident on a spiral will cause
equal currents toflow in opposite directions.
If sufficient coupl ing between
a
driven spiral and a
parasitic spiral can be obtained such that the parasite
radiates a field e qua l to tha t of the driven spiral , the
combined fields would be linearl>- polarized. The direc-
tion of pola rization would be fixed by the paras itewhile
phase would be determined
by
the driven element. Pat-
terns recorded with
a
parasitic spiral separated from the
drivenelementbya&inch ucitediskresulted nan
Fig.
13-Spiral
trough
array.
Fig. 14-Parasitic spiral in front
of
and close
to
a driven
spiral.
axial ratio (or on-axis ellipticity ratio) of 15 d b a t 1500
mc,which ndicates adiation rom heparasitewas
down about 2.5 d b from th at of the driven spiral (see
- 4 x d
Rat io below). The luc ite disk was emplol-ed t o in-
crease the degree of coupling between the driven spiral
and parasitic spiral. 3,Iaximum axial ratio without the
plastic separator was approximately 10 db. The se axial
ratios are relativelyasl; to obtain and do notecessarily
indicate the greatest egree of coupling obtainable wit
proper care.
PoluYizatioTz
Dixlersity
A spiraldoubletwithsomerelativephasebetween
its two elements will radia te a field linearly polarized in
some arbitrary direction. f the input (or intrins ic) pha
ing to one elementf the doublet
s
changed by lS0 the
direc tion of polar ization will be otated
90,
just
as
though hatelement were otated mechanicall): 180"
h
doublet fed from a ring network as shown in Fig. 15
allows selection of either of two orthogona l polari zat ion
of
arbitrary direction. Currents fed in to arm 3 of the
ring network divide equally and leave arms
2
and
4
in-
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390
Fig. 15-Polarization diversity circuit.
phase,resulting na inearlypolarized field from th e
doublet. Currents fed into arm 1 also co me out of arm s
2
and
4
equally but180" out-of-phase, resulting in linear
polarization orthogonal to t hat obt ain ed when currents
enter arm
3 .
Similarly, orthogonal shifting f the polari-
zation according to the input te rmina l used can be ar-
ranged for an array of doublets.
~'IISCELLXNEOUSPIRALNTENNA OXSIDERATIONS
Axial
Ratio
Anellipticallypolarizedwave can be esolved into
two circularly polarized waves of opposite sense, which
have a ppropriate relative amplitudes and hases.I4 Th e
relationship is
EL
E R
EL ER
ellipticity ratio (in db) 20 log
where -EL and
E E
are the amplitudes of the opposite
sensecomponents. A specialcase esulting n inear
polarization arises when the two amplitudes are equal.
Another special case where the amplitudef one circular
wave is zeroyieldscircularpolarization of the sense
corresponding to that
of
the circular wave of finite am-
plitude. In general, the latter case is desiredof individ-
ual spiral radiators.
The Archimedean spiral should n heory radiate a
circularly polarized field along its axis with a sense cor-
respo nding to the inding senseof the spiral. Frequently
in practice he on-axis field of a spiral is found to be
elliptically polarized, indicating generally th e existence
of c urren t flow on the spiral in a s ense oppos ite to that
of t he cur ren ts flowing from the nput ermin als.
For
example,whenhe entererminals hownnFig.
l(a ) are excited, t he current
flow
gives rise to a right
circularly polarized field travelin g away from the iewer
of th e figure. Currents originat ing n some fashion a t
J .
D.
Kraus, "Antennas,"
hlcGraw-Hill
Book C o . , Inc., New
York,
N
Y.;
1950.
the spiral periphery, on the other hand, are in a sense
opposite to those traveling from the center, resultingn
a radiated field which is left circularly polarized. Th e
sum of these two fields of opposite sense from the spi ral
isaradiationpatternwithanaxialratioother han
unit);. T he rev ers e cur ren t flow may arise from reflec-
tion at the oute r ermina ls of currents either eaking
past the radia tion region or being induced on the spiral
by t he field reflected from a backing ground plane or
cavity.
I n
an y case,' th e reflected curre nts retur n to the
region of the one-wavelength ring and are there radiated
in a sense opposite o that desired.
Currents existing beyond the radiation ring are there
fore enerally ndesirable. The y an be att enu ate d
quite simply by placing lossy material such as resistive
card or aquadag on the outerm ost turns f the spiral or
a t some radius less than tha tnecessary for higher-mode
radiation . Aquadag painted between the two mires of
the la st turn of a spiral, for example, will absorb inci-
dent currents in both the radiation mode and transmis-
sion line mode. Th is
is
so because the lossy material is
parallel t o the ele ctr ic ield for both modes. In pr actice,
axial ratios have been reduced from 2 or
3
db without
aqua dag to less than db after applying aquadag.
Beam
Cock
Anotherhenomenonrequentlyncounteredn
spira l patt erns is that of beam cocking or pointing of
the beam other than along the axisf the spira l. T his s
a condition brought about by simultaneously exciting
both the first and second modesf radiation. Ina transi-
tion from a coaxial line t o a two-wire transmission line'j
there exists on the two-wire line, unless suitable precau-
tions are taken, an in-phase component of cu rrent
as
well as th e usual anti-phase or transmission line mode
currents. The in-phase component along the two-wire
line is out-of-phase with the corresponding current on
somegroundsystem,whichmaybe heoutsidecon-
duc tor of the coaxial ine. Considering such a discon-
tinuity at the inp ut terminal s of a coaxial fed spira l, it
follows that the in -phase com pon ent of cu rrent will ex-
cite the econd radiation mode f the spi ral s sufficiently
large, while the usual transmission line mode currentx-
cites the first modeof r adia tion. The resul tant field ob-
tained from adding the first radiation mode, character-
ized by maximum gain along the axis and
360
phase
change per spiral revolution, and the second radiation
mode, characterized by maximum gain in the plane of
the spiral and
720
phase change per revolution , is gen-
erally
a
beam that does not exhibit symmetry about the
spiral axis. The amo untof beam cock is dependent upon
the relative amplitudesof the two radiation modes, and
the direction is determined from the relative phases.
Fig.
16
shows two axial cuts f a coax-fed spiral which
was large enough to support the first
wo
modes of radia-
E b c t r m i c s , vol. 17, pp. 142-145; December,
15 N . Marchand, "Transmission-Line Conversion Transformers ,"
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1960 Kaue r :.he. r c h?me de an 1 wo-Wzrep?.ral4ntenna
32
Fig.
l b B e a m
cock associated with
a coaxial
line fed spiral. Scale: 360 .
tion. One pattern was recorded with the spiral so ori-
ented as to shift the beam as fa r as possible off axis in
one direction. The spiral
was
then rotated 180" in its
ownplaneand heotherpatternrecorded.
I t
canbe
seen that a beam cock of approximately
30
exists and
rotates with rotation of the spiral. In practice i t was
found hat a coax-fed spiral only a ittle arger han
necessary for the first mode of radiation produced suffi-
cient second-mode radiation to cause some beam cock.
A balanced feed for the spiral eliminatedall evidence of
beam cock.
Ground Planes
A
flat ground plane is one type of backing used with
spiral antennas. Then-axis gain is-not much affectedy
ground-plane size providing the ground plane has a min-
imum dimension greater than approximately
0 .6
wave-
length. The faroff-axis patterns however are a function
of the ground-plane sizewhen i t is small. T his latt er
factorassumes mportanceprimarilywhenarrays of
spiralsareconsideredand
low
sidelobe evels arede-
sired. For
low
sidelobes in any antenna arra)- , the radia-
tion pat tern from each element should coincide exactly
with each of the other element patterns. Identic al ele-
ment patterns for all directions nspacecan onl . be
achieved with adequate ground-plane size.
CONCLVSIONS
The
flat
Archimedean spiral antennan the first mode
-the input terminals excited anti-phase-is a versatile
broadband antenna which radiates circularly polarized
energy with constant beamw idth whose far-field phase
depends upon angular position of the spiral. Excited in
the secondmode, i e . , the nput erminal s excited n-
phase, heL\rchimedeanspiralbecomes
a
broadband
radiator with
a
beacon pattern; that
is,
radiation is a
maximum in the plane f the spira l and the phasef the
far field again
is
dependent upon angular position.
Two spirals
i n
th e first mode, of opposite sense and
excited equally, radiatea combined field which is every-
where linearly polarized. The directi onof polarization is
controlled by rotating one spiralof the doublet relative
to the other,while phase is independently controlled by
rotating both spirals equal but opposite amounts. An
array of doublets can be employed to produce a linear
polarized beam of an)- arbitrary direction which can be
made to scan through an angle of
as
much as f50" by
rotating he ndividualspiralradiators.
A virtual doublet, with which linear polarization of
variable phase
is
obtained, can be realized by placing a
single spiral in a right-angle trough. Direction of polar-
ization
is
not rbitrary as with he piraldoublet,
but linearpolarizationand canningcanbeaccom-
plished with one-half the number of elements .
Nearly linear polarization can be obtained by placing
a parasitic spiral in front of and close to
a
driven spiral.
Rotation of th e parasi te rota tes the major axis of t he
combined far-field ellipse, while rotation of the driven
element changes only the phase.
Polarizationdiversityutilizing any woorthogonal
polarizations can be obtained by feeding spiral dou-
blet roma ingnetwork.array of doub letswith a
corporate feed can have one input termina l for inear
polarization in one direction whilesecond input termi-
nal feeds the orthogonal polarization.
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329 IRERANSACTIONS
OhT
ANTENh7ASNDROPAGATION M a y
APPENDIX
The Archimedean spiral is defined by
where
r =radius from spiral center
=angular measure (in radians)
a = a constant which controls spiral pitch
0,
7r
for
a
two-wire spiral.
The length
S)
of
a
spiral filament
is
approximately
Change of phase due to line length in electrical de-
grees along a given filament relative to the input
s
(360') (360')
x 2x
where is the current wavel ength along the spira l.
Table I showsvalues of for hreewavelengths
(assuming
1
and input termi nals excited anti-phase)
and for
=0.1.
Fig.
17 is a
plot of these phases (small
numerals)alongeach piral ilament tarting at he
center erminals.Largernumerals epresent hedif-
ferencesnphasesbetween djacentilaments. The
shaded circular areas are those regions in which the d
ference of phases between adjacent filaments is approx
TABLE
I
TYPICAL
HASE PROGRESSIOX
L ~ O K G
N
ARCHIblEDEAN SPIRLL
FILAMENT
7.88 inches (1500 mc)
1c
11.8 inches
(1000 mc)
15.f5 inches (750 mc)
(radians)
S / h
(360) S/h (360) 180
(360) 180
360)360)
S / X
(360)180
ir
2 2 202
15
102
8296
76(16)
4
ir 564(204)
080
1
81ir 361(1)
282
0215353
ir
225
5
40
00
2
70
1r
191
1
95
(degrees)degrees) (degrees)degrees) (degrees) (degrees)
812(92)
226
06(46)42 182)
72
Iir
1 OS(2.5)
13
53(193)
98
38(18)
05
1443(3)
228
128(48)
46
506(66)
44
0ir 2254(94)
1414(194)19219(139)061r 1826(26)
182
4
64(244)
83
Fig. 17(a)
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196
Sis hid a: Coupled
L e a k y Waceguides
I : T wo
Pa.ralle1 Slits
n a
Pla.ne
343
Fig. lf( b) Fig. li (c )
Fig. 17-Progressive phase change along a spiral antenna and phase differences between spiral filaments.
(a)
A
15.75 inches
(750
mc):
(b) A=0.1 , inches (1000 mc): (c) A=0 .1. inches
(1500
mc:).
mately zero. I t can be seen that as the wavelength in-
creases, th e region where the currents are in phase pro-
gresses outward rom hecen ter of thespiral.Addi-
tionally, i t can be n oted that the egion
of
in-phase cur-
rents at750 mc is one of anti-phase currents a t 1500 mc.
The spi ral sed for illustrative purposes hasive turns ,
and , since
a =0.1
inch per turn, the maximum diamete r
is slightly greater than
6.25
nches.
ACKKOWLEDGMENT
Theautho r wishes to hank
E.
klarston,head of
theMicrowaveAntennas ndComponentsBranch,
Electronicsivision,avalesearchaborator?.,
Washington, D.
C. ,
for his contributions and for the en-
lightening and encouraging discussions. The author a
wishes to th an k J . DonnellanandR. IYiegand
of
the
same organizationfor their assistance.
Coupled Leaky Waveguides I:
Two
Parallel
Slits in a Plane*
S.
NISHIDA?
Summary-Theoretical expressions are derived or the effects of
mutual coupling between two parallel leaky wave antennas located
inan i n h i t e plane. The eaky wave antennas reated slitted
rectangular waveguides, the propagation constants of which are
modilied by the coupling. It is shown that the attenuation constants
influenced signscantlybut that the phase constant s are hanged
onlyslightly,
so
that he coupling is different from hat between
neighboring surface wave lines. The natur e
of
the coupling effects
are illust rated by numerical calculations.
vised manuscript received Jan uar y 18, 1960. The research reported
Origin manuscript received by the
PG.qP,
Xugust
8,
1959; re-
was conducted under Contract AF sponsored by the
.Air Force Cambridge Res. Ctr., Air Res. and Dev. Command.
York, N. Y.: on leave of absence from Tohoku University. Sendai,
t Microwave Res. Inst., Polytechnic Institute of Brooklyn, New
Japan.
I .
INTRODVCTIOK
HE longitudinally slitted rectangular waveguide,
with radiation characterized bl, leaky waves, has
already been investigated by employing a trans-
versenetworkrepresentationand perturbationpro-
cedure to solve the resulting network resonance prob-
lem. The above investig atio n has been carried out for
a
single (isolated) leaky waveguide. I n this paper, two
coupled leaky waveguides carr\-ing the HI( , eak>- wav
L. 0.
Goldstone and -4. A . Oliner, Leaky wave antenna :
Rectangular waveguides, accepted for publication in I R E TRAX
OK
qXTESXAS AKD PROPAGATIOE; .