the archimedean two-wire spiral antenna-efc

7/23/2019 The Archimedean Two-wire Spiral Antenna-EFc

1/12

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

AlultIXDoM1a1UfIX Ra


2/12

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.



3/12

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.


4/12

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



5/12

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



6/12

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.



7/12

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



8/12

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-



9/12

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 ,"



10/12

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.



11/12

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)



12/12

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; .

the archimedean two-wire spiral antenna-efc

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