Directive Gain and Impedance of a Ring Array of Antennas

7/22/2019 Directive Gain and Impedance of a Ring Array of Antennas

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I EEE TRANSACTIONSON - 4 h ~m 3 ~am PROPAGATIOX VOL. AP-14, O. 5 SEPTEMBER 1966ture dist ribution and the feed line reflection lobes

f tuning devices in the properms of the transducers attached to the feed lines.The beampositions were close o those predicted. Th e

L~CKNOWLEDGMENTTh eauthors wish to express heirappreciation o

in this program; to Dr. ,4. T. Villeneuve, for hisysis of waveguidedistortionandmode solation;H. Nonnemaker, for his assistance in making

REFERENCES[l ] M.Y .Silberberg and J. P. Campbell, Space vehicle applicationsof self-containedDoppler radar, Natl. Conf. on Aeronaut icalElectronics, pp. 10&109,1959.[2] H. Saltzmann and G. Stavis, A dual beam planar antenna forJanus type Doppler navigation systems, 1958 IRE Natl. Conv.[3] A. J. Simmons, 0. M. Giddings, XI. Diamond, and J. Gindsberg,Rec. , pt. 1, pp. 243247.

I E E E Innternatl. Cono. Rec., pt. 1, pp. 56-69.4 multiple-beam two-dimentional waveguide slot ar ray, 1963[4] F. J . Goebels and T. S. Fong, Four independent beams from asingle h e a r array, IEEE Trans. on Antennas and Propagat ion,[j] R. L.. Fogeh Orthogonal mode transducers and waveguide step

vol. 4P-13, p~,.83-691, September 1965.transltlons, Microwave Lab., Hughes Aircraft Co., Culver City,Calif.. Tech. Memo 467. March 1957.[6] s. Silver, ~ l ~ u r m a z ~ entennaTheoryandDesign. New York:McGraw-Hill, 1948, pp. 182-188.[7] S . P. Morgan, Mode conversion losses in transmission of c ircularelectric naves through slightly non-cylindrical guides, J . -4ppl .P h p . , vol. 21, pp. 329-338, April 1950.

Directive Gain and Impedance of a Ring Array of AntennasG . 31.ROYER, ~ M B E R , E E

Absfmcf-Ring arrays can be made so that they concentrate thein the plane of the ring a nd are also omnidirectionalso ) in this plane. This paper deals with ring arrays which

hese properties. For antenna engths which are equal oX/4, graphs are includedwhichshow,ormake t

o calculate, antenna mpedance, the ratio of maximum odirectivegain in the plane of the ring, and hemean

i n the plane of the ring.

I . INTRODUCTIONHE RIN G ARRAY, as considered in this paper,consists of identical cylindrical monopole antennaswhich are mounted perpendicular to a perfectly

e circumference of a circle (see Fig. 1) .The amplitudef the currents in all the antennas in the array is th e

but he phase changes progressively round heotal phase change for one revolution around

If there were an infinite number of antennas in theay, he field strength would be independent of a.a finite number of

the field pattern, 0 constant , is serrated (seeFig. 2) . If desired, this variation in field strength can be

t small by a proper choice of the numberof antennasof the ring, and the nu mber of360 phase changes of current round the ring.

of 360.

Manuscript received September9, 1965; revised March 31 , 1966.The authors with the Defence Research Board,Ottawa, Canada.

Pages2 an d Chireix3 have shown th at (if the rad ius ofthe ring is not too large, and the current phase changea t least once through360 round the ring) the horizontadirective gain (e=90) is greater than thatof one of theconstituent monopole antennas isolated from the array.Thearraymay hereforebesuitedasanazimuthlyomnidirectional,antifadingantenna.This paper investiga tes the properties of ring arraysfor which

1) the serrations n he horizontal field pattern aresmall

2 ) th e mean horizontal directive gain is greater thanth at of one of the monopoles from the ar ray.

For antenna lengths which are equal to and less thanhi4, graphs are included which show,r make it easy tocalculate,antenna mpedance, heratio of maximumto minimumhorizontaldirectivegain,and hemeanhorizontal directive gain.Hickman4s5s6has computed antenna mpedances for

neer, pp. 102-109, April 1948.October 1948.

3 H. Chireix,Antennas 2 RayonnementZenithalReduit,LOnd&Elec., vol. 15, pp. M M 5 6 , 1936.C. E. Hickman, Current distribut ion and terminal impedanceof a circular antenna array, M.S. thesis, University of Tennessee,Knoxville, $ugust 1960.Scientific Rept. 5, Dept. of Elec. Engrg., University of Tennessee,Knoxville,March1963.

6 C. E. Hickman, H. P. Keff and J. D. Tillman, The theory ofsingle-ring circular antenna array, Conzmutz. and Electronics, May1961.

H. Page, Radiation resistance of ring aerials, Wireless Engi-2 - , Ring-aerialsystems, WirelessEngineer, pp. 308-315,

5- , Firstorder mpedances of acircularantennaarray,


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ROYER: RING ARRAY OF A N T E N N A S 56 7

S I ANTENNA NUMBERFig, 1. Geometry of ring array.

4.

Fig. 2. Normalizedhorizontal field pat tern ,8=90 , s=7, n=2, g=3.0.

ring arrays where the elements of the ar ray are half-wave dipoles. In Hi ck r~ an ,~ anxtensive set of tables ofmodified zeroth-order impedance was compiled. In th ecomputation of modified zeroth-order impedances, i t isassumed tha t the cur ren t is sinusoidally distributed onthe antennas. Thiss only approximately true. A less ex-tensive set of tables of modified first-order impedancesis shown in Hickman,j where antenna half-length/an-tenna radius =75. These impedances were obtained byan iterative process, and should agree more closely withexperimental results than the zeroth-order solutions. I twas pointed out that there was no great difference be-tween he solutions, and hat, for many applications,modified zeroth-orde r impedances are sufficiently accu-rate. In this paper, the current is assumed to be sinus-oidally distributed on the antennas.

Knudsen7ns has investigated ring arrays where thele-ments of the arr ayare not perpendicular to, but are di-poles located in, the plane of the ring. The dipoles areeither normal or tangential to the ring. He has shownth at these arrays can also be made to havehigh direc-tive gain in the planeof the ring.

infinite number of tangential or radial dipoles, Proc . RE, vol. 41,7 H. L. Knudsen, (The field radiated by a ring quasi-array of a npp. 781-789, June 1953.* -, Radiation rom ingquasi-arrays, IRE Trans. mAntennas a d Propagation, vol. AP-4, pp. 452-412, July 1956.

11. FARELECTRICIELDSome symbols are definedelow (see also Fig. 1):s=number of an tennas in the ringa =ra dius of the ringp=29a/Xff=@--n/2

I , 0, and are the coordinates of the f ar fieldy,=29x/s--a; a+y, and a locatehentenna

numbered x- 2 r x n l s is the current phase in the antenna num-bered x, comparedohatnhentennanumbered s; n is an integerH =height of each antenna in the array

9=dG,hich was set equal to1207r for computingthe impedance characteristics f the ar rayp =2a/X.

Currents and ields appear, in general, as complex rmquantities.

Refer to Fig. 3 and consideraverticalcylindricalantenna on a perfectlyconductinghorizontalgroundplane. If the current is considered to be sinusoidally dis

t

Fig. 3. Geometry of monopole antenna .

tributed on the antenna,10 sin [ p ( H- ) 1

sin @ HI = (1)where los the current at the base of the antenna, theni t is well known that the fa r lectric field is givenby

j v Ioe- jor cos ( P H c o s e) - os p HEe =2 ~ rin PH [I sin 0 -1. ( 2 )~ T Y , in PH [ sin e 1. ( 3

Refer now to Fig. 1. Using ( a ) , the electric field dueto the antennan the array numbered is

jqIoe-jn(r*a)e-jorz cos ( p H cos e) - cos p HEeZ,=I n the far field, r , can be replaced by I in the denomi-nator, and by

Y - siny,sinOin theexponent.Theelectric field du e o all of theantennas in the array becomes

8Es = Ee,Z=l

=&e-i(BTt.no) [2 j ( n s i n (w ) sin O-n-rs)-1


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568 IEEE TRANSACTIONS ON ANTENNAS A h ?PROPAGATION SEPTENBERwhere

?r0COS @aos e) - os p a ]Eo = 2 ~ rin @a) in e - ( 3Page2 has shown that he unc tion in thesquare

brackets in (4) can be expressed in terms of Bessel func-tions. When this is done,o becomesEo=g ~ o e - j I B + n ( Q - - / 3 ) 1 r sin e ) e - j k s ( + w / z )k= O0+ (- ~ ) k * n ~ ~ ~ - ~ ( qin )e+Jzs(+-rr/2) ] (6 )

I t will now be shown tha t if, for a given value of s,the antenna impedance and field pattern properties of aring array are known for the values of n shown in ( 7 ) ,then these properties are easily determined for all posi-tive and negative integer valuesf n.

k = l

0 5 n 5 s/2 s an even number.0 5 n 5 (s- )/2 s an odd number. (7)

In the derivation of (6) , he phase of the curr ent in theantenna numbered 1, compared to that in the antennanumbered s, was made equal to

- a a / s . (8)An array with the same impedance and the same,r (aswill be shown in the next paragraph) almost the same,radiationpatte rn could havehe following cur ren tphases in antenna 1

zk [2mn 2 ~ a / s ] , ?n = 0, I , 2 . . . .Let the equivalent valuebe nl

andnl =5 [ms n]. (9 )

Substi tut ion of the values of n defined by ( 7 ) into (9)mak es it possible fo r nl to range over all positive andnegative ntegers. We herefore need to consideronlythose values of n given by (7).

Consideration of (8) shows tha t, when 05 n


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1966 ROYER: RING M A Y OF ANTENNAS 56 913-12-II-10-

9-

8--B=I7-l? 6-

5-4-3-

2-

WHEN n IS 1 , 2 8 3USE SCALE AT LEFTWHEN n IS 4,5&6 USE SCALE AT RIGHT**A

n - IP

q [RADIANS)

6.0

5.55.04.5

4.0

3.5 -g


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570 IEEE TWSACI'IONS ON ANTEhThJASAND PROPAGATION SEPTEMBERis a plot of the radiation resistance, divided by s, whenH = h / 4 (i.e., Rl/s ) .I t was found that the rati oR / R l , where R is the radi-ation esistance when theantennasareshorter hanX/4, was nearly independent of n, q , and s. R/R1 as afunction of H/X is shown in Fig. . The error n the dataused toplot R/R1 inFig. 5 was oundnever to begreater han3percentover he angeofargumentsdealt with in this paper.

Th e curves for radiation resistance, as well as thoseshowing the directive gain and reactance properties ofthe array, range from the value of q where R 1 = lQ , othe value q where either the mean horizontal directivegain becomes less than 3, or the maximum divided bythe minimum horizontal directive gain becomes greaterthan 4.

The radiation resistance or ant ennas whereH


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1966 ROYER: RING !&RAY OFANENNAS

- EAN HORIZ. DIRECTIVE GAIN571

Fig. 6. Mean horizontal directive gain when H / X = : (Le., D l ) ,and when H/X-+O, (i.e., DJ . Also maximum horizontal directivegain/minimum horizontal directive gain, which s independent of antenna height. IZ ranges from1 to 3.


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3 IEEE TRbhSACI ' IONS ON ANTENNAS A N D PROPAGATION SEP"3ER

35

30-00

r0Wuz

E25

::02WCa

a 15zW0

10

5'

0.

-5'

-10.Fig. 8. Induced reactance: n ranges from 1 t o 3.

40-

35-

30-Er

25-2E 20-0a

W03

n

9 15-

10-

5-

LFig. 9. Induced reactance:R ranges from 4 o 6 .


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1966 ROYER: R ING ARR4Y OF ANTElvhTTciS 573Due tophysical symmetry,

z s z = z s , s - x .The current phase in the antenna numbered -x , com-pared to tha t in antenna number s, is

- ma 25mfl.x(s - ) =- ~ n-S

When s is an odd number, (17) can therefore be written(s-1)/2Zi= z s z ( e f ( 2 r n z / s )+ - j ( 2 z n x / s '1z=

and the induced reactance becomes

When s is an even number, the induced reactance is

If the curre nt s assumed to be sinusoidally distributedon the antennas, X,, an be expressed in terms of sineand cosine integrals (see JordanlO).

Tables showing Xi were c ~ m p u t e d . ~ome of the in-formation in the tables appears in Figs. and 9. Plots ofinduced reactance are shown only for those arrayshichappear to be the most promising.To get the total reactanceor an antenna, add theelfreactance to the induced reactance,

x,=x,,+xi.The self reactance of cylindrical antennas has been con-sidered by many authors. Brown and Woodward1' havemeasured i t experimentally.One of thegraphs romtheir workll also appears in Jasik.l"

Englewood Clifis, N. J.: Pren tice-Hall , 950, pp. 352-353.10 E. C. Jordan, ElectrotnagtzeticTraces a d Radiat ingSystems.mined impedance characteristics of cylindrical antennas ," Proc. IRE,11 G. H. Brown and 0. M. \Voodward, "Experimentallydeter-vol. 33, pp. 257-262, Bpril 1945.

12 H. Jasik, - 4 n t e m an g i n e e r h g H a d b o o k . New York:McGraw-Hill, 1961, pp. 3-5.

Induced reactance instead of self reactance has beenplotted,because assuming that he curr ent issinus-oidally distributed on the antennas and the spacing be-tween antennas is large with respect to their thickness)induced eactance snearly ndependent of antennathickness. The otalreactance,however,doesdependcritically on antenna thickness, and therefore presentinthi s would have necessitated a much larger number ofgraphs.

I t should be noted that the induced react ance is fre-quently much smaller than the self reactance (particu-larly when the antennas are short), and so can often beignored.

VI . DISCUSSIONI t has been shown that the re is no point in consider-

ing arrays with valuesf n no t in the following intervals.0 5 n 5 s/2 n even0 5 n.5 (s - 1)/2 n odd,

as an arra y with n in the intervals can be found whichhas the same impedance and almost the same radiationpattern characteristics.

Th e properties of arrays wheren=0 and n= / 2 havenot been computed, because when fz =0, the horizontaldirective gain is low, and when n = s / 2 , the horizontalfield pattern is deeply serrated. Therefore, graphs areshown only for values f n in the interval

0

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Directive Gain and Impedance of a Ring Array of Antennas