Traveling Wave Linear Antenna !!

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384 IRE TRAhSACTIONS O N ANTENlVAS AND PROPAGATIO;\T

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The Traveling-Wave LinearAntennaEDWARD E. ALTSHULERf, MEMBER, IRE

Summary-It is shown experimentally that an essentially travel-ing-wave distribution of current can be produced on a linear antennaby inserting a resistance of suitable magnitude one-quarter wave-length from the end of the antenna. A theory for the resistively-loaded dipole antenna is formulated on the basis that the insertedresistors (one in eacharmcan be replaced by equivalent generatorsand tha t the resulting triply-driven antenna can be solved by thesuperposition of singly- and doubly-driven dipoles. Approximately 50per cent of the power is dissipated in these esistors.

With a traveling-wave distribution of current on an antennaavailable, the properties of this antenna are then investigated andcompared with those of the conventional linear antenna. It is oundtha t he input mpedance of the traveling-wave antenna remainsessentially constant as a function of antenna length, whereas that ofthe conventional linear antenna varies considerably. It isalso shownthat the input impedance of the traveling-wave antenna varies onlyslightly over a 2 to 1 frequency band. The directional properties of thetraveling-wave and conventional dipole are compared, and it isshown that a minor lobe does not appear in the radiation pattern ofthe traveling-wave dipole until it is much longer than the conven-tional dipole. Also, it is s h o w n hat where the directional propertiesof t he conventional dipole are quite sensitive to a change in fre-quency, those of the traveling-wave dipole are not.

received, October 3, 1960, and January 1, 1961. This research was* Received by he PGAP, June 30, 1960; revised manuscriptsmade possible by support extended to Harvard Cniv. by ;\FCRLunder Contract No. AF19(604)4118.rence G. Hanscom Field, Bedford, Mass. Formerly with Cruft Lab.,t Electromagnetic Rad. Lab., AF Cambridge Res. Labs., Lau-Han-ard University, Cambridge, Mass.

INTRODUCTIONHE properties of the linear antenna have een investigated in considerable detail by King.l I t habeenhownheoreticallynd verifiedxperi-

mentally that an essentially standing-wave distributof current exists on short antennas of this type. Thisreport deals with a linear antenna very much like theconventiona l one, except that it has beenmodified sotha t a traveling-wave distribution of current exists onall but its end quarter-wavelength, which has a standing-wave. The trav eling wave is produced on the an-tenn a very much as a traveling wave is produced on atransmission line. According to transmissio n-line theoa pure traveling wave can be created by terminatinline in itscharacteristic mpedance. If the ine isas-sumed lossless, itscharacteristic mpedance s a purresistance. If th e line were terminated in an open circuit , one could produce a traveling wave by placing aresistor equal to the characteristic resistancef the linin erieswith he ineone-quarterwavelength romits end.

University Press, Cambridge, Mass.; 1956.1 R. If. P. King, The Theory of Linear Antennas, Hanrar


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X linear antelma is i n two ~ . a \ - s imilar to an open-i t ends i n an open circuit

nce th e boundary condi tions state that t h e axial cur-must go o zero at th e en d of the antenna. Sec-

standing-wave distributionof cur rent exists oni t may therefore

ible to creat e a traveling n-ave 011 a inear an-

Unfortunately , the antenna does not have a charac-i n the TEM sensethe transmission line. Therefor e, the correc t valueof

ce is not mmediatelyobvious.However,byt can be shown th atexistsbetween hecharacteristic esistance

f a transmission line aud the expansion parameter $an anten na. The inpu t impe dance of an ideal, open-

transmission line is

h is the length of the line and P o is the free spaceIhe zeroth-order input impedance of azi,,=- -o I) cot $ o h ,

277h is th e half-length of the dipole a nd j-, is the

Therefore, X, or-l0 /2r$.

Th e expansion parameter is a somewhat arbitrarilyof the vec-

at an y ross section on the outside surfacehe an ten na to the tot al axial current in the conduc-

cross section. It ca n be shown that this ratioreasonably constant overall par ts of the antenna, ex-

is veq- small or zero. I t can be$ A 0- , where G 2 I n 2 h j a , where

is the half -length of a dipole, anda is its radius.? Sinceparameter js a function of the length of

anten na? while the characteristic resistance is inde-ent of the length of the tra~z sn~i ssionine, i t is obvi-

s that this correspondence is not precise. It does sug-however, an order of magnitude of the resistance

o approximate a raveling-wave distribution60 $ ohms. Since the quantity

- 2 has a value in the range of 9 to 15 for reasonablydipoles, a resistance of theorder of magnitudeo2 ohmsmightbeexpected, for example.when

= 12 .The heoreticaldistribution of current on the re-ti\:e-loaded antenna is calcu lated as follons. The re-

is first replaced by a constant-voltage generator.is made possible by applJ-ing hecompensation

? Ibid., p. 77.

theorem of network heor)., which stat es hat a 1 1 im-pedance i n which a current I is flowing c;m be replacedb>-a potential difference equal to - Z , without chang-ing the electrical behavior of the network. I n replacingeach resistor by a constant-voltage generator, one ob-tains a dipole driven b! three separate generators. Dueto he inea ritv of hiaswellsequations,onecansitn-plify the problem still further b\- applying he super-position heorem, which st at es hat i f severalsourcesare present i n a linear electrical network, the networkmal- be solved by finding the currents or voltages in thenetwork resulting from the presence of one source a t atime, and then superimposing the results. The voltagegenerators omitted are replaced by connections of zeroresistance. This enables one to treat the three-generatorantenna as the uperposit ion of two ymmetrically -driven antennas; one driveny a single generator at t hecenter, the other driven b>- wo generators, each locatedone-quarter wavelength from the end. In order to ana-lyze the doubly-driven dipole, superposition may be ap-plied again.This ime t is thesuperposition of twoasymmetric ipoles.The symmetric ipole an esolvedapproximatelyby reating ts opandbottomparts separately, as i f each were a base-driven antennaover an infinite, perfectly conducting plane. The cur-rent distribution has been calculated for a loaded an-tenna of half-length h =3 Xj4.3

Once a sound experimental setups available, it is pos-sible to producea traveling-wave d istribu tion of cur ren ton a linear ant enn a by inserting a series resistance one-quarter wavelength from the end of the antenna. Theinputmpedance, urrentdistribution nd adiationfield of this a ntenna the n can be measured. From thesedata, the behaviorof the travel ing-wave linear antennacan be completely described. I t is found that it differssignificantly from the correspond ing standing-wave an-tenna. I n order o how hesedifferences,numerouscomparisons remadebetweenhe esultsobtainedfrom the two an tennas.

ESPEKIMESTALESYLTSI m p e d a m e a n d i ld n zi tt an .c e

Th e first experimental task was to determine whichvalue of resistance,whenplacedone-quarterwave-length from the end of the anten na, produced a d istr ibu-tion of cur ren t which most closelq. resembled a travel-ing wave. Carbofilm resistors having dc values rangingfrom 3 ohms o 1 megohmwere selec ted. The inlped-ances of these resistors were measured a t 600 > IC, andit was found tha t as the val ue of resistance increased,the dc and R F values began o differ. For resistancesgreater than 500 ohms, the correlation was very poor.The microwave impedance of the resistor was measured

Lab., Ham-ard Universi ty, Cambridge, M a s s . Sci. Rept. So . 7 ; 1960.E. E. Altshuler, The Traveling \\-a\-e Linear Antenna, Cruft


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by locating the resistor at th e en d f the center conduc-tor of a coaxial ine in series with a short circuit , andthen measuring he nput mpedance.

-1s has been previously mentioned, the input imped-ance of a traveling-wave transmission line is independ-en t of the line length. I t therefore seems reasonable toassume hat he nput mpedance of a raveling-waveantenna is alsoessentiall>- ndependent of its ength.Therefore , b! measuringhenputmpedance of atraveling-wave antenna as a function of its length, it ispossible to det erm ine Ivhich value of resistance, n-henplaced one-quarter wavelength from the end of the an-tenna,changes hedistribution of current so that tmost closel!. resembles a traveling wave, without hav-ing to actuall?, measu re the distribu tion of cu rre nt tha texists for each resistor. Xfter extensive measurementswhich nvolved the use of numerous esistors, it wasfound hat he nser tion of aresistorhavingadc re-sistance of 240 ohms produced an antenna that had aninputmpedance whichwas almostndependent oflength. The R F value of the resistance differed b! lessthan a few per cent from the dc value. It was also dis-covered that the impe danc e char acter isti cs of this an-tenna were not sensitive to a small changerom the op-timum resistance.

i37ith a 240-ohm resis tor fixed a t a dista nce of one-quarterwavelengthfrom heend of the ant enn a, heinput impedance of t he ant enn a was measured a t 600YIc as he half-length h was changed rom0.5 X to

I ,I y - - - - - h ~ ~ TRAVELING WAVE CU14 +

e, > STANDING WAVE - n 40 fl

1.5 X in 0.05 X increments. Thenormalized input impeance of the monopole above an image screen is plo ttei n Fig. 1. For the purpose of c omparison, the measureimpedance of the corresponding standing-wave antenis also plotted on the same graph. The actual measuimpedance of the monopole can be obtained by multipl!.ing the norma lized value by123.6 ohms. The impeance of the corresponding dipole is simply twice thatthe Inonopole. It is interesting to note that the impedance of the raveling-wavedipolehasavalue of aproximatel!. (32O+jllO)hms. herefore, i t seemreasonab le to assume that the input impedanc e of tunloaded dipole should approach this value as the dlength approaches infinity.

I n order to investigate the broad-band properties the traveling-wave antenna, the input impedanceof aant enn a of half-length, Jz =31.25 cm, was measurover a frequency range from 300 3 Ic to 900 l l c in 101 I c increments. The result is shown in Fig. 2. The 24ohm resistor was located 12.50 cm from the end of t hantenna whichcorresponded toone-quarter h a t 60> I C . Onceagain, he mpedance of thecorrespondinstanding-wave antenna is plotted on the same graph.

Distr ibut ion of CarrentThe distributionof current on th e 240-ohm loaded a

tenna was measuredoralf-lengthsangingromh = X ; 2 to h =11 X/4.3 The relative amplitude I I1 T~ c& 2.0i2 1 31 25cm-q250cm TRAVELING WAVE-> STANDING WAVE -

40 il

Fig. 1-RIeasured normalized impedances of tral-eling- and Fig. 2-Measured normalized impedances of traveling- andstanding-wave linear antennas a t 600 hIc. standing-wave linear antennas ( h=31.25 cm).


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0=ar1I:I, and real a n d imaginar>. compo-I/ l-oaand I!,! are lotted for antennas ofh = 5 X18 and 11 h:4 i n Figs. 3 and 4 along

BT , which is a reference phase that varies linearlyalong theantennaand herebl-corre-

to the phase of a pure traveling \vave.Since the relative amplitude decreases almost expo-

and since the phase varies al-i

sx

l l c -.& s the esis tance is incrcased bove 240 ohms.hestanding-u:ave ratio begins to increase. For the limitingcase of K =x , one n.ould expect the current distribu-tion to resemble rhat of a1 1 alltenlla of half-lengthh = 3 X;?. I t is for this reason t ha t the standing-\~--a\,,epatter11 shifts by 90 ; I S the resistance is increased frombelow 240 ohms to above 240 ohms. The phase of theunloaded antenna oscillatesomewhatinusoidall>-about the linear traveling-\vave phase. s the resistanceis increased, the amplitude of the sinusoidal oscillationdecreases until at 240 ohms i t is essentiallJ- zero. LA s theresistance is increased above 240 ohms, he amplitudebegins to increase. The shift that the sinus oidal- phasepattern undergoes \\-hen the resis tance is increased f rombelow 240 ohms o abo\Fe 240 ohms is 180. This cor-responds to the shift that the phase patte rn of an un-

Fig. 4-Distribution of current for k =2$ X: Fig. 5-Distribution of current for lz=7 A!4


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328 I R . E T R A N S A C T I O S S OAV A S T E N ; Y A S A N D P R O P A G AIO X Julloaded antenna undergoes when it is reduced in lengthfrom h=7 X/4 to h = 3 X/2.

I t is expected that the standing -wave dist ribut ion ofcurrent on the unlo aded antenna eventually approachesthat of a traveling wave, as the antenna is madeongerand longer. The curren t dist ribut ions of the unloadedan d 240-ohm loaded an tennas of half-length h= 11 X/4(the longest antenn a that could be measured with theavailableequipment)areshown in Fig. 4. rls canbeseen, there is little indication that the unloaded antennais beginning to approach a traveling-wave distribution.Therefore, it seems reasonable to assume that, asn thecase of the open-circuited transmission line, the an tennamust be extremely long before a traveling-wave distri-bution comp arable to t hat obtained by the insertion ofa 240-ohm resistor is produced.

Radiat ion FieldThe relative power patterns of traveling- and stand-

ing-wave dipoles ar e shown in Figs. 6 and 7. -4s is ex-pected, hedirectionalpropertiesdonotdifferverymuch for short dipoles, since the current distributionsaresomewhatalike.However,as hedipolebecomeslonger, a significant difference arises i n the respectivepatterns. A minor lobe does not appear n the radiationpat ter n of the raveling-wavedipoleuntil i t ismuchlonger han hecorresponding tanding-wavedipole.This behavior is in agreement with the power patterns

I I I I I I I I I I I

Fig. &Measured power pat tern of traveling-wavedipole a t 600 Mc.

I 1 I I I I I I I 1 1

Fig. 7-iMeasured power pattern of standing-wavedipole a t 600 Mc,

which were calculated earlier.3 I t seems th at th e nulwhich ordinarily appears in the radiation pattern of thconventional dipole, s essential ly filled in for the traveing-wave case. Therefore, he sidelobe n he conven-tional dipole pattern becomes part of the main lobe inthe corresponding traveling-wave dipole pattern. I tinteresting onote that some raveling-wavedipoleshavehalf-powerbeamwidthsof pproximately loowhich is considerably larger than the beamwidths thacan be obtained with conventional dipoles.The adiationpatte rns of traveling-andstanding-wave dipoles were also measured as a function of frquency for dipoles f half-length h=32.6 cm. The owepa tt ern s of these dipoles ar e shown in Figs. 8 and 9 .can be seen that where the directiona l properties of t hstanding-wave dipole are quite sensitive to change ifrequency, those of the traveling-wave dipole are relatively insensitive. Therefore, the traveling-wave dipolin addition to having a broad-band impedance, also a broad-band radiation pattern. Naturally, as the fre-quency is changed from600 Mc, the frequencyat whicthe resistor is at an opt imum d istan ce of one-quarterfrom the end of t he antenna , the trave ling -wave distbution of currentup o he esistor ends owardstanding-wavedistribution.Therefore,onewould epect the directional properties of both loaded and unloaded dipoles to be very similar a t 1200 Mc, the fre-quency a t which the resistor is t X from the end of thantenna.

I I I I I I I I I

20"

Fig. 8-Measured power pat tern of traveling-wavedipole ( h=32.6 cm).I I I I I I I I I I )

iVIEASURED F'OWER PATTERN OFSTANDING -WAVE DIPOLE (h=32.6 cm1

Fig. 9-Measured power pat tern of standing-wavedipole ( h=32.6 cm).


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Altshuler: T h e I'razding-JT*are Linear .Antenna 329

Let he efficient!. oi anant enn a be defined as hef t he pon-er radiated by the antenna to the power

ower th a t is deliveredrtenn a and is not radiated is usually dissipated

oi heat. I n general, the conventional linearenn a has radiatin g efficiencl; of close to 100 per cent .

he onl!- losses which a re presen t are those due to theconductivity of th eantennaand he nsulatorsh may be used to suppor t it . Th e 240-ohm loaded

pproxinmtely 50 per ce nt ef fi ~ie nt. ~C oh- C I > vs r oh- s

The result s which have been reported here representextensive investigation of the traveling-wave linear

its comparisonwithhe onventionalnear ant enn a. It has been shown experimentally that

essentiallg; traxTeling-wave dis tri but ion of c ur renton ;I inear antennaof !!A 10, by insert-of approximatelq~ 40 ohms one-quarter

from the end of th e antenn a. The radi ationnce of the traveling-wave monopole above an irn-

eplane is approximat ely 160 ohms.Therefore, heitude of t h e cur ren t at the esistor must always be

t h e amplitude at the input of the antenna,re power must be delivered o the ant enn a tha n

n the r esistor. For this reason, the cur-amplitude on the traveling-w ave antenna s always

Xs the resi stance is increased from its opti-of 240 ohms oward nfinityordecreased

distribution changes from anwave oastandingwave.This

ransition is quite gradual. It is expected that the cur -distribution would undergo imilar ransitionthe resistor is moved, for example, from its opti-

um position of one-quarter wavelength from the endf the anten na to 4 wax.-elength from the end.

The input impedance of the traveling-wave antennahas been shown to remain essentially constant s a func-tion of antenna length. I t is for this reason that this an-tenna is very broad-band compared to the conventionallinear antenna. A broad-band antenna s i n practice verydesirable since it allows a good impeda nce match to beobtained over a wide band of frequencies. As has beenpointedou tearlier, hebandwidth imitation esultsfrom the fact that upon changing frequency, the electri-cal distance of the resistor from the endf the antenna schanged rom tsoptimum ength.Therefo re, he es-sentiallyconstant nput mpedance of the raveling-wave ant enna as a function of length tends to the vari-able input impeda nce of the standing-w ave antenna.

The direction al propertie s of the traveling-wave di-pole have been shown to be quite different from thoseft h e corresponding standing-wave dipole. IYhether theyare more useful depends on he particula r applicatio nfor the antenna. The radi ation properties of the travel-ing-wave dipoles are superior to those of the conven-tional dipole in two respect s. First, the traveling-wavedipole can be operated over a relativel!? wide frequencyrangewith only a smallvariation n tsdirectionalproperties. Secondly, i t can be designed to hav e a half-powerbeamwidth which is over 20" larger han hatwhich can be obtained with a convent ional dipole.

411 investigationdirected oward mproving he ef-ficiency of this antenna is present]!, being conducted. I tmay be possible to replace the carbon resistor bl; moreuseful resistive element, for example, a resonant antennan-ith theappropriate adiation resistance.Therefore,energy ordinarily dissipated in ohlnic losses will insteadbe radiated by the second antenna.

A C K N O W LED G MEN TThe aut hor s indebted to Professor R. IT. . King for

h is very helpful guidance and encouragement during thecourse of this research.

Traveling Wave Linear Antenna !!

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