an experimental study of the dipole antenna with non-reflective resistive loading (1966) shen

8/6/2019 An Experimental Study of the Dipole Antenna With Non-Reflective Resistive Loading (1966) Shen

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AN EXPERIMENTAL S T U D YOF THE DIPOLE ANTENNAWITH NONREFLECTING RESISTIVE

I Scientific Report No. 7

LOADING

-.I

September 1966

GPO PRICECFSTl PRICE(S) $-ard copy (HC)Microfiche (MF)ff653 July65

"Reproduction in whole or in part i s permmed by the U. S .Government. Distribution of this document i s unlimited.

NATIONAL AERONAUTICS AND SPACE ADMINISTRATION

Prepared under Grm? No. NSG 579Gordon McKay Laboratory, Harvard University

Cambridge, Massachusetts


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AN EXPERIMENTAL S T U D Y O F THE DIPOLE ANTENNAWITH NONREFLECTING BESISTIVE LOADING

BYLiang-Chi Shen

Scientific Report No. 7Reproduction in whole or in pa rt is perm itted by the U. S.Government. Distribution of this document is unlimited.

September, 1966

Pr ep are d under Grant No. N s G 579 atGordon McKay Labo ratory, Ha rvar d Unive rsityCambridge, Mas sachus et sfor

NATIONAL AERONAUTICS AND SPXCE ADMINISTRATION


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-1-1. Introduction

Traveling wave antennas a r e desi rable for purpo ses of broadbandand direc tiona l communication. A trave ling wave antenna m ay be obtainedby introducing dissipative elements into the antenna system [l], 2]. Theintroduction of loss y elemen t wil1:inevitably res ult in a dec rease i nefficiency, but the lo ss of over all efficiency in a transm itt ing sy stem isoften the pr ic e to be paid fo r an improv emen t in the broadband and thedirect ional proper t ies .i t sel f , it ma y be added to the feeding network in ord er to m ake the syste mbroadband however, the traveling-w ave pro pe rty is then not achieved. Onthe oth er hand, efficiency should not be of ma jor co nc ern in a receivingantenna for which the req uir em en ts of a broadband, direc tivity and as impl ici ty of s t ructure a r e usual ly the most important factors .antennas a r e being designed for use i n sa tel l i te communication.

If the lossy element i s not added in the antenna

Resist ive

In Al tshulerD swork [l] it is found that a t raveling wave may ex iston an antenna with lumped re sis to rs located a qua rter wavelength fro mthe ends of the antenna.depends line arly on the wavelength, such an antenna cannot have a verybro ad band.beforehand.t o 1 megohm had to be teste d sepa rately on the antenna in Alts hule r 'sexperim ent in or de r t o find the suitable r es is to r which could induce atrav elin g wave on it.

However, since the location of the resistor

Fur therm ore, the resista nce of the resis tor cannot be knownIn fact , re si sto rs with d-c re sistan ce ranging from 3 o h m s

In t h e work of Wu and King [ Z ] i t i s found that i f the antenna is made ofres i s t ive mater ia l mch t h t z i, the internal impedance per unit length, is


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-2-a p arti cu lar function of the position along the antenna, a pure outwardtrave ling wave can exist on an antenna of finite length. It is found tha ti f

i CoQ az (z) =-2Pthen the zero- order curren t is

The constant f& is determined byh-h9 1I(z) = I I ( z ) )eikR/ R d z s l (3)

2 2 1at the maxim um of I(z ), where R = [ z-z ') t a ] z . In the aboveequations, z is th e axial coordinate,f ree space, h is the half-length of the antenna, k is the free-space wavenumber, and a is the radiu s of the antenna. The antenna i s assumed to

-iutbe dr iven by a delta-function gene rator which ha s tim e dependence eand an e mf of one volt. Note that he re the distribu tion of the z alongthe antenna that is necessary to support a travelin g wave i s determinedpredominantly by the physical distance ra the r than the elec tric al distance,with the freq uenc y dependence appe aring only in f&logari thm [ref. 2, 4. 291.band. Moreover, the current distr ibution (2) s a simple function whichcan be easi ly integrated to get the field pattern.

co is the intrinsic impedance of

i

in the fo rm of aTh mf ore the antenna should have a very broad-


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- 3 -The purpose of this experiment is to me asu re the cur ren t

distribution , the input adm ittance, and the ra diati on field pa tte rn of thecylindric al antenna with nonreflecting resis t ive loading in or de r to com-p ar e th em with the th eo ry of Wu and King [Z]. Due to technica l reason ,

iantennas with z varying in the form of s teps rat he r th an in continuouslyvaryin g fashio n have been built.have been tr ie d in o rd er to simu late the continuously loaded antenna.

Various de signs of this step antenna

F ro m the ana lytic point of view, the antenna with step -fun ctionizpa rame t e r as tepwise var ia t ion of zpa rame t e r aper turba t ion of apat tern is sma l l for a nea r 1. In this sens e the com pari son between thetheo ry and the meas ured resu lt of the antenna with step-function zbecom es meaningful .

is inconvenient. In an analysis ca rr ie d out by Shen and Wu [3] th ein (1) is not restr icte d to unity as i t is in [2]. Hence the

i ca n be viewed as the discontinuity of thein (1) and i t ha s been concluded in [3] that the effect of the

on the cur rent distr ibution and the refo re the field

i

In t hi s e x p e ~ m e n the frequency range i s chosen to be f ro m 450to 900 MHz.construct ion of, among other things , e lect r ical ly sm al l pr ob es .t ion to this rea son, the difficulty in obtaining the right ma te ria l to mak ethe effect resist iv e coating at higher freque ncies is also a majo r factor .The indoor m etall ic imag e plane which w as avai lable for this exper iment

A highe r frequency range would cau se difficulty in theIn addi-

res t r i c t s the iise of lower freqrrency range.The inte rnal impedance of the antenna to be me asu red h er e i s many

t im es higher than that of the ordina ry br as s antenna; such h igh re s i s -


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-4 -tivity is obtained by spraying resistive paint on a dielect r ic cyl indr icalrod. In ord er to be able to me asu re the intern al impedance after therod has been spra yed, the thickness of the resist iv e coating mu st be madesm al ler than the skin depth of the res is t ive m ate r ia l at the frequency rangementioned ea r l ie r .can be me asure d e asily and accur ately, would be a good indication of theinte rna l impedance of the coating in the r - f field.coating is thin, the field due to the antenna pen etra tes into the coatingand the o rdina ry intern al probe with metall ic coaxial transm ission l inecannot be used to me asu re the cu rre nt distr ibution on the antenna. Anexter nal probe with a se ri e s of detuning sleev es built on the coa xial conduc-tor in orde r to minimize the current excited on the lead w ire [4] wil l notwork eithe r because in the prese nt c ase the operating frequency is notfixed.high res is t ive w ires used as leads is thus proposed. A diode rectifier,however, can only detec t the amplitude of the field, the other imp ortan tinfor ma tion about the phas e of the field i s sacr i f iced. Thus in this exper i -me nt the antenna wi l l be shown to have a relat ively invariable distr ibutionof the amplitude cu rre nt , of the driving-point admittance, as well as,the field pa tter n against changing frequency , which we sh all cons ide r asa proof that the antenna has a broadband.antenna wil l be d om onstr ated by 'me asur ing the field pat ter n of the V-antennawhich is for me d by folding down the two a r m s of the dipoie antenna ..The existence of a trave ling wave on the antenna is not dem onstrated di-rectly but is believed that it will be suggested by the experim ental results.

The refor e the d-c resista nce of the coated rod, which

Inasmuch a s the

An extern al probe w i t h diode re ctif ier attached to the loop and with

The directio nal ch ara cte r of the


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-5-The phy sica l length of the antenna that wi l l be under test is

chose n to be 50 cm long, or 1 wavelength long at 600 MHz.for this choice is as follows.s is , the radiatio n efficiency of the antenna i s known to in cre ase a s theantenna becomes longer ( see ref. 3 Fig. 10).antenna length is favoured. With a longer antenna the d iffer enc e betweenthe theory and the experiment can be see n mo re clea rly s ince the for me ris only of zer o-o rde r acc ura cy a s ra diated power has not been taken into

The reasonAs a resul t of previous theo ret ical analy-

For th is reason a longer

account.antenna length on one hand and on the other hand longer resistive wiresa r e needed for a longer antenna in orde r to feed the s ignal detected bythe diode from the loop to the measu ring equipment, consequently the sig-nal-to-noise ratio is reduced. Pe rha ps the dominant factor that l imitsto 50 c m is the fact that i f the length is increased the required internalimped ance ne ar the dri vin g point would become too low to be obtained inthe laboratory.

However, the limited size of the indoor ground plane re st ri ct s th e

2. The Free-Sp ace Room, The Transmitting: System-and theDetecting: Sy ste m for Curre nt and Admittance Mea surem ents

F o r the measur emen ts of cur ren t dis tr ibut ion and driving-pointadmit tance of the antenna, a metallic im age plane is used,as usual, so thatthe obs erv er and the equipment a r e completely out of the field due to theantenna under test . The ground plane used in this experimen t is made of

-inch aluminum pla tes. It is 305 cm high, 3 6 6 cm wide and i s surroundedby absorbing mater ia l s to form a room about 244 cm high, 33 0 c m wide, and208 cm long. The antenna is located near the cen ter of the ground plane.


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- 6 -The deta i l s t ruc tur e of this free- space room and the ground plane canbe found in Wh iteside's work [5], who orig inally designed i t in 1962for experimental s tudy of various p robes .over the near f ield of an antenna operat ing at 600 MHz, it is found thatthe room is al so suitable fo r purpose of cur ren t d istributio n and inputadmit tance measurem ents over the frequency range of 450 to 900 MHz.F o r purpos e of testing the facili ty, the cu rre nt distribution,and the inputadm ittance of an ordi nar y br as s monopole antenna have been me asu red byconventional shielded loop probe with superheterodyne detec tion over thefrequ ency range ju st mentioned.with hem isph eric al cap at i t s end; the slo t along the antenna was 0.159 cmwide. The slo t w a s cove red with a br as s s lab during the measureme nt ofthe input admittanc e.relat ive dielec tr ic constant equal to 1.04 approximately.the measurements a re shown in Fig. 1 and 2 and they a r e found to be i ngood agree me nt with both the theory [ 6 ] and the expe rimen tal data obtainedby others [7 ] . It is fel t that this test gives a good indication of the useful-ne ss of this free-spa ce room for curre nt and input admit tance meas urem entsin the frequency range of 450 to 900 MHz.

While his concern was mainly

The antenna w as made of br a s s tubing

The antenna w as supported by a polyfoam table withThe results of

The transm it t ing system consi sts of an U HF osci l la tor made byth e G en era l Radio Company of Ma ssa ch us et ts (Ty pe 1361-A) with modulatingpower supply (Type 1264-A) which can provide ei the r C W o r 1 KHz squarewave modulation.1050 MHz and the frequen cy can be set within 0.2 perce nt of acc ura cy bymeans of a vern ie r sca l e d i a l once ca libr atio n has be en done.

The frequency range of the osci l lator is $.om 450 to

The freauencv


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I-zW30L L0w133

-IQ5

aa

kaw>I-Q-1W

-a

/250 I I I I20 15 10 5 z ( c m ) 0( C ) f.451 M Hz

--

-% /0.2 /I

-0 1 I I I

10 5 Z ( c m ) 05 20 15(a ) f =901 MHz

/-

O I I I I I5 Z(crn) 05 20 15 10( b ) f = 606 M H z

0.8

FIG. 1 THE CURRENT DISTRIBUTION ON A BRASS ANTENNA


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.

m0zW3ULLI-zWUWLLLLnI-

ws

-aaZZWI-zaammmlxw-I0a0z0ELL0W0zI-I-2naa

a-I-3zcu-6-LL


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-8 -with Type B plug in unit), it i s capable of displaying a s ignal f rom 0. 05volt per cm to 0.005 volt pe r cm in 4 step s.manu factured by the United Tra ns for m er Co rpora tion of New York(Model 4c).of Harva rd Universi ty.detecting syste m i s illu stra ted in Fig. 3.

The band pa ss f i l t er was

The voltage am plifier w as mad e by the Acoustic Lab orato ryA block d iagra m showing the ar rang em ent of the

3. The Ex ternal ProbeThe extern al probe co nsists of a silico n video de tecto r diode

(mo del num ber MA-4123A manu factured by Microwave As soc iate s ofMassa chuset ts) and a capacitor of 330 farad d-c capacitance which,toge ther with the diode, fo rm s a squ are loop about 1 cmX 1 cm in d imen-sions. The diode is 0.24 cm i n diameter and is 0. 75 cm long, and thecapac i tor is of similar dimensions.to r s spaced about 3.0 cm from center to center , a r e connected to t he twosides of the loop serving as two lead s for the d etected audio signal(se e Fig. 4).is perpend icular to the antenna under measurement,and is about 50 cm long.It consis ts of res is to rs wi th 390 ohrns d-c res is tance, 5%pre cis ion, and

wattage rating, except the two r es is to rs ne are st to the loop which a r e

Two s t r ings of res is tors , wi th res is-

The fir st section of the resis t ive wire s is erected ver t ically ,

470 o h m s with 10%prec ision and 1/8 wattage rating.the res i s t ive w i res is horizontal, is para l l e l to the antenna, and is about55 cm long, while the d-c res istan ce of each resi st or is 200 ohms with 570precis ion and 4 wattage rating. The total d-c re sistan ce of each wire i sabout 10 K-ohms.wire s a r e confined in a plexiglass tube of 1.27 c m 0. . and 0.94 cm i. d.,

The second sec tio n of

R e s i s t o r s ar e so ldered together and the two res ist ive


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tt

We@ g0v)0

I 1eco=3, uu20I * I


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FIG. 4 THE EXT ER NAL PROBE


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- 9 -and they a r e cemented by epoxy ma ter i a l a t seve ral places in orde r tosec ure the junction and prevent the w ires from short-circuit ing.

The vert ical section of the res is t ive wires is furthe r embeddedin a polyfoam block which in turn r e s ts on a polyfoam p latform so thatthey form an inver ted T-shaped s t ructu re (se e Fig. 5).tion of the resistive wire is at one end connected to the v ert i cal section ofthe wire at the top of the inverted-T and the other end of it goes through andr e s t s

The horizontal s ec -

fre ely in a hole on the ground plane and lead s to the audio am plif ier.At the bottom of the polyfoam platfo rm th er e a r e two teflon wheels o

The wheels can rol l or sl idne side and a set of two keys on the other side.in a t rac k which is embedded in a polyfoam table on which the whole struc-tu re r es ts , including the antenna under measurem ent. The keys a r e to lockthe platfo rm in position while it is being moved.slotted plexiglass tube of 0. 70 cm 0 . d. and 0. 32 em i. d., so hat the plat-for m can hard ly be shifted either sideways o r upward a s i t is moved by ahorizontal force along the direction of the antenna.

The track is made of a

The polyfoam platform as well as the extern al probe can bemoved at the back of the ground plane by means of a plexiglass rod of1.02 cm in diameter .end, goes throug h a hole on the ground plane and has a n indicator attachedat the other end.tion of the ext ern al probe.antenna and is 10. 0 cm above the polyfoam table. ,

This rod is firmly attached to the platform at one

The indicator re st s on a s tee l scale to regis te r the posi -The rod is 19.2 cm away from the ce nter of the

A s he polyfsam platform is pushed by means of the plexiglassrod and moves along the track, it is found that the distan ce between the


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FIG. 5 T H E E X T E R N A L PROBE A N D ITS SUPPORTING TRUCTU RE


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-11-

t rave led along and above the antenna.in the ra ng e of 0. 3 to -0. 3 db at the cu rren t maxima and 0.8 to -0. 3 db a tthe current minima. The differe nce between the two sets of readings ob-serve d with the two different probes at the current minima some t imesamounted to 2 to 3 db as seen f rom Figs. 1 and 2,cur rent nul l is attributed to the fact that the exte rnal probe has l a rger d i -menaians (1crn X 1 un)than the shie lded loop (0 .02 c m n diameter) so hatthe form er responds to the averaged field at the cu rren t null which is l a rge rthan the field strength at. ha t point. the in-ability of the extern al probe todetect accurately a current minimum is not a serious defect in the presentcase because for a resi t ive antenna the curre nt distr ibution is expected tovar y smoothly.

It was ob served that the signal varied

The difference near the

In platting the exp erim ental data, the mid-point of the diode in theexternal probe is ar bi tra ri l y re fe rre d to be the posit ion of the external probeBut it is seen f romFiigs . 1 and 2 that the agreemen t is bet ter if the anode enthe diode is chosen to be the r efe ren ce point instead.measurements , the positi on of the ex te rn al prob e is determined by theposition of he anode end of the diode.

Hence, in dl following

4. The Res ist ive C oatingThe r es is t ive antenna is composed of sections of dielectric rod coated

with resist iv e paint . The dielec tric rod is made of 1/4-inch plexiglass rod.The ends of ea ch sec tion s a re machined so that sections can be screw ed intoone another afte r having been spra yed individually. Two bra ss ends a re mad


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-12-to f i t each rod.against re sist iv e paint in the pro ce ss of spra ying and also a s a goodelec t r ica l contact f o r d-c res i s tance measurements .ends a r e removed when the 'individual sections a r e connected togetherto become a resis t ive antenna.

They serve a s a protection for the sc rew ends

These b r a s s

The brass-ended plexiglass cylindrica l rod is put on a latheready for spraying. After many tes ts, the resist iv e paint f inally chosenw a s co m m erc ial ly called "Shielding Paint'! (NO. RS-14, ma de by M icr o-Ci rcu its Company of Michigan).paint ca n be thinned to be spra yed in a spraygun and s t i l l be adhesive,the resi sta nc e stay s relat ively constant aft er spraying, and the paintdoes not settle too quickly fo r uniform spraying along the r od.

The choice was made because this

The Shielding Pa int i s f ir st thinned by adding an equal amount ofsolvent (N orm al Butyl Ace tate), then fil tered through two overlappingdisposable paint str ai ne rs with 60x48 m es he s pe r square inch. Thespra y gun i s clam ped to the automatic feed er of the lathe.sprayed , the plexiglass rod is revolving at a speed of about 3 revolutionsp er second, the s pr ay gun advances about 1 c m pe r second, the distancebetween the s pr ay gun and the rod is kept at about 8 to 10 cm , and thenitrogen p re ss u re feeding the s pra y gun is regulated at 12.5 pounds persqu are inch.

While being

F o r obtaining d-c res ist an ce in the vicinity of 6000 ohms p e rm ete r , two to four coats ar e enough; for resistancem e t e r , as many a s ten to twelve coa ts a r e needed. In addition to thenumber of coatings as a variable to control the res istan ce of the rod,

8CC ~ F i i i s e r


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-13-the dista nce between the s pra y gun and the rod can be adjusted to getthe pro per thickness of the coating.opening of the nozzle of the spr ay gun and the nitrog en pr es su re , a rekept unchanged.also depends on the liquid level of the paint in the conta iner of the spraygun, precis e control over the resis tanc e is found very difficult.of this difficulty, exc essive coating is som etim es reduced by sanding.This is done with the coated rod revolving on the lathe and with the au to-ma tic fee der guiding the sand paper which is held by the hand.pape r has ve ry fine ( N o . 320) gri ts and e ach sanding stroke i ncr eas esthe res is tance of the rod only about 1 o r 2 ohms out of about 100 ohms.Sanding is used only for the low resi sta nce range (about 1000 o h m s perm et er ) and to increa se the resis tance of the coated rod by not mor e than20 percent . Under a microscope the sanded surfa ce can be seen to beroug her than the unsanded surf ace , but in gen era l the roughness is nom ore than 20 per cen t of the averag ed thickness of the coating.aged thickness of the coat ing on the rod can be est imated as sl icedsamp les a r e viewed under the micro scope . Some of the re sul ts a r eliste d in th e following table:

All other factors , such as the

Nevertheless, sin ce the rat e that the paint is sprayed

Because

The sand

The aver-

Table 1Thickness of the C oating and the Conductivity

Sample

1234

Re s ist ivi y(ohms met e r )703793845960

Thickness( c m )0.004- 0.0050.00350.00350.0035

Conductivity(mho/meter )1 . 7 8 ~ 1 0 ~1.42 X1.8OX1O31 . 6 9 ~ 1 0 ~1 . 4 9 ~ 1 0 ~


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-14-Table 1 (Continued)

9 9 7102510401220

0.0035 1.43x1030.00 3-0.Q04 1.63 x103-1 2 2 x 10.003 - 0.004 1.6ox1o3-1. 20x10.0025 1 . 6 4 ~ 1 0 ~

According to the above rough estim ate of the thickn ess of the coating, t heconductivity of the r es ist ive paint c an be put to be equal to l . S y l 03 mho perm e t e r .at 900 M H z and 0.061 c m at 450MHz. The in tern al impedance per unitlength z of a conducting tube of outer radiu s c and in ne r rad ius b is ,according to eq. (3 ) , p. 356 of [ 8 ] .

For this conductivity the correspon ding skin depths ds a r e 0.043 c

i

-2 P I C J,(F,C) Y1 (Fib) - Y0@f 1J1(Blb) 30 C Jpf Yo (Fib) - Y1@f ) Jl(F1b)z i = r ( l - + ) ( y ) b (

where ro i s the d-c resistance of the tube and1 -

dS = 1/ ( II f 5 rl ~ ) z , P, = (1-j) / dS (where f is the frequency;. p and Cr a r e respect ive ly the permeabi l ityand the conductivity of the conducting tube.

1 1

In the present case, t= c - bA0.005 cm, c=Q3175 cm and t < ds so hat (4) can be reduced to (6) :

for t < I C and t


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-15-

3080(t270) 2980 (-1.3%1450 (+2.1(!70) 1 400 (-1.40/907 tl.2%) 886 (-Oe8

997 t2.2%) 960 -1.5%

until i ts d-c resi stan ce has the des ired value of the inte rna l impedance.

sect ion A2.99 c m4780 (t4-8%)1640 (t3.8%)735 (-3%)793 (-470)

The uniformness of the coat ing in the circ umfer ent ial or in

sect ion B5.98 c m4430 (-2.4%)1550 (-1.9r)769 (91.570)845 (t27o)

the axial di rec tio n of the rod cannot be me asu red . However, with therod revolving at the speed of 3 revolutions per second and the sp ray gunadvancing 1 cm per second in the process of spraying, while the jet of thespra y covers about 1 cmXl cm ar ea a t the surfa ce of the rod, i t se em sreason able to believe that the rod should be uniformly coated in the c i rcum-ferent ial direct ion. As o the question whether it is evenly coated alongthe axia l dire ctio n of the rod, som e tes t sprayin g has been done and theresul t s a r e lis ted below. Each tes t s amp le consisted of two sections ofdielectr ic rod joined together by br as s ends. It was sprayed as one unit.The resul t ing resis t ivi ty of each sect ion is l is ted in Table 2.

Table 2Resulted Resist ivi ty ( in ohms /meter) for

Uniformness Tes tOpe rat ion

f i r st sprayssecond spray sth i rd sprayssanding

Sample 2sec t ion A sect ion BI3. 31 c m 1 5.00 c m

~ _ _ - _ -In the above table the number in the paren thes is is the percen tage of thedeviation of the resis t ivi ty in the indicated sect ion from the averaged res is-tivity of the two section s combined. According t o the above resul t i t s eem sthat the coating of the rod is reasonably uniform in the axial direct ion.

The evenness of the coat ing in the circu mferen t ial and inthe axial direct ion was also checked under the microscope and no signi6icanunevenness was observed.


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-16-The resi stiv ity of the coating does not become stable until

about f ive days af ter the spraying, for resist iv ity near 1000 o h m s p e r m e t eit would take longer for thicker coatings and shorter for thinner coatings.The res is tance in general drops 3 percent every day in the f i r s t few daysafter spraying. In order to save t h e , some of the coa ted rods have beenput to us e only one day af ter the spraying, without waiting for the irresista nces to become stable. However, al mo st all measurements foreach antenna were completed within ten hours in or der to minim ize theeffec t of the changing res isti vity .

Warning for those who want to obtain the re sist ive coating byfollowing the foregoing proc edur e: The Butyl Acetate used a s the thinnerof the resist ive paint is highly ev aporative and flamm able.University H ealth Serv ice, prolonged contact with the sk in or breathingvapor or sp ra y m is t should be avoided, the sp rayin g should be done direc tlyin front of a n adequate ventilating facility, and a ma sk with a proper a irf i l ter should be w orn by the worker during the spraying.

According to th

I

5. De sign of the Stepped Inte rna l Imped anceFrom he previous description of the spray ing proc ess for ob-

taining the resist iv e coating and the cri teri on as well as the method ofchecking the result ing intern al impedance, it is c l ea r that it is notpossible t o make an antenna with a n interna l impedance pe r unit length thatvaries continuously accor ding to a cer tain pat tern such as hat descr ibed in(1). In ord er to approx imate the variat ion of the intern al impedance of (l) ,the only possibility s ee m s to be dividing the antenna into a cer tain numberof sections each with a constant zi at a value clo se to the zi of (1) at the


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-17-corresponding place. The result ing variat io n of intern al impedancewill then be in the f orm of a step function that zigzags around the smoothcurve of (1).discontinuity in the a - factor i s smal l , it is believed tha t the ste p functionvariat ion of z made according to (1) wil l be a good realization of thetheoretically requi red smooth variat ion of z descr ibed by (1).

If the number of s teps is sufficiently larg e s o that the

ii

The f ir st design of an antenna with interna l impedance varyingilike a step function i s shown in Figs . 6 and 7. It allows z of the antenna

to v ar y between two fixed value s of asection. The length of eac h sectio n i s then decreased, but an interes t ingfea tur e of this design is that the total resis tance of each sect ion is a con-stant, excluding the las t section.aistics of the antenna a r e theor etically known to be not crit ica lly dependenton he parameter a , it was hoped that this design would simu late bes tthe antenna with the continuous res istiv e loading assum ed in the theory.Two anten nas of thi s design have been built and tested and the res ult isdesc ribed in the next section.

nea r a = 1, except for the last

This design res t r ic ts the var ia tion ofwithin a ce rta in percentage fo r mos t of the antenna. Since the ch aracte r

iA second design f o r the ste p function variation of z used in thisexper iment is as follows.tions of equa l length, with the int er na l imp edan ce of ea ch equal to thatcorresponding to the ce nter point of this section that is prescr ibed by ( l ) ,as i t is shown n Fig. 8 . This mak es the deviation of a f rom 1 largeraway from th e driving point than near it.should have l es s effect away from the driving point than that near it, it is

The antenna is simply divided into seve ral sec -

However, the deviat ion of a f rom


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2 0

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I I I I I I I I I

III---iI

-

I I I I I I 1 I I0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0I /h IFIG. 8 DESIGN O F Z (ANTE NN AS NO. 1, 4, 5, 6 817 )


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-19 -Antenna No. 1 was intended to be put into a slot ted br as s tube

of inn er rad ius b to form a coaxial-line-like struc ture . If the cu rre nton the inne r conductor (the resi stive PsantennaP9)s assum ed to be equalin magnitude and opposite in phase to that on the o uter conductor (th ebr as s tube) , which is approximately co rre ct , the curre nt dist r ibut ionalong this s t ruct ure should be mor e accura tely described by the zero -or de r theo ry than that of an antenna. The proportionality constan t !&defined in (3 ) for the %oaxial l ine" i s equal to 2 log (b/a),not involve the frequency at all.tube used in the experime nt is 2 .42 cm , which ma kes 9 of the coaxialline equal to 4.06. Thus the a factor of antenna No. 1 is equal to

which doesThe inne r radius of the slotted b ra s s

unity, and the curr ent distribution is expected to decay linearly,a nd thephase to p rogress l inear ly as descr ibed by (2). The experim entalresu l t is .shown in Fig. 9, where the magnitude and the phase of thecu rre nt have been measu red by mea ns of a n ordin ary shiklded loop withsuperhete rodyne detection.experiment i s rem arka bly good.the resu lt of the meas urem ent brightened theLhope that the r es ist ivecoating and the step-function des ign of the i nte rna l imped ance should workfavorably in ca se of other antennas.

The ag reem ent between the th eory and theThis antenna w as first built and tested ,

Fig. 10 thr oug h Fig. 15 show the re sul ts of the me as ure me ntof the current distributions and the input admittances of the other sixantennas l is ted i n Table 3. The curr ent distr ibut ions ar e plot tednorma lized to the input admittance.in the fo rm Y = G t j B where j= -i. Fo r an antenna, the proportionality

The input admittances a r e plotted


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33/65

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THEORYrTIT111lrl EXPERIMENT

I I I I I I I I I I I I I I I I0 60" 80" 8 100" 120" 140" 160" 180"20" 40"FIG. 23 FIELD PATTERN OF RESIS TIVE DIPOLE ANTENNA AT 490 M H z

THEORY1 E X P E R IM E N T

- 3 0 I I I I 1 1 1 I I I I I I I I I I0" 20" 40" 60" 80" 8 100" 120" 140" 160" 180"FIG 24 F IE LD PATTERN OF RESIS TIVE DIPOLE ANTENNA AT 605 M Hz


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La-1 -2c

- 25

- c

T H E O R Yl3IUED E X P E R I M E N T

T60" 80" 8 400" 120" 140" 160" 180"" 20" 40"

FIG. 25 F I E L D P A T T E R N O F R E S I S T I V E DI PO L E A N T E N N A A T 705 MH,0

- 5

I0 -10

c m t E A SU R E D \LW-lfad -2 0CL

-25

-30 "L L0" 40" 60" 800 looo 120" 140" 160" 180"FIG. 26 F I E L D P A T T E R N OF R E S I S T I V E D I P OLE A N T E N N A A T 800 M H z


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(80) l3MOd 3 A l l V 1 3 t lI I0 LnI


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- 2 6 -490 to 900 MHz.pa red with frequenc y change.

The change in width i s considered to be sma l l as com-

8 . ConclusionsAntennas with step function zi have been built to simula te

In view ofhe antenna with nonreflecting continuous re sis tiv e loading.the analysis carried out i n the previous report [SI, the comparidonbetween them is meaningful as long as the deviation of atak es into account the discontinuity of z , is not large.amplitude of the c urren t distr ibutions a r e found to decay l inearly on theantenna, which ag re es with the theory.been me asure d and the agree men t with the theory is in gen eral good.curre nt , the input admittance, and the field patter n are found to be veryinsen sitive to changes i n frequency which is als o anticipated successfullyby the theory.

from 1, whichi The mea sured

The radiation field patter ns haveThe

The zero-ord er theo retical input admittance does not agree wel lwith the experim ental data, but the the ore tica l input admittance of aninfinitely long resistive antenna which is obtained by m ore rigor ousFou rier Tran sform method with an approKimated kernel , ag re es with theexper ime ntal data remarkably wel l .

The rad iation field pa tter n of a V-antenna with the angle betweentwo a rm s of V t t equal to 90" has be en measu red when each a rm of the iantenna is made of a monopole antenna with nonrefiecting s tep fmctiorr zThe agre em ent between theory, and experim ent is again good. The front-to-back ratio of the V-antenna was found to be mo re than 14 db and themajor lobes a re at leas t 7 db higher than the minor lobes in the frequencv


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.

-27-range of 490 to 900 MHz.insensit ive to changes in frequency.

The shape of the pattern is found to be v er y

iThe above evidence pro ves that the antenna with step wise zdoes have a ve ry broa d frequency band and it se em s that the existence ofa t r ave l ing wave on i t s a rm s is suggested by the experimental results.

Although the antenn as we re built with a physica l length equal to50 cm only, the above conclusions se em to be rat he r g ene ral sinc e thefrequen cy range under which the antennas were teste d i s rather wide.It is believed that they should be appl icable a t leas t fo r antennas withelec trica l lengths not muc h gre ater than one wavelength.

It i s observed f rom F ig. 16 that the imaginary p a rt of th e inputadmittance obtained from the zero -or de r theo ry does not agre e with theexper iment . It is se en that z on the dipole antenn a with nonre flectingresist ive loading is relat ively constant ne ar the driving point and theessential characterist ic of this antenna is, just l ike an infinitely long re sitive antenna, the existence of a t raveling wavei t se em s reasonable to suspect that i t s input admit tance i s clos e to that ofan infinitely long re sis t iv e antenna which c an be obtained by a m o r er igorou s Fouri er Transfo rm method using an approximate kerne l .input conductance of a n infinite antenna fo rm ed by a cyl indr ic al tubular coductor of constant z ha s been studied by Shen and Wu [12]. The inputsuscep tance of this antenna is obtained i n the Appezdix.the or eti ca l value of the input adm ittan ce of an infinitely long tubularantenn a of con stan t zreflecting resi st ive loading obtained exp erime ntally (se e Fig. 16a) .

i

on i t s a rm s . Therefore

The

iIt tur ns out that t

i is ve ry clo se to that of the d ipole antenna with non


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-28While the input admittance of the infinite antenna is not se nsitiv e tothe value of z , a s it can be seen in Fig. 2 of [12] and in Fig. 16aof this repo rt , nev erthe less physically this antenna and the dipole antennawith nonreflecting resist ive loading do have a sim ilar ch ara cte r andthe agre em ent between the two se ts of data of input admittance is thoughtto be mo re than a mere coincidence.

i

ACKNOWLEDGMENTThis sub ject was introduced to me by Pr ofe sso r Ronold W . P. Ki

two yea rs ago and without his patient guidance and many helpful sugg esrtions which he ha s given m e since then, this w ork could neve r have beencompleted. I am deeply grateful to him.

I wish to express my appreciat ion to M r . E. J. Joh son whoconstructed the exper imental apparatus .


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-29-REFERENCES

1. Altshuler , E. E. ,T h e Traveling- Wave Lin ear Antenna," IR E Trans .AP-9, 324-329, July 1961; doctoral disserta t ion, Har vard Universi ty,May 1960.

2. Wu, T. T. and R. W. P. King, !#The Cy lin dr ica l Ahtenna withNo nre flec ting R es is tive Loading,'f HEEE Tra ns. AP-13, No. 3,369-373, May 1965; Scie ntif ic Re po rt No. 1, Gordon McKay Lab .,Ha rva rd University, 1964.3. Shen, L. C. , a nd Wu, T. T. ~ 'The Cylin drical Antenna with Ta per edRe sist ive Loading, Scientific Rep ort No. 5, Gordon McKay La b.,Ha rva rd Univers ity, August 1965.4. Hatch, R . M. J r . , "Current Distrib ution on Conducting Sheets

Exc ited by Ar ra y s of Slot Antennas,If Tec hnica l Rep ort No. 103,Cruft La b. , Ha rva rd University, July 1950.5. Whiteside, H. ,Wl ectr om agn etic Field Probes,31 Technical Re portNo. 377, Cruft Lab . , Harv ard University, October 1962.6. King, R. W . P ., Aronson, E. A. and Ha rris on, C. W. Jr., "Deter-mina tion of the Admittance and Effe ctive Length of C ylin dri cal Anten-na s ,t'Radio Scien ce, Vol. 1 [New Series), No. 7, 835-850, July 1966.7. Mo rita, T., !!The Me asure men t of Cu rre nt and Charge Distr ibut ions onCy lind rica l Antenn as, llTechnicaP Re po rt No. 66, Cruft Lab. , HarvardUniversi ty, February 1949.8 . King, R . W. P. l 'Fundarnental Ele ctro ma gne tic Theory, W ov er , 1963.9. Iizuka, K . , !'Experimental Studies of the Traveling-Wave V-Antennaand Rela ted Ahtennas, Scientific Rep ort No. 2, Gordon McKay Lab.,Har vard U niversity, October 1964.

10. Duff, B. M. 1fThe Re sis tiv ely Loaded V-Antenna: sc ie nt if ic Re po rtNo. 3, Gordon McKay Lab., H arv ar d Uni versity , October 1964.11. Iizuka, K . and King, R . W. P. 'OThe Traveling-Wave V-Antenna,'8Scientific Re po rt No. 4, G ordon McKay La b., H ar va rd Univ ersity,M arc h 1965.12.. Shen, L. 6. and Wu, T. T. 9vR adiate d ow er and Ohmic Loss c?f theInfinitely Long Cylind rical Antenna:' Scien tific Re por t No. 6, GordonMcYay Lab. Harv ard University, Feb ru ar y 1966.13. Wu, T. T., 'PTheory of the Dipole A nt em a and the Tw o-W ireTra nsm issi on Line,"$. Math. Phys .1961. Voll. IT.9No. 4, 550-574, July -Augu


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-30-APPENDIX

In thi s append ix the input susc epta nce of the infinitely longitubu lar antenna of rad ius a, with uniform z , and dri ven by a del ta-

function gen erato r, is evaluated.I(z) on the antenna has been obtained in re f. 12, Eq. 2):

The Fourier Transform of the current

The input susceptance of this antenna cannot be obtained by integra-t ion along the r ea l axis of the imag inary par t of the left-hand side of (A- l)sinc e such an integration does not exist . The singulari ty of the imaginarypa rt of the driv ing point c urr en t ha s bee n known to be a consequence of theassumption of the delta-function gen erato r. In view of the s uc ces s of theemployment of a n approximate kernel used a s a subst i tute for the exact ker -ne1 K ( 5 ) in Wu's th eo ry on long an tenn as of infinite conductivity [13], in

-the sense that such a substitution yield s a finite value of input admi ttanc ewhich ag re es with the experim ental result , the input admittance Y of thisinfinitely long resistive antenna is hereby defined as

d5 ZI'0, i y n2 9(k2-52) [ & 2 y t i ~ - log (1-5 /k )] t ik2%where % is the path wrapping the left bran ch cut shown in Fig. A-1.

This is permissib le s ince for ZI=O, ;fr< g , the zeros nearthe branch points a r e in the next sh eet of the Riemann sur face . This i s


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L e f tbranch cut

5 - planeRightbranch cut

FIG. A-1 THE BRANCH CUTS OF 5;? ( 5 )


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- 31-proved as follows.

The zer o is near f=k, thus the denominator of the integrandof (A-2) can be ap proximated and equated to z er o a s follows

and -a /Z2( e2 = a r g ( St k) < 3 z / 2 .L et c=ky=k(ltutiv), (A-3) beco me s

(v2-2u-u2) U-2v(ltu) 8 + Z I = 0(v2-2u-U2 ) 6 tZ v(lt$ Q - 5 = 0

2 2 2 2here Q = c-4 og [ (2 tu ) t v ] [u t v 3and

e = e t e1 2Therefore

v 5 / 2 Qand

uc Z I t 5 (5-46) /4Q] /2QF o r ;k = Z I , the zero is a t c = k [l t(ZIti%)/ZQ].0

F o r ZI 0, 5 < 2 n , assume tha t u is posit ive, then O N - 3a/2 , but(A-7) gives a negative u. If u is assum ed to be negat ive,(A-7) gives a posit ive u. Therefo re the ze ro is actual ly on th e other

e-" - 3 X 12, but

(

((

Riemann s urf ac e, not on this defined in Fig. A-1. This com pletes the proof.


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.

2111y = -{O

for

where

-32-By a change of variable, (A-2) becomes

Z 1 = O , y 2 n

Num erical integrat ion of (A-8) shows that the r ea l pa rt of Y is equalto the input conductance obtained from prev ious calculat ions carr ied in[12], a s it should be.in this way has been calculated for a n inf ini te antenna of radius a = 0.3175 cmand zf r o m 450 to 900 MHz.

The n um eric al value of the input adm ittance defined

i ranging from 720 to 1440 o h m s p e r m e t e r at frequency rangingThe result is shown in Fig. 16a.

(A


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Security Classification .DOCUMENT CONTROL DATA - RLD

ORIGINATIN G A C T I V I T Y (Corporate author)Division of E ngineering and Applied Phy sic sHarva rd Universi ty, Cambridge, M a s s .2t3 R E P O R T S EC U R IT Y C L A I S I F I C A T I O NUnclassified -

6 G R O U P

I. R EPO R T D A T E 7.9. T O T A L N O . O F P A G E 5September, 1966 62Shen, Liang-Chi

7 b . NO. O F R E F S1310 C O N T R A C T O R G R A N T N O .

NsG- 79b. P R O J E C T N O .

9 a . ORIGINATOR'S R E P O R T NUMBER(S)

Scientific Report No. 7C

d.

Ob . O T H E R R P O R T NO(S) (A ny other number. that may be aasign adt ~ aeport?

3 ABSTRACT The amplitude of the current, the input admittanc e, and the radiationfield pattern of a cylin drica l antenna with a step-function in terna l impedance a r em ea sur ed in the frequency range 450 to 900 MHz.function a r e tr ied in or de r to sim ulate the antenna with the smoothly distr ibutedres ist i ve loading which has been studied in previous rep ort s. The experimentalr e su l t i s com pare d with the theory. It is pointed out that such com paris on i smeaningful in the light of the ana lysis ca rr ie d out in previous r ep or ts. It ha sbeen found that the z ero -or de r theory gives acc urate d escriptions of the c urr en tdistribution, the field pattern, the prop ert y of a ver y broad freq uen cy band ofthe antenna, and the existence of the traveling wave on the antenna. The agree -ment of the input admittance is not good, but it i s found that the th eore ticaladmittance of the infinitely long resistive antenna which i s obtained by ae r Transform* method fi ts the experim ental data sa tisfactori ly.

Se ve ral designs of the step -

1 SUPPLEMENTARY NOTES

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UnclassifiedSecurity Classification~~4. KEY WORDS LIIR O L E

experimentdipole antenna with nonreflecting re sis tiv etraveling wavedirectional

loading

Iide freq uency bandcu r rent distr ibutioninput admittancefield pattern

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an experimental study of the dipole antenna with non-reflective resistive loading (1966) shen

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