AD-A!35 975 ELECTROMAGNETIC NEAR-FIELD COMPUTATIONS FOR A BROADCAST 1/,MONOPOLE USING NUMERICAL ELECTROMAGNETICS CODE (NEC)(U) NAVAL POSTGRADUATE SCHOOL MONTEREY CA D 0 THOMSONUNCLASSIFIED6 EP 83

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MICROCOPY RLSOLUTION TEST CHART

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NAVAL POSTGRADUATE SCHOOLMonterey California

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SECURITY CLASSIFICATION OF Tmis PAGE (fhm' note Entered)

PAGE READ INSTRUCTIONSREPORT DOCUMENTATION PAEDEFORE COMPLETING FORMI. REPORT HUMUEN Ii.1 GOVY ACSON N0 3. RECIPIENT'SCATALOG MU.89ER

4TITLE (40d SuMillo) S. TYPE OF REPORT & PERIOD COVERED-:ectrornagneti-- Near-Field Computations 'Master's Thesis;r:cr a Broadcast Monopole using Num~erical. September 1983Electromagnetics Code (NEC) 6. PERFORMING ORG. REPORT 04UMOI

7. AUTHOR(o) 11. CONTRACT OR4 GRANT %UMIER(e)

:avid Duerr Thomson

6. PERFORMING ORGANIZATION NAME AND ADDRESS 10. PROGRAM ELEMENT. PROjECT. TASK

Naval 7Postgraduare School AREA II WORK JNIT N4UM9ERS

'Mcntere':. California 33943

It. CONTROLLING OFFICE NAME AND ADDRESS 2. REPORT DATE

aalPostgraduate School Ie Tt ember 133.Nornrerey, Calif-4ornia 9394~3 i. N~UaMoR OF;AGES

14. MONITORING AGENCY NAME A AORIESS(i diffeent fro Coaaaelilf* Office) 1S.- SECURITY CLASS. '21 :hA report)

IS&. DECLASSIPICATiON OWNrPaOING

SCHEDULE

10. maSTRGUTlON STATEMENT (of hi Rle port

Aknoroved for Dub!i release, d istributionuni te

17. 01STRI11UTION STATIMENT (of the obotreel entered in Stock 20. it diferet Ito, Repor)

10. SUPPLEMENTARY N4OTES

Is. KEY WORDS (Cemfimdan ,ewev. alie it necessary and Idefftifr bp black nmbeer)

E~z:rcagntis ; Iea -i- ; oua :icns; A.me ric-a

20. AISTRACT fCa*nu.~ on reerse add Of necoosme INd Ideify by black aMeer)

7--e onn-as is the haract-eriza- icn D- -thelr near-1 t :nutSr---ra:, 7:a -' (1 3

:jc::,i-noutZare ner-ll: a( -oa o-l a-cnc-ocl. nn 'ords '" ~ - a~

>in- i.....n~enrna -:)r i ar c*:o ; zan ce 7n~ ~rE :r-~le E- -a a l 1 15 : o a; a's a fnn~ ail i:a:

00 , 1473 EIINOn O 5I ~LT$.'N 0102- LF-0Oil.6601 SECURITy CLASSIFICATION OF 741S P040E When Daoes Enter.,

A-oooved for o)ubiic reilease, ,-Js-:ribut-on rhmz

Electromagnetic Near-FEjeid Computazions

for a Broadcast Mono~ole using

'Vimerical El.ectromagnetics Code (NEC)

by

David Duerr T-homsonLi'~enntCommander, UJni-Led S-az es Nav

U n iversit:y of .Tashingror, -17 .

>z a7 -:,in1 ff1 men c erecqu-- -menzs fo7*e e e ~ Acession For

Justificatioll

Zoom -.he

:!A*A7 7, R2A D UATT 7C! C OL £AmIlabiluy Codes_-3- vif and/or

at special

/ (7r

Sz fcr:Rae

rma , -- 7 -le 777 T0

AE S T RA CT,

An of-.en ignored aspect of eiectrornagnetic radia-tio-n lfror

antennas is the charac-terization 3ff their near-fiel.ds. A

cornvuter Drogrxn, Numnerical 7BlectroragnieTics Code (NEC); is

Validated for accurate near-field conmmuzations and applie: to

a model off a b-rcadcast monzoople. and --i1~are lte

as a o-'zcna ooslZion abong r-a alenfla -Icrvaiu

di Stances fromI tnve sur'ace. -'-e filsare also lc e as

3. Z' flc--infl ra~il& ditac atar )r *rarious :ie-i.:"r-.

TABLE OF CONITENTS

I INTTRODUCTION -------------------

A. PROBL1EM ENVIRONMENT --------------

.THESIS STATEMVENT, SCOPE AND Li.MITATIONS ----------

M.DESCRITI ONj OF SELECTED ANALYSES------------------ 1

A. 2LASSTCAL AINALYS------------------------------

B.CONTEMPORARY ANALZSS--------------------------2

-. he -nt-i; a1 Equation 'Mezhod -------------

2.The Sween-Of f Method----------------------- 24

3. Moe Trheory : An-ernnas-------------------

4. Discussion-------------------------------- -1

C. N UMER I CA L A NA LYSIS---------------------------- 2

7- ~1. Hallen's Aooroach-------------------------

2. Paraboliz Inerolative F>Aooroach-- 2

3. esse' ruriction i Aooroach--------------

7iscussion--------------------------------

ITT DECFTN 'F i Z ---------------------------------

A. rBTATUTR E S CF H~E C 0DE -------------

3. zo:::~q-------:-------------------

cuacS------------------------------------

~run Pan---------------------------------,

2. ::rqAL )A'TONS----------------------------

ziec 74ri: Fil nt egral Equat4-n (FE

2. ~ - 7' P1t~ -:el Inrewal £.cua-~n F)-

-7- r :F:M:--------------------------

D. METHOD OF MOMENTS AND THE MATCH POINT -------- 4

1. Mathematical Concet ---------------------

2. NEC's Application ------------------------

IV. MODEL DESCRIPTION AND COMPUTATIONAL RESULTS ------- 53

A. MODEL DESCRIPTION ---------------------------- 53

!. Assumed Current Distribution------------- 53

. Modal .Modeln- ---------------------------

3. Sub-domain Modeling ----------------------

B. M.DEL CCFrURATCNS -------------------------

EXPE CT AT :ONS / O SZR.A-I N S /A,,-'.AL -1-S------------

I. E(Z) ?lots --------------------------------

2. (R) PTs-------------------------------

3. O() Plots ------------------------------- ,7-

----------------------------

V. A ,AL:DA C-ELD -ALCULAONS-----

A. COMPARIISH :1 :c:H CLSS-CAL AM ALYS:3

REUL" -7-3 - -T ---------------------------------------------------

3. CCMPAR:22M -,E "'J '17 7H,:C: A i A-YSSR EST - ---------------------------------------

-??~?-------------------------------------------

-N117 L, D:ISTR IBUT: 1:37 --------------------------------

. INTRODUCTION

A. PROBLEM ENVIRON=N1T

Maxwell's equations describe, for all space, the Electric

(E) ana Magnet-ic (H) FZields that are the medium for trans-

M.tLing information (virtually) ins tantaneous 1v over

extended distances. Thi 4S ractical a-_ptlication of electro-

magnetic (EM) radiation has generated considerable itrs

_n its 'ar-fielde* Characteristics. The anmd MJ vectocrs can

be analyticall,,. d-_etarmined when -the current_ C() on t he

radiat.or (from which th--e -Field vectors are grenerated ) has

been :Aescrizet. B'or the far-fiead regic-n of 7-oncooles an,,

Doles, acceoc)-able resut-s are ob-ained- by assum:i-,7 a

inusoidall-zvarvit- current. .'oeewe h

Avect-ors are calculacec :t r :ze: cints at ~Is--ances les-

-han X/2i (the near- ield re;ion), si ,.nificant errors occur

be-ween cacltdvalues and eiicl meas-.red ;4 us

- .. :icre7:ancv, _3 not the isu i:ao:rce n

Ma w ells :1a-r., but a.- be whollI a -Lri d t0 a n

_naccuratedsrt.t.o he:r-

~hefarfiedf~r a mncoole o-r ioeis defined as Iostances from -:he rad iat'o- gre ater th-an '2,whnere X is tnhe

**:aelenth. horfree -so-ace, \cfwhere =the freq,*uenc'; at

wn~h he -' :>tc ~ xcte-, nd ct-he s-_eedI li3ht :n

In the past, the inaccurac'>s of the near field cabcul-

tions were not a ?roblem--there was no nractical application

to which the eneryy could be aoDlied. However, in recent

years there has been an escalating interest in the close-in

problem. This inzerest has been generared by an increasing

proliferation of devices which use Radio Frequency (RF) energy

in such a manner that the user is exoosed to near-:ield

radiation (e..z. microwave ovens, hand-held walky- "<-talk'ies,

wireless telephones, RIF sealers, etc.).

:he U.S. Navy was one of the firs- organizations to

exoress an interest in these =ields. The interest was the

result of a concern for the hazards these fields might ocse

to fuels, ordnance, other ... oerational and ':es: ecuimen:,

and to nersonnel. The hazards posed b! fuels, ordnance,

and other -! .. uipmen7 result in over ef-ects; the hazaZ,-'s

nosed to personnel are not so obvious,

... h virtual unanimous consensus, the literature

identifies -he heating of boav ti3sue as the =_rmar; hazard

to rersonne. However, o:e n 1-- - ncn- hermal efects

have b-een obser... Some of -. ete effects ref7 ] _ic ue:

a) ninor :han-es in blood oroDe ies

D) a "Zuzz" heard bv cer--ain Deocle when exposed to

mi_ .....w.ave r. diation "

eThe "buzz" 's assume. to be a n...n of the seo_ 7u13 nrate ( r,°) ranher than the :arr:- .r...ec.

c) abnormalities o'E the chrirnosorne structure

d) movement, orientation, and polarization of rt'

molecules

e) changes in the transoort rate at the blood-brain

barrier

f) cofort mbalances, such as enigastricdsre,

emotional upset, and nausea.

The signif--icance of these ef'fects is not lvet 'nderstod.

The general oublic has not b)een exnosed to near-fi4el'.

radiation hazards orf surr-icient _4ntens_:vor uraio t-o be

cause for alarm; however, there are certain vocations in

whi7ch the incumbents have an elevated orcbab4lir': o

exoosure to this tvo7e orL field.*

B. TH.-SIs S:LA-'l:-N7, 3CCOPE -VD "_L'Y::A:I

:- order to orovide miore accuratLe data 'r nec7,?

researching bDiological fecso- near- fielA radiation, t~

id,, wIll valid*,ate a romurr o=a"' whir>::ru- --'e

near el eC-r4o, a n.i cor anek

erbitrar,7 rad-_iatLor. The :or c zr am aIso tbe usie to

Comoutle th.ese near fi_--2liS -'-r a reesrbdbbw

--he nrozgram, Mumerical crman~ - 2oe (12E), -.as

Ievloda-- Lawrence_ LIver~nore at-.raory inder the

a r e _a e or e ~n aeek n 3 r ac er.tn na r: a I'r s

soonsorshiD of the Naval Ocean Systems Center (N1OSC) and the

Air 'Force Weapons Laboratory. it can be easily learned and

applied directly by a researcher who has some knowled~fge of

electromagnetic theory.

The model to be used for the investigation will be a 75

mIeter high broadcast monoocle radiating above a oerfectiv

conducting around olane. -he 7roicA nlane i*s located in tne

X-Y olane; the mononole is co-axial with t.he Z-axzs. The

antenna will b-e excited at its bDase with a voltage sufci ent

to oroduce a radiated Do wer of 0 9,a wt ts. The exciLat*cni 3

at -- a frec uencv of 'I M e gah ertz, whic-h has -a wave length of 32

met7ers; hence, the monopole is a ciuart.er-waveiengt:hrdao

oorerat_1nz at resonance. A liagram of the model i*s 3shown i

n~ s7,_ -ai th I*s 7,o de, EC r ec1:i r e- t hat te antena

r b o boen I ito virt-uial s hc rt st3:r a i ht ~e me n t. .In

consonance t*~c h I s re~iu i rce n, thre e dfeetcn-1

tzns will _e isec :orcmuca a -n e comoose: ;

e~ n_ 17 Z - -nd4 -7e er , re, I-:.1..

§jnrcl:~'n'ethe ra -1a and -:ar a e

s, , an_ magne-i.

:cmut:. ie -;alue3 wille c~o~di 1meter

=nrenen-3 'or ocints 7arallel to -hea z-axis a- -distances -_7

-. 1, DD 1 and 1101 r aii Irdis . met-ers)

Pc P r; ctI '(IC Cowjuc ifl3

Field values will also be calculated along the radial axis

('-axis) in increments of .5 meters for heights (h) cf 2h,

lh, 1/2h, 1/4h, and 2/100ths h.*

The near-field examined in this study is the cylindrical

volume bounded by a c-iin(er of one wavelength radius

cenzered on the Z-axis, r3ing frcm the 7rournd lane to a

hei:ht twice that of --he monooole.

- , ,' p> 5 ?.r 2. f

II. DESCRPTION OF SELECTED ANALYSES

A. CLASSICAL ANALYSIS

The antenna utilized in this study is a member of the

class identified as 'thin-wire' antennas. The criteria

which adumbrate the thin-wire approximation are [Ref. 2]:

a) Transverse currents are negligible relative to axial

current s

b) irufeezilvariations of axial current a e

negligible

c) The current can be reoresented by a ::iament curren

on the wire axis

i) Bcundarv condi-ions Dn the electric field need be

enforced onlv in -he axial direc:ion.

f, car, _he largest subset of -:'in-wire in-ennas s a

-lass known as short an-enna3. 7 -r-c-n3--.. are _;ef:in--,

as naving one -ension (h) nuc. _rearer-ban -ha oter

dimensions, but h is alsc muc -eo,: -Ian a ::aelenc-h.

u -et, -s es reasonable -hc- --- e :sa s a moue.

-or claosical analysis.

!ase. on 'a:<wels Equations and ,eo'etr_ ,cons etisnsas shown in Ficure , the f lowin non-zero -om,"e ca!_r

.......... - n... . re :

--,-a:-, 1e

144~

sine + ,----)

n Br= as (0 + 1

- Sin3 9 -7 .z. )e> 3?

where: =:he intrinsic imoedlance of' tne rned UM, 7 antenna

-. ren, X wavelength, 3 27Ahi = nhase constant, h

monoocl-e r~h: = stance 3.' field observat~on -oont

:rOM Moncoc<e 3 _-zinc e 7here is no vari-ation In ~

:e :neoec.:n: hese C'uLFs nder c-sja

a he is a n ce TTe fiel os erv a:on cin t i s d r Se

r a:v ~ toTe -ion. --o'1 a h-?i;h:, a nc

~)An -mn:a- ~ne vrngcurrent _;3 u'niform over

-- e heigh"t Df the monooole.

~efrtof these as-um:oti:ns I's made -o ':o-cus a--t-nt'_on to0

-2-a- volume of- s7oace where -he lines or- o -rce h-ave? Jezached

7*-M34rfls-7e3 frm hea--:nna andj ar-e a--rcachnz -he 7 "m 0-f

a olane wave front. The second assumption is to form a

first approximaticn of the current distribution on the wire

which is solvable in closed form. Extensive analysis. over

many years has shown this to be a valid assumption when the

antenna is excited at a single point.

In this study, we will be interested in fields where the

observation points are not at distances considered large

relative to the monopole heihz. T hen -his is the case, the

diagram of Figure 2 must be modified as shcwn in Figure *.

From the geometr oy, of this figure, the foliowin non-zero

complex scalar field compcnents can be derived:

r r~

i+

_."A

, - 9 (- h ____ + z =_ _____

4 r - (e r : s h -

iin t= wh le nuai-h ( e -j r1 -j " ' have zo n.z .- :.. .-:, vlin ric l :c rdin tes

p

I.

-

Monopole

Trva 3 ,e of MonoepoleRpe;lected thoIJ>h

&rovidPlane

A current of the form:

1(z) = 1 0sinBh for 0 < z < h (3)

has been inserted into Ecuations (5) through (7).

Ecuations (5) through (7) indicate that each field

comoonent is the phasor sum of contributions from three ooint

sources. The first source is located at the toD of the mono-

oole, a second image source is located in a symmetric tosition

when the first source is reflected through th!.e ground n lane.

The third source is located at the base of -he monooole; its

relative amolitude is modified by the (-2cosSh) factcr.

Since we have a soluti'n for ccmnutng the fieldd

it is now reasonable -o -Jetermine the range over wnicn = i

-al By inspection we note that ror r -ats

(i) through (i), the ma~ncude of each non-:ero term in the

oarenthesis is -u-l This imnies that r = /2- may be a

transition roint. Further investa-cn ndiates tha- fcr:

a) r ' r t he 1' tr ns in H H., an,- the I/r

-erm - re :om:nan-

b) r<x/2: -The 11 -erms in -and , 'nd the l -

term. in H are ominant.

Since we know -hat o-wer irots off as the inverse square cf

iistance, and -hat the oower "!ow at a :e... _ ocnt can oe

:efined in terms I: -s --e J as:

-a-

2we can extrapolate from a) above (E'a/rnw k/r ,where k a

constant) t hat the far-field begins at r X/2T and continues

out to infinitv, while the near-field begins at the TiofloDole

and continues out to r

i: s interes-.ing to note thz! comolementarv 'ela-ionshiD

that ~s maintained bv the Dower in this transition region.

7nstantaneous power flow atz a point in space is given. byte

comp'Lex Poynting vector:

:or the short monopole, -he complex P ovnt-_nq -ector is

orlented in t he radial directizon and tive s:

--he real -)a-.- Df 7hi 'atin is the avera,:7e rate of flocw

of eal oor.-;er (-'/r-) -hl he -m~nr ar- is -rcoortional.

:o the d iffe.rernce be-.ween average -na.~netic energy :4ens-4:;-

C~h3 ag~mnt s :fer'~not as a -:rccf, 1-u-7 as a reasonab'le-a-crai- no.c- nircl~ :r~

and average electric energy density (-l/r'). Interoretation

of this equation indicates that for:

a) r>x/2 : Reactive pcwer flow decreases rapidlynr

Real power flow decreases not so raDidly (m-7)r

b) r = X/2,1: Average Real Dower flow and average React~ive

Dower flow are equal

c) r<\/27: Reactive cower flow; becomes 7nuch ,ea-_er

(-r5) than Real power flow (-r)

The transverse componen-: of the comp _ :x Pov.,n vec-r:

."= -- )>cossin(-(-- --- 3 (12)

is comple-v -mazinarv, fni: -int no Real tocwer f1nw, and

it faS - off raoiU.x with "-ir . ue 7- -. '

_l/r contributions."

7'e 'e~ envo f:he f~~*r.~~e'~e

:'stanc es r--\'> the r e.. - -, :"- -n r 1.

the lines of f-rce are 2lsei - - ees nachin z

ane wave :frnt, -o re~i:n .a. - . ... .

maintain a st n;., 3:ner2 w,2'.e front ain/ soe toe - ne

are still tracheaj to t-he antenna. Even tn :he si:les7 of

*Also noted is the :act -hat the 7.ectric fiei chan -s froml'iotical Lcearizatian to er o a,.

from r>\/2- to "!ale -f r l- ;.herf -0, 'CO, ,)or these -nc-es -'e o clari:.ticn of -he el.... c field

linear -n Zoth 5e7. r '

- - - -- - a

cases, the current ,Jistribution in c:onductors is CCrnol:,.

This complexity -Is the result of non--iniform curr-ents-- an:4

charge iensities, capacitance and inductance generat.ed bny

these non-uniformities, and discontinuities from imcressed

forcing functions.

it is well established that as the field observation roint

moves within the X/21r distance from the antenna, that --he

measured values deviate f"rom those ore-4C-e, 07 zui a -.1on.s S~

through (7). it is also well establishe th-,at MIay,,ells

ecuations are valid for all soDace. -oneqenly te co n-

clusion is that the sinusoidal current distribution :S! o

suffici'ent>v accurate for determining field -o-'Ino w~znin

the near-field regi'on. The problem then _J3 to fida better

d escriD-tion of the current d-ista-ibuti4on. 7--is I's -he d-omain

o- cont-emporary analvIsis.

Before oroceeding, t 'necessar,; torerlect t-hat trh.&

analyss: performed thus far hI'as been f or a short antCenna.

The -model f or this s zuc_-v is a resonant nononole; -,hnne

antenna is 1 ~~ee oresonance_ 32:ne -:trestinZ

c:aracte i3st-cs appear. :?riMary amonj thes.? -13 t frc-

that the react _ e ccmi'cnent orthe im.-ec ancfe van: 4n3', 3 nc

3ais -,he nutreactance 7oes to zero. Th-e current :n nthe

antenna and --he -107 tage required to :)"ac-- -t here are

-etemined 3olel by the resist-ance, the rea-, -tart of -he

d-~arce:. ',qhe n a S4 nusoidlal cu-rr is assumned onte

an .ena, t- -3nqential fl eli :cmonen-t :-3 :_%-_n

o te e_ __

7he (-2cos~h) term representing radiation from the !)ase of

the :onooole has disaopeared. The monopole a-Dears -as a

Doint source -radiating from its height, and an image source

found at the reflection through the ground plane.

Also, the resonant condition occurs at a length less

rnan thatc exnected from th-e X/4~ relationshio. This is the

result of an "effe-ctive" lengtheni4 ng o' -the ant!enna by

ca-oacilcance -and "-fringing" at the end-cap of thne wire.

Caoaci-tance is caused by a build-upo cr charge at the en-, of

a Wire of f~~ewidt:h. :-he chani-e in directioDn of the

,yeometrJ at the end of -he w~re also chan-es -he dfreczticn,

othe lines of force emanating -ernencicular frTmit

4s -he frinqin7 - fet These ffactors cause treconance to

occur "or an antenna leng= fr h S w.,here 3 is a

Z-nctio-n of t he caoac-4tanc-e zase > te Ltw7 e-ff-ects

scuss-2d above. _

The short: mono cl -evelo7pment diLscu,_ssed albuve- --svr.

etrtieHowever, when -h eo-n eua aaceis

tics mentioned are tkn:t ::.rtctee l~.

'eecoment! will fo'7ow the same :rcdrea se-. -:7r h

-I'tnno e. 3 :r 7.7e r :atn' t ~ ~ _

3. CCM::M-r'11POR-ARY ANA1LSS

Sch-el'unoff [Ref. 3: nzz. 370-374] identifies thr-e'EmZ~d

-,:o r obtaining, a closer aoDroximation --o the actual cuirren7

distritution on an antenna. Thev are:

a) The Integral Equation method

b) The Sweep-Off method

c) The Mode Theory of Antennas method.

Each are diHscussedj below, .4- succession.

L. The Integral Equation Method

The assumotion Is made th'-at, 7he c-.r-re:nt_ is itib

on the surf~ace of a hollow cylind er which-. i'S divided -

fil4aments of angular 4ensity(Tz'/v and angu-lar w~z

(d') he 'Kernel Tin Ct4 on :s modifie -to alow or

v-mriations in o and is ex-:ressec a~s an 4_n-:, :7r aroun-' -hne

=~cum_,:erence n: the w.,ire as:

.rfi'eld inesiyf.r a stagtcurrent_ filament:

+ ~ 0Z

is modi ied by inclusion of Xquation ('4), wit-h the bcunoar;

condition: (7-- + 7- 0) enforced to give:

Z2 1 2 2,7

This In-tegral EQuation (:frcm wnh- - one name of tne method

d erives) iS --he1 -lii (as o--):of a series of -quazo-*ons of-

--ne f rm

wlhich is a~so of the formi:

"n

Z zi1o-4n (1 ',3 -~a ri'c 4i oaz o' 1- -:r an anoe~nna -and :an

te -o' ved, in a manner analczous 7n -.-e -ise 07 iohor

E2.lati-ons for I1:moed networks-, t-) an a:rr'

accurao': tnoL :n se

7- s instructive at t.his~ii opuea

consider how accuratelvoutwinita. a:)trsx4_mazo of-4zurn

approachedi reality. integrating Ecuat ion (16) by 7aros and

setting -E i(z)=O, as it is an the sur-face of the antenna, ve

obtain:

d2-

-'1,i4S erUat, ion Dhoqs 7hat a3 -i antenna racss -. 3= o-racr--

zero, the fir-_st te3rm of : Lc'.aton (1,) -a-,roachies a con-an

:z~ or all Z, ' et z or z =ZI.-

o m the ends -,his const-ant 1* 3s mal I '-e ':,7') acto-r in

tese-ond term is -niieat z 5' -e

-4:nit-,; -ence, th"e + f~ a ct-o r 7,us 7ze ol

ehre fore , a Sh --:1u o_1 ,3 f t he an-- F-nna a-rc aclxe~ 5r0

a---- a -3s ch e rfc m

-h .e 7wee-?f" eh

e9 ec _at in 'or a --lament, lur 'n t n7tio<ra

0' art:. oen an, za- cx ma -- n to tecurre ntZ:7I

ona raris -t:ng antenna o i> ~ ~ _

A 2033sz' 4 3 sin( :)

.subst ituted into the integrated form of Eaua-4cn 7I) o

yield:

r3 3

: equati1on is an exact exnre S4 3n for -he ele C:r4 _C f _e

.t -2n si iarallel - a 3_-:-.,uscc_-_a_ cirrenrt fillamen7. Te

-2 n.. na ~ce :.o a7a z3cnstn amrse ~

-7d th :r--t0 erms f-cm 7he :r a:orcx-a"-'-

a r' : n e_ -- n nam -crf o -li

-:rnce7- -_f T he s71rface th .e an-7enne z-

-~ ~~'-' nte~t-~ zv a7t0.-,':.7R an -

an 7 Dnc 7:-2 zntn:

0t ehu -e n:e ae a7 h,: u~ Ec i;n ) r.s a n

eztes:a: -:r 7, tht oe- not vanish alcn=tn

:.-amen-. Thii 27Tnarnt ihcn. sus rrom rne roeu

-) o ~n :rn' cnver c' n ce f tr *in ate:v n

nver-nc n i 'Drm a t where i is --e

fl--- ----- --. an-enna ri~zll~s r a.

f

there e xiSt s a re mainder te rm Lz) in addi tio cn -_o ( z

(z) i s sui5ffici-;en t o c a use E (a) ". As a-0,

oonsouenlvI's contribution to E_ for any fixed v u

j, 7reater than a, w111 appnroach zero with. a. *n -'n~ - -

i s aivef by E-nuation (21) 'f'or o>J, utat o = Eat

(-'I) ices no-t hol.

:3 Moeheor, of Antennas

Thisneo-od s bas ) n -- e uin:fa.~~

-,UationSs ubflc- t-o -ounda-v conditio--ns -,he antenna

7;irface. and t-e surface of :te sDoure -)f :nower.Th eo-

cons4,s-1 of, cazatn oues c:oo taonzossen ;t

the !zoundjarv atuo~n a:he >trisurfaces of t:he

antena, ten t-he :nocc:s wonso -::h free-sopace :caa

.-3n. Th ese 7ooz4e s ar e combin-ed to s at a boo -ar

L) n on a nd h cu r~n - _ - - ane, as th'-e m

omnonents:teC!o rn rl3.ae n - ~~__

wavie eossi~ f l ice ore rcs ch I' * ial

2: ter Ms of3 i:D' o~acIa c: ne an: on,_"i ic-

he 7n 1h-1ce S;e' L-_: is2

e Ic Tor', c' Anerna xc;--3 a creto 0 ooco

ho he TE aoe ra a :u rrcrz sor t1e 77' M'-,a : ;vave

-: -7 e

the 7eormetrical configuration of the system; hence, a

-enera2.ized solution requires a number of: termis w4ch reo3.D;

aDoroaches infinitv. T-his overwhelrninz Drotlem of accOuni,: in;

'for all termis limits the attractiveness o_,- this me hod.

The Tnte-ral Enuation method ap~rears most risn

'Dor genierat ing, a better approximation to --he current. M.an-i

difretaDrcaches t-o solvincg the ecuation h-ave teen

o)rcncse:4 and virtual>v all of them le nd th em7,sel v e s to7

73 0 -n by dligital com-Du~er Three of -.hzse apprcac'es :-:±i

be 23iscuiscec ;. the next see tion.

'FU f EJC A A NALYSTS

1. M-allen's A-ooTroacn

-ne of- -he earliest solott-: s to the - - n

-.-a.eao n -DrocOSec by! Ma! Ien,: the basis ot jhmn:. -s

3D~tx~at:ns c te trrent. M all-n l.ses

-~~~_ -a -- wil --- -o, -- '

.. te: ~rent :7 e ~e 'nutrrn

-- , 3 -. e

'E' ieldoutside the conduct!or (expressed in terms Df

vector ootential, 'A'). The wave equat -ion is s olved as a s- m

ofr a cornol-:.imentary function and a -Larticular inte 7ral A

constant, C-), In the soluticn is evaluated in terms of' inpuit

-cnditi.-ons at the terminals, and the vector no -rnr-' , A, is

exoressed in termis of -the antenna current. (I') and A are

-nsertLed in-h-2 so~ution "or -h= wave ecuat4:n obrcaining an

-ntec-ral cuat ion i-*n cu-lrre2nt, hich 11s HaI e n ' s :. ton .

-oartia- solution f'--r the cu.rrent-t is Iraie b'! va tng

on e o: fn ~n -e 7a 1 s s o c- ~ent, 4 3 e x.r e-se,: a s he 3u

of .3ev eral te r ms, som 77e of w hi ch a I incllb tecure

~e 1 e -ing certain t-erms i ,an aorxmm zer

solu ti4on is Dobtain ed foDr 7 his !u e ss -ubt 1mue bac K

-hi13s orDce s :3 7:n minued -o -2 1 su-c ce 73sivl o::r Drr -S

3l 0s1 ,ton. Th e D:roces7 S 7"ed a>z ~ ~ '

-~~ ~~ cc:al:s om nd, t- contan r-, at~~~~

toe -ndatre term-,-c 7f nurent r3 cv~ae

-r.to an-enna (as o-<f~ to .. nmur

a D :, r n) ma r ax.. 7arito1 en:r. also -:cres-)

a-:,- n- -, ax a

IA

- -Z(7(.~)+ 32T) ~WLI E:

which he claims is more accurate, since continuit-i of higher

order u-'erivarives o' 111 o not have to be soecificall,

considered at seament boundaries when solving the nreqral

qcu aio n. He then assumes a Parabolic Ttratve '71t f-or

t-he current di4st-rib-ution over each segment (-he t~stri:outeicn

over t-he whole antenina 1's not necessarily :;arabolic) where

orecise val ues of' curre2nt are exact-: de-7ined :;- Salmo3<e cit

"e a"lso: defnes three mcment functions -hat- d-escribeth

,<erne-L Functi on and its varation wit reoc t n

over a se=. ent. - e n cn -:ze ro f e Ii -:Dio s are -the n -_xtre sH;eI

as ~c e s ummat ions of:h hea mmnt- fu n c ton s o-v er e-a cnhI n er -

-al c,: bvi :h cbe s immt -ns, ce :z 7 -,t: th e '.,"e-r

zunc -on in-to tw acto-:rs (a -7ecncue uIsed by n-n,-s

;e _,) 4ho :ao:~ t-b -oonua n --hte domi nant, term

(7 1 -e wh a 7:mcete .- iiti'n~-7a :

',e .e..: ne as an -?e' -_-ra

:io''r :xlm*-~ "'ma nd er. -Jih-4 -ht erne! '-e th"en

-' _" ,nC 4- _ _ fineJ a -)v-e o 2 --

a r_-a---r -' -ee OzJ_"ferent 3ceowa 3 t-,-at- _- .

:'-m mcme-n cuar. to eeue n numerically%

<a-- v -~--' '~in echnit:ues, suhas us~~nr

- 7n 7 nc:> 7 ent -a' anct

3. Bessel Function ""it ADroach

An o ther recent a-oroach (:981) is that 7Dronos-Ec '21-

Balzano et al, [Ref. 71 Salzano also :e~sby rdfnn

the Kernel Function to account :--or azimut.hal varla-tionS, tut

cas-.s it into the 'form o.' an integ7ral of a d-ankei 7Funo tion Df

the second kind, which also can be representec as in infinite

3cma:i'On of Bessel --cios he nano- euo ceial

-.hnen ex-oresSec is a 'doible i nte~ratIcn Dfon cur-rent

~ens-;tv. on the conductor times the inte~ra o he_

m n..atioDn o f 3 e ss e Fu nc t - Dn s d e s c rib*'-ed ac,. . 'form,

all t.'at. is needed_ is -an accurate Jeonto -he axial

current diti'ton (z'' over t.he C-'l4idrical a:tCenna.

From t-he -eatc'-,ofte vecto-r onza .:.

7:, d fields, an '-s an "-e written 47,r a

:s- t na r ,- -i C -.

-n'~"ma. :nc--Irns which 3zai':-. zhe- bo':ic oc'-

-r r, nn h e cur-ire n - x nre s se' 1:z -a

- ~ : 4". 7-,'- - _-'-- ' - . -

moo .....- or~-~22 :c

hi (z )ej' A /Tn c~ :

where: s ( is the Fourier Transform of the currentn

harmnonics, A is an infinite series of constants. Equaticr,

(2L) is substituted into Equiarion (?2) and 5.olved b y aling

*7alerkins Method.* T~i yielts an infinite sysiem of

equations which can be truncated and srolved for th7e 1ur..now;n

A A similar treatment can be aoolied -:: t:hz )-:her ncn-zero

field2 equations to cast them into solvable fcr-i. However,

the e-,,,ations so defined converge slowlv, therefore, add-

tional mani:oularion is required . :7he a-Jitional manioulat ion

Decornes ra-:ner in-.,-: ved ant q-' ii nit t b dscs here.

etails :an be fcund in ?e.7.

Di cuss -on

All t!-ir :f !:he ab ove methc- are h~~~ ~

sound, all nhc cier-sn±I ut ~r lar~e 3rrios

nc the near-Liell re~lor', an! KlL throc -a.> hmslt

numerical solaion by zomou ncr. Df conc-ern h ere is the

*amount of 7ala: ccmoir~ _ scur- (-ime czre, and Cost

* cncuedin mnakin, nhece calculations. ?alzano indicazac the

Yalnrkin 3 Method solves an 7nte-r- Euati: n ,,ia the M-ethod'

t----------------------- ------------------- a------ --ai:

exoressions he der-*ves for fipil comvonent-s are sloi inl

c onve r g ng, and4 even after moiiainzo his basic

derivation to hasten the convergence, h-e states that 7cr-

than 15CO hnarmoni*cs (a 1500t-h order l-Inear system o_ ecuaticns)

are needed to satisfac-coril- miatzch boundary con-I.iticris.

Chanz- does not i:ncicate direc> vh mutc

computer resources consumned by his method, but_ he doe; ly'

his3 method is a.dooted b-ecause a simol:-.er mehd(7-a Method- o-f

Momenrts) is iaaccurate:

.he niumerical ccompucati~n .eit a r - - :-

is usually subjdivi;ded! intD -a -- ni-e number of 3e-ments ;ineach seg-mentz --he clurrer.: i-S inter-pclated ty a 7,Cvn7m-a"

wihcoef'fic ents exoressiblie in term=s of valules of_ cur-rent-at a ew samo-1- Doints itnthat segment. --h hig-ar

eriuiao__Ies ocf '(z) are therefore isntucsat tounzar'v.cints bDet-wee n any, tw segment.s." Z. .~

Th of' th!e _ntent::--ns of cnhis 7.to show -'hat

the 'Tumeri-ca. Cetcmie z C) , which u'Ses the

Mehdof' Mments, h-as been ac-ce t ccount fr -:ne

JiSco-nt ni ies cf th fi*rs: ierivati.' -t::..n ollndafies,

area C' a 7 -1

:.DESCRIPTION OF NEC

ENumerica! "-'etromagnetics Code, is a COMDUter oro-

gram 'for -the analb;3iLs of -.he electromagnetic response of

antennas and other me-zal s-zrxc-tures. It comoutes a nurner cal.

soiu- ion zo intezra. er~uations 7*.'at d escribe :he irrents

:nffcet on a 3-r-uczure tv *:ol a:ge-r current eaos nc

;ncident fields. Tc: 2s thte lat;est 'n a series o: o)rczram's.

--he first , callaJ 3R.7ACT , was d'evelone-I b 'EA X soclatLes :r, :er

~inding fOrcn the Air Force 3-cac-2 and Missile SvIste:is ~ma

:his was follcwed by Arl?, a--ain dieveloned by>ssatr

thiS- time -und-er an OfcI: e of:7~ java -search cont ract-. Z:'

evol ie.d 'from AM!P an.d w..as dev.elonet by': awrence Livermore

Laboatoieswit'h 'fdio rom th e Maialec tronics rts

C , man. i i 3 -a user frieniP; :od h which incororazcs th7*e

A. 377JE :iH' D:7

'n~ :egral :,--a ;on C:: -fr mod eling the curren -3MO(t'- srfaces 3s 7,z~e 7it an 1 c r c re t m~ Ln

on t-hin -ir !:o describ e t he elleccr'xiaznet:- rcn-soD:a

arbitrar*7 Structure. --he :Structure, :or -:ar-s:3: of ma,. be

acc iv, or c: as 34 , ocace' over a nerfect_ or impnerfect: ground

-D.- l, and -Odv h-a ue-em or dsrbtdl~-

7*?:T f ra;c rm ;oe: :rct oucso o

structure, an incidenz :olane wave with either li-near -r

elliptic oolarization, or the field may be r'ue to a Hoerr::an

ip-ole. Ou:--Dut miay include current and char~e Aenscx7:, -. ower

g7ai n or di4rective gain, near- or far-zone ele3ctr--c or mnagnetic

fields, i.medance or admittance, total radiated 7ower or input

power. _t is suitable for either antenna analysis oDr cross-

secionscatt ering and electromag-netic DUlse (-'4P) 3-,;dies.

code wil Ihandle !jun;ctco;nS of .,;res oruneven r3--_4-u3, free

end s or wires rhat have finite radius, wires of ',ariamble radius.

andco~~l 'g etween wires.

_IC utlie 4 he *auss-Dool-ittle MIethodfrsoin th

rarx eiluat ions -enerat ed by the M ethod of M-oments ,.hen

So -I n~o the int-e-r al e u ati:;o n s z alZc allo ws fr use of

utatonalor lane 3y77.me-r, -c rec-_uce -acta~nce .~n

an :ran c 7a r -x *s too lareto -- cont-a'neA core, '17C

as5 -I-.-i'-:n 3- oron- ocrticns utorcore. allow t".e

'se'-''-ract~on atrix c fr a stru=cture t ecrotd

-- ra new ant7enna -r-at - ~~-nitos n':oretrequ-res 7nly

natrlx facualns7r a oar _ t_*naI 7nacriX z, t~

Ia rioee3nln oewhere a somole2xstctr

~~~~~~~~~dp 0b~ fs~~l eeet qrso

nia-es) to which the Flectric ' T nte:gral Equ.ati:n ( 77- 7

or M!agnet!_ic Field ntegral Equation are)_ ~n

with any descriotion of rhe real world, there are ai:rc:xlma-

tions, but because of the versatilitv in miodeIng-, -the -eo-

metry of a structure, its aDproximat~ons mnore closely

resemble nature. The resemblance :4s Strongly inflIuenced by

the conoice of- ZO_n7 (i.e. Aissectina) -he structure in the

-:rc: ram. The smaller t-he geoDmetrit' elements, --he clcser -:he

model comes to realit-y. :Icwever, th;e small-er -he elements

-he larg7er the num'ber of elements, which -7.eans the -'ar-7e r the

Matr4:< re,]uat~ons and hence, -- e more costly the solu_,ticn.

There is a ocint bevond which s7maller zones Jo not yeda

3_Tbstantilally more -accurate solution; it may be- necessarv t

re ne rb'-a ; -hncr-asi*n.:ly smaller elements to fin4

te nn of fi minishing returns. The onrc o ooer z on in L

I:e s -aine .,ith' exner-*=nocE and be cones as much of an art:

as itis a sclince. The uieln for the siceasreot

are 3.s ___

____ sould :~o -:he 7o -h -- conductorsusn

a orc-oe rer7to u-': nrlv e-menT: !-enz-hs

4 3. should e les t han e1, fctr s egme_ nt -.S~ r lss-

m ay nee-.e at cr-*t-oca, rerion (.ntons -or ourves) .

7e7en-s 7mall,-?r t:han 12 hcl e oi-elsnceth

M ~a rt- : snstan-7 an':: n -cmocnencs lead -,o

:n9L~r.~:u~':y.C-c:-eii f-he rsi ', 3) relative t o

I _ eoends on thie Kernel used in the integral Ecuation. l;;o

oot~r~ eist. The th~n-wire Kernel models a iomtt 2rrent,

while the extended Kernel models a un-Irorm current osr

-ton around the segment sur-face. The field of the :stiu

'ted current is approximnated by the first two terms in a

sres exoansicn Df the exact field in -- of ei.cThe

:T~r't (d) zrm :s -in'ical 'to the thn-wi're Kernel: -hne

secor. d ter-i exten : s 'teacuay :r larce-r vausOf a.

3oth ',*Kenel incurnorac e --he -hin-wir3- nciairs(e

S e '~n .A ' and b!oth reqcuire _T a / < < 7L he 'thin-w-re

<er-el reursa _ /a>5; the extendai= _Kernel r-elaxes thi

'to !/a-,". :hese values ensure e-rror-s are less thnThe

<xenedKrne- is u.sed_ a-7 f re -. re- -nds and be-ween -cerallel,

e c ed 3 -7, ntS. --he 'tin ir ernel is al;av ued a't

-C-nucn s77ac - (ClC<e by sma, :a-t su-r "ace

catches~~~ n:;-~ confr a cecva osbetocre ucc

c-e aramete-r :'efinin7 a acc - aIs a ncrmal n' etr

:r~ocatc~ ~m n ceterof-he Dat ch, -eind n Cartes-an

_cor :cte. m; acc -eus cc cnnecteu by a i-r -h te

Dcacc :ecr - r -ne rooram -c I anceo rate te surface current

cer~ iv easc- catc n'o f -uir ec ual c-atche ahcu'tto

7,: _I -e -c'e crr nt - - toeeTi 4 aI71 - 7

pat c-hes , and t he f un cti:-*on i;S nume r ic a2 vi .ra- -

4:h wires connectad t o them (aczive ates ou:

chosen to be aDoroximare I%, scuare with sid es 7-,,L 0

unit vect ors Jefining tine surface. Jnily one wire nayr :o-rect

'to a natch-, zhat wire mav not be connected 'to anothner Datch

and it may not lie In the -)lane of -he oatch. A mni-mum o'

a-ou7 25 -:a72hes sn ould '-e used -rer ;waveien-7h -,: -Surr_'-ace

ar-e a ; 7one maximum- size r7or an cno!~antIn s zu

square wavelenaths. The number of ,;ch~ set nress

and the size o:-" eachn -catch '-ecreases, as the r''

cur-!azure d-ecreases. Smlir atches shou>' beizec a:

edzes since the cur-rent amolT)'-udfe mna' var'; rao7i:4_ -'- n "'I s

region. ucn aro atcnes Should eaoe.?-zb

-,arallel surfaces oni C07osit -3ies ca:nnot bDe ocos

3.'>'cund Pl1ane

oa errecol, o:u1ncvuud the coe ene-a-ec

a cefleced im7a7ge. ituorsma'.' --lose Lo r -ont-act.

th e zground; hcw .=;er, focr a bo rizo ntalwire: h_ - + a-"

-iaea = wire radious, in hei.w r a xc abc te

ground -dane, and '.-/a;.

A' fiie> -nductinz tro~n, ma-' be mcd ee- an

Mmcise odfie-d 1-7 thez resnel 0 1an e- j a,.z_ R fe C T: 0n

n- 7:11-: mehdsfast, btc zie cua.

cc: ncu.litotbe se~:crsocuours :se o tne rou2. r

having a largYe horizontal extent over -he ground. :he

Sommerfeld/'Norton mcdel uses -.he exact solution anai _3

accurate close to the ground; the horizontal reszricz-*on 47

the same as for a perfect --round. T-his model Is only used

for wire-wire interactions, for surfaces -he code reverts to

Fresnel ?Ref :lecz;icn coefflcoents. At the Dresent time, a

7.round st-ake cannot bDe 1-sedI, tut wires mav end on a rec-clv

2oriducting- ground- plane if --he i4eri';ativ-e of the current: at:

tn n o h wr s eo or wires, ther- are 0o1)t 4ons for

aradial-wire --round screen anproximar-'= and a t-m.-redium,

7,round ao-Drox.-1:4-~n based, on modified rezlect,4on coe:::c~ents.

These ootions allow considerable savings in cornuatilonal t-ime

when liitd ccuracv can bDe tolerated.

:N:T77_SAL 72UA::o:Is

7- _ cr ieid :-nte.ral 7Zc.,ation T

:he 1 E is usdfor thin-wire Structures wit4 h zmall

7onducr 7oue -~drvdfo he e lectri"cfil

reoresentetio n fo r a curn itrbto onienote

wter: r~i-:he source 7o int,- ~s 3toser-ia.~ -i noi-nt,

7 a siir'ace cuirrent ensitv--, z

.Lmnedance of medium. The Torincinal valu7e integraIL / L 3

indicated so rr in the im-it.

An integral equat7ion f'or the current ind-ued, -r, .7 b y

an incident field E ' can be ob'tained -from ': uaricn (25) and

the 'boundarv condlit4on,:

n(r) [ ()+ (r)1 0(

AS 4

where rES, n(r) is the uni-*-. normnal vector a-- T, othe

felAd due to --he -Induced cu-rrent . This nerlcain

's Oriven bv:

-n(r) NE ) n(r, x<

e ci~ztn::r :'ietn~nw~re:oze. n :e 7Eu;r7ac- curre-it

:4ensit- aelcdb filment_ :urrent_ an,- -he bcndr

-Dn iin enforced_ in the a-a diretin ths :ive;-s:

r d~S 9

7n: re %'Ire axzs3 at r, and 3'

v!ec7:r a r aX 3 __s is rhe ET: S7- ?

a . .ie nezra -c7ati (MFTE)

The ~'~is erived from the in~egralrz~etto

=or the Xagnetic fiLeld o-f a sur-face current dis-_ribct1_io

u - -

3 i induce by an ex-:erna'l inc t fieen , -nen -n-

-a I -aneti-c fi S in3durenef~a*ncine

mLust Ze:

- ~ ~ r r -a I.~r- C

- --j-

3 c- S 0

§rizs e*:zr esol.ve.,. ln~o o &oala equations alcng 7he

ar g -\ v-

7 T

0 D

-7 r L~ r' '

-r j A<

'- FT-",

3. Hybrid F/ E

NEC 7%od-Is thin -..14 uin ET and fo s-ae

Uses *MFT-i. For a structure ,:-izh both- wir-- and surfaces, r

4-n 7quation (23) is restriczed zo the -4ires, with -,he in-egral

ur s(r) -2xtending over --e como 1 ere strricture. H-ence,

:quatIon (23) i sed ftDr r*iewie hE -ntre 7eneral form,

.2a-~r (Y' is 4 s3 r for~'= e,, r I

r-est.ricsted to sr fa ces i E~aic n' a ~)~d(5'n t he

~ntesrals Hrr ~ et nn y~r h e 7 2o

e s- n c7 I - r ~ a a ns

7-~r I -:

and

- -Ti

D.~L "1 -'0 4I!7! S r-:: -A

:>.e Method o'f Moments is a : echnique whereby an I-t:a

e cua -on is reduLced to a system of' linear al-etbralz ecuat:_-'rS

w-i c h are e a& han dled_ b!y h i h 3 ed diLa I ccmnu er

'lanhemat~cal Conceo-,

ne ~ ~ ~ ~ c meO O L st n i nDojenecus 7-:rnear

ooeratzOr :-f-7e :z"rm:

w'in i's :ven, and found U-- e -in 7e f L.

a a so-ition -7 -:iat -n (3'11 t an'

-he:n: -he ~ - 7-- atr, ex(3 -c--h-

r -e.

-he unknown funct'on v, la e ex~andea in 3r:i

'I linearly independent asis :unc--ions s7oanning

= a. f!. (K

Subs-!-4uting Equarioin ( O in , 1ain() rd:kn

t he inner product it a s~zt 'Dz near-~

r- functions -:eYage anl -an=

:ce::~et a 3., 7-- :Ua-4n (4) >3se-- z e~zuat::nrs:

:ro Scr :r o ste 7-ace e nt the iu~Ce an,

(-3) a__ -v

e n,-- if a -!:n o 7-i-,a:ixn ( _) _ :s an. -

-nie :,-r all -, ten -:-)e Inverse ooera-or, L -al~so

c_ _ vh ha:

Which iS a solu4tion to Equation ('43).

T-he efficiency of computations and accuracy of

solution is largelz d ecendent on the choice of Basis Function.

Factors which sflou!l auide this coice are:

a) accuiracy of solut _on dIesiredJ

b) ease of evaluation of. matrix elements

c) size of the matrix -!hat can beinver-,>,_d

-. he real ization of a t wel-cnirond'o .

Thiere are two general ClaSZeS 0: 3"4S43 unc-ions -_:rcm ~hc

-o choose, e nt ire doma in 3n-, sub-d--omaIn . Th"e sub'_-domain class

'-as -fewer 'nemenns --*its execu-.ic n tim-e IS less, I

s~othes:e evaluation of T-he inner Drotuc t 4 nre~ral a7nd

~ n;re s -_he matr~x 'I3 ~I LIl be I wel 1-cod ion,'

:~ s AD ol Ic a - On

~ in rooanicn_ currentc on wires -_S oce

2r aure n, .a hre.eniva em

Ths ~--~adit.:airs _ zon n oecurrent_

* nai -_'-7 r _ eio rseco to -ance aLona -.ne

:nciiC -Dr. f-i§rces thDurn n tne cnuort ao

*- -- ~ utonat soeii ocios oese '7at!c- to~n-s'

are- :cee a -entr-er orf -sach zeTerr.

~C3 7-, 1ationr cf The "etho otcf M oment.s starts

~~ _ '7 n 3s a ~r:~)'n >)

3 or- E cu ari o n'Is (35) c ( 3 8) '1e e cu aton s el1ec-t ed

oeoendinz on the structure being modeled. These inte~ral

e uatclons are the 'oasis from which -lie s-vstem of linear

,Eauatzons will be generared.

A source r-cde.' with a k.nown excitatiOn voltage can

:erelazet -z~ 3nedir~rssdc the antenna; >e-nce,

e frm m~a~in (3))-s krcw...ie '<:-cw we are looking

.or- a 7nore accura-- c5 -c,~zo he curre n- iriuio n

o n --he ant enna; h-ence, -")e c-irrent I ~::o nuto 3)

s th-e _inkn-iwn reins.Te oDeracr (an r, zra

ocrio n -.-I's case) 17, the com-oosi-ce of all o-t.,er terms7

:-efle, thes7F 7erms can 'cc cast into -.he 3or o9T'a~o 3)

-: ~cnrace te :-cm~ere.-'uat: nns, -wepnav;e

ic~lt re 7uzz o3 secmentZS

~urn :srbon:n -7n>. ant:?nna now, aooro.x~ma-:-jda

h L- ch , 7,nat -o P, c ur r ens found on each s Iment. .Tat

Ak ~

which has -.he same form as Equaticn (41). Here z. are tne

Basis ?ct.nsand I. Is the svstem of uefce~. >

Wires:

A. + 3. sin(B(S-S.) + .cos(3(3-3.))* (47)

,.,here: s. cenr e- .:-, the jz.h sub-section, and 3 = free

s-ace 'wave nur.As =result :f- curren:_ conze inu__*iv

=13ns4--raezcns a: se~men-. ends, each sub-sec 4 on w-l- have

o r ~a c e s, the s u r fa cz!u r r en 7 cen :1: s j

.7(r) ~K .+*~K(3

.~.r:K a nd are e ~ enet s -he srf -a c e

eurn en si, I 7_ ;n ca: ~a c- ach .I's cons tant:

-:'-le natch, 'D-- ~ - ecaglr ut can 'De an-,

reasonable 3 nace n cur't:nzn. os ra'-r.'S

::r -he _-nl- - - -;-o un-cnownS f :e re ac-.:e-:n

-_a_--f -- e nature tf he_ K-ernelfntosi the-

r ecu atrs, on 47 o 4z .7: 1e Znct 7re

- n -7re han -Dn -ir ace s

-sfr a enfu~v rovid' ra:: 7-K:ic :vr -n; -.-. - - - a -S

.'~ ~' ~c:7,th -- ~sr of -his section wil'

.3 r:2e -3 t-e case -,:cr Dn7- wtres, -as this i

:_,nscnance -,-t te syte rr this study. A ss umni n the

,71re I's ai-n ed w it h the z --a x s ( as it s i n t h1s zd)

Equ~ation (45) Can be re-written as:

7-z = (9

where th-e z' iicesthe curren-: Is on -,,he surface 3f --he

wire. 71-uat,4on (1'6) can. 'be re,.-ritten as:

j.:ton (50) 3efi3e Dh-eto sub-d:main b-asis "llnczicns

D: e used in2 7o~~tcs hrfnt .te~mo . ('

cannct ezc:', e,,-al 1'~ ;eeauzrn :sro or.Y Z's

7:h-2 z.(z') needl to b;e a-:--n =- lse t7h :e auea

?i StrI-u t13 P as Sosbe C: 'I -his Is acroi~o2 etitn

h Suzcortf _rL -.' o -a .cca7-iZe 4 -iln fr to ~ Ce

near -he center or -hne se~ltrent . 7ac- c-aso *s ru'not~on _--a a

oea z oIn tnie r;egent on Inc s ::oz30extenus o~

-'he aror:-oxitat ion can ou i ' -a-4>os to)S

29 ~ ~ ~ a .3na~ ac'rcte e oband n-, w~ ie.:ith ama -num.-er ----- ~ -

onto secments to which it is directly connected, going 7c

zero with zero derivative at the outer ends of connected

segments.

Ecuation (53) is then substituted into Ecuation (42)

to give:

j! NZ-(z): L[ : ; .(z')] :Z _.L (']

where: and the summation have been 7noved outside the

domain of7 as a result o1 3ts linearity.

-he next task is to i"entify a set of weightinc

functions, w. t K ,Then the weizh-ting functins are set ecual

to the basis functions (i.e. w. =.), this is known as

alerkins Method." :n N,[EC, w. is chosen as a set of Dirac

Delta Functions:

w.(z ;~~Z.)(

where: s e set of 'atch aoint- -*n et center r

each se.men- ii. i se of this wi: _no fnc-icn results in

a 7oint ::amlin- or tne , ncc -raons "-nown as the"colloc tion -etho" =f sui "

-ion Ha - n' a7trroacn:-' -n

Jsing this weight-ing -function (Equation (52)) anr.:

za-king the inner product ofeach side of Equation (tE) ~,z

wnachl has t-he form:

v] [T] [2]

where: 4 s -a matr-*x or- weihing "unc-j;-saD14,4c t~,

known im, ressed field, L21 is a matrix of' Znnw 4ofoons

and [Z1 is a ma- -i mat-rix of w i -7 in fu nctions aTooLlied o

toe assume:4 :-aszs*3unczions.

7ror Devc argu-ment-s, we Know.- 7na- o a oon

-o7,uaz--'n (54) exists and' is unouefr K£,-

Equati4on H-4) can b:e zransoosedl to:

[7 - vi (~]5)

~n oo :rm te 3\'3em Or- eoa.tis*an be sov v x

mosiog 7,he :bcundar, .ccoon:

- (56)

on E-, which then states that -the tangential scatter-!d J

E*'(which zgenerates the current), is equal t-o the neg7a.--,,-

or the known impressed fi-e-ld, Stated in eatiL4on form:

-1 (57)

Hence, -the 2sster of' equations can '-e so.lve. -rh:e exact

current. at -- e maton -o~nzs, and ')7 enforclng -:urrent anc-

onarge cont-nu1t:; at segment end s, a verv close =arox4 mt~n

-:o zne acotual current c- stri Dution can 1)e otained.

joat 4on (54) is solved by, the us-citD eod

:n this mietao d the m atri []. is ie fi ned a s t wo su ib --atr _4s

,;iere sub-matrx [A] with -e.-mentsA.rce t h et~

:eld a th e c en e r cf 3 egm ent u de to the zh a s is

rnct-cn , :_er~erec. on s !cm7ent j b 2u-m atr-: x LJ, wit-h elEments

reoresents ~ ~ ~ ~ -:O( manei :-ls e''. v n ai

function n _-te exectin of this meth- --he mLrx[

ac ret~C nrth rocuct ofT an utt,:er trasa a~r

E2 Iani a lower tran-7u'a arx L a is:

IEL

Ccuation (S14) then becomes:

IV] = [I] ELI LUIJ( ')

and III is computed in two stages:

[V] [zLI [71(e

an.:

wih e re 7qu a ion (I ) i S 3,':,, fiv rst for [I(an it e eI*a

Ta-trix) b~f:rward sabst ut i-n, and -h e- f or [1 ay bck:

':)w -:hat zhe cir-ent has b.een. -hemneoe ot-er

non-zero sca'ar '4elid corooonents (7 and H can

!'I. MODEL DESCRIPTION AND COMPUTATTONAL RE--"-.)

A. MAODEL DESCRIPTION

The basic model used for this study is a SimDo!c moncoooe

colinear with the -ai an-- mounted Der-nendicular to a )E-

fetyr'efec-.ing -,round plane, that -i's itSelf located' in. the

o- Y lan e As can be seen rc igeIheant-enna is 7:-

meerIn heigh- and .6 meters in diamezer. t-r is rado-at-;*n-

a-. a rfreauencv Of I _le -- ert: ( the middl"e of t-he A" '-road-

cast band) wit'h a waeegh(~/)of 30C mnet:ers; it 3

3uarter-wavelen:-h mornovole ooera-ing at -4-s resonant -'re-

_;en cy. 7rans-mot oc;.;er is f:ed to hemod'el thr3ough it-s bDase

:vavolt:age thiat 13 normai~ t4 ao obt,:ain 133wts or

racrate 2wer.

*:roal~all modeling- noncemes start- from t ha'e Dsac

7remise -hat an, ifil comoonent! : ,alues can be 'etermined

from a kn c wle -qe oDf th'ie or r en Jitiuin o iea

noe ~ee r a 1z -2 me _i c,-s tor os cr i -h te --crrent oso:

butonwil h dscu~e hee: 1)ass'mn a current:

_3tiuin )rdlmdeig n )stdmz mote -ng.

I.Ass' irej >-rrent Distributij7on

:his is t-he lasc method, as incr> ~ ]

.7~l~ -he __7~ itiuini iuodl hr

repi.7- sn m aa~nta -iec :cmncn s:stntia r,.

-.e 'far-field, but in the near-field where st-ored energy

strong>;,. Ierencis on the current s:-aDe , larg~e errors

zen eralliv occur.

2. odal Modelling

-O:mrove on tne assumed distri4bution, the mnodal

moeigmethod .was devise'- . Bv this method th'e current

fisriutoncan te zlescribed as the sum of: an _nin-.

system of eq-uations w"-ich rciev:sre

diS~r4u:jo*n in the limit 7his is the aoroach used by7

7Balzinc LRe,!. 71. "~s in,. anr infI n;te e S~e o s Bessel ro

-.qrls hic'h can bDe truncazed to'&-low f Thsired-

accu.raci, a Sssem orc-se form equations can b-e sene-ated

woo'-h __if :htemsel,;.s -o comiuter solut-ion. This metn-oc

n_ orces oouinciarv~ 'ond _-ions ( .e. over -'-e silrface

tone antenna woo r-cisi-on in the ii bt te~ _

:r~toz~ .ao ,tat must_ : * ' s )n to'e :soze 7:_ toe

sys_-ci of --aon 'tat- Drecludes an e3Xact_ Sc.:,tion. :-toe

_,rent o s:Dres 3e ; : sm ccnroosteot nmr

oD f ' r-mc -- c w-.;h -.ustet. 22a

-D, nd~' j o~~ asi etdt r,,.- ec aooo oo

IDr/~ nuc cz o ma-'a-r-l tmlxt:o moja]

~-dcnio mde~ig ~'~ a ~'~n rrue ont

:;ncatsnat71 ;er-e Dc s n-:rcrs r lret

.~~xn on~ ~o stsotue o

aooroximated by geometric dist ritut,.ions (sin, cos, and line:ar

constants) on the elements. :his i1s the method _,sed b.4E

[.Ref. 2]. The NEC code uses -,he scalar form of the intec-ral

ecuations to eterrnine the current in each of the ele-ments,

then combines the results from each substructure to s:educe the

Derfrormance of the total st ru.cture.

3. MO()D EL1 C C N 71 ] jRA T O1MS

In this studyz three confirurations of -the model were

assumes- ano_ valuies for -.-e -tangenti4al , rad;a a nd -eaf, m~e

and scazial) fields were calculat.es for eac-. -.he three

conrigurataIons were f-or a st-ructure moceledi -w7ith 5, 15, d

25 sub-domains. I n each of the conf-"igurat ions. a null value

'Zor the tangent ial 7-field was iLmoosed at the center Do;=t o

ech sub-d4omain (thi-Ls Doint -:s called the -atch Pooint). Sin c e

a: cissed form sov-abl'-e functi_-or. has not '_e identarrfed which

:escri*:es :nhe current on tne antenna, whille maint aining; a

t-an-ential E-ild-r eglal_ to) Zero, ht as become necessarv -o

aonroxim-ateth curre:nt titio n. 's I:on. -n '17C

tnrcuih the M!ethod of M-cmients as discussed o econ M

--~g his method t~ie curent -an beaooiae oan

ar:rav .~reof accurac- b7 1'n c r ea sIn ~ 7. -urate>:,

reasonable- accuracy1 Is ob-,ained i*n -iost s3ituatao;ns with a

reatve=,sall number of seom-ent!s, z-rnicall; '1 1)/%.

C. EXPE~C:_AT ICOS/OBS:RVA::GNS /AM O MALI ES

This s tudyi utiliz~t:d t-hree con fi aions to determne two,-

relevant facts: a) whethe r the calculated v7alue of

near-field was denendent on the number of se,7ments 1.sed,

and b) whether --he size ofT the segment conformed or. --he

:guideli- nes used in the f"ar-fielai.

A non-anal -tvc o~verview of --he olots 7enerate-d by -his

_3 d -n - c a t e t hat t ,h e c alc ulaed v al-u - o' h e n e r-:ec

was indeoend'ent of- the number o-F- sec-ients into which th

structure was d ivid4ed. Thswas 1'' ' vov erlIa I*ng

Dlots o. -"iv and fif teen segments ona twent.v-::,ve segrment-

Doot . An exarnole of -)ne of- these olot s iS sho)wn I- 7?:iure ~

The sourious field emited' fromi the base of t-he antenna

siniicantlv lifferent values. These *,ariaet ons werete

resut ofusz~ inntrrentva~s or:nzr vota ,,hen -roe

o.nfi.uration was chancges, -t3 maintain a no rma ___e. -da~ed

.ower cout ofl-Ovts h vle eog-h enna

an , at its to ar- F eetal - te same, nor reso-ective

:h :Cmanual_ rTf o rcme n ts =ewent r.gt~

!l-Ts th'an /Df~rnre oe it r ------ ~a- -,e-oCnS

a i ' romme n e. Fr a w ae n a D of 3 1 et-_er -s

a used Cot csuv snetlnth r LC

Sn t, -1-7 -nuornne n te ~- en~ t ooth.:

Plo Exv tw5 5. *tW 25 .. ,.em me"s

PWh* at~ two P"L.3 molof above ihe sw~em.

.. .. .. . .... .

meters, or A < 300/20 = 5 .meters are suzgested. et:: s:

in each c onf, gurat ion we re: A 7S/ 5 =15S me ter s, F4 51

5 meters, and a 75/25 3 meters. Again, from a non-

analyi overview of plots similar to Figu.re4,i as

Idetermined that reasonable additional resolut-ion was obtained

~n going from a five segment_ to a fift -- een segment con'figura-

to (ie. A 15 me-ters tLo 5 meters), --the incre:ased,'

resolutio:n in g-oinz :'rom the --cee s-:ntt he rwenz,!-

ove seg-ment confrogurat oon :.e.A 5 metes toD 3 -e-=r,

w~as not- jutf t y t:he i;ncreased ocotr-sources-

c cn sum-ied. 7rorn this obseriati.D- it, cu_la be tocludez' that7

smaller segment l-engthrs are required' fo-r near-fiel] zalou

Let ions, and th at the Lengt-hs are on th-2 orter' Df /E 7he

_aue -tc~ or t:he :a-i.d ie </0for normnal

_2.7a:on3 45-A\:23fr rtoa are as). A~ttC

r-X.ton '.-ow mat nen t e a3 a moon0

otot:o~a0; e ntnn. a.7i~ te se ob~rv ato* ns, a

n m :r-,e -D me D Stoatto 71o. OZ e a r

crmthe b~ase or --he mononole to it-s eghand also _f-,

-he 1base to -:wice -he he :gnt -,-te mono-oole. :: ,07-

ostz the heizht of the monooole were run to Obta:.n _:ncreaseu_

resolution as a function of Dosition along the mcncno-le.

Examination of t!he single and double height plots, side bv

s'ie, revealed no i-ncreased resolu-tion or a,-d4 - 4 ca: _ nfr-

7natc*on was clt :a~hed from a single hieig-ht Dlo)t th at was n,

av a 'ae on -he ocube4,eiht -,lot, so oni;' nlits to -wc

the antenna he47h- are -4 4S cuSs3ed in thi4 z ect:ci.

Addi t-i4 nal z, oos e =aceA r iots wit:n a sezment were

run to .- e-ermne 7 -tere ja-3 an,,- variatio4 n as -a f3co :

:ntr-sementros ti'. :~s pe :Doo was run at

--enter a: -he antenna "or: a) the end of asezmert, t))th

oca -'z-et, and o a hosition half-wa b.et-ween the

7sc I~n ~c eb -In a) and b hS tvo t7: lot -a s -aIs o

cc 2 - a n---nna , '_) a -u,ar-_r c: a segm7en-

a:e e~c D-,., e -7> n, c) a 'a---:a~c atove a

-~ :c.-icase, cnre: -;az noc~e'a~

.c~~:-~ ccr :>~n 3c~e Sn Ie iscfon fKc o

- --- 'd4

ac i~~ :f ce ~ n ~ I i r

::t:Inc ri-J InAroedixA:

2.~ ~ E-?:l Dos (,E,~as a functilon o-f R

a disiancte o:,; one (1) wavlelength from the monopole, for

heig-hts of'2i~ts 1/4, 1/2, 1, and 2 times th.-e ih

of the monooole.

3. H-field plotS (H) as a function of Z to twice the

'neigh-. o' the mcrno-ole, at:Hdstances of 1, 2, ID 1, 123

- fieldi OIc-s (H) as a function of R t-o a distarnce co:

one (1) wa.'elength' for hitsof 2/lO0-ths, 1>/L, 1/2,_

ard 2 times -,:le :eizh-o the monoz)cle.

Each of these categories are diiscussed in furt-her dti

'-elow

As shown in 5, ---- (7) alonz t-he anen s-,r _=c-

.qas much low..er In manz~e(ab-c-u: 6C i- 1-ower) -hnis vale

a-- t-he to:7. Thee lwer valu--es *,aried o a n --,r-er o: magni-

a rua 7-ng valuies (from one cure'- -r'itu-i)ele

~isaco ie ra,_4 (Ki re 3), he in - r ain; efc

rve -also d-ecreasedl -- e -f--rneI

vs ie att-e to -h te ant.ena and -hose a.L:n,- _t enzt

'*P* mceo to ance f 1)') racii. the neroz

-:-7-~fI:~; rae namot uiomm iu- ln

Plot Ex vs Z for a model of 15 Sollffint.

Mtt is of *o, redlos. the Surface of the Monopl.

25 ISO tG t2 5

Distance Z (Wl

Plot Ez vs Z for a model of 15 sejmonts.

Plot Is at ten radii. 2.7 Motors above he Surface.

Au ,.

.3

:2

22

tU

0 2 5175 t0 125 ISODistance Z (Wn

t-he antenna, and this uniform magnitude will continue ro

decrease in absolute value as the distance of the 0.?. m _e

radially from the antenna.

The magnitude of E and E are approximatel, equalr

at the 'op of the monopole, but Er maintains a valie within

an order o" manirude of its neak value all along the antenna

surface (?igure 7). As a result o: boundarv conditions on Z

for the ground oiane (similar to those for n he antenna

surface), the magnitude of 7r cuick! apDrcaches zero at _he

base. The shaDe of this curve remainS pretty much the sane

as observaions are made at greater iszan--es. The -ai-tu e

of the curve decreases slowly and aoproaches a unifor-n value

along the antenna.

teak as :orpC74osi of B and . "ear -he antenna,

iocs D : '- (-ure 3) stron v -resemble olos of - This>_eak

imols ....... :he om....nan ctmoonent :n -he near-f:i-

reion .however, ae s h , fre -Dyed :u-h.r cu-ward,

-he B/B resemnene -adean Tn :here a _ - co-n runw e" r -, a n c

,/_> (see, -zu. tz r 9) where th -_ n inan- .. .\,-i t; st'' :t .. ."

- . ' =nen ... ecm omes : .moe te> cminnant, the value of Eak

7r a uniform value aLon the antenna. Th i

results from -he electromane.. . -;avec, eneratedy h

ooin- source a- the -_oo of the antenna, a2proachi n a Diane

,vave -r:n-t a- ar:e, tis-nces. AIo noted i 'irre r ee

.harn iecine -- ove toe -h ;f the an-enna. Bi

ter a . f n h

Plot Er vs Z for a mode of 15 segments.

Plot Is ot one radius, the Surface of the Monopole.

1000

low

le-

I

ina

2 5s ,0 50 oG 125 ISOOstance Z (in)

".4

Plot Epook v# Z for a model of 15 $0910011111

plot is at one radius. the Surface of the Monopole.

NM

25 so 79 )Go 125

Distance Z (in)

m" 404 s z fw a amw Of 15 soomefu

PhIsg at00 roil 29-7 Me~on sbey. She surf.,.

2S soIN f" n1het

g'reatest ' 7ercentage is di-rected radially out ward!. A more

Sone e set oE:(7) Plots are found i!n ziure A-! through

A-18 in Aooendix A

2. E(R) Plots

Figure 10 shows the very large value of 7, ound at

tne to- of the antenna decreases raoidlv in magnizude as tn-e

C..moves radially awa,, :from the monooole. At, a radial

di stance of aonroximately X /'C- the razi _d decline in Es u b

sides and- anoroximates t.he attenuation with di4stance

observed-- at, other Doints along the antenna (se-e Figu,,re 11).

oZ'nce ': = at the surface, as shown in 7igure 11 1 the

magnitude of the field rises rapidly with iadial --is7tance to

a oeak at about 20 met!ers -trc-i --n, antenna, tramo~ wn--ch the

mag-nitude lew.' -4ci'-es.

--he rat-e of_ lecline of E,(7) appears t o b e -.milorm

'Cor a'los~~n al ong the antenna, t:he on; ifference

oengthe magnitu-de from -anicn th'e d'ecline eis(iue12

_loe t o -he a7ntenna, th-e -~l&~ he

cure.At so me 1=kno~n no.t a C)hs diminis-hed

7,a-r.t-de I S; than B() ecthe E cu~rve .t.5to

follw C) (icur It. -e -oint at hch ths 3T'it

occurs fal -at: a g-reater radial cf-cnc r D*.* 's at

C'reater he1ns Ti is thssl of -a larzer sta-ti-zz

ma~crue (t feat-r e;ts frcm io

un:rmrate 1-2cline. Frlrr tro a"v'ea

Plet E2 wo r for a model of 15 segments.

Pot i at the W~ght of the monopole along the r axis.

IGO-.

Iwu I

a*0 0 0 0 011anoR m

Plot Ez vs r for a model of 15 segments.

Plot Is at 1/2 the monopole height along the r axis.

101

0.1 ____

0 too 200 200 400 500 600Olstance R (m)

-a4

Plot Er vi r for a model of 15 segments.

Plot Is of 1/2 the monopole heSWh along ther axis.

14l

0.1. 00 200 30 .0 o 0

Ditne2 m

Plot Epook vs P~ far a model of 15 segment.

Plot is af the height of the Ofenopos. along lie r axis.

too

1

0 )Go 3:00 400 Sao bOO

larger radial distance is allowed for it to decline b~r

the magnitude of: E., exceeds . he Doint at whichq -thi

occurs is so sharoly defined, that the curve or EaI nas a

"fa~oarent discontinuity" in it.

At twice the monopole heighz, the curve ofE

(Fig7ure 14) has an inverted cuso- . This result-s : rom thessm

shift in IT dominance dis4-cussed above. Directlv- ab)ove the

antenna, E j; hence, E is lar-er' i-han 3u7 as --he 37r -

moves ra'diall1y, -:- eclines wmile ~,rises to a peak. s:i

orszne- inverted cuso; then, also begins a o-ecoLne.

not as raoiZd as 7. More )lot-S of a() re -fou'nd in :ue

A-1 1 through A-33 in" Aooendix A.

3. ':(Z) Plotzs

At tne surrface of the monc7role, th-e mgi'

_s ;r -ia'. : ons-an: ; tnere -sa cso- -h -ecrease near -:-e

-:)r (Figure 135). Above the n7onooole, there a Shar-,~o

.ouz 3 Bs) in int-enS~t 4 s 'h il i tav

trom he anenna -fDI!:ow tn 3ame --:-e Os:)-F , xeo~n

caniud O tnie -il: - :raUlel to tne_ ant enna oecreases wt

incrasin disanczes from the antenna, and_ -he s ham ,)

on ntnstvabDove the h ei.ht Df oh.- antenna bDecomes 7less

a _ stance o-f one wavel-nn Th, h ifenc

-ewe he naPLio :e of H ar alla! t-e ant-,nna an] atcve

:?. Mre o~: h()are f'In,: o

o~~~ -~" 1-~~~ : ~i. An-ene4 ixA

72

La

PIot Epeok vs r for a model of 15 segmenti.

Plot I at twice the monopole height along the r axis.

I

I Oo 200 200 4;0 IGO booDistance R (m)3

"M. vs~ Z to twi.. *emon s.*.15,beft

ph. i at am- eoddha& O Sswfm *4 the Menopel..

0.000 5 10 "5 6

Dtoe" Z CO)

- 4

4. H(R) Plots

Again, at the sarface ofT the monopole the magnit'ud'E:

of H 0is virtually constant. The magnitude of H decreases

rao lJl1v with increasing radial distance, and uniformly for

various antenna heights. Figure 16 is an example curve which

Jelineates the behavior of H all along the axis. Az indicated

above, fo"-r O.P. Is directly above the antenna, H~ i s virtually

..on-existent. As the 0.?. moves radially out wart, at -:w.ice

~heheiht f te atena, rises quickly to a :eak, then

slowlv dfeclines in mnagnit-ude. More :Dl.ots o." H(R)' are

ound in Figure A-40 through A-44 in Ao~endix A.

Pkt HPhI VS P few. moe 811Of 15 segment..

Fis ofe 2/100th th. .oel h.I lse the f Oxis

'a 0' io n

OkO.m

mokU

V. A VALIDATION OF NEC 'NEAR-FIELD CALCULATIONS

NEC is still evolving. On-going efforts toward refining

and imoroving its calculations are constantly occurring. In

its Dresent formi, it has been extensively used, and docu-

mnented -to orovide accurate results in the f'ar-field; its

v7alidity in close to the antenna is not so well -ccumenteJ

To show that NEC Dovides reasonable results in near-f-eld

regions, three tests have been run. :hev are described _'

the following D aragraphs.

A. COMPARISON OF NEC WITH{ C TLAS SICAL ANALTYSISRELS

'lills C~ef. 91, using equac.ions similar to those found

in Ref. 4 (?p. 333 to 333) , calculat ed theoreti-cal values

-or as a flnction of radial 'i stance from the antenna,

:.Ir 3ncr-: antennas of vari;ous lrts zoof his Dlots are

::oners t to sud;thev are for -Doles : half

'ength (h) eclal t:o .1' and .?\. Te results of his

oalcatD-s are dotdas bnroken lines in 7i:,ure 17, t:he

o-D 1. D ?s c al ul ato ns o,2 t he anme a nt17en n a ar e sh Ow r

a 3 1*: n es ReReierin.g, !-he assum~ation o1Tsinuscijal

c,;rrernt Is accuratle only. f"or --he -iuarter-wavelencthmoo1oe1

*As~ -he an-enna z-ecomes snor-ter, the sinusoid,-al :oeak occursi r a c.- on -the fe J ine a no ane :3trozuton Con hne

antenn=a beccmes7 7ore linear.

77I

I TheoretegCal

-NEC

-) 7

,7 33

it is interesting to note NEC's calculations are more clcsel'7

matched as the antenna length aoproaches the resonant

condition., esoecially for radial distances greater than

X/2n (= 300/2 = 48 meters for this study). 3alzano [Ref. 7]

points out, that inside this distance, the classical approach

breaks down, "...because nowhere in the near field (p<,\!2 )

Joes the dinole look like an elementary source (infinitesimal

dimension) from the observation ooinc". Balzano also Doints

out that the classical approach has a constantl7 increasing

E field un to the dioole surface which is incornruent with

energy density boundary conditions at the antenna edge.

Therefore, the leveling off of the magnitude of E z , as

nredicted by NBC, is the more reasonable olot.

3. COI'MARISCM OF NEC '-17TH TPIRICAL ANALYI3S RESULTS

Balzano in Ref. 7 (Part 17) nerformed some measurements

on a iocle constructed from bronze rods of .3015 meters-3

.iameter ( 3.75 0 1 \) that was .199 meters in length

(= . ,l2''), :ncldin7 a .93013 meter -aD at the center from

which it was fed.

A model of this antenna was constructed using NEC. The

-on-fiuraton chosen w,.as a moncpole of 19 segments, each

segment being .*0u9 meters long. The monopole was mounted

azcv a ce:ec:>r conducting ground olane in a manner

... Sed. f tis study. ?Iots of 7 and - were

..... 5:-: for radial dis-snCes of .2>9, . >9,

=man

.01, .02, .03, .04, .05, and .06 meters from the dipole axis.

The results of these plots are shown in Appendix B. dith

the exception of a scaling factor, the information contained

in these plots is the same as that discussed in Section IV.C.

for the study. To further compare the results of NEC with

the measured values, the measured peaks of the square of the

electric field intensity, for both axial and radial polariza-

tions, at the radial distances indicated above, were extracted

from plots in Ref. 7. These values were plotted in Fizures

10 and 19 along with : square of the oeak of the fie"l!_Js

extracted from the olots of the model run by NEC. As can te

seen, ver,, close correlation between the model and the

measurements were obtained. The largest diScreancy -was at

.003 meters distance where the calculated value was inordina-_elv

hicher than the measured value, relative to other calculated/

measured Dairs. Balzano's calculated value was also quite a

bit higher, which would indicate the measured value was a bit

-ow. Credence for this argument sopnorted by alzano's

statement, "...at closer distances, capacitive effect3

ecame predominant".

CZYPAR:SON OF "t 'i7h ' AXWEL' IS UACNS

Chang [Ref. 6] noints out that "...on the surrace of the

mononole the f:d ccm-oonent -. should be roicortional to the

:irrent ditrriut.icn i::)...". The '1-C ,alaulted 'alie of

:was :ono _red ~t-'e - ... n. ~:"win7 o; -he model. The

7- i

LW - DE

iJ I I~J. ____ __ I I

____ ____ I _____________ _________

t _____ ___________- r - £

4 -,

I --- c ---. ______________

-t - 4* -1

-t ---- , - --- i---.--4---

I - ____ -. I.* I

Ii- - __________ . I __________ 1~~~~11

- -. . -~--------------------~---------- I_________

I ________________ _________________

___________ ___________ ____ _____ I _____ ________________

_______ _________ j ,. * _____

V

i: ir:f

4-

I - -~.--- ____________________ - _____________

- t

_____ --...... _

I _______________________________________________________________

NEC~NOD~1i

Lmil27I7 7 - jTI7Til7ZZ72J

3

32

results are shown in Table 1.

TABLE I

COMPARISON OF NEC COMPUTED H-FIELD AND CURRENT AT -.-MONOPOLE SURFACE

____ H~ 25 7(7

2.49 2.573 4.950 4.97.50 2.577 4.858 4.853

" 51 45,313 94.81117.52 2.497 4.707 4,707

2 41 1 4. -.3SID -5 .413 .:4 71 .

27.51 2.300 4.335 4.337,32.52 2.161 .73.37.:: 1.97 3.7 S.7;7-2.5 1 * 10 3. " . 1447.5 1.601 3.C183.1

5-. !.36- 2.531 2.58457 5 i 1 2.107 2.1112,

j ~4737 .56 •5562 .O-'8 1.266

3 7od reemen- _3 naintained all alon the antenna.

....... .varia-ion ocours at the end DL e antenna and

-n:' varia-:' n is s"!e_ than 1..

an.- 3 te s -he '- _erance - et ean:

Sand

33 N

a~prox-Lmate This relationshr4T is:

= ~ ____)H z )--i(z )33-h z3-~ z 3 ~ 2

-s aD.lication to the data from the study at sarnp>- ocints

TABE:

CCMARONOF EsT:'MATED AND ECALCULATED YN

2j

32.53

* rr -a c -e-ee n e

3..l-i - 3 -4 - -JcJ 320ve a o ox- a-e

n.* -, e r-at r nt -i -cn t

:--! t -, o ns 4 i -i a ---

:n z.-'.e nonohe i Th n~~ -aztc a o~cn

7": fie'm enteo:'on e bDase of' -- e mcnonle,

eja

which is not considered in the o'imt oMaxwell's

eouazlons. Cons idering -tnece t-,o :factzrs, the correlat-Ion

is surcr: singly good.

E~is expected, by Maxwell's equations, t-o te ze ro on the

surface of the monooole. I- NJEC, this -;~Cr- is3n

enforced at the match Doints,. The best esi.az o hw well

-EC ao-rox~mates E '?can be se:en rsm the noo : j at

the surface of the monoole, iue23. T Te magnitude of

that is radiated can be found at the top of -he mononcle,

as exrected. ':his value, fro-i Figuire 22, Is nominally 103q

!//,n; a: oDther points along the antenna, --he nominal value -,an

be avcroximaL-ed as 1 v/rni. This dron, of three orders of

magni-tud--e, or SO tD, isa reasonable apToroxirnatio-cn olf zero

tv v-_rt-ual1 lv any engineering standard.

Plat Es vs Z for a MOCIel Of 15 seg4Rmns

PNot Iston* radius. the Surface of the Monopole.

wool

AU

0.10 25 50 so 100 125 io0 . 0 4 1 D i s t a n c e Z ( a )

4iue 2

VI. CONCLUSIONS AND RECOM4MENDATIONS

From the results of Section V, it can be seen that :!E, is

an effective analysis tool for near-field calculations anc:

can be used and trusted to give meaningful results. The

tool cannot be applied thoughtlessly; care must '-e exercised

to ensure the model accurate>,Y represents thp actual z hvsi';Cal

structu-re. oningr consideraticns must b e factored into -.he

orocedure to ensure that sufficiently small seg7ments are used

to ,et: the desired resolution, btnot so mnany a to be

wasteful of resources. Electrical Darameters must '-e con-

sidredto ensure tnhev reoresent t!he ooerational environment

:nowhich the st ructure w-l b1'e immersed. T7hen t tes items

are ad equat.ely cons-'dered, NEC -will --rovi-de the desirec.

reuls'n a tzm .elv and cost e-"fect'Ive manner.

Areas of urhe study could, include exn-anded invest-_

~atcns:no se ax~umsegment len=thfrneril

ca:.xt~cne ineT Ig:-ati:o n -fhe -hrce~~- he

-e frcm tne casei insulatc re7ion, and effects

o)n -"e near- fieldj of using multiple 7narallel wires- _It cr 2S 7

:rnnict__ons in :he manner in whnich broad'cast -Dwers are

-jactlil- :onStruc-edi.

APPENDIX A

Plot Ez vs Z for a model of 15 segments.

Plot I at ce radius. ?he Surface of the Monopole.

moo

0.0 2 50 75 loo 129 1so

Distance Z (m)

Figure A-1

- :?-res A-! -hre'ia: A-6 are )Iots of a s a 'i n c~r various ::is-ances from zn .(axi.

13

Pet Es vs Z for a modo; of IS togment.

Pilot Is f two rodl. .3 Meters above the Surface.

low,

10.

Distance Z m)

Figure A-2

313

Plot Ex vs Z for a model of 15 seglments.

Plot is of five radii. 1.2 Motors above the Surface

Li LUr' /

Distance Z (m)

7igure A-3

Plot Ex vs Z for a model of 1S egments.

Plot Is of ten rodill. 2.7 Meters above the Surface.

1-

m /S/

1[ \ 5 15,0 25 5

Ditne I

~,, '~'~!

*'- "' i "l "I .... I -.... i: I ... ....... ,, , " .At

P~ie t at 100 reft 29.7 Moont 4bv* tho Surf...

23

lDktwws Z (MIL

PW at~ M0 raft. 299.7 #.#o 4ovo Sw~54.

M*1

4i7,r -

Pot Er vs Z for a model of 15 segments.

Pht Is e one radius. the Surface of the Monopole.

'o

*1a

: 0.o!

S is s0 75 ,00 1oDistance Z (m)

Figure A-7

7igures A-7 through A-12 are oiot3 of E -as a function ofror various ]istances from the Z-axis.

?42

Plot Er vs Z for a model of 15 segments.

Plot is at two radii. .3 Meters above the Surface.

,00

!s-

0.! 25 so 79 100 125 S9.031Distance Z (m)

-igure A-3

AD-A,135 975 ELECTROMAGNETIC NEAR-FIELD COMPUTATIONS FOR A BROADCAST

MONOPOLE USING NUMERICAL ELECTROMAGNETICS CODE (NEC)(U) NAVAL POSTGRADUATE SCHOOL MONTEREY CA D D THOMSON

UNCLASSIFIED SEP 83 F/G 12/I NLEEEIIEIIEIIIIIIIIIIIIIIIIIEIIIEEEEIIEIIENDmhmhhhmh

-21 1112.2

11111_L25 _..

MICROCOPY RESOLUTION TEST CHART

N. .NA fO 1 A, 1 T .-

Plot Er vs Z for a model of 15 segmentii.

Plot is at five radii. 1.2 Motors above the. Surface.

V9 S

Plot Er vs Z for a moclol of 15 segment%.

Plot Isoe ton racill. 2.7 Motors above teSurface.

79 10 1

Ditne m

FiueAI

03

nos rr V's Z for a medol of Is somw

Pot k a 100 roil. 29.7 Melon o.v o On Sewfm&.

Figure A-il

33

Iawz foa me"s of 15 Segfft~

Rletse of0I ro"L. 2997 #eftn 4"w Uh wf me

Dist.W z wew

Figure A-12

PIs Epook vs Z for a model of 15 segmens.

Pot ft at on* radius, the Surface of the Monopole.

040111

tu 100,

C

ur

I0

is50 7 100 2 ISO

Distance Z m)

Figure A-13

zigures A-3 hrough A-13 are Dlots o a n cnof z for various distances from the Z-ax s.

ao0

Plot Epak we Z for a model of 15 segments.

Plot is of two radii. .3 MO'.. above t Strface.

10

* 25 50 7 ~15 100,Distance Z (m)

?iueA-14

No~t Epeok vs Z for a no"e of 15 segments.

Plet Is of five radii. 1.2 Motors above the Surface.

X

* 25 5 7512oDistance Z CM)

~iueA-15

Plo EP0 ve Z for a moelm of 15 2e,,,ots.

Plot Is at ton radio. 2.7 Motors above the Surface.

a!

,I /

0 25 5 2 100 ?90

-Distance Z

i ri

No mm vs Z framedai o 15 sugmeeh.

Ph* fte atO redLt 29.7 M4ftn above the Smw~ugm

iI

25 gDhtene Z (a)

Figure A-17

• , . ...... I "-' - .... .. 7 . .... -04-- -

iqW Epoch s Z for me" of 15 soom

POW ft of 100 vdK 299.7 At~ A@, a the kwfum

11)

JHI

Dis Z W

Figure A-I

Plt Ez vs r for a model of 15 togments.

Plot ti of 2/100th the monopole height along the r axs.

I4

0

Io

ti co 2 0 3; 0 400 Soo ,ooDistance R (m)

Figure A-"

iZ:ures A-19 through A-23 are ciots of as a function of R_:r various heights above --he zround iane.

136

Plot Ez vs r for a model of 15 segments.

Plot Is at 1/4 the oapolo 1M clamsong the r axl.

us

a,

Distance R (m)

-re

1

a]. .. ..I I _&"

Plot Ez vs r for a model of 15 legments.

Plot isot o 2 the monopole height aong the r axis.

5 . 1

Distance Rf Wm

.3,

0.II

z:iUr A - 1

Aoos=~~ 32S=

Plot Ex vs r for a meiel of 15 segment$.

Plot ts at the besot of the menopole along the r OR.

ai

.1

0 1" 200 200 400 goo 40Distance R Gm)

, J

NtF Ez vs r for a model of 15 segments.

"lOt Is at twice the monopole height along the r axis.

Distance R (m)

I'gU

i*-i

i Fistane U (s-t

Not Er vS r for a m ol of 15 segment.

Plot Is at 2/100th the monopele holoit a" ther axis.

" G

Dltance R (M)

Figure A-24

Figures A-2" through A-28 are nlots of E, as a function of R:7or var,,us he-hts above the ground oiahe.

Plot Er vs r for a model of 15 segmonts.

Plot is at 1/4 the monopele height along the r a312.

IMI

-10

0 10 200 200 400 So0 600

Distance R (m)

Plot Er vs r for a model of 15 oogmons.

Plot Is at 1/2 the monopole height olong the r ais.

0.1

01

:t ii

1[

11"20Distance R (m)

i-A-21

Plot* Er vie r e a moel of 15 segments.

Plot isat th, height of the monoposle along the r amls.

Ism

.. 4

0 100 200 300 400 500 400

Distance 2 (em)

4L

Plot Er vs r for a model of 15 segments,

PMet Is at twice the monopale height along thor axis.

03S

i15

t mu

II

wi

!.S

.. ~~~~~ ~~~ ~~. . .. . : :.- ... iI tOO 200t00.400 tO

Pot Ep*,ok vs r for a model of 15 segments.

Plot is at 2/100th the monopole height clong the r asis,.

I* o-

0- 0 M00 300 400 so 600Distance R (m)

Figure A-23 through A-33 are 7!ots Df E ak as a function of .

for various heights above the ground 1T,.e.

• 42-

Plot Epoo we rfor a amof @15 segments.

Plst Is ot V/4 ffie mionaola height along thee r*Ms.

W"

Ca

to Vi i .6601tno m

:-ur

Ii

Plot Epeok vs r for a modei of IS segments.

Plot Is at 1/2 the monopole height along the r axis.

IG

allt Ia ,00 20 300 0a 0 0I Distance R (M)

-iure A-31

Ui3

Plot Epook vs r for o model of 15 gegments.

Plot is at the height of the monopole along the r axis.

H)0001

Uh

' I000,

0

10 200 3io 6000o ,oDistance R Cm)

'iuire A-32

, !

Plot Epoak VS r for a model of 15 segments.

Plot Is of twice the monopole height along the r axis.

'1

20 0 ;0 30 ZDitne m

i

p1.9 HPhS we Z to 1wh antefle Wowg. 15 Goemefu.

PW to ait oe .edha, the Sewfue ef the. Monopele.

CA

irsA-'4 -hrough A-311 are Diots of H as a 'unction ofr .,ariu .:.s-ances f-rom -he ::-a-,:s.

PIW HPhI VS Z to twice orw.. helght. 15 sega..,.

Plet to a two rediL .3 Metert abovo the Swu'4ese

Distance Z (m)

wCow

P2t is 1"v mdli W eeeoe.teSw~

z reA-3 6

12 3

P~ev H#II vs Z to twkeotm foa belM. 15 s.m"eh

PIO ft o ton ,.diL 2.7 Moton abev* The Suwqfs.

25 n o li S ISODkftnee Z (m)

Plot "mN v, Z to !W im enotse hmel. is .,gMONOu

"mt st 100 rLdn 29.7 Meten a ove Sete.

1 Z "

~- -e A-8

125

PWe tob V tu - WOehtI415 #

plo ~t 1000 mdL.297Mtr v theSu4e

GA

4t

'Ut'_______________

a 21 2

Plot " I r for a m-JO of 15 s~met..g

Plot Is af 2/100th the mnopole heIgh, a" the r mois.

0 10 00 300 400 0 600r Distance R (m)

Figuires A-4) throuc4 A-1 ar'e oiots ofT asauc-tion of-or *,-:r ous he; hts a:bove t he --round o-Ia~e

Plot H"bI vs r for a moel of 15 segments

PIt Is at V4 the SMopeo height al e the , axds.

0-

0.01

0 OG 20 30 4N0 Sig 00Distance A (a)

Figure A-al

123

I P WSidv r for a mOdl of 15 segsm~e

Nlo is at V/2 the maopole 6*1h. oIle" the r axis.

S 0 200 3i0 400 S00i0Distance 3 (m)

zure

Plot ~ HIwo 6 me" ofd. .15 selmentS.

too 3 Cm

A-!43

S-------

£am

PlOt HPI VS P fec 6 model Of15 IO.M.ew,.

Pialigt te e ft e ,pole height on thee rneis

SAO

06 li6 26of 601st... R (m)

i 31

.-

APPENDIX B

Pst Ex w aw e mds of 19 soo.m...

Ple. h .3 c from =*%*eel*e a" Ow. x. nk

low

0.M L O-t LW00 0.10 0.12Dletne Z Cm)

4i ,-ire -

iures '-I through 2-8 are -)ots of E as a fun-tin tf 2fCr ,arious tanes from the Z-axis.

13 ?

PWe Es vv.3 for a mede of 19 segmenit.

PWn to Ahm froo *4r woepsis af oin hs ak.

-14

Plot Gat vs for aewe" of 19 6entsu.

Plot IS I M fvMM thb NWWPd. OIS al" th. I W1e.

6 002 C66 6:00go oDitm*. Z (m)

-i.~re -

1 LL

PI. Es vio a for a so"e of 19 s,.o.eg

U .e2 0.64 ..eDistess. Z Cm)

Plet ES "t S for OM mof .19 ,.mets.

Pft i ,sm 3 tem e from meep.li, ea sis, aia.d

.o o.o1 oo4 0:.0 LW 0.w o.,,Dkts.,ce Z Cm

Plot Ex vs a for so ofda It1 eog.....

Pa. ft 4ma fr.. oenp. -. 0- m ~g tbe a ei

ir

Plo i am from the meopoe a" a"se Z Se

I

1 *18

0.4 00 O . . _@ , 12 ,

NLDm ._ " Z "m

Pio E vs a fo omodd of19 .t.ogew

Plot k 6m m e menepea l redo a" O s xdo,

I

GAS 001 0.04 0.00 am0 .10 0.11DIkese Z (a)

::ue -

1% .:r -

PW r we3 v a mds of It egh

MW 1 .s GO Er,. .b. menepoeid* o iong 'he a-af

0:43L

OkeIez(

?:igures B-9 through 3-16 are Dlco7 of a's a function ofZo~r var Ojs -lis-tances frmthe Z-axis.

vs fy a for a so". of19 .. w.

Poo k, Am frm lb moeopd. aft Wse e x aft

4ii

6.1

4- Dlseww Z W.

.. igure 31

41

EI. fr vos 2a fo 0 010 of 19 "0".

91.4 is2 4 wm ee O'SP s sm ,.z s

Detm

S.SM S. S .S .S01DM .

Nlir " 31 fo a meda of 19 sogmawn

Meoto g 3m ffw .* heOsel wk alo the: euOW

I-

Ditfte Z (M)

Figure -13

Pst •Er w fr a md of 19 sogom,,.

fIt t. 4 an from the me oe ads olong x atk.

I,

9.00 0.0 0.04 L" LOO 0.10 .,CD hsm Z (sk

Figure 3-!4

2>

Ph*9 Erv z er a mdeof E19 segmosh.

PW. k, 5m frm the mefeqiele m" sl a he ad.

0'3 .U'em

14

Plot E r i f ,. a e de of 19 ,eg ,,em . .

Pow b 6 em ,. moe eds w the z sf

IO

I.

ALOO La 0:4 06 0:" 0.10 L12Dhteus. Z Cm)

Fiqure 3-16

147

LIST OF REFERENCES

1. MIL-HDBK-238(NAVY), 10 August 1973.

2. Naval Ocean Systems Center Technical Document 116,NUMERICAL ELECTROMAGNETICS CODE (NEC) - Method of Moments,by 3.J. Burke and A.J. Poggio of Lawrence LivermoreLaboratory, January 1981.

3. Schelkuncff, S.A. and Friis, H.T., Antennas Theory -and?ractice, Wiley, 1952.

4. Jordan, E.C. and 3almain, K.G., Electromagnetic Wavesand Radiating Systems, 2nd Ed., Prentice-Hall, 1968.

5. :Kraus, 1.D., Antennas, McGraw-Hill, 1950.

. Chang, D.C., Halbzewachs, R.D., and Harrison, C.I., "TheElectromagnetic Field Very Near tco a Monopole",Transactions on Electromagnetic ComDatabilitv, Vol. 7YC-17

No. 2, May 1975.

,. Balzanc, Q., Garay, 0., Siwiak, K., "The Near Field ofDipole Antennas, Par: 1: Theory" and "The Near Field ofDiDole Antennas, Part II: Experimental Results",Transactions on Vehicular Technology, Vol. VT-30, No. 4,November 1981.

3. Mills, A.H., Fields Near ?,adiatinq Antennas, Unpublished,'Jndated.

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