AD-A!35 975 ELECTROMAGNETIC NEAR-FIELD ...cornvuter Drogrxn, Numnerical 7BlectroragnieTics Code...
Transcript of AD-A!35 975 ELECTROMAGNETIC NEAR-FIELD ...cornvuter Drogrxn, Numnerical 7BlectroragnieTics Code...
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
THESIS:Z- VP-r' "D - 7 .
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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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