Preview only show first 10 pages with watermark. For full document please download

Ssn 71, D. E. Merewether, Transient Electromagnetic Fields Near A Cylindrical Antenna Multiply-loaded With Lumped Resistors, Aug 68, Sandia Corp., Sc-dr-68-549

   EMBED

Share

Transcript

,- e~-. ““ ) ,.. -.. , .. I “ 1. .— . ...-7 . .. . . . . . . . .. .. . . . . ,:, —. -. ,,. ,, ,-. ; /’---. , ‘“. ,. “\ .,, ,/ ,. , . .. ,. ., ..”” SC- DR-68-549 ,- ,, ,., ,, ,,. ‘ TRANSIENT ANTENNA ELECTROMAGNETIC FIELDS NEAR A CYLINDRICAL MULTIPLY-LOADED. WITH LUMPED RESISTORS . . . ,. ., D. E, Merewether, 2625 Sandia Laboratories, Albuquerque ., ,.. ‘. . . ,.. . > .. ,.. ., . August ‘“1968 ,. ,. .’. ,. .- ,.. ,, . ., . . ,., ,, ., —.’ 7%...””;. . :. . ..,, . . 2620 ., .,. . .. . -. .. . gG G. W. Rodger<, “.. ,. . ,. ~;l . ,. ..- . . ,.. .. . ..,., . . “. . “ “ . .. . . . . ‘. . ““ j’ ‘. “.. ,. . The cylindrical antenna,. driven at its center by some transient voltage input “ .. . 0&nd symmetrically loaded with lumped re-sistorsj has been found. to be.. a useful “ electromagnetic pulse generator. In a previous study, a procedure was developed “_ . ,, for selecting resistor paitis to be used to load the antenna.. When these resistors transient approximates some pqe - ,, , ., . . ,are in place the radiated electromagnetic-field ,. scribed fast rising generally decaying function of time when a voltage ste”p is . . . ,.-. impressed across the center terminals of the ante’rma. . ,. “ . . “.+-- ,. ,’ .“’. ABSTRACT ,. . ., ., . . ,. . “, ,“ ” ,.’ .. ,., .’ Iri this report, the components” of the transient electromagnetic field near the antenna are evaluated and the antekma synthesis procedure is extended to allow the selecti6n of resistor pairs so that the magnetic field at a point of ‘observation in the” near zone approximates some ~rescribed transient wavesha~e. “- ,--. -4’— ‘ “ .., :“’” .. . .. . .1 ,,, , . -t,” . ,. ‘1 I I , ., . . ,. . .“ . ,,. ,i‘) ‘, f-’) 1“ .,-. ,,.’ ,.”, i ,.. f . ..\, . .. .. l-. (D sc+ ,.. l;: . ,’ ‘:, 11 ,, ,, : ., ,! l“! ,. ,., :, ,’ ., ,. I 1, o E$ ./ g .. .. .,, ,, ., ., ., .. ., . . .: . .. .. “. .. . ., .’ ; ‘. ..” .. .,. .! .: . ,, . . . . .,’ ,. . . . . .. . I . . , . . ,. . . ,. . . .. . . . ., . “. ,:,, .. .’. ,, .: ... ., ,,. ,. ’,, “w ,. -.-- ..:... some desired transient or so that ez(t) approximates some desired transient,. but .:.,. not both simultaneously. Selection criteria for either choice are given in the text ..- of the report. . ..- . r’ci?,-.:’: -i’: i. of ~:~:~:~:- ,’ ---- . ‘,. ,, .,– ..--- ;. ; Analysis of Near-Zone Electromagnetic Fields ~. +-.% ... . ge.Wfi%i& ~ection, approximate ‘formulas, are developed for the transient ‘ . . . ele&&b’rnag’n-et~c fields observed near a cylindrical antetia mtiltipl y-loaded with ., “. ., ., resistors’ d~iveri by a “transient voltage sour,ce~ -. --, ~a&:,:.~ ., ., .It”n-J_?j:’:. ““ .-.. : -’:- “ .-”. - ‘“ . . of length 2h, symmetrically . ,.-+” .;, ..= . . --,. “>, . . . .,’. .:. . . .. . . . ., driven at “ ‘ .‘ “ : ~ For the ynl~aded cylindrical antenna, . . . .. . .. +j~t points z = ~ d by monochromatic voltage sou~ces V.e . (Figure 1), “the nonzero “ . . .. . . u. ..” .,. ..’. . “ . .. of the elecfromag~etic field in cylindrical coordinate; are ‘, 4. :. . . . “: . .. , .c@npone@ .. . ,., .-, . . .. . ..-— ,. .“ . .. ., . . ., . . . . -....._——— .—. . 4. ., . . .. .“’ .. ,’ . ,, ,“ ., .,., <,. . . . . ., ,,, ,’ ‘, :\. ,“. ’.’. .2.,. . . . ,.. ,, -’ ,. [>;,,. .,, .. :,. .. .. . .- ,,. . “.,”, ;.:’$ ,.:: :. ..../.;”. .... .,.. :,.. . “.,,: . ,. .,, .’ :, .,. . .’s ,, . . ..., ;. .,,. .. .. ,/., .,. . ..”. ,’. , ‘-.. ,, . ,. ,,. .. ”’, .~, , ,., ., ,, ,.. , ””’ ,,. .. ,,, , ,, ,,... .. . . .: .,.., ,. .. .... !’. ,. . ,., ,, ,. .. .! . -.. , .,. ,., z=i-h ,, ,. ,.. ,,, . ., .’ ,., ,“,-. . ,. .. ,...,. .. z=+-(j ‘d, ., , * .. ,, ,. ,.. : .. .. ... . . .’ ... ,“ .. . ., 2=0 ,.. . . ., ,.. ,. .. . . ,.’ . . .. . ,. . . ..” . . . ,, ., ., . . . . ,’ — z=- d . . . . .. . . . i.. . . . .-.. .– , . . ‘d . ., ,. ., ., -,, ..” . .. ,. J ,,- “.. ,. .._, ?. .,... . ,. .. ... . .,, .... ,. ,, .. . . . ., . ,’ . —Z. . . ,. -h .’ .,..’ ,. .. .. ,. .. ,,~ ., ,. .,. ., ,,, 9 1 1 . . “..”--’. :.“ / ,,. /. .. , ,,. where c’”” ,) .* ., ,, . ,, D ‘ ,, ,’. - jkoR h “ . PO Az(r, z) + ~n ‘[ I(z!, d) e -- dzl ~ , (4) .- ,. .. .,. ,. ,, . . . . ., “R=l-==. ,“ ,, (5), 1 ,. The approximate current mined (3.11 ).2 ., ./ I(z, d) ‘= #Z. ,, COS sinko(h koh [ –- ,. n .performing L “. ; the operations ,.. , ., .’ . . ‘, +-e Ez(r, z) = - ~ ,“ ‘2d { . ,,. *.’ ..’ - ... ‘r(r’ ‘) ‘d Or . . 1 .:-> ,,. (6) . . .-. .. “i ‘jkoRld (Z ,0 . . + (Z R~~) e + d e . . ;, ,,” cOS kod .e -.jkQR1h . ‘jko132h ,,. +’e — , COS koh Rlh ‘2h [ 1) ., ‘jkoR2d ‘Id .’ - Iz + d[) .---”’”~~ ,Vde ‘&#ld ,. ., - Iz - d[) + sinko(h ~ -,—_t . deter- distribution into the integral equation for Az&, z) and .: indicated in Equations (l), (2), and (3) yields ! . . ..,. ., t ,“ !, ,:., . . .i \ .’ ‘Subs~itution of the current [,” .,’ . . j2rVd ., on the antenna w“as previously distribution , (7) ,.. . -jkoR2d. ‘2d { . ‘1 Cos kod COS koh (~ . ‘lh L. ~) e ‘jkoRlh * (Z + h) e -jk ,0R2h (8) ‘2h . 1) “ .“ ‘ 1 . . (9) ‘-, .. ,. ,, ,.’ ,. ,. . ., ., ,’. ., . , . ,.- ,, -,. ., ,, ,, :. L .,, Here ,. .”. ,.-, . F “ ! ,.. ,.. - .,.“.,, ,. .. . ,~’ ,. . . .. . . .. ,. ,. ,,.’ ,. .“ . ,., - ‘Id = ,,, . ... ‘., . .— . ” ..— ,,. , ,’, Following the inverse discussion field observed loaded ,,’ ,. .,, N . ,.,., .. ., . —’vo+t ‘R2d . .’ ,. i ., . . . . .. . . . .,,,.... . . .,-, .,. . .. . . . . .,, .. . . . .. . .. . ,. ‘ is applied to Me ,.,’ ,. .,, , ‘., ,, i, (. “: - “2(j. 21. ..- . ‘V. ( ; L ,, .“ ,’ , ‘ (10) . ,“ . ,, .’ . . . . . 2’(j ~1.jA/;)’ i’. ,. “, R2d . ,. .,$ :. ..., ‘(z+ij:” -: -’ l)A/c) “, f ., ‘.. ,. ,“lj., . . . ,. . .,. . . . . of, the ,,, ,. ,.. ,. ,,. ,’. ,er(r$ z) ,= +Vy 0 “ 1- >‘o”v~)~~$Ai:j[~~o(~’-’tli”.=. ,. ,.. . . ‘. { .,, .. “.. ...., .. . causal voltage ,. in the form j=l 1 .. . . “...- the components .,... ~ i=l . . in the previous tli-2i’,’)Aic) ~ ~2i2ZAi:j[*vo(;- ..’. ‘! 3.3), “{ .“.,,., ’.,, ..._, ,,—. ,.,, . . . employed , -’,-,. ,., (Section antenna are obtained -’~ 1’ ez(r,”z) = ,v~vo(t)+ ., o ,L ,:. . ,’. . procedures when an arbitrary ,.. ..’ ,, transform field problem ,, symmetrically ,,.,,, ,, ,. Fourier of the far-zone ele~t~omagnetic t,- . . . . t2i - 2(j ‘ .. - II,’ l)A/ C) ., (11) ., . !. . .“ ., .’?, ., .:.;-.:&[v::)+$~”*i; ,. ‘+(r’‘) 4+ .. .. . ....- .’, ,, ,“ . . ,L ., J, ,./,., ,5 ,.. ---- .. . -. ‘, ‘.. ,.. ,, . . All of the components are given in retarded time, . where ,, /-- ‘/ //. .. ‘3 ,, ” RO=J- R,,= ~~ -“ i .. . ., . and . .. ’.., ,’ ‘Ii = ( ‘i*Rld i “Ro )1 c ‘2i = ‘ ( ‘i+ R2di-Ro )/ c“ ,,. Equations (10), (11 ), and (12) are the desired field near the, radiating structure. description of the electromagnetic ,, > ,’ It may be noted that: “ field is Z. times zone. at a point (r,+, O),,the-initial amplitude the initial amplitude The subsequent of the magnetic shape of the pulse is different, ., field, of the electric just as it is in the far however. . Transient-Voltage r“”,-’.’”. \ In the synthesis voltage ,. ,$ procedure. Input to the ‘Antenna ‘ . .“’: previously developed for far,-z,one fields, a step was the assum”ed input to the ante~a and a staircase ..app~oximation ~ . . . ,, to the desired field transient was obtained.’ The procedure previously developed ,, . can be extended to .any..causal voltage. source wijh only a slight modif~dation, .,O . That. . . . . ..’ ,.. ‘“ ) .. ., . . ./ ,. . .. . . . . .~, ., !’ .,, . . . .. . . . ,. . ... . ‘. 1. . ,, . w u v [I-)’ .“. . . . x“ ., .. ... RN-2, .. ..’ -. .. . .! . . ..” .“. .“$ .. . .. .; Figure 2. . .. . . . . . / ,-., Let vo(t) be some simple in retarded ., time. where f(0) = O, and f(A/c) .,. causal input of the form vo(t) = VBf(t), = 1. For this type of’ input the normalized ,, ,-. ,., D . far-zone f---- electric-field ‘L. transient .,, . The synthesis normalized is of the form . proceeds electric-field ., -“ by finding an approximate transient expansion of the desired in the form ,. r“ ,, es(t) = .’ Mkf(t - M/c) f(t) + E I_ 7 03 ‘(15)’ . .’ J ,< i= 1 ..” ., ., A solution . for Ak ~ is then obtained by equating > coefficients of f(t - .kA/ c): .: JM . ,, P ‘k, ,, k- 1. ,. . . ., ,., . . ,. ‘ . “ ~;6)”’ e. -. . . . ,. .“” .-, . ”,. . “ ...? .. . ., -: : “,. . . ., . . j ..,. . ., ,. ““.: k= 1, .“. .,, ;(N”-1) = Mk 2 -“” “A . “k-2(~-l), lx ., “ j:2: ., ., !- ~ ., -. .: f.. -. -. . and, {M =, Int [(k + 1)/2]. of Rk is determined .’ Int [x] means the’ inte’gtial part of x. - The .requifled+val~e. .. . from” (3.32). “ .. ..’ . . The reinaining.ques~ion-is development, the coefficient .“ ,, . ,. how shall the Mk’s be selected. M4 was selected . , j , ,,’, ‘. ‘,, . — In the:previous so that the step approximation .-, ., . ‘ es(t) “ Y , ., . yielded an average fit to the desired normalized electric-field transient eN(t) during = .13A/C. when the input is not a voltage step, ‘he ‘nterval’ !J < t < tj+l’ wh~r: tj , ., !“ !..’ .’, this selection is not appropria.$ej several other m“ethods’ of selection are possible, ‘ “ , ,“ “ : , ~ ,. ..,, .’. .. -’ .. . . since f(t) is’ causal, ,,. ,. ”,, ,, ,, f(t) = O if t < 0,’ and s nc”e f(0) = O, the desired ., ., ,,, The coefficients ,,, loaded ,,, are obtained As a guideline resistively ,,. . . field, .-.”. antenna, value of M4 is ., ,, ,. sequential~y.””’ of type of electric-field is’ likely to’ be less than f(t), ,, ,,, ,. . transient that may be generated it should be noted that the normalized since the resistors Also it should be noted that, if’ the desired waveshape have a degenerative, field waveshape effect is very by the observed on the simi’lar to ., ,. .. ..: . . .. . .. ‘, ..” ., ,, s, ~. ,. . . .. . ,’ .. . .. . .“ ,.. .“ . . . . ,, . . . ..- -. _:. .: . and .. (-., , ..... . . . . . . .... . . Sl:ic’: A,$b.~. --- ~~=:-.-: ,, ‘Rdi= ,/’ ,, --,...- ..- .,::.-,. -~.’ m--, ~-(:, )-:’.: ~\ L+i ., ,’. . .. “ ,., . .i-- ; - ..---. __. —.—, .- .—..— When r >>h, t~~ ‘iA and changes-’inA tie far-zone of A/ c. ce~’er Signal changes caused by higher .. ,., . order ,“ .,’ field. occur bounces z: + cu. =.-.=-- . . signal caused by the passage ,. “ ‘-: “ — of t$e antenna arrive, at.the point of observation Lne co:.~lcl~?::.: “,’; ,.‘P . >. of another resistor peri~dicd-ly- between resistors at the precise by the primary at intervals” near the time that the current wave arrives. .’ ‘The.- ant.enna. designey has some. control over every change in the radiated -~-s c..$-.....--.-;: ‘-- -. ; .. ,., ,, field. ___.. -,. ~ ~J:e:::.,:,. . ~ =C+,Z-. T->. .,. ‘ J,..,~--.-..! -., $ LQ=,:..: . . ,L. ,-==-~ -;-. .:$ ., , . . .,. .. ....- . .-..--,..: z----“---- .’ ------~ When the point of- observation is in the near zone, signal changes caused by, ... . . . .. . . . ..-:----- .7--m- .-.. . ultiple reflections between resistors arrive at the point of observation between. ‘ .-. --------. . ----. ..-..,. ----, -, the times that correspond to ~e” a;~ival of the~primary wave at another resistor, . ~~~~~:, -q:~;~:~~~-~cv,-, c .: r . .. because of the differences in signal time delay. Since the designer may exercise .. “ . . control over the waveform a somewhat only when the primary dej$c~ded:w~tefoi-”m” wave passes another resistor, c’an ‘be expe et ed. , For this ca”se~ the synthesis : “’-l>roceeds by finding an app;oximat~on’to . . -....,. ‘the desired r~this SC2J.:L:-, .2z... =.G.- .-. .. magnetic . . field .,in the .. form “ .. ; . . . ..---., ,. ..=. — , . ,. .,. . . ,, at the point of ~bservation represents ,,, ,, is exa@ly bqfore tj+l. the ,. point where the travel equal to the travel ,.. In Figure 3, the point Ze on the antenna -, ,,, time from J?Ato Ze to the point of observation ., ,, time from i?4 to (J + I)A to the point of observation. ., ‘,. ,. .:. ., ., ,. . . .“ Al- ,. ““’”.1[ - ‘ ,,. ,. “. . . . ““’””’-””” ‘“”: . . .,, .’ .,,- omparlson -. ... . ,, / ,,. ,. ,, ,, .’ . . . . .. . . . . . .. -. -y.,-< . - - /-” ‘II 4 (23) ( -- ,- .-,,’ --. ,.” , . . ‘1 ,- = :--- ,, .:a- (J - l)A. Higher order bounces from resistors “ ‘:-;-”” “ ‘ ‘“’’”-” and arr,ive ,at the. point of observation before. :----... . . Ioaate< @qY? ~@;.ntl?e !?v?~!.e. -!g~ I -. . . . .. . . ... . -.. ... t =l,$]s~. #@emthe contribution A ,..1 !S .fact~{e~ frorn:’Equation” (21),-. .the, .- .-=-. .total . . . -----T- ------ of -,g where ., D ‘ ‘-;” form below is obtained. .. . .. . . . . ..— .. .. . .,. —.. ---- .“X k=l”. . . .. JJU” .J3... . . ... . . . Mkf(t4+1 - tk)” = ,2 ~ZAi,$~~+l 1=1 j=l , - tin- 2(j - I.)A/c) . ,.U . . . ‘“, . o AJ,l ‘ ., “. .. ., .. . . ,,’ .,, . .,. ,. +’%(-: -‘~+’-j - 2(j -l)ALC)-” .-C(’)fb+’ .’ (24) ,. ,, ,. ,, /----”” i_ . .. . .. .- ““. ., I’CJ= In~ ze/A] [ .“ ., “ , ,, .. .. . . -.... .<4. . . . . ,, /’t’ “, . “. “. . c(1)= 1 , ,’. ,., . . .. ,. / .. . . . ..’. . -. :.$ . .,—. ‘- 1 ._”.. . C(j) ‘r~+l-j k m. —- C(m) , ‘ and . ,. j>l . . 1 .- ‘.,“ . . ,. .“ J. . .. ,, ., ,. , where, . . 1: : ,. ~ . . ,, . . . . . -, ,. i, ., ., -. . “. . ,. . . . .. . . . . .“ .. ., ., .> .. .-,:, ,.’” . .,—---., r —-- . . . ..-— —- ~ .-.. ,. (25) ,,, ,, .,’, ..,, !. .’. ,— ,.’ .. ,. H tie desired . . . values Of AJ,,1 are determined R~ ,rqay be determined . ,. . from. Equation (3.32) in the far-zone . ~“ ,. ‘“ ,. t ‘,. ~ . E Mf(+:pk)-z . ‘~ .’. -. .~. .,. ..--~ , :. ,, “, ‘kJj ‘ft. ‘Rdk ‘, ...” ,. ..= . value of The selection . c(j) “L;=l : ‘, ~“, r J–A ., ‘f tj+l ( d~+l-j ‘- ..– .“, ‘ ‘J+~_j - Z(j An. 1 “.4 =O (2’6) ‘ ~---+ - ) .,, the desired .’. electric ., .. i)A/c’ :. .. . where .,. the approximate shapeof ...’ , . . . ..” . .“ ,) )A/ ~ -tk-2(j-l ..”. ,. ,., ‘1 ,.. ‘, “.,”:’ ’,, J +’1 1 J,-IU3, ‘ “~ ~ , ( ..’ , “,, ,,. .’+. . “r l“’-k”’”,j k=-1[ ““AI, 1 = ~ ,,. ,. ,, . study. ,.. ... .,,... 1 .“, /, . . r, the required is essentially the end of the synthesis problem for near-zone magnetic ‘OfAJ,l fields. An equivalent formula :.for the synthesis of the z,- component of the., elec~ric’ ,, .,, .‘—. ,— field ‘may also be obtained in the same manner; .the result is .. ,. ,,’ ,. ,,’, . .. ,.. ,. . sequentially, .“ .’ .- field” is ‘ . .. . ,, .’ . . ., (27) ., . . ..,-,. . ... .. . As in the ~ar~zone case, the antenna ‘designer’,loses shape when ‘the primary of the ante~a, ,. . wave of current must be chosen. so.that simulated ,wlien the primary reaches control the end of the antenna, most of the desired wave reaches of the radiated V=veshape the end of the antenna, has wave- . The length been As an example “ , of ,.’ ,. .“ ,, ,, ,.’ .q.::y . . . . . .. . .--. k. . . . The spacing between .. resistors ,, was chosen to be ‘o, .’{ n!, (29) +$= cT/12.5 . ‘ 1 ;:-. , ‘1 ., .4 ) ~ /. .:-_~:,,z _-’’< a_:__l_)dJc:::: -.! . . , ,-; :),:,.!’.:.; . ~ - .- .-.. , ‘,T .... . . :. ,_ +-. _ f-_._’ J- _... _s=2.; :;. — -..= ---=%== : I~w~as&%ed-that the ~~~~agein~ut to the antenna was a voltage’ step and that the ..’ ,, ,..4 ,., ,, J; ..- ..- . was consid”ered~ f=-. .... . . .. ,’ .----- ,k-. ““”’ ,:- ., ‘ ● - ‘-- - syn~h;esis range was 3A, ~A-ntemnas.with @df -lengt~s. I-ti,-,,_,-, 10.~, and 64 were conL 1.{ ‘;’’- l’:--: ‘~-:-’ sidered. Figure 4 shows ,sthe normalized magnetic, field at the point of observation, produced by each of the antennas. The portion of the waveform that is of interest ‘i this is the portion he~e-.is the portion after t = (h + Rh - r)/ c, Rh = m; ~ ,. the designer has no control over;”. the current wave has reached the end of the antenna and the subsequent waveform is controlled entirely by the-previous ,’ . choice of resistors. For, the.longest antenna, the reflection from the end of the anteima . . ,, .“ is ~ppar”ent at t = “2, 02T; the gradual decay of ,the magnetic field after this’ time is ,.’ not too dissimilar from the desired waveform. As the antenna is’ shortened, ,. . . . . less —. of the, desi~e’d ~wavefocm is genera~~d before .th.e wave-r e”aches the end of the a~,d a~,la,:ger curqent. wa~e a~proach&. s the end of thej str,u.cture. Accord/ ingly;” th=e_&hange’ ‘ in th~ m“agnet~c &ld caus~ & by ..—.—...---—- —..—____ --------.. ..... . .~ef~e ctio-n from the end’ of the’ -K~ antennii is “larger, and a ‘pooi~~~’over - all approximation ‘results”. ” : -.’ .,-~.(j:. : ~ -. . . ...” T. \, -:’.,. ...” . . . ,:;..”../’ ‘ . . $., . ,.. . J=z ‘In Figure 5, the normalized electric fie~d for each of these three antennas’ is . ., efiibit’ed. These, waveforms all, approach a static dc value b“ekause.the poi~t of ‘ antenna, L..- ‘. observation is well within the “static type of input, obtained an estimate zoner’ of the antenna. of the final ,value of the, observ~d from the zero freq~ency limit of the electric For a voltage elect~~c field produced by an u~oaded —— .— “ ,.‘“; . . : . : .’ . “ o “ ‘ , . ~_. ., . .. . . .. step field may be ,., . .—, . . “ . “. . . ,Y . l“ u %-l $ ,, ‘“.$ . . z. C...,. ,. “, ,, ,. ,,. ‘d. ,&’., :“7J ‘ .,. . ,.” .. . .,. ..: .,, . .’. ,., . ,$. ,. g “ ., .. ,’ ,, . . .. : . . . . .. . . . ,’. . “.!, .,. . . ‘ O . .. ,, —.- .- L $, ““”’. .“. ., . . 1“ . . ’,, . ,. ,, ‘, .. . .’ , -%” . .’ ,. . ,. . . . ,.. -.. . .. . “,. . ., ... ,. , .. .. ” ., . ..’ ,. . ‘ ,=6~..., ,. ,.,’ .: -. . . ., . ‘o . . . .. .* . .’ .. ,. ..” ,. .“ .’ . . . . ..” . . ,,. . . .. . . ,.. . . . . ,, .,” ,. P .,.. . -. ,“. — . .. ,.-. ,“. . ,.. ,. . ,. ., ,,. ‘, ,/ .’,., J.. _., , ‘.”—’’,.+ ,’ ,. ,, ./’, -. .D .’, ,, ~ .’ J* .. -,’< l;’ . . -. -, 1 /., . I ‘h= 14A ( .,, , . . .’ ‘. ,, .. ,, ,, . ,. . . h = 10A ., r’ ----. ‘, ‘d la) .. ,’ .,5 “G, G .8 z .. . . -; -, . iii “r- . . !. . . . .. . :.. “. .,, .. . . . . , ..” ,.. . . .’. .. ...” 5-” . ., . . . . . . .. ,.. . % . . . .,, .:. - h=6A . . l.’ . ..”~, . . .. . . . . ._ .. ,. . ,, .!- r-if. “o” . . . I .40 I I :80 I I I 1.20 I 1.60 Normalized I I 2.00 I 2.40 I \ I I I ,2.80 3.20 Time .. Figure .. ‘ 5. The Effect of Truncating the Antenna on the Observed Electric Field Waveshape r = 3A .. . ,. ,,, . .— .. .“”’ . ........ — .. .. . I I I 3.60 4.00 ● , ?, ,, f: ,.i=; “3 ,, .,, ., ,., ,. . .,...;.,. ,,-, .. ,,. ) ;. ,“. ,. . . . .. -+, is retained . as a static ,.. . component is ... . . . ,. ,’. ., ., ? ,,, ,, .,, . ,.,, “f- .,, ./, . —.. . ,, ?.- ““of. ‘ /y~~~ti~ - inn.. - r, - ‘Uv + I L - ...’. .“.., “. :!. ..’ ,. .’: ,., . :, . -. ----,, .,.. “.,-.4. ..; . “. . .. . w .= —. eventu~ly goes to zero; hqwever, the static component is not ,.a very serious . ,:,,. .:.= . ,,, ,. ,,. pieces of electronic apparatus will respond to a static consideration since very’ few . . . ., .,. .. ,, . electric .. . .. field. ,-, ’., --The . .. . sharp discontinuities . .,. ,,,’ .“ .,. ,., ... .“. , that occur in’ the waveforms (4) and (5) are primarily .. exciting step. ,. . asso’ciate~ with the assumed .. If a voltage step-type of waveform”tiith zero ,. . “ . ,, . . ”..’...;. ,,, -., . . . shown iq Figures ‘ :“. rise a noniero ripe time is ..’ Analysis ,., antenna theory “ , ] “’” . . . “ “ “ ‘ ,- that the analysis . .“ . . . . ,,, . ... ..”” . . , ,. , time on the .‘ ,.” is . . .. . . ._, source (P.: !.< - is Qrnpr$ss .-—k_.. ed across _ -..-the ...-.-,-in-put .. -.. _~erminals ._-..-cwrrent of the antenna, ,3 is~~.yuls e.of. identical shape given by -——— .+___ . . .. . .=.,. deveio~fi< &in... -j:rr ---------- -,.. length of ,tie highest approximat~on ‘quantitative significant cf the effect results For thi~ker frequency actually antennas, .’ in the -----neighborhood ... . . . is a voltage step, form , rapidly . . ~, .,’ ., .. .. ’..- compared this response to the waveis an excellent and very good ‘theory. . , , ,, onto the structure to, char”ge up . . . ~f the drive terminals .,, ., so that,. ., if the input,”voltage the input nur.ient has a ‘significant spike on the front of the wave. . and the’ 1’characteristic impedance, “ Za, cannot be considered’to be frequency independent. Use of the simpli~ed theory can only yield a qualitative picture of the !,,’ y: transient respo&e ~of ; t$iclt’ a~te-niia, For the antenna synthesis problem, ~e “use . of a thin antenna is, certainly desirab~ej for then the synthesis procedure ,will yield ‘ ‘ . ,-.. , the; desired resistor with reasonable accuracy. - IIowever, ‘struciu~al ~ -. —..~---- . ....values . .... . —..-=----+ ,-< considerations and driving voltage conditions may “require the use of a thick antenna. ., . . When a thick antenna must be used, the synthesis procedure. cs.TIonly provide an . initial selection of resistors; final adjustment of the values experimentally . . be anticipated. . . In the Section entitled Tq~~ie-n~s2.~~,.formulas i-. . -- - “Antenna for theselection for Near-Zone of jhe-values load-_ the antenna >... ..... -..>.,. ,., were r, based upon the synthesis . magnetic-field transient.”or transient ‘h a des-ired electric-field in the near zone. that has no static mn;mls into the %n%nnai---F@ pai!s “ ‘‘ must ‘ . ..”. ,. Magnetic-Field of the resistor . “ - ,usd to . .<”---- near the antenna has a static . :, C.._..,, Synthesis syc~:~~~~all~ observation -. .-—-—— —.- —— . . ,. in the laboratory, rushes ;’0 ,— from the use of-the simplified current .. the capacity of the pulse, observed can be expected . . * .,c ~.-;. ..-. - s_..._:,.. Vin(t) ‘- iin(t) = ~ . .,. ~-[, -; a=_- _~!;k’ ? “E ,. .~, !2 -::Stz:ic . .. . .-r.L For thin” antennas, where the radius of the antenna is small ., the initial input It should be noted, component component transient however, ,$ at the ~oint df that the electric so that the synthesis cannot be accomplished ~tliis type of input voltage, of either” a desired. the magnetic field of an electric-field with a voltage field is more s~ep easily “ . ._ ., ,’. .~-.~rlando,’, Florida 32805 ,“4: .-.,.,... ... , ,., ,...,.. . . . ..’ .,..’ ~..,. .. :, . . ..,-,,.. ,— --..’ -. .,,,’... ”,. *-Bi-Dinger’ ---------------, “.. -.,“. ‘,,., .. .. . . .. ,:, ::U. S. Army Mobility Equipment . ,and Development Center ,.. -. ‘.”. ,.” ~;, ,: B. F. Hefle~, 8232 (5) .,- ., ~~T. H. Martin; 9143’ 34~~ -:._;.- --- -x --~~;-Gi~le~pie; Research ~ B. R. “Allen, 3421 ‘“, . . . C.” H. Sproul,3428-2 (10) ,. :. Men permission by the manager ........ . .’. ,,_ .;,,:_ ... ,, !.-”-. ,., ., “ ,’ . ,, . . ,,,.. , ,.. 25 .,