of Radiation from Lightning

Transcription

1 b NASA Technicl Meorndu Review of Mesureents of the RF Spectru of Rdition fro Lightning Dvid M. Le Vine jnbsatm8778&) REVE OF MEASREHENTS OF THE RP SECTRM CF RACATCEi F GB LGHTNNG (NASB) p CSCL 4B NB71658 ncls G3/47 b49 MARCH 1986 i

2 i NASA Technicl Meorndu Review of Mesureents of the RF Spectru of Rdition fro Lightning Dvid M. Le Vine Lborto y for Ocens Microwve Sensors nd Dt Acquisition Systes Brnch Goddrd Spce Flight Center Ntionl Aeronutics nd Spce Adinistrtion Gwr Spce Fiigni Center Greenbelt, Mrylnd

3 . NTRODCTON The electrognetic rdition fro lightning t icrowve frequencies nd below is generlly referred to s the rdio frequency or RF portion of the spectru. Rdition fro lightning in this portion of the spectru is iportnt both for scientific investigtions of lightning nd for engineering ssessents of the interference environent during thunderstors. Mesureents hve been reported fro frequencies below kilohert to frequencies bove gighert. The word spectru is generlly used in the literture on lightning in this frequency rnge to en the gnitude of the Fourier trnsfor of the electric field E(t) rdited during the dischrge. n pplictions to lightning, two ethods hve trditionlly been eployed to esure this spectru. n one, the spectru is obtined fro the electric field wvefor itself by Fourier trnsforing. The electric field wvefor is recorded first using instruenttion such s fst field chnge syste nd wide bndwidth recorder, nd the spectru is obtined nuericlly fro this record by ens of Fourier trnsfor. This technique hs the ppel of being stright forwrd, but it requires wide bndwidth recording devices with lrge dynic rnge becuse the power t high frequencies tends to decrese rpidly with frequency. The second technique is to esure the energy rdited t prticulr frequency directly using filter nd detector syste tuned to the frequency of interest. Stndrd rdio receivers suitble for this purpose re vilble in this frequency rnge. The jor difficulty with esureents of this type hs been in identifying the eleent of the lightning flsh (e.g., leder, return stroke, etc.) which is the source of the rdition. Ech of these techniques will be described in this report nd sury given of the dt obtined with ech. 11. SPECTRA OBTANED B FORER TRANSFORM A lightning flsh is not single event but, rther, is sequence of ny discrete events. Soe, such s return strokes nd the leder steps preceeding first return stroke, hve received uch ttention nd re resonbly well known, wheres others such s the ny different events which tke plce in the cloud re only recently beginning to be studied. The electric fields rdited fro these events tend to hve chrcteristic (tie doin) shpes which perit the events to be identified nd spectr to be obtined seprtely for the vrious events. For exple, t the top in Figure 1 is shown n electric field wvefor E(t) recorded by the uthor in Florid during the Thunderstor Reserch nterntionl Project (TRP; Pierce, 1976). This wvefor hs shpe chrcteristic of those observed during first return strokes (n nd Krider, 198; eidn nd Krider, 1978). t begins bruptly with rpid rise to pek nd then decys irregulrly towrd ero. Frequently, the brupt beginning is preceeded by string of sll pulses ssocited with the stepped leder (Krider et l., 1977; eidn nd Krider, 198). The lst such step is visible in this record just before the beginning of the return stroke. The grph t the botto of Figure 1 is the gnitude of the Fourier trnsfor of the wvefor, E(t), shown t the top. The Fourier trnsfor ws obtined nuericlly fter the wvefor t the top ws digitied. Figure shows the results of verging wvefors fro return strokes. The dt ws recorded in Florid during short period of strong ctivity ssocited with nerby thunderstor on July, At the top is the verge of the tie doin electric field wvefors, E(t), nd t the botto is the verge of the gnitude of the Fourier trnsfor (the gnitudes were verged). This dt ws collected by the uthor during TRP76. One of the erliest pplictions of the Fourier trnsfor pproch ws de by tt nd Mxwell (1957). n the course of describing esureents of low frequency ttenution due to the erth, they de Fourier trnsfors of electric field wvefors recorded by Norinder (1954) nd Florn (1955) nd fro the fored coposite spectru; however few detils were given regrding the wvef~s. ter, Ty!~ (1963) reperted cxcfti!!y docuented esureent of the spectru in which the lightning dischrges were locted nd propgtion losses 1

4 1.o FREQENC (kh) Figure 1, Electric field wvefor (top) nd its Fourier trnsfor (botto) for first return stroke. Recorded in Florid during TRP76.

5 TME (ps) LL FREQENC (kh) Figure. Averge electric field wvefor (top) nd verge gnitude of the Fourier trnsfclte cf the indisridu! ssr~.lef% (Scttc). Dt reccrded frc frst retiii strokes in Florid during TRP76. 3

6 tken into ccount. Tylor recorded return stroke wvefors nd de Fourier trnsfors over frequency rnge fro 1 1 kh. The spectru he obtined is shown in Figure 3 (open circles) norlied to rnge of 5 k. The norlition hs been done ssuing (distnce)' dependence for the plitude. The spectru obtined by Tylor peks ner 5 kh nd then decys roughly s (frequency)' to 1 kh, the liit of the esureents. n obtining this spectru, Tylor used the recently verified theory for the effects of ttenution due to propgtion over the erth to correct for the loss of signl t low frequencies. He hd both this theory nd tools for locting the lightning dischrge t his disposl. The Fourier trnsfor pproch ws lrgely ignored until Serhn et. l., (198) gin reported spectr of rdition fro return strokes. sing ode techniques for locting nerby return strokes (Krider et. l., 1976; Krider et. ]., 198), Serhn et. l. were ble to seprte first nd subsequent return stroke wvefors nd copute spectr for ech. Their dt for first return strokes t 5 k re shown in Figure 3. These dt fit well with Tylor's (1963) esureents nd extend the (frequency)' trend to severl hundred kh. The spectr obtined by Serhn et. l. (198) forsubsequent return strokes hs substntilly the se shpe but is soewht lower in plitude. eidn et. l., (1981) using substntilly siilr techniques lso reported spectr of first return strokes (squres in Figure 3). Their dt, collected fro lightning over the ocen to iniie effects of propgtion, extend the spectru to 1 MH nd continue to show decrese proportionl to (frequency).'. eidn et. l., (1981) lso reported first return stroke spectr t higher frequencies which they obtined by recording the derivtive, de/dt, of the electric field wvefor rther thn E(t) itself. Recording the derivtive iproves the sensitivity of the esureent to higher frequencies (becuse the spectru of the derivtive is the spectru of the wvefor ultiplied by frequency). The dt obtined by eidn et. l., (1981) in this nner re shown with solid tringles in Figure 3. Notice tht the dt show decrese with frequency which is greter thn the (frequency)" decrese chrcteristic of the dt t lower frequencies. The eidn et. l., (1981) results were obtined using only the first few icroseconds of the rdition wvefor. Since, this portion of the wvefor is ost strongly ffected by propgtion losses, it is not cler whether the rpid decrese evident in the dt is rel chrcteristic of first return strokes or n rtifct of the esureents. On the other hnd, there is soe theoreticl evidence to suggest tht decrese in the spectru s (frequency) should nifest itself t high frequencies (Le Vine, 198). A few esureents using the Fourier trnsfor pproch hve been de of the spectru of events other thn return strokes. All of these hve been reported recently by eidn, et. l., (1981). Figure 4 shows the spectr obtined for positive (top) nd negtive (botto) intrcloud events. The curves show the spectr of the intrcloud events superiposed on the spectru of first return strokes (solid line). On the left in Figure 4 re exples of positive nd negtive intrcloud events recorded by the uthor (Le Vine) t the Goddrd Spce Flight Center, in Greenbelt, Mrylnd in 198. Notice tht t the high frequencies the spectr for these events tend to coincide with the spectru of return strokes, but t low frequencies the spectru is sller thn the spectru of return strokes nd decresing. This is the behviour one would expect of dischrge with the se generl physicl chrcteristics s return stroke but of shorter length (e.g. Le Vine, 198) SPECTRA FROM DRECT MEASREMENT n ddition to the pproch described bove, it is lso possible to deterine the spectru directly by esuring the power incident t prticulr frequency. The procedure is to use filter to ccept signls only in nrrow bnd of frequencies ner the one of interest nd then to use detector to esure the power being rdited in this frequency bnd. The precise reltionship between the spectru t the noinl frequency, v,, to which the filter is tuned nd the output fro this syste depends on the specific filter nd detector eployed. An iportnt specil cse occurs when the filter is very nrrow ( sll percentge of the center frequency, v,) nd the detector is n 4

7 E x w (3 Q / rc : / h N x > w 3 w L v1 8 N.C d VJ s e VJ E, e i;] (3 5

8 n 1 1 F E _ ' 7 E 5:7 7 6

9 envelope detector of the type eployed in conventionl AM rdio receivers. n this cse, if the input is single ipulse, the spectru S(v,) is proportionl to the pek vlue, ep, of the output. This reltionship is derived in Appendix A where it is shown tht with n idel bndpss filter of bndwidth B nd syste gin G one obtins: ep S(v,) = GB Dt obtined using this technique re illustrted in Figure 5. The plitude of the spectr hve been norlied to lightning t 5 k using (distnce).' s the rule for scling plitude nd (bndwidth)'' s the rule for converting fro pek field esureents to spectr when necessry (Eqution 1). Aong the erliest esureents of this type re those of Schfer nd Goodll (1939) who were interested in ssessing the potentil interference lightning presented for trnsission of television signls. Their dt t 139 MH is shown with solid tringle in Figure 5. Extensive esureents over wide rnge of frequencies were de by Horner nd Brdley (1964). These dt re shown with the solid line in Figure 5. Additionl esureents by Kosrev et. l., (197) nd in 1963 by Hllgren nd McDonld (dpted fro Cinos, Oetel nd Pierce, 197) re lso shown in Figure 5. The spectru which eerges fro these esureents is one which peks ner 5 kh nd then decreses s l/f to the liits of the esureents (1 GH). The preceeding re only soe of the esureents which hve been de with this technique. A lrge nuber of esureents hve been de, but under gret vriety of circustnces (e.g., distnce, type of receiving equipent nd bndwidth). t is often difficult to reduce the esureents to coon units. Nevertheless, severl ttepts hve been de to cobine the esureents by norliing the dt to coon bndwidth nd distnce (e.g., Hoer, 1964,; Oh, 1969; Kipr, 1965; Cinos, Oetel nd Pierce, 197). Additionl dt gthered fro these reviews re plotted in Figure 6. The reltionship (distnce)" hs been used to convert to lightning 5 k wy nd the reltionship (bndwidth)' hs been used to convert pek field esureents to spectr (Eqution 1). Shown with open circles re dt by Tkgi nd Tkeuti (1963) s reported by Kipr (1965). Dt by wt nd Knd (1967) s reported by Cinos, Oetel nd Pierce (197) re shown with X's. Finlly, esureents of severl reserchers using rdr receivers (Atls, 1959; Hewitt, 1957; Pwsey, 1957) s reported by Oh (1969) nd Cinos, Oetel nd Pierce (197) re shown with open tringles. Notice tht these dditionl dt tend to fll soewht below the l/f spectru suggested in Figure 5 nd with significct spred of the dt, especilly t the higher frequencies. A jor proble fced in interpretting spectr such s presented in Figures 5 nd 6 is tht the dt do not represent rdition fro single events (e.g. return strokes) but rther represent soe generlly unknown collection of events in the flsh. To illustrte the nture of the proble, the output fro severl AM rdio receivers s seen during representtive cloudtoground lightning flsh is shown in Figure 7. The records t 3, 3 nd 3 MH re dt fro rel lightning recorded by the uthor in Florid during the Thunderstor Reserch Project (TRP76; Pierce, 1976) using stndrd AM rdio receivers with coon bndwidth of 3 kh. The records t 3 nd 3 kh re the uthor's ipression of wht rdition fro the flsh would look like bsed on reports in the literture (e.g., Hoer nd Brdley, 1964; Mln, 1958). The slow electric field chnge for this flsh is shown t the botto for reference. Notice tht the rdition consists of ny discrete ipulses. Soe of the ipulses correlte with identifible portions of the dischrge. For exple, the initil ipulses in this record occur where one expects to find the stepped leder, nd the return strokes (which occur t the brupt chnges in the slow electricl field chnge record) re ssocited with lrge ipulses of RF rdition. However, these re only few of the ipulses seen during the ilsh. The others re probbly ssocited with intrcloud portions of the dischrge bout which we hve only begun to lern. The discrete nture of the rdition is chrcteristic of the dt recorded by this uthor fro both cloudtoground nd intrcloud dischrges (e.g., Le Vine, 1976). Another iportnt chrcteristic of the dt is tht the rdition does not pper to chnge fro series of discrete ipulses t the lower frequencies to continuu t the higher frequencies s reported in soe investigtinns (e.g., Hcer s~:! Brdley, 1964; Mi?iii, 1958). Rther the rdition consists of sequence of discrete ipulses t ll frequencies in the rnge (3 3 MH) investigted by this uthor. n ddition, the ipulses tend to correlte well ong the frequencies. Tht is, 7

10 rn rn CD 9 rn E x (3 Q [: /5 Q) n 1 c Q \ Q) n 7 G w > & (3 4 1 v, 1L 6 rn h 3) 7 > n Q [: & [: \ Ln r\ (p) nuxids c N x >. 3 [: LL c h E rn 1 M.e L4 8

11 E w (3 Q 7 1 Q 1 ~~ 1 1 ' 1 / % % h 8 F > Q dj w 1 w \ 6) F.d cd E.d 8.d c E 41 ru!= cd.r( 3 E ru 5 M i 9

12 ~ SLO E o TME (seconds) Figure 7. Rdition fro cloudtoground lightning flsh. The signls t 33 MH re dt recorded by the uthor. The exples t 3 nd 3 kh re n estite bsed on esureents reported in the literture. 1

13 prticulr ipulse tends to be present t ll frequencies. The behviour is consistent with lightning flsh consisting of sequence of individul dischrges (leder steps, return strokes, Kchnges, etc.) ech rditing over very brod bnd of frequencies. Certinly the return stroke is dischrge with this chrcteristic (Figure 3). The proble which occurs with spectrl esureents using the filterdetector pproch is distinguishing between ipulses. The ipulse response of the esuring syste is inversely proportionl to the syste bndwidth; consequently there exists fundentl contrdiction between the requireent for bndwidth nrrow enough to be close to the noinl frequency of interest nd the bility of the esureent to distinguish between closely spced ipulses. For exple, with bndwidth of 5 H, the ipulse response of the syste is on the order of.5 seconds. This would include ny ipulses in typicl lightning dischrge (Figure 7). Very few investigtors hve ttepted to distinguish between events with esureents of this type nd those who hve tried hve hd difficulty (e.g., Tkgi nd Tkeuti, 1963). The spectr which hve been reported using this ethod generlly ust be regrded s n integrl (verge) over ny events in the flsh. The exception is t VLF frequencies where, becuse of the low frequency, return strokes tend to be the doinnt source of rdition. V. DSCSSON Notice the siilrity between the spectru of the first return stroke (Figure 3) nd the coposite spectru obtined fro ll the filterdetector esureents (Figures 5 nd 6). To fcilitte the coprison, the spectr hve been plotted together in Figures 8 nd 9. Figure 8 shows the return stroke spectru (Figure 3) nd the spectru in Figure 5 together, nd Figure 9 shows the return stroke spectru nd ll the filterdetector esureents (Figure 6) together. Considering ll the vribles tht enter such esureents, the spectr re very siilr. This is especilly so t frequenices below 1 MH, but even t higher frequencies where the spred in the dt is gret, the two spectr overlp. The siilrity between the spectr is not surprising becuse of ny fundentl difference between the two techniques. n fct, in principle the two techniques for esuring the spectru of lightning dischrges ought to yield identicl results. n prctice, they should be coplientry, the Fourier trnsfor pproch hving dvntges t low frequencies nd the direct (filterdetector) pproch hving dvntges t higher frequencies. However, becuse of the reltively nrrow bndwidth eployed, the filterdetector technique does not esure rdition fro single event, but rther is n verge over ny events in the flsh. Furtherore, the dt in Figures 5 nd 6 were obtined fro esureents of different bndwidth nd without ny ttept t identifying the portion of the flsh onitored. Consequently, it would see resonble to ssue tht Figures 5 nd 6 re ore representtive of the coposite flsh rther thn of ny prticulr event. ht is surprising, then, is tht the spectru of the coposite flsh nd the spectru of one prticulr event, the return stroke, re so siilr. The siilrity between the spectru of one event, the return stroke, on the one hnd, nd wht probbly represents the spectru of the coposite flsh on the other hnd, suggests to this uthor physicl process coon to ll the vrious individul dischrges which ke up the lightning flsh. There is soe dditionl evidence supporting this view. For exple, eidn, et. l., (1981) esured spectr of intrcloud processes nd stepped leders, nd these tend to fll on the spectr for return strokes (Figure 4). The difference is roll off t the low frequencies which is to be expected for identicl dischrges of shorter length. Also, Le Vine (1976, 198) hs been ble to predict spectr for the return stroke nd coposite flsh which gree with esureents by ssuing trnsission line odel coon to ll events. (The events differ in such preters s chnnel length, pek current nd tortuosity.) A criticl test of this hypothesis occurs t high frequencies where ll events should behve siilrly. But this is where the dt is ost scttered. Consequently, it would see iportnt to obtin relible spectrl esureents of individul events t frequencies bove few MH. This would resolve the biguities in the spectrl shpe pprent in Figures 5 nd 6 nd would dd insight into the physics of the lightning dischrge. 11

14 1 1 x Ln u CT / / / f \ \ \ / n Q) Q) J F n (3 & LL v) 4 ~~ 1 Ln r Q) n \ Q) c i G >; v) 7 7 Ln 7 // / A e CD Q) F > n J & v) [L v) 3 \ 7 h N x > 3 K LL w s M.C( 55 s %.C( c( M c e M.C(. 1

15 E x h \ CD 6 1L l n s X n / s w x / / \ \ \ \ \ \ /) // s \ 7 i 6 > cn x H cn L 1L v> 3 K cv) \ 7 \o 8 5 M." k 4 V h % N x N." c( > ti 3 E LL e e." e M." * *.d c) Q)." B 8 u 13

16 REFERENCES r 1% Atls, D. Rdr Lightning Echoes nd Atospherics in Verticl Cross Section, in Recent Advnces in Atospheric Electricity, L. G. Sith, ed. New ork: Pergon Press, 1959, pp Born, M., nd E. olf, Principles of Optics, Pergon Press, Cinos, N., G. N. Oetel nd E. T. Pierce, Structure of Lightning Noise Especilly Above HF, Lightning nd Sttic Electricity Conference, right Ptterson AFB, Deceber 197. Dennis, A. S., nd E. T. Pierce, The Return Stroke of the Lightning Flsh to Erth s Source of VLF Atospherics, Rdio Science, 68D (No. 7), pp , Florrnn, E. F., Ntionl Bureu of Stndrds Report #3558, Noveber, Hllgren, R. E., nd R. B. McDonld, Atospherics fro Lightning fro 1 to 6 MH, Rep. No BM Federl Systes Division, Hewitt, F. J., Rdr Echoes fro nterstroke Process in Lightning, Proc. Phys. SOC. ndon, 7, pp. 1 4, Horner, F., Rdio Noise fro Thunderstors, in Advnces in Rdio Reserch, Vol., Acdeic Press, J. A. Sxton, ed., pp. 14, Horner, F., nd P. A. Brdley, Spectr of Atospherics fro Ner Lightning, J. Atos, Terr. Phys., 6, pp ,1964. Kipr, A., Electrognetic Energy Rdited fro Lightning, in Probles in Atospheric nd Spce Electricity, S. C. Coroniti, ed., Elsevier Pub. Co., pp , Kosrev, E. L., V. G. Ztsepin nd A. V. Mitrofnov, ltrhigh Frequency Rdition fro Lightning, J. Geophys. Res., 75(36), pp , 197. Krus, J. D., Rdio Astronoy, McGrwHill Book Co., Krider, E. P., C. D. eidn, nd R. C. Noggle, The Electric Fields Produced by Lightning Stepped Leders. J. Geophys. Res., 8, pp , Krider, E. P., R. C. Noggle nd M. A. n, A Gted idebnd Mgnetic DirectionFinder for Lightning Return Strokes, J. Appl. Meteorol., 15, pp. 336, Krider, E. P., R. C. Noggle, A. E. Pifer nd D. L. Vnce, Lightning DirectionFinding Systes for Forest Fire Detection, Bull. Aer. Meteorol., SOC., 61(9), pp , 198. Le Vine, D. M., et. l., The Structure of Lightning Flshes HFHF: Septeber 1, 1975, Atlnt, Georgi, NASA X Le Vine, D. M., The Effect of Pulse ntervl Sttistics on the Spectru of Rdition fro Lightning, J Geophys. Res. 8 (1), pp ,

17 Le Vine, D. M., The Spectru of Rdition fro Lightning, Proc. EEE nterntionl Syposiu on Electrogfietic Coptibility, pp. 4953, October 198. Mln, D. J., Rdition fro Lightning Dischrges nd its Reltion to the Dischrge Process, in Recent Advnces in Atospheric Electricity, Proceedings of the nd Conference on Atospheric. Electricity, pp , Norinder, H., The vefors of the Electric Field in Atospherics Recorded Siultneously t two Distnt Sttions, Arkiv for Geofysik, (9), pp , Noveber Oh, L. L., Mesured nd Clculted Spectrl Aplitude Distribution of Lightning Sferics, EEE Trns., EMC11 (4), pp. 1513, Pwsey, J. L., Rdr Observtions of Lightning, J. Atospheric Terr. Phys., 11, pp. 899, 1957 Pierce, E. T., The Thunderstor Reserch nterntionl Progr (TRP) 1976, Bull. Aer. Meteorol. SOC., 57, pp , Serhn, G.., M. A. n, D. G. Childers, nd. T. Lin, The RF Spectr of First nd Subsequent Lightning Return Strokes in the 1 k Rnge, Rdio Sci., 15, pp , 198. Schfer, J.P., nd.m. Goodll, Pek Field Strengths of Atospherics due to cl Thunderstors t 15 Megcycles, Proc. RE, 7, pp. 7, Tkgi, M. nd T. Tkeuti, Atospherics Rdition fro Lightning Dischrge, Proc. Res. nst. Atos., Ngoy niv., 1, Tylor,. L., Rdition Field Chrcteristics of Lightning Dischrges in the Bnd 1 kc/s to 1 kc/s, J. Res. Nt. Bur. Stnd., 67D, pp , n, M. nd E. P. Krider, A Review of Nturl Lightning: Experientl Dt nd Modelling, EEE Trns. on Electrognetic Coptibility, EMC4 (), pp , 198. tt, A. D., nd E. L. Mxwell, Chrcteristics of Atospherics Noise Fro 1 to 1 kc., Proc. nst. Rdio Eng., 45, pp , eidn, C. D., nd E. P. Krider, The Fine Structure of Lightning Return Strokes vefors, J. Geophys. Res. 83, pp , eidn, C. D. nd E. P. Krider, Subicrosecond Rise Ties in Lightning Return Stroke Fields, Geophys. Res. Lettrs., 7, pp , 198. eidn, C. D., E. P. Krider, nd M. A. n, Lightning Aplitude Spectr in the ntervl Fro 1 kh to MH, Geophys. Res. Lett., 8, pp ,

18 APPENDX A RADO RECEVER RESPONSE. t is the purpose of this ppendix to derive n expression for the ipulse response of n RF receiving syste typicl of the sort used to esure the spectru of rdition fro lightning. The syste consists of n ntenn, usully verticlly polried, connected to stndrd AM rdio receiver nd followed with post detection filter (Figure Al). Assuing tht the ntenns re verticlly polried nd isotropic over the bndwidth of the esureents, they cn be ssued to deliver voltge proportionl to the incident (verticl) electric field. Except for phse which is ultitely lost in the detector, this proportionlly constnt is d L / k where k = COG = d A, G is the gin of the ntenn in the plne prllel to the ground, nd A, is the effective receiving re of the ntenn (Krus, 1966). The receiver is device for detecting nd plifying the envelope of n plitude odulted sinusoid (crrier) t prticulr frequency. This is norlly done by trnslting the input signl to n interedite frequency where the ctul processing is done. However, the frequency trnsltion is done for engineering purposes to ke the detection ore efficient, nd it is not necessry to do this in order to odel the receiver output. The idel device is perfect envelope detector in series with filter which represents the equivlent bndwidth nd gin of the syste. For systes whose bndwidth 6 is sll copred to the noinl frequency, vo, of the esureent, these opertions cn be written explicitly in ters of the Fourier trnsfor of the incident rdition. To do so it is convenient to write the verticl coponent of incident rdition, E(t), in the for: E (t) = Re f?e (v)ej7f"t dv where Re ens "rel prt of" nd where E(v) is the Fourier trnsfor of E (t). The integrl is clled the coplex nlytic representtion of E (t) (e.g., Born nd olf, 1959). sing this nottion, the signl V(t) out of the ntenn nd filter nd into the envelope detector is: K V(t) = Re (v)h(v)e (u)ejn"t dv where H(v) is the Fourier trnsfor of the filter h(t) nd (v) = (A/k)d?FT;TA, is the cobined effect of the. ntenn nd n plifier with gin, A. Although in prctice the post detection filter is pplied to the video output of the receiver, theticlly the effect of the post detection filter cn lso be included in H(v), This will be done here nd it will be ssued tht the equivlent filter H(v) hs pssbnd centered bout frequency uo which is very nrrow copred to v,. Tht is: nd 6/vo << 1. sing this ssuption nd king the chnge of vribles 6 = vucs Eqution A becoes = j e (v,,t) 1 COS(~T,~ + +) A 1

19 where J e (v,,ti = (v, + S)E (v, + S)H(S) nd where the ssuption tht H(v) is nonero only in nrrow bnd bout v, (Eqution A3) hs been used to forlly extend the lower liit of the integrtion in Eqution A4 to infinity. Fro Eqution A4 it is cler tht V(t) hs the for of n plitude odulted sinusoid, cos(.rrvt+~), t frequency v,. The output of the detector is the envelope, le (v,,t), of this crrier. Thus, the output, e,(t) cn be written: e,(t) = 1 JT, (v, + 5) E (v, + 6) H(S) de Now, suppose tht over the nrrow bnd of frequencies pssed by the filter (v, + 6) (v,) nd E(v, + k) E(v,). Then, where E(vo)l is the gnitude of the spectru of the electric field t frequency v, nd where h(t) = l (v,)h(s) ejst ds is the ipulse response of the syste. (Note: e = e e*) ntegrting both sides of Eqution A7 nd using Prsevl s theore for Fourier trnsfors, one obtins: eg(t) dt = E(v,) J, h(t) dt Finlly, solving for the spectru, one obtins: where A = 1 ds H () (v,) H(O)/ J s The integrl in Eqution A1 1 is coonly clled the bndwidth (power bndwidth) of the syste nd l(v,) H(O) is the gin of the syste. Eqution A1 sttes tht the spectru of the input signl cn be obtined by integrting the output nd dividing by twice the gin ties the squre root of the bndwidth of the syste. This result only A

20 pplies to individul input signls, E(t), whose bndwidth is uch lrger thn the bndwidth of the syste (i.e. pper s ipulses on the tie scle of the ipulse response of the syste). This restriction is consequence of fctoring E(vo) out of Eqution A6. f the input were sequence of such pulses rther thn n individul event E(v) in Eqution A6 would be su of the for Z Ei(v) dn ti where Ei(v) is the spectru of the individul pulses nd 4 is the tie between pulses. n this cse the spcing between.pulses cn ffect the spectrl estite (Le Vine, 1977; Dennis nd Pierce, 1964). An iportnt specil cse occurs when the syste cn be odelled s n idel bndpss filter: Then, fro Eqution A6 one obtins: J 131 = ((vo) E(vo)lHoB sinc(.rrbt) = ep sinc (TBt) where ep is the pek vlue of the signl out of the receiver. Now, squring nd integrting over ll tie, one obtins: 1:e:(t) dt = ep s, sinc (nbt) dt = e,/b Finlly, putting this result into Eqution A1, one obtins: where G = l(vo) H() is the gin of the syste. Eqution A15 pplies only if the tie between pulses is long copred to the response tie of the syste. Another iportnt specil cse occurs when the input is rndo process. f the process consists of sequence of identicl pulses with rndo plitude nd/or rrivl tie, then the nlysis proceeds s bove with odifictions s indicted in the text nd described in detil by Le Vine (1977). However, if the rndo process is noiselike (Le. continuous, fluctuting signl), then the nlysis ust be odified. n this cse, the pproprite definition of the spectru, S(v), is the Fourier trnsfor + of the utocorreltion function, R(T) = <E(t)E* (t + T)> of the input signl. Assuing tht the detector is n idel s urelw detector nd tht the input, E(t), is sttionry, ergodic rndo process, nd defining E(v) = S (v) 1, one obtins A3

21 vlue of the output signl by dividing by the squre root of the bndwidth nd twice the syste gin. This result hs been eployed to copute spectr of lightning in soe cses (e.g. Oh, 1969); however, s indicted in the text, lightning is intrinsiclly ipulsive in nture nd s result this forul ust be used with cution. > FLTER DETEC FLTER TOR n t Figure A1. Exple of rdio receiver used to esure spectru of rdition fro lightning. A 4

22 ~~ BBLOGRAPHC DATA SHEET. Report No. NASA TM Governent Accession No. 3. Recipient s Ctlog No. 5. Report Dte 6. Perforing Orgnition Code Code Perforing Orgnition Report No. L Perforing Orgnition Ne nd Address Lbortory for Ocens Goddrd Spce Flight Center Greenbelt, Mrylnd Sponsoring Agency Ne nd Address Ntionl Aeronutics nd Spce Adinistrtion shington, D.C. 1. ork nit No. 11. Contrct or Grnt No. 13. Type of Report nd Period Covered 14. Sponsoring Agency Code 15. Suppleentry Notes 16. Abstrct A review is presented of the esureents reported in the literture of the spectru of electrognetic rdition fro lightning in the frequency rnge fro 1 kh to 1 GH. Mesureents hve been de either by onitoring the power received t individul frequencies using nrrow bndwidth recording device tuned to the frequencies under investigtion or by recording the trnsient (tie dependent) rdition with wide bndwidth device nd then Fourier trnsforing the wvefor to obtin spectru. Mesureents of the first type were de extensively in the 195 s nd 196 s nd severl coposite spectr hve been deduced by norliing the dt of different investigtors to coon units of bndwidth nd distnce. The coposite spectr tend to pek ner 5 kh nd then decrese roughly s (frequency). upto nerly 1 MH where sctter in the dt ke the behviour uncertin. Mesureents of the second type hve been reported for return strokes, the stepped leder nd for soe intrcloud processes. The spectru of first return strokes obtined in this nner is very siilr to the coposite spectr obtined fro the nrrowbnd esureents. 17. Key ords (Selected by Author(s)) Lightning Spectru Lightning Noise 18. Distribution Stteent nclssifiednliited Subject Ctegory 47!9. Secnrity &ssif. (ef this repnrt! nclssified g. Secnrity C!ssif. {cf:hi; pge) 1. \!=. =f pge;. p;ice* nclssified