NBSIR 73-310

Electromagnetic scahering by a thin wire

with continuous impedance loading -

part ii: time domain analysis.

Tommy C. Tong

Electromagnetics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

April 1973

US. DEPARTMENT OF COMMERCE, Fr«cl«rick B. D«nt, Secretary

NATIONAL BUtEAU OF STANDARDS, Richard W. Roberts, Director
1
NBSIR 73-310

ELECTROMAGNETIC SCATTERING BY A THIN WIRE

WITH CONTINUOUS IMPEDANCE LOADING -

PART II: TIME DOMAIN ANALYSIS.

Electromagnetics Division

Institute for Basic Standards

National Bureau of Standards

Boulder, Colorado 80302

April 1973

Tommy C. Tong

U.S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS
nI1
PREFACE

This is the second part of a two-part work on electromagnetic scattering by a thin wire with continuous impedance

loading. In the first part [1] we have solved the problem in

the frequency domain. Since the frequency domain and the

time domain analysis are related to each other mathematically

by the Fourier transform, the transient scattering of a time

pulse by a thin wire can be synthesized from the results

obtained for the scattering of plane waves via the Fourier

trans form

.

iii
1
CONTENTS

Page

PREFACE iii

ABSTRACT 1

I. INTRODUCTION 1

II. FREQUENCY DOMAIN AND TIME DOMAIN 3

III. NUMERICAL RESULTS 6

IV. INCIDENT FIELD OF ARBITRARY TIME DEPENDENCE 8

V. CONCLUSION 9

ACKNOWLEDGMENT 10

REFERENCES 11

ILLUSTRATIONS 13

APPENDIX A - COMPUTER PROGRAM 2 3

V

ELECTROMAGNETIC SCATTERING BY A THIN WIRE WITH

CONTINUOUS IMPEDANCE LOADING PART II: TIME DOMAIN ANALYSIS

Tommy C. Tong*

ABSTRACT

The scattering o£ electromagnetic pulses by a thin wire with continuous impedance loading is

investigated theoretically. The basic approach used

is the numerical Fourier transform of the frequency

response. The incident pulse is assumed a truncated

periodic Gaussian pulse. Numerical results for the

transient current distribution and the transient

scattered field in different directions of observation

are presented. It is found that the shapes of the

transient current distribution on the wire and of

the scattered field can be controlled by loading

the wire with some impedance.

Key Words: Electromagnetic scattering; Impedance

loading; Pulses; Thin wire.

I. INTRODUCTION

In recent years, the time domain analysis of field

problems has been receiving increasing attention partly

because of the demand for generation of high power pulses

and partly because of the fact that radar interrogation is

essentially a transient process. In the case of wire structures, substantial work [2,3,4] has been devoted to the

study of transient radiation of a dipole antenna. But

very little work [5,6] has been done on investigating the

*Pos tdoctoral Fellow.
transient scattering characteristics of the dipole, and

apparently none when the dipole is modified with some kind

of impedance loading.

' The present study investigates the scattering of electromagnetic pulses by a thin wire with continuous loading. In

general, there are two different approaches to obtain the

time domain response to an electromagnetic scattering problem.

The first approach makes use of numerically evaluated frequency domain solutions and the Fourier transform. The second

approach [7,8] is one which originates from a strictly time

domain viewpoint , and requires solving the time dependent

differential or integral equation directly.

The first approach is preferred in the present investigation, because mathematically it is easier to solve a time

independent differential or integral equation than a time

dependent one. Moreover, recent development of the fast

numerical algorithm has made this approach more appropriate

for this study.

Here we assume that the incident pulse is a Gaussian

distribution, but any band-limited real time function can be

used as well.

2
II. FREQUENCY DOMAIN AND TIME DOMAIN

A. Incident Pulse

As shown in Fig. 1, the thin wire (a/L << 1) which is

loaded symmetrically about z=0 with a continuous impedance

function Z(z) is illuminated by a truncated Gaussian pulse

varying periodically at a frequency oj^ = Zir/T with T being

the period. The Gaussian whose pulse width is t (T >_ 4t)

is given by (Jig. 2 (a))

p(t) = exp(-tV2a2) , |t| < T/2 (1)

where o" is a time constant.

The frequency spectrum of a truncated single pulse is

CFig. 2(b))

CO P(w) =

/ p(t) e"^'^''^ dt

- 00

=i a /TtT exp (-a^to^/2) . (2)

Since p(t) is a real time function we must have

P(ca) = P*(-^) C3)

where * denotes the complex conjugate.

B . Scattered Field

In the frequency domain the scattered field is given by

E ro,) = ^

e-j^^ sin 9 I (z ' ,a))e-^^^ ' ^ dz ' (4)

" 47Tr -L/2

where is the intrinsic impedance of free space, and I(z,a))

the current distribution for an incident plane wave of unit

amplitude.

3
Then, the scattered field in the time domain for a

periodic pulse can be obtained by superposition (since the

system is linear) thus

n L/2

EP(t) = I

ja3. P(a).) / sin 9 I(z',c..)

47rr 00^=-°° -L/2

-3^ A -J'^.-i^ z

' cos 0 L_

c c

i oj . t

' 1

' X e ^ e ^ e ^ dz' (5)

where o)^ = i = ±1, ±2,

which after terminating to a finite number of terms 2N + 1

is approximately given by

D N L/2

E^Ct) ^

I

jo). P(a).) / sin 6 I(z',a).)

^ 47Tr a3^=-N ^ ^ -L/2

-jo)^ -joj^r

z' cose joo-t

X e ^ e ^ e ^ dz' . (6)

Using Eq. (3) and the relation

I(z',-a3.) = I*(z',a).),

we obtain

N T /?

EUt') - —° 5: ja3. P(a3.) / sin 6 I(z',a).)

4TTr 0)^=1 ^ ^ -L/2

-jo).

Z

' cos e 10). t

' X e ^ e^ dz'

+ complex conjugate term

where t' = t-r/c is the retarded time, and c the velocity of

propagation.
In the frequency domain the scattered field due to the

pulse is given by

00 .

^ =

/ E^(t')e"^"'^ dt

n =° N L/2 - I { I

joj. P(a3.) / sin 6 I(z' ,lo.)

47Tr -°° C0j^ = l -L/2

Z

' cos e j CO . t '

.

, xe^ e^+cc} e"^'^^ dt ' (8) n

=° N L/2 —^ Re / { I

jco. PCoj.) / sin 9 ICz','^-) (9)

27rr -°° 03^ = 1 -L/2

-jo:

z

' cos 9 i oj . t ' . ^ , X e " e " }e^"" dt

where c c represents the complex conjugate term.

C. The Surface Current

In a similar manner, the transient current induced on

the wire is given by

°° j 0) . t

I(z,t) = I I(z,a..)P(a3.3e ^ . (10}

OJ . =-co

1

5
III. NUMERICAL RESULTS

Fig. 3 shows the transient current at z = L/2 for a wire

with L = 0.125 A and a = 0.00 5 A at the fundamental frequency

for two different impedance loadings . The width and the perio

of an incident pulse are equal to 10 ns and 40 ns respectively. The Gaussian pulse is truncated when the amplitude

is equal to II of the maximum amplitude. It is seen that

there are marked differences between these two current distributions. If we take a Fourier analysis of them, we

would find that the one corresponding to no loading (Z = 0)

is rich in the second harmonic while the one corresponding

to loading is rich in the third harmonic. This indicates

that it is possible to control the harmonic content of the

transient current response by loading the wire with some

impedance.

The transient scattered fields for different angles of

observation for the same wire and same incident pulse are

shown in Figs. 4-6. The kind of impedance loading used here

is distributed capacitive . Properties of antennas with such

loading were first described by Hallen [9] who made a monopole

antenna in the form of a row of small conducting cylinders,

between which dielectric discs of increasing thickness toward

the antenna end were inserted. In this manner the antenna

had a variable capacitive impedance which increased toward

the end. It is seen that in each case the response with

such loading decays at a faster rate than that without loading. Perhaps it should be pointed out that the shape of the
scattered field in the time domain is closely related to the

first derivative of the incident pulse, because Eq((jo) has a

j CO factor (Eq . (4) ) .

Figs. 7-9 show the scattered field versus the retarded

time for a wire with longer length (L = 0.75 X and a = 0.01 A).

Besides the continuous capacitive loading, a nonreflect ing

resistive loading is also investigated. This kind of loading was used by Wu and King [10] in antenna analysis. It is

seen that except for 9=90°, the shapes of the scattered fields

with or without loading differ significantly from those we

saw previously for shorter wires. This difference can be

understood if we realize that when the wire is illuminated by

a pulse, a transient current is induced on the wire. This

current travels along the wire at the speed of light, and

when it encounters the ends of the wire, it will be reflected

back. This process will continue until the current dies

down. The longer the wire, the longer the time the current

takes. Since the electrical length of the antenna is proportional to the frequency, the contributions due to the different harmonics would not add in phase in the far field. The

case for 0=90° is a special one, because the phase factor

cos 0 z

'

e in Eq. (4) is equal to unity under this

circumstance. Note that the scattered field for the nonreflecting loading is not shown in Fig. 9 for 0=90°, since it

is very close to that for the no loading case.

7
The effect of reducing the pulse duration is illustrated

in Fig. 10. As the pulse width reduces, higher harmonics

will become more important. For the numerical calculations

we used ten harmonics (N = ±10) for the longer pulse (t = 10

ns) and twenty two harmonics (N = ±22) for the shorter pulse

(t = 5 ns) . In each case the period of the pulse is 40 ns

.

IV. INCIDENT FIELD OF ARBITRARY TIME DEPENDENCE

For a linear system, the superposition theorem says

that the time response of the scattered field from a dipole,

illuminated by a plane wave of arbitrary time dependence

y(t) is given by the convolution

t

E (t) = / y(t-T)h(T) dx (11)

" 0

where h(T) is the impulse response of the dipole and is

related to Eg(aj) , the frequency response, by

00 h(t) = — / EqCo)) e^'^'^ do). (12)

2 IT - 0° Therefore, once we get the impulse response we have solved

the time domain problem entirely. Numerically, the impulse

response is difficult to obtain because its frequency spectrum is constant. In other words, the delta function is

not a band limited function. But there are various approximate functions that can be used for the delta function.

However, we will not pursue this matter further in this study.

8
V. CONCLUSION

The scattering of electromagnetic pulses by a thin

wire with continuous impedance loading has been investigated

using the numerical Fourier transform of the frequency

response. Numerical results show that the shapes of

the induced current and the scattered field in the time

domain can be modified by using the impedance loading technique .

9
ACKNOWLEDGMENT

The author wishes to thank Dr. Paul F. Wacker for his

helpful discussion in this work. Thanks are also due to

Janet R. Becker for her excellent work of typing.

10
REFERENCES

[1] T.C. Tong, "Electromagnetic scattering by a thin wire

with continuous impedance loading. Part I: Frequencydomain analysis," unpublished NBS Report, (Dec. 1972).

[2] T.T. Wu, "Transient response of a dipole antenna," J.

Math. Phys. Vol. 2, pp. 982-984, (1961).

[3] R.J. Palciauskas and R.E. Beam, "Transient fields of

thin cylindrical antennas," Proc. Intnl. Ant. Prop.

Symposium, Boston, Mass., pp. 165-167, (1968).

[4] H.J. Schmitt, C.W, Harrison, Jr., and C.S. Williams, Jr.,

"Calculated and experimental response to pulse excitation,"

IEEE Trans, on Antennas and Propagat . , Vol. AP-14, pp.

120-127 , (March 1966)

[5] E.P. Sayre and R.F. Harrington, "Transient response

of straight wire scatterers and antennas," Proc. Intnl.

Ant. Prop. Symposium, Boston, Mass., pp. 160-164, (1968).

[6] R.H. Ott, "The time domain backscatter from dipole

antennas illuminated at broadside," AFCRL Scientific

Report No. B-2, Air Force Cambridge Research Laboratories,

Bedford, Mass., (July 1968).

[7] C.L. Bennett and W.L. Weeks, "A technique for computing

approximate electromagnetic impulse response of conducting bodies," Report TR-EE68-11, Purdue University, (1968).

[8] G.W. Soules and K.M. Mitzner, "Pulses in linear acoustics,"

Northrop Nortronics Report, ARD 66-60R, (196 7).

11
[9] E. Hallen, Electromagnetic Theory , pp. 501-504, Chapman

§ Hall Co. , (1962)

.

[10] T.T. Wu and R.W.P. King, "The cylindrical antenna with

nonreflect ing resistive loading," IEEE Trans, on

Antennas and Propagat., Vol. AP-13, pp. 369-373, (May,

1965)

.

12
A

Fig. 1. Geometry of the Thin Wire

13
H

b

CM

-l->

I (U

1

/

/

/-

/

/-

/

/

/-

/

/-

I

/

/

(^)d

\ O CO <X) C\J

\

\

v

\

\

\

\

\

\

00

o 3

I

I

CO

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14
(J) I QBznvwyoN

15
16
1

VD^CNJ O CsJ ^ U3 CO

I I I I

17
CNJ CO ^ O ^ 00 I— I I

18


21
22
APPENDIX A - COMPUTER PROGRAM

Subroutine FORTID performs the fast Fourier transform

on a one -dime ns ional array of complex numbers A. It assumes

the real parts of the elements of A are stored in the oddindexed locations and the imaginary parts in the evenindexed ones. Suppose it is desired to evaluate

F(X) = / exp(-j2TrAx) f(x) dx

where f has limited support

fCx) =0 |x| > a. Then F(X) is approximated by

N/2-1

F„ ^ 1//N y exp(jmn/N) f , -N/2 < m < N/2 ^ n=-N/2 ^ ~

"

where f^ = f(ns) and F^^ = FCm/T) . The range of sampling T

and the period of sampling s are related to the number of

samples, N, by

T/s = N = 2^, p is an integer.

23

• J0B»2727277 »T0NG»2

'FTn»L»X»*

PROGRAM FOURIER

DIMENSION A(256)

COMPLEX Ul

DO 1 I =1 ^256

A( I ) =0 • CONT 1 NUE

Ul= (6. 53490E-003

1*(0. .1 . ) A( 131 ) =REAL{U1

)

A( 132 ) =AIMAG{U1

)

A( 127

)

=A( 131

)

A( 128

)

=-A( 132

)

Ul= (2. 26778E-001

1*{0. .1 .)

A( 133 ) =REAL (Ul

)

A(134 ) =AIMAG( Ul

)

A( 125 ) =A( 133

)

A{ 126

)

=-A( 134

)

Ul= ( 2. 09957E+000»

1*(0. ! . ) A ( 135 ) = REAL ( Ul ) A( 136 ) =AIMAG( Ul

)

A( 123 ) =A(135)

A ( 124

)

=-A (136

)

Ul= (4. 28172E-t-000»

1*(0. »1 . ) A( 137

)

=REAL(U1

)

A( 138 ) =AIMAG{U1

)

A( 121 ) =A( 137)

A( 122 ) =-A( 138

)

Ul= (3. 46354E + 000

1*(0. »1 .)

A{ 139

)

=REAL(U1

)

A( 140

)

=AIMAGI Ul

)

A( 119) =A( 139

)

A( 120 ) =-A( 140

)

Ul= (2. 75311E+000.

1*(0. »1 . ) A( 141

)

=REAL ( Ul

)

A( 142

)

=AIMAG(U1

)

A( 117) =A( 141

)

At 118 ) = -A ( 142 ) Ul= (2. 35476E+000*

1*(0. tl . ) A( 143 ) =REAL(U1

)

A( 144) =AIMAG(U1

)

A( 115 ) =A( 143

)

A( 116

)

=-A( 144

)

Ul= ( 2. 08824E + 000 » 1*(0. »1 . ) A{ 145 ) =REAL ( Ul

)

A( 146

)

=AIMAG(U1

)

1 .57600 E-0 01 ) * ( 5 .40 7 5 7E-00 1 ,2 . 4394 5E-004 ) *1

.

9.20442E-001 ) * ( 5.29174E-00 l,4.50751E-004)*2.

2.06968E + 000 ) *( 5 . 10402 E-00 1 5 . 8 893 5 E-004 ) *3.

1 .633 52E-001 ) * ( 4 • 8 5 205 E-00 1 » 6 . 3 745 7E-004 ) *4

.

1 .78828E+000) *( 4.54582E-001 » 5 . 88934E-004 ) *5

.

2.163 72E+000 ) 4. 19705E-001 »4 . 50 75 lE-004 ) *5

2.26 216E+00 0 )*( 3 . 81846 E-00 1 »2 .43946E-004 ) *7

2.31764E+0 0 0 )*{ 3 . 42 3 04E-00 1 » 4 . 64 752E-0 10 )*8.

72 10 24 PAGE 1
A ( 113) = A ( 145 ) A ( 114 ) = -A ( 146 ) Ul = ( 1 • V29dV h + OOO

1* ( 0 • 1 •

)

A I 1 / "7 \ 1 4 M _ (-» (r A 1 MM \ A ( 1 A-8 ) = A I M A G ( U 1 ) A ( 111' = A ( 147 ) A ( 112) =-A ( 148

)

U 1 = { 1 • 80 j56E + 000

1* ( 0 • » 1 •

1 A I 1 49 ' = REAL I Ui J A ( 1 50 ) = A I MAG I Ul ) A ( 109) = A ( 149 ) A ( 1 10 ) =-A(l50)

U i = ( 1 .67960E + 000 » 1^- ( U • » i A ( X J 1 1 - D F A 1 (111 1 A ( 1 J c. ' = A T M A G ( LJ 1 ) A ( 107) = A ( 1 5 1 ) A ( 1 Oft ) = -A ( 1 5 7 ) U i = ( i • 5 3 167E + 000

1* ( 0 • »

1

, ) A ( 15^) L ^ J ' = RF Al ( U 1 ) A ( 1 54 ) = A T MAG ( U 1 ) A ( 105 ) =A ( 15 3)

A { 10^"!) = _A ( 1 54 )

i 1 ^ U 1 = ( 1 . 320 86E + 000 » 1 ^ I 0 • »

1

, ) A I 155 ) = REAL ( Ul ) A ( 156 ) =AIMAG( Ul

)

A ( 103 ) =A( 155

)

A ( 104) =-A( 156

)

1 1

1

u i = ( 1 .05350E+000

1^ ( 0. ! . ) A ( 157) =REAL ( Ul

)

A ( 158 ) = AIMAG( Ul ) A ( A \ 101 ) =A{ 157

)

A ( 102 ) = -A ( 158 ) Ul = ( 7 .06912E-001

1">^ V 0 . »

1

.)

A I 159 ) =REAL(U1

)

A ( 160 ) =AIMAG( Ul

)

A ( 99 ) = A( 159 ) A ( 100 ) =-A ( 160

)

U

1

= ( 3.06016E-001

0 . »

1

. ) A ( 161 ) =REAL ( Ul

)

A ( 162 ) =AIMAG( Ul

)

A ( 97 ) = A{ 161

)

A ( 98 ) = -A( 162

)

U

1

= ( -1 .01943E-001

1* ( 0 . »

1

.

) A ( 163 ) =REAL ( Ul

)

A ( 164 ) =AIMAG( Ul

)

•2.39637E-t-000)*( 3,02 3 36E-001 -2 . 4 394 3 E-Oo 4 ) ^i- 9 .

•2 ,52007E + 0O0)*( 2.63087E-001 -4 . 5 0 749 E-0 0^ )*10

-2.696 70E+00U)*(2.25546E-UUl»-5.88932E-UO4)*ll.

-2,92654E+00U )*(1.90 506E-0 0l»-6.3 74 56E-U04)*12,

-3 .19377E + U00)*( 1 . 5 8 549 E-0 0 1

» - 6 . 3 74 56 E-0 04 ) *1 3.

,-3.48155E + 0 00)*(1 .30038E-Oul , -4 . 50 75UE-O04 ) *14.

,-3.73998E + 0 00)->^( 1 .05134E-0 01 , -2 . 43 944 E-U 04 ) *15.

-3.92222E + 0 00)^( 8 . 3 8 1 70 E-0 02 7 . 5488 1 E-0 1 1 ) *16.

»-4.00l39E+0 00)*(6 . 5 92 0 5 E-0 0 2 , 2 . 4 3 944E -00 4 ) *17.

10 24 PAGE 2
A(95)=A( 163)

A{96 ) =-A( 164

Ul= ( -4.55164E-001 »-4.01742E + 000 ) * ( 5 . 1 1 6 9 1 E-0 0 2 4 . 50 7 5 OE-QO 4 ) * 1 8 . 1*(0. »1 • ) A( 165 ) =REAL ( Ul

A( 166 ) =AIMAG( Ul

A(93 ) =A( 165

A(94)=-A( 166

Ul= { -7,52346E-00l »-4.00 571E+000 ) * ( 3 . 92 1 66 E-00 2 , 5 . 8 893 3E-0U4 ) *19.

1* ( 0 . » 1 . ) A(167)=REAL(U1)

A(168)=AIMAG(U1

A(91)=A(167)

A(92 ) =-A( 168

Ul= (-1 .0l354E+000»-3.99996E+000 )* ( 2.96826E-002 ,6.37456E-004 ) *2 0.

1*(0. jI .

) A( 169 ) =REAL ( Ul

A( 170 ) =AI MAG(U1

A(89)=A( 169)

A(90)=-A( 170)

Ul= (-1 .2 7136E + 000 »-4,012 66E + U00 )* ( 2 .2 1831E-002 »5 .889 33E-UU4 ) *21 . 1* ( 0. » 1 . ) A{171)=REAL(U1)

A( 172 )=AIMAG( Ul

A{87)=A(17l)

A(88 ) =-A( 172

Ul= (-1 •55684E + 000,-4,0 3862E + 000 )*( 1 . 63 5 52 E-002 , 4 . 5075 OE-OO4 ) *22 . 1*{0. »!• ) A(173 ) =REAL(U1

A( 174 ) =AIMAG( Ul

A(85 ) =A{ 173

A(86)=-A( 174)

PRINT 3,( I»A( I) ,I = 84»175)

CALL FORTID( A,128»l ) PRINT 3» ( I »A( I ) ,1 = 1,256)

3 FORMAT (15 ,E20.5

STOP

END

SUBROUTINE FORT I D ( A , N , I FS

C A=1D ARRAY»SIZE 2*N

C N=2**P, NO. OF COMPLEX ELEMENTS,? AN INTEGER

C IFS=-1, FOR FOURIER ANALYSIS

C IFS=1, FOR FOURIER SYNTHESIS

DIMENSION A(256)

NN=2*N

FN=N

PI=3. 14159265

C SUPPLY PHASE TO A TO SHIFT THE TRANSFORM TO THE CENTER

DO 1 J=1,N

JJ=J-1

L=MOD( JJ,2)

A(2*J-1 ) = {

( -1. ) **L ) *A( 2*J-1 ) /SORT ( FN)

A(2*J ) = ((-!.) **L) -x-A ( 2*J ) / SORT ( FN)

1 CONTINUE

72 10 24 PAGE 3
C PERFORM BINARY SORT

J=l

DO 34 I=1»NN»2

IF (I-J)2»3»3

2 TEMPR=A(J)

TtMPI=A(J+l)

A ( J ) =A ( I )

- A ( J + 1 ) =A( I + l ) A ( I ) = FEMPR

A(I+1)=TEMPI

3 M=NN/2

4 IF(J-M) 6»6»5

5 J=J-M

M = M/2

IF (M-2) 6*4 »

4

6 J=J+M

34 CONTINUE

C START MAIN LOOP

MMAX=2

7 IF (MMAX-NN) 8»11,11

8 ISTEP=2*MMAX

THETA = 2.*PI/ ( IFS^MMAX

)

SINTH=SIN ( THETA/2.

)

WSTPR = -2.*SINTH*-SINTH

WSTP I=SIN ( THETA

)

WR=1.

WI = 0.

DO 10 M=1»MMAX»2

DO 9 I=M»NN»ISTEP

J=I+MMAX

TEMPR=WR*A ( J ) -W I*A ( J+1

)

TEMPI =WR*A( J+1 )+WI*A( J)

A( J)=A(

I

)-TlMPR

A( J+1 )=A{ I+l )-TEMPI

A{ I )=A ( I ) +TEMPR

A( I+l )=A( I+l )+TEMPI

9 CONTINUE

TEMPR=WR

WR = WR*WSTPR-W r^WSTP I+WR

WI = WI-s^WSTPR + TEMPR^-WSTP I+WI

10 CONTINUE

MMAX= ISTEP

GO TO 7

C END OF TRANSFORM

C CORRECT PHASE ON TRANSFORM DUE TO SHIFTED A

11 DO 12 J=1»N

JJ=J-1

L=M0D(JJ»2)

IF (L .EQ. 0) GO TO 12

JR=2*J-1

JI=JR+1

A { JR ) =-A ( JR

)

A( JI ) =-A( JI

)

12 CONTINUE

72 10 24 PAGE 4
RETURN

END

SCOPE

• LOAD

»RUN»10»1500

72 10 24
FORM NBS-n4A U.7«)

II c nppT nr rnMM 1. PIIRI irATION OR RFPORT MO 2. Gov't Accession

BIBLIOGRAPHIC DATA „^ No. SHEET NBSIR 73-310

3, Recipient's Accession No.

4. TITLE AND SUBTITLE

Electromagnetic Scattering By a Thin Wire With Continuous

Impedance Loading-Part II; Time Domain Analysis

5, Publication Date

6. Performing Organization Ccnle

7. AUTHOR(S)

TnmTYiy C. , Tnng

8. Performing Organization

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS, Boulder Labs.

DEPARTMENT OF COMMERCE

Boulder, Colorado 80302

10. Proiect/Task/Work Unit No

2727277

11. Contract/Grant No.

12. Sponsoring Organization Name and Address

Same as Item 9.

13. Type of Report & Period

C overe d

1 ^ Soon ^nrin c A ffpnfw

15, SUPPLEMENTARY NOTES

16. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here.) The scattering of electromagnetic pulses by a thin wire with continuous impedance

loading is investigated theoretically. The basic approach used is the numerical

Fourier transform of the frequency response. The incident pulse is assumed a

tr\ancated periodic Gaussian pulse. N\americal results for the transient current

distribution and the transient scattered field in different directions of observation

are presented. It is found that the shapes of the transient current distribution on

the wire and of the scattered field can be controlled by loading the wire with some

impedance.

17. KEY WORDS (Alphabetical order, separated by semicolons)

Electromagnetic scattering; impedance loading; pulses; thin wire

18. AVAILABILITY STATEMENT

I I UNLIMITED.

[Xl FOR OFFICIAL DISTRIBUTION. DO NOT RELEASE

TO NTIS.

19. SECURITY CLASS

(THIS REPORT)

UNCLASSIFIED X

20. SECURITY CLASS

(THIS PAGE)

UNCLASSIFIED X

21. NO. OF PAGES

32

22. Price

USCOMM-DC 66244-P7I

USCOMM - ERL

I