REFERENCE

NBS

PUBLICATIONS

A11102 b 3 1 3 7 fl

NAT'L INST OF STANDARDS & TECH R.I.C. NBSIR 86-3063

All 102631 378

Hill, David A/Far-fleld transient respon QC100 U56 NO. 86-3063 1986 V19 C.1 NBS-P FAR-FIELU l kanSiEnT RESPONSE OF

AN ANTENNA FROM NEAR-FIELD DATA

David A. Hill

National Bureau of Standards

U.S. Department of Commerce

Boulder, Colorado 80303

December 1986

-0C

100

-U56

86-3063

1986

NBSIR 86-3063

NBS

RESEARCH

INFORMATION CENTER msz.

FAR-FIELD TRANSIENT RESPONSE 0F»^

AN ANTENNA FROM NEAR-FIELD DATA' 2 "

David A. Hill

Electromagnetic Fields Division

Center for Electronics and Electrical Engineering

National Engineering Laboratory

National Bureau of Standards

Boulder, Colorado 80303

December 1986

Sponsored by

Defense Nuclear Agency

Alexandria, Virginia 22310

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

CONTENTS

Page

Abstract 1

1. INTRODUCTION 1

2. PLANAR NEAR- FIELD SCANNING 2

2.1 Frequency-Domain Approach 2

2.2 Time-Domain Approach 4

3. ANALYTICAL EXAMPLES

3.1 Rectangular Aperture..

3.2 Circular Aperture

4. SINGULARITY EXPANSION METHOD 12

4.1 Input Reflection Coefficient 13

4.2 Near-Field Data 14

5. CONCLUSIONS 15

6. REFERENCES 17

iii

\0

CT\

CT\

FAR-FIELD TRANSIENT RESPONSE OF AN

ANTENNA FROM NEAR-FIELD DATA

David A. Hill

Electromagnetic Fields Division

National Bureau of Standards

Boulder, CO 80303

The theory for calculating the transient far-field response of

an antenna from planar near-field data in either the time domain

or the frequency domain has been developed. A double integral

must be evaluated if we begin with time-domain data, but a triple integral must be evaluated if we begin with frequencydomain data. However, the frequency-domain integrals are in a form that is suitable for three-dimensional FFT. Two idealized

examples are studied, and identical results are obtained

starting with frequency-domain or time-domain data. The main

practical difficulty in determining the transient response is

the large number of near-field samples that are required. If

data are taken at only a few near-field points, then the

singularity expansion method (SEM) presents a possible method of

determining the complex resonances of the antenna under test.

Key words: antenna; complex resonance; far field; frequency

domain; near field; singularity expansion method (SEM); time

domain.

1 . INTRODUCTION

The response of antennas to out-of-band frequencies [ 1 — 4 3 plays an important role in interference and jamming problems. Earlier work in this area at the National Bureau of Standards ( NBS ) included an analysis of

reflector antennas [5] and an analysis and near-field measurements of

antenna arrays [6].

This earlier work applied to single-frequency cw signals, but many

interfering signals, such as high-power microwaves (HPM), are actually

pulsed signals with a fairly complicated time dependence. Thus it would be

useful to be able to determine the transient response of antennas

illuminated by pulsed signals. The transient far-field patterns of HPM sources are also difficult to determine because it is generally difficult to

make measurements in the far field of the HPM source. In either tvpe of

1
application (reception or transmission) with electrically large antennas,

neai—field measurement techniques need to be extended from the frequency

domain [7] to the time domain [8]. In this report, we consider the

calculation of the transient far-field response of an antenna from near- field data taken in either the time domain or the frequency domain.

The organization of this report is as follows. Section 2 considers the

theory of the calculation of transient far fields from planar near-field

data in either the time domain or the frequency domain. Section 3 illustrates the techniques with two idealized analytical examples. Section

4 explores the possibility of obtaining complex resonances of the antenna

from near-field data via SEM. Section 5 summarizes the results of this

study and includes recommendations for future work.

2. PLANAR NEAR-FIELD SCANNING

In this section we derive expressions for the far-field transient

response of an antenna in terms of near-field values measured over a planar

surface. The near-field values can be taken in either the frequency domain

as in section 2.1 or the time domain as in section 2.2. We include no probe

correction for pattern effects or frequency response; thus we assume that we can measure the electric field at any point on a plane for any frequency or any time. The results will be given in terms of two-dimensional integrals over a planar surface, but the integrals can be put in discrete form if

evaluation by fast Fourier transform (FFT) is desired.

2.1 Frequency-Domain Approach

We first consider the time-harmonic case where the fields vary as exp(ju)t). The geometry for planar scanning is shown in figure 1. An

arbitrary antenna under test (AUT) is located in free space to the left of

the plane z = d, and the values of the electric field E(w,r') are measured

on the plane z = d. An expression for the electric field E(w,r) for z > d

is available from Harrington [9, p. Ill]

2
E(w,r) = V x //

S'

z x E(u),r ' ) dS’ , ( 1 ) -jkR

2tiR

where R = | R | , R = r - r ’ , k = w/c, c is the speed of light in free space,

and ~ indicates a unit vector. The S' integration is over the plane z = d.

If we take the curl operation inside the integral and carry out some

algebra, then (1) becomes

E(oj,r

)

-jkR

// ^5 + ~) [z x E(w,r ' ) ] x R dS’

.

s

, 2n R

r

2

( 2 )

In the far field (kr >> 1, where r = |r|), we can approximate R by r in

A amplitude terms and R by r - r • r' in the phase. If we make these

-2

approximations in (2) and neglect the r term, then (2) reduces to

E(w,r ) = jke-jkr ^

2irr r x //

S'

x E(o),r f ) e

^ kr * r ' dS 1 (3)

The far-field result in (3) is equivalent to the expression given by Johnson

[10, p. 332].

The Fourier transform nature of (3) is more evident if we write r in

terms of polar angles 0 and <p and r' in terms of rectangular coordinates:

r = x sine cos<(> + y sine sin<j> + z cose AAA (4)

and r' =xx’ +yy' +zd.

If we substitute (4) into the exponent and the differential in (3), we obtain

3
E(u>,r) = - jke-jk(r - dcose) ~ “> ~

2irr r x // z x E(w,r '

)

i ksin0(x’ cosd) + y'sindi)., , . , • e

t j t dx* dy* .

( 5 )

If we wish to know the transient far-field response of the AUT, then we consider the far-field response in (3) or (5) to represent only one spectral

component of the total transient response. The transient far-field response

E(t,r) is given by the inverse Fourier transform of E(w,r):

E(t,r) = F

_1

[E(w,r )

]

_1_ 2tt

00/ E(w,r

)

— 00 e Jut

da). ( 6 )

The evaluation of (6) involves a triple integral over x* , y', and w. If we require samples in x’ , samples in y* , and samples in u, then

the total number of samples required would be 2N N N . The factor of 2

x y id arises because both tangential components (x and y) are required. The

samples could be obtained either by sweeping (or stepping) through frequency

a) at each near-field point or by doing a complete near-field scan at each

frequency. Either method appears to be very time-consuming for typical

values of N , N , and N . The evaluation of the triple integral does not

x* y’ w appear to pose any particular problem because each integral is of the type

that can be evaluated by FFT . Thus (6) could be evaluated by one threedimensional FFT to obtain a grid of values of E in 0, <j>, and t.

2.2 Time-Domain Approach

In the time-domain approach, the AUT has a transient excitation, and

the measured field values on the plane S’ are functions of time E(t,r’). We

could derive an expression for E(t,r) in terms of values of E(t,r T ) directly

in the time domain, but it is easier to derive E(t,r) from (3) and (6). The

4
jk factor in (3) transforms as a time derivative, and the exponentials in

(3) transform as time shifts. Thus (6) can be rewritten in the following

form

E(t,r)

-1 ~ 2irrc x //

S’ z x

r - r»r'

r') dS’. (7)

In some cases, it is more convenient to use a shifted time, x = t - r/c, and

to rewrite (7) as

E(t,r)

-1 ~ 2irrc x //

s*

x lt

g(T

r »r r

f ) dS’. ( 8 )

From (7) or (8) we see that the time derivative of E is required at

each near-field point r*. Thus a time waveform would need to be measured

and stored at each near-field point. If we require N^. time samples at each

near-field point, then the total number of samples required would be

2 N N N . As in the frequency domain case, this is a very large number of

x y u samples for typical values of N , N , and N. . The time domain result in (7) x y u or (8) requires evaluation of only a double integral rather than a triple

integral, but the double integral is not of the form that can be evaluated

by FFT. If the probe measures the value of E, then the time derivative of E

would have to be computed for evaluation of (7) or (8). (This could be done

by finite difference.) However, some probes actually measure the time

derivative of the electric field directly, and these probes are usually

called D-dot sensors [11].

The results in this section have been given for the electric field, but

the same equations apply for the magnetic field. There are also probes

available for measuring the time derivative of the magnetic field, and these

probes are usually called B-dot sensors [11].

5
3. ANALYTICAL EXAMPLES

In this section we study two idealized examples where we are able to

determine the transient far field analytically from the planar near-field

distribution. We consider a step function distribution over a rectangular

aperture in section 3.1 and a step function distribution over a circular

aperture in section 3.2. In each case we perform the analysis starting with

either frequency-domain near fields via (5) and (6) or transient near fields

via (8). Even though the examples are idealized, they illustrate the

differences in the integrations that must be performed. The examples also

illustrate that we can obtain identical far-field results either working

entirely in the time domain or working in the frequency domain followed by

an inverse Fourier transform.

3.1 Rectangular Aperture

We consider first the rectangular aperture geometry shown in figure 2

where we have set d = 0. The time-dependent electric field in the z = 0

plane is assumed to be a step function inside the a by b aperture and zero outside the aperture and is assumed to be x-polarized

a E( t ,r ' ) = x E U(t) p Cx') p (y’),

S cl D (9)

where p (x '

)

a

< a

> a

’

U ( t ) is the unit step function, and E is a real constant with units of V/m.

s We do not need to consider what type of antenna would actually produce such

a field, but a step-excited aperture antenna is one possibility. For

evaluation of (8), we need the time derivative of the electric field — E(t ,r ’ ) = x E

s 6(t) Pa (*’) Pb (y’) » (10)

where 6 ( t

)

is a delta function [12]. If we substitute (10) into (8), we

obtain the following expression for the far field

6
E(t,r) ( 11 ) 2^ P X y X

6

9

b a where I = / / 6[x + (x’sinecos<t> + y ’ sinesin<j))/c] dx ? dy’

6 -b -a

and r x y

= -x cose + z sinecos<j>.

For arbitrary e and <(> , (11) can be evaluated, but the result is rather

involved. The results simplify in the two principal planes (<j> = 0 or ir/2).

For <(> = 0, we have

E(t ,r)

<p=0

e

E b

s irrsine P T

(t) , a( 12 )

where T = (2asine)/c.

a

For 4> = tt/ 2, we have a similar result

E(t,r)

<p=ir/2

„ E acose

X

irrsine P T

(t) ’ b(13)

where T. = (2bsine)/c.

b

Both (12) and (13) are indeterminate for the on-axis case (e = 0). By

taking the limit as e approaches zero in (11), (12), or ( 13 ), we obtain

^ 2abE

E(t,r)| n

= x ——- 6 (t). (14)

1 6=0 irrc

Thus the far field for the on-axis case (6=0) is proportional to aperture

area times the time derivative of the aperture field. In figure 3, we show

the two principal plane results. In either case as 6 approaches zero, the

pulse narrows and approaches a delta function as indicated by (14).
We now treat the same rectangular aperture example starting with

frequency-domain values in the z = 0 plane. The frequency-domain values are obtained by taking the inverse Fourier transform of (9)

- E

s EU,r') = x -7- p ( x ’ ) p.(y') , (15)

j co a d

where we have used the inverse transform of the unit step [12]. The far

field is obtained by substituting (15) into (5)

E(w,r

)

E e s

-jkr

2irrc r x y I 9

where I e

j f e jksine(x T cos<|) + y’sin<}>) dx , -b -a

( 16 )

The double integration in (16) can be performed to yield

-2abE e" jkr

w s 2 _ ?. sin(kasinecos<j)) sin(kbsinesin<f>) fArT ^

tj \ (jo * r* j

* p x y . . , . . • \ I (

)

irrc kasmecoscj) kbsmesin^

This is the general frequency-domain, far-field result, but it simplifies

considerably for the principal-plane (<(> = 0 or tt/2) or the on-axis (0 = 0)

special cases

^ 2abE e E(w,r) 1=6 —

1 4>=0 Trrc

-jkr

sin(kasine)

kasine ’ ( 18 )

E(u,r)

— 1 kr

^ 2abE e

J cose . . s sin(kbsine)

= x

<()=7r/2 irrc kbsine (19)

and E(w,r)

^ 2abE e

s

„ _ = x

9=0 irrc

-jkr

( 20 )

8
To obtain the transient far-field response from the frequency-domain

far-field response, we use the inverse transform relationship in (6). It is

possible to take the inverse transform of the general frequency-domain

expression in (17), but the result is rather involved. For simplicity we

consider the special cases in (18)— (20). The simplest case is the on-axis

case (0 = 0):

F

1 [E(u>,r

)

a 2abE

] = x 6=0 J irrc

S(t) . (21 )

This result is in agreement with the direct time-domain result in (14). To

take the inverse transform of (18) or (19), we need the following inverse

transform [12]

^-1 r sin(a)T) n PT

(t)

F [ u/f

] " ~2T

‘ ( 22 )

Using (22), we can transform the principal plane results in (18) and (19) to

the time domain

F

-1

[E(o),r)

<j>=0

]

- E b

0 T—r- irrsine PT(t) , a (23)

and F [E(w,r

)

a E acose

g

. /0 ] = X

~r~T~

' q P rri (t)

<b=TT/2 irrsinS T,b

(24)

These results are in agreement with the direct time-domain results in (12)

and (13).

3.2 Circular Aperture

We now consider a circular aperture geometry as shown in figure 4 where

we have again set d = 0. The time-dependent electric field in the z = 0

plane is assumed to be a step function inside the circular aperture of

radius A and zero outside the aperture and is assumed to be x-polarized

9
E(t.r’) = x E (25)

s U(t) p

A

(p ' ) .

The time derivative of the electric field is

E(t.r’) = x E

g

6 (t ) P A (p’) . (26)

If we substitute (26) into (8), we obtain the following expression for the

far field

E(t,r)

E

s

~ ~ 2^ r X y : A (27)

where I,

A

2tt A , / / 6[x + sine cos (V -<{))] p’ dp’ d<j>

T . 0 0

c

( 28 )

It is easy to see that I is independent of <j>. The p' integration can be

performed using the properties of the delta function [12, p. 274], and the

<j>’ integration can then be performed to yield the following result

E(t,r)

-AE

s

:—

t

r x y irrsine

1/2

P T

(t) , A

(29)

where T. = — sine

A c

The waveform for the circular aperture case is shown in figure 5, and it

differs from the rectangular aperture case because it does not have a step

discontinuity. For the on-axis case (0 = 0), the expression in (29) is

indeterminate. If we take the limit as 6 approaches zero, we obtain

E(t,r)

0=0 6 ( t ) . (30)

10
The on-axis results for both the circular and rectangular apertures are

proportional to the aperture area times the delta function.

We now treat the same circular aperture example starting with

frequency-domain values in the z = 0 plane. The frequency-domain values are obtained by taking the inverse Fourier transform of (25)

* E E(w,r ' ) = x -r^ p (p ' ) . (31

)

J W A

The far field is obtained by substituting (31) into (5)

E(w,r) = E e

s

•jkr

2trrc r x y I (32)

where I J JJe , . j kp ' sinecos (<t>’-<p) , p

0 0

dp’ d<t>' .

The integrations can be performed using the integral representation of the

Bessel function [13], and we obtain a result which is equivalent to that of

Johnson [10, p. 333]

2 — i kr

-A E e

J ^ ^ J. (kAsine)

s 1 E(co,r) = r x y rc kAsine (33)

where is the first-order Bessel function [13]. For the on-axis case,

(33) simplifies to

* A

2

E

s e-J kr

E( “' r) 8-0 * -£~c ( 3 ^)

To obtain the transient far field from the frequency-domain far field,

we use the inverse transform relationship in (6). The necessary inverse

transform of is given in [14, p. 300], and the time-domain field is
F ^EU.r)] (35)

-AE—s - r irrsine

2 , 1/2

“ T ) PT

(t) . A

This result agrees with that obtained in the time domain in (29). The onaxis result is obtained from the inverse transform of (3M)

F

- 1 [EU,r)

a

2 e

] = 9=0 2rc 6 ( t ) . (36)

This result is also in agreement with the direct time-domain result in (30).

4. SINGULARITY EXPANSION METHOD

A major difficulty in determining the far-field transient response of

an antenna from near-field data is the large amount of data that must be

taken (either 2N N N or 2N N N . samples). It would be convenient if we

x y a) x y t could extract some useful information from data taken at a single near-field

point or at the terminals of the AUT (either N or N. samples). This type

10 t of data has been taken in the frequency domain at NBS in an attempt to

characterize the out-of-band response of antenna arrays [6].

During the past 15 years, a great deal of work has been done in

characterizing the transient responses of antennas and scatterers in terms

of natural resonances. This general approach has been named the singularity

expansion method (SEM), and a recent review paper by Baum [15] contains an extensive bibliography on the subject.

Under some conditions a scalar response f(t) can be written as a sum of

damped exponentials

* st # s t f(t) =T(ae n +ae n

L ) U(t)

n n n

(37)

12
where s = a + jw , n n n

a) is an angular frequency, o is a damping constant, and * denotes complex

n n conjugate. The n summation contains an infinite number of terms, but a small number of terms is often sufficient except at early times. The terms

appear in conjugate pairs so that f(t) is real. Here f(t) could represent a scalar component of the surface current or radiated field of the AUT. The

coefficients a^ of the exponential terms are functions of position and

excitation, but the complex frequencies s^ are characteristic of the antenna

and are independent of position. Consequently, if we know f(t) at any

point, then we can attempt to determine the characteristic frequencies s^

from that single waveform. There can be computational difficulties in such

a procedure [15], but the Prony method [16] has been used by a number of

investigators.

To work in the frequency domain, we take the Fourier transform of (37)

* a a f(w) = F[f ( t ) ] = l ( -r g s

+ 2_) . (38)

n n jai - s n

Each term in (38) represents a first-order pole singularity in the complex

frequency plane. In some cases there could be other types of singularities

in the complex frequency plane [15], but the form in (38) has been used for

most numerical work [17]. In sections 4.1 and 4.2, we discuss the

possibilities of determining the complex resonances from frequency-domain

measurements of the input reflection coefficient or the near field.

4.1 Input Reflection Coefficient

The input reflection coefficient r is a useful quantity in

characterizing the out-of-band response of antennas because it is directly

related to the mismatch loss [6], However, the input admittance Y is more

useful for SEM analysis because it has been shown to have the same complex

13
poles as the surface current expansion [18]. Thus YU) has the same form as

( 38 ) and can be used to obtain the complex resonances s^.

If r is measured as a function of frequency, then Y ( w

)

can be

calculated from

YU) Y

1 - r 0 1 + r

* (39)

where Y^ is the characteristic admittance of the transmission line.

Schaubert [19] has used a related expression to obtain complex resonances

from time-domain data via Prony's method. Noise in the YU) measurements

will cause errors in the computed s^ locations, and the general problem of

determining the pole locations from noisy frequency-domain data has been

studied by Ksienski and Willis [17]. The number of poles that can be

extracted from the frequency-domain data is limited by the quality of the

data.

4.2 Near-Field Data

Near-field data is also a good indicator of the out-of-band response of

antennas because it relates to both the radiating and impedance mismatch

properties of the antenna [6]. If E U, r ) is a scalar component of the

a m electric field measured at a frequency w and at a location r , then we can

write E in the SEM form of ( 38 ) a

E a U,r) - l ( . n m , n J» sn jw - s n

(40)

The usual procedure would be to take swept-frequency measurements of E^ at a

single near-field point r and to calculate the s values based on that data m n set. However, if we take swept-frequency data at several points, then we

14
would have several data sets to use in the determination of the s values,

n and we might expect to improve the accuracy or the number of s^ values that

can be determined. The use of multiple frequency-domain data sets for

extraction of pole locations has been studied by Ksienski [20],

If we are only interested in a rough estimate of where the antenna

response peaks in w, then there is probably no need to search for the poles

in the complex frequency plane. The raw data will show peaks in w

[6]. Such peaks are sometimes used in estimating how many poles can be

extracted from the data [21]. The SEM analysis of the data does appear to

be attractive because the complex resonances of the AUT are independent of

r . Hence the complex resonances ought to show up in the far-field response

of the AUT.

5. CONCLUSIONS

The theory for calculating the transient far field of an antenna from

planar near-field data has been developed. The near-field data can be in

either the frequency domain or the time domain. For frequency-domain data,

the required triple integral could be performed by a three-dimensional FFT.

For time-domain data, only a double integral is required, but it is not of a form suitable for FFT.

Two analytical examples have been studied, and identical results are

obtained starting with frequency-domain or time-domain data. The two

examples, a step-function electric field over a rectangular or circular

aperture, are idealized, but they illustrate the integrations that must be

performed. In each case, the integrations can be done analytically.

The main difficulty in determining the transient far field from near- field data is the large amount of measured data (2N N N or 2N N NL samples)

x y a) x y t that must be taken. If time-domain or frequency-domain measurements are made at a single near-field point (or at the antenna terminals), then SEM

might provide a means of determining the natural resonances of the antenna.

15
The theory presented in this report is preliminary, and a number of

theoretical, numerical, and experimental extensions are possible. More

theoretical work could be done on sampling and probe correction [ 7 ]. Other

near-field scanning surfaces, such as spherical or cylindrical, could be

considered. The examples in section 3 were chosen so that the integrations

could be done analytically, but it would be useful to study some less

idealized cases where the integrations would be done numerically. Such

cases would allow sampling requirements to be studied numerically. Further

experimental and computational work could involve SEM analysis of near-field

data at a few near-field points or the complete near-field to far-field

transformation. The question of what time-domain probes are most effective

[8] also deserves further study.

16
6 . REFERENCES

[1] Lind, W.R. Out of band performance of antennas. Moore School of

Electrical Engineering Report No. 65-18; 1965.

[2] Levinson, D.S. Transmission-line measurement techniques. More Air

Development Center Technical Report No. RADC-TR-65-1 87 ; 1965.

[3] Cown, B.J.; Cain, F.L.; Duffy, E.G. Statistical prediction model for

EMC analysis of out-of-band phased array antennas. IEEE Trans.

Electromag. Compat., EMC-18: 1

6

3 — 170; 1976.

[4] Cown, B.J.; Ryan, C.E.; Weaver, E.E. Antenna pattern measurements to

characterize the out-of-band behavior of reflector antennas. Georgia

Institute of Technology, Engineering Experiment Station, Report ECACTR- 83-OO 3 ; 1983.

[5] Hill, D.A. Out-of-band response of reflector antennas. Nat. Bur.

Stand. (U.S.) Interagency Report 85-3021; 1985.

[6] Hill, D.A.; Francis, M.H. Out-of-band response of antenna arrays.

Nat. Bur. Stand. (U.S.) Interagency Report 86—3047 ; 1986.

[7] Kerns, D.M. Plane-wave scattering-matrix theory of antennas and

antenna-antenna interactions. Nat. Bur. Stand. (U.S.) Monograph 162;

1 981 .

[8] Lawton, R.A.; Ondrejka, A.R. Antennas and the associated time domain

range for the measurement of impulsive fields. Nat. Bur. Stand. (U.S.)

Tech. Note 1008; 1978.

[9] Harrington, R.F. Time-Harmonic Electromagnetic Fields. New York:

McGraw-Hill; 1961.

[10] Johnson, C.C. Field and Wave Electrodynamics. New York: McGraw-Hill;

1 965.

[11] Baum, C.E.; Breen, E.L.; Giles, J.C.; O'Neill, J.; Sower, G.D. Sensors

for electromagnetic pulse measurements both inside and away from

nuclear source regions. IEEE Trans. Antennas Propagat . , AP-26: 22-35;

1 978.

[12] Papoulis, A. The Fourier Integral and its Applications. New York:

McGraw-Hill; 1962.

[13] Abramowitz, M.; Stegun, I. A., ed. Handbook of mathematical functions.

Nat. Bur. Stand. (U.S.) Appl . Math Ser . 55; 1964 June.

[14] Roberts, G.E.; Kaufman, H. Table of Laplace Transforms. Philadelphia:

W.B. Saunders Co.; 1966.

[15] Baum, C.E. The singularity expansion method: background and

developments. IEEE Antennas & Propagation Society Newsletter, 28 ( 4 ): 15-23; 1986.

17
[16] Van Blaricum, M.L.; Mittra, R. A technique for extracting the poles

and residues of a system directly from its transient response. IEEE

Trans. Antennas Propagat., AP-23: 777-781; 1975.

[17] Ksienski, D.A.; Willis, T.M. Numerical methods of noise reduction for

frequency domain SEM. Electromagnetics. 4: 393-405; 1984.

[18] Pearson, L.W. ; Wilton, D.R. Theoretical aspects of the physical

realizability of broad-band equivalent circuits for energy collecting

structures. IEEE Trans. Antennas Propagat., AP-29: 697-707; 1981.

[19] Schaubert , D.H. Application of Prony's method to time-domain

ref lectometer data and equivalent circuit synthesis. IEEE Trans.

Antennas Propagat., AP-27: 180-184; 1979.

[20] Ksienski, D.A. Pole and residue extraction from measured data in the

frequency domain using multiple data sets. Radio Science, 20: 13-19;

1 985.

[21] Drachman, B. ; Rothwell, E. A continuation method for identification of

the natural frequencies of an object using a measured response. IEEE

Trans. Antennas Propagat., AP~33: 445-450; 1985.

18
X

Figure 1

.

Near-field planar scanning geometry for

under test (AUT). an arbitrary antenna

19
X

Figure 2. Rectangular aperture (2a x 2b).

20
r>u E

(a)

nu

E

(b)

Figure 3« Time dependent far field radiated by a rectangular aperture: a)

4> = 0 plane, b) </> = tt/ 2 plane.

21
X

Figure 4. Circular aperture of radius A.

22
r>u E

Figure 5. Time-dependent far field radiated by a circular aperture.

Emax

r x y I AE /(irrsine)

.

1 s

23
NBS-114A (REV. 2-80) U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR

REPORT NO. NBSIR 86-3063

2. Performing Organ. Report No. 3. Publication Date

December 1986

4. TITLE AND SUBTITLE

Far-Field Transient Response of an Antenna From Near-Field Data

5. AUTHOR(S)

David A. Hill

6 . PERFORMING ORGANIZATION (If joint or other than NBS, see in struction s) 7 . Contract/Grant No. NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

8

.

Type of Report & Period Covered

9.

SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City. State. ZIP)

Defense Nuclear Agency

Alexandria, Virginia 22310

10.

SUPPLEMENTARY NOTES

Document describes a computer program; SF-185, FIPS Software Summary, is attached.

11.

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 theory for calculating the transient far-field response of

an antenna from planar near-field data in either the time domain

or the frequency domain has been developed. A double integral

must be evaluated if we begin with time-domain data, but a triple integral must be evaluated if we begin with frequencydomain data. However, the frequency-domain integrals are i.n a form that is suitable for three-dimensional FFT . Two idealized

examples are studied, and identical results are obtained

starting with frequency-domain or time-domain data. The main

practical difficulty in determining the transient response is

the large number of near-field samples that are required. If

data are taken at only a few near-field points, then the

singularity expansion method (SEM) presents a possible method of

determining the complex resonances of the antenna under test.

12.

KEY WORDS (Six to twelve entries; alphabet! cal.order; capitalize only proper names; and separate key words by semicolons)

antenna; complex resonance; far field; frequency domain; near field;

singularity expansion method (SEM) ; time domain.

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Xj Order From National Technical Information Service (NTIS), Springfield, VA. 22161

U.S. GOVERNMENT PRINTING OFFICE: 1987-774-183/65064 USCOMM-DC 6043-P80