Download IA Simple Technique for Obtaining the Near Fields of

I
A Simple Technique for Obtaining the Near Fields
of Electric Dipole Antenm+s f rorn Their Far Fields
;- . -.
Bharadwaja K. Singaraju
Carl E. Baum
Air Force
Weapons Laboratory
... ..... . .
... ..: ,, ;..!’
:,. .:i.’:,,
Pi/i?~
.
+;5/97
Abstract
In this report a technique of obtaining the near fields of axially and
lengthwise symmetric
electric dipole antennas from their far fields is
.In particular it is shown that if the 6 component of the far
discussed.
electric field is known either in time or frequency domains, all other
electric and magnetic field components including their near fields can be
An example involting the fields of a resistively
obtained very easily.
loaded dipole antenna driven by a step function generator is discussed in
detail.
L
Introduction
In the calculations
as involving
electric
of fields
or magnetic
have a very simple behavior.
fields
and are proportional
due to simple current distributions
dipoles,
In general
linear
considered
point.
Because of the ease with which
far field representation
in cases such as large vertically
in the testing of aircraft,
polarized
etc. , the observation
dipole simulators
point in general
the near fields
being predominant.
of such structures
such simple technique.
degrees
used
cannot be
At most fre -
and within useful distances from the simulator,
field components contribute to varying
Iow frequencies
in most
in general is sufficient.
to be in the far field of the antenna (simulator).
quencies of interest,
field
these fields behave like the radiated
can be obtained and also because of their applications
antenna problems,
However,
or magnetic
to 1/r, r being the distance from some reference
point on the antenna to the observation
the far fields
the far electric
such
with their contribution
near
at the
As such, a simple way of calculating
was desirable.
An example involving
dipole over a ground plane is discussed
2
This note deals with one
an impedance
in detail.
loaded conical
o
II.
Electric
and Magnetic
Dipole Moments
and Their
Far Fields
@
Consider
a volume Vt bounded by a closed
system is as described
in figure
contains electric” current
2.1.
Assuming
S!.
The coordinate
Let us assume that the volume Vf
density 7(J’ ) and charge density ;(~’ )0 Here a
tilde (-) over the quantity represents
quantity.
surface
the bilateral
that the charge and current
Laplace
densities
transformed
are zero before
time t=to and requiring
no current density to pass through S!, the electric
1,2
dipole moment can be defined as
;(t)
z
1
(2. 1.)
;I p(;}, t)dV’
v!
or in terms
e
of Laplace
transformed
quantities as
dipole moment while ~ is frequency
Notice that ~(t) is a time-dependent
dependent.
Equivalently,
in terms
of the current
density
(2. 3)
Similarly,
s being complex radian frequency.
+
2
m can be written as
the magnetic
dipole moment
(2.4)
in the time domain and
+
m=-—
o
1
(2.$}
4
in the Laplace
domain.
can be written
as
In the low frequency
3
limit these dipole moments
●
~1: surface bounding
the sources
Position
a
✎
vector
.+
Is
outward normal
volume containing
the sources
Position vector
the observation
to
point
v
.
Figure
2.1.
Coordinate
system describing
4
the source and radiation
region
*
J
;=
4-+
rlp(r!)dV[
= $
~(:’)dVl
(2.6)
Jv!
VI
-
where ~(;’
magnetic
) and ~(;’ ) are charge and current densities
dipole moment can be written
respectively.
The
as
+
.
(2. 7)
Low frequency
then be written
far fields
due to electric
and magnetic
dipoles 1 can
as
(2.9)
(2. 10)
+
@
where
lr is a unit vector
in the radial direction
and
No = free space permeability
e
o
= free space permittivity
c=
1/~
r
= speed of light in free space
u
Z.
Yc
=
n—
—
e
s
u
= 377Q = characteristic
= complex
propagation
It is clear that if the electric
magnetic
9
fields
space
due to an electric
dipole moment are known, other components
and far field relations
or
can be simply
cal -
of the electric
and
quantities.
If we consider
magnetic
of free
constant
or magnetic
c ulated using the complementary
magnetic
impedance
o
fields
can be written
an electric
due to an electric
as
dipole source term alone,
electric
dipole~ with 1/r2 and 1/r3 terms
and
included
(2.11)
(2. 12)
From the above equations,
a general
relationship
1/r term to the 1/r2 and 1/r3 terms.
as a frequency
This relationship
the
.
can be thought of
scaling along with a simple proportionality
clear that in the case of the electric
constant.
It is
the 1/r3 type field is more
.
If ?r is perpendicular to ~+ certain simpli-
important at low frequencies.
fications
exists which relates
.
field,
result in (2.1 1).
If we consider
a magnetic
dipole instead of an electric
dipole,
its
fields can be obtained by setting
*
+
+
P~~
(2. 13)
ip(~)
-
zo~m(x)
(2. 14)
_
- +
(2.15)
++
Hp(r)
Em(;)
o
in (2. 11) and (2. 12).
A general
source distribution
may contain electric
dipoles along with their higher order
counterparts.
to (2. 11) and (2. 12) may be found for multipole
and magnetic
Relationships
terms.
terms,
one may expand the Green Ts function in series
spherical
Bessel
and Hankel functions and spherical
tion.
This procedure
of this report.
harmonics.
to the order of the multipole
is quite involved
and is considered
similar
.
To include these
multipole
of these functions is related
*
involving
The order
under considersoutside the scope
:!
o
III.
Expansion of the Fields
in Spherical
and Cylindrical
Coordinates
—
In practical
magnetic
drical
fields
applications
in terms
it is convenient to express
of their vector
Let us consider
components.
density symmetrically
components
the special
dipole moment is present.
electric
dipole moment can be written
In terms
Y
in spherical
and
or cylin-
case of the electric
situated as shown in figure
directed
the electric
current
3.1. such that only a z
f spherical
coordinates
the
as
(3.1)
Using this representation,
the electric
field given by (2. 11) can be written
as
Note that the radial
electric
field does not have a 1/r component.
that the e component of the far electric
Suppose
field is known, let us represent
this by ~fo as
s2p
= -&
Ef
-
(sinepe
()
-yr
(3. 3)
)
e
then the 1/r2 component ~20 can be w:ritten as
Zos
--yr
E2
= ( sin ()flpe
4m2
e
while 1/r
3
=&&
sr
f
component can be written
as
)
7
e
.~~
yr
f~
(3.4)
r
h
X,X1
Figure
3.1.
Axially
and lengthwise
8
symmetric
dipole antenna
.
:
--yr_l*
1
=——
sint)pe
= ~E
(
()
) - --; E2
22f
30
4~r3_c=_=
o
.= -___ .= -=_= -=- !Q 7?
Representing
written
the total 0 component of the electric
(3.5)
8
field by ~. , it can be
as
(3.6)
Hence in the dipole approximation
the far electric
of an antenna, if the 6 component of
field is known, the total 0 component of the electric
near the antenna can be calculated
In a similar
be written
fashion,
Zos
a
with the help of (3. 6).
the 1/r2 part of the radial electric
field can
as
E2 = --y
r
field
(cos(@)~e
“l’r)
.
_- 2cot(e)~
-yr
2cot(6)E2
n
2?rr
(3. 7)
f.
e
while the 1/r 3 component is given by
E3 = —A(cos(0)pe
r
213
- ‘~r) . 2cot(e)E3
= 2f20t(e)~
e
‘o
y2r2
Hence the total radial electric
and the 1/r component is zero.
.
of the electric field Er can be written as
E
r
(
= 2c0t(e) *+—
The only non-zero
1
y2r2
)
fe
(3.8)
component
Ef
(3. 9)
e
component of the magnetic
field fi$ is given by
(3. lo)
and
.
.+
‘4
o
(1+ #
Ef
(3* 12)
e
Note that the radial electric
the 6 component.
component falls off at a faster
rate than
Not e also that the @ component of the far electric
field is
,
sufficient
to reconstruct
the total radial and @ components of the electric
field and the @ component of the magnetic field.
Let us now consider
the case when the 0 component of the far electric
field is known in the time domain.
transform
.
Using basic principles
of the Laplace
we can write
(3.13)
(3.15)
A.s should be expected,
in time domain,
if the @ component of the far electric
a simple process
of integration
field is known
yields the total near fields.
If Er and E ~ are known, z, fI and ~ components of the electric
magnetic fields
in cylindrical
coordinates
can be written
and
as
+
Ez(~)
= Er(;)cos
Ep(;)
= Er(~sin(6)
(e) - E6(F)Sin(O)
(3. 16)
+ Ee(I)cos (0)
(3. 17)
10
(3.18)
In the case of dipole type antennas it is generally
the far fields.
very easily
Using the procedure
described
If the far fields
obtained.
above,
are measured,
good measurement
namely Efa(;)
this measurement,_
the n.ea.r.f~eld calculation
expedient to calculate
the near fields
it suffices
either in time or frequency
becorn.gs a trivial
In this connection it should be pointed out that this procedure
only if r >> h, i. e.,
the observation
point is far compared
height .’ For distances
of the order
order multipole
in the expansions
regime,
terms
the reconstruction
can be
to make one
domain.
Using
exercise.
is accurate
to the antenna
of h, one may have to include higher
for the field.
of the field is not accurate,
are small.
11
In the high frequency
however,
the errors
N.
Calculation of the Near Fields
Antenna from its Far Field
Consider
a typical axially
as shown in figure
3.1.
of an Impedance Loaded Dipole
and lengthwise
The coordinate
symmetric
dipole antenna
system is as shown.
loading on the antenna is assumed to be A(z’ ) per unit length.
In our present
mission
analysis
of the dipole antenna we also use the trans -
line model for calculating
We assume that the generator
Cg and a voltage
domain.
feeding the antenna has a generator
line model,
mated as shown in figures
impedance
The geometric
g
Elements
3.1 can be approxi-
of the incremental
line are related to the characteristic
section
impedance
o
/2)]
(4. 1)
factor fg is defined as
m
= *In
ZO
for a biconical
lcot (@1/2)]
antenna.
(4.2)
If the biconical
antenna is of half height h and 01
radius a << h, then the antenna can be considered
metric
radian frequency.
Z ~ is given by
Z.
= —ln[cot(el
03
7
z
capacitance
If the bicone has cones at # = 01 and 0 = ~ - @l , the charac-
of the bicone.
~_
the antenna in figure
4.1 and 4.2.
of the equivalent transmission
f
on the antenna.
source VoU(t) in the time domain or Vo/s in the frequency
In the transmission
z
the current distribution
Here U(t) is the unit step while s is the complex
teristic
The impedance
3-7
factor f
g
can be approximated
to be thin and the geo -
as
(4. 3)
where the mean radius of the antenna can be used.
biconical
antenna is in free space,
of the equivalent transmission
parameters
Assuming
that the
of the incremental
section
line are given by
12
.—
e
-
+
I
Open
Circuit
Generator
I
Transmission
I
Line
I
Figure
4.1.
Transmission
line with generator
~--‘-r
—.
J?igure 4.2.
Incremental
section of the transmission
13
line
~1 . /Jf
(4.4)
c!
(4. 5)
Og
‘c/f
Og
and
Zf(f)
= a~(~)
(4. 6)
We define normalized
retarded time Th as
_—
7 _ct-r
‘h
h
(4.7)
where
h=
half height of the antenna
r=
distance to the observer
t
from the center of the antenna ,
= time measured in seconds
‘h =
h/c
We also define
‘h
=—sh = normalized
c
c!
=1+$
radian frequency
c
g
Ca
c
~
= antenna capacitance
= generator
capacitance
Using transmission
line can be calculated,
on the antenna.
A(F)
=
line equations the current on the transmission
this current distribution can be used as the current
For a special impedance loading of the form
w
(4.8)
-w
Baum5 has calculated the 6 component of the far electric
field in frequency
domain to be
●
14
(4. 9)
d
where
sine
r
qe)
.
;-2_
(Sh + CY)
sin (0)
shsin4 (e)
-Sh(l-cos(e))
cos2Fj
+2
-Sh(l+cos(e))
+ sin2 ~
()
e
e
sh sin4 (6)
1]
[
(40 10)
in the frequency domain.
It has been found very cliffic ult to cbtain the near fields of this antenna
analytically.
a
However,
if we use the technique discussed in section 111,the
near fields can be obtained very easily.
first,
Considering
we can write the 0 component of the electric
frequency domain
field as
(4. 11)
while
+1
-yor
Voth
h2
e
——
E3
= —
2?i-f
r
e
g r2
[
=
[1
Vt
oh h2e
2?i-f 5Y
gr
F\ (e)
‘h
-yor
Y;
[1
.
(e)
-.
—
15
(4. 12)
. .
We note that the normalization
of normalized
frequency,
of a by varying
factors
~! ( 6), ?;(6)
@ and a only.
and ~~(e) are all functions
These are plotted for several
values
= jwh. Notice that at low frequencies ~~( 0)
h
while at high frequencies F!(6) is more important.
(3and setting s
is more predominant
~’ {e) is insignificant at most frequencies compared to the contributions of
-2
~\(6) and ~~(d). We can write the total O component of the electric field as
“Voth
——
-1
.1
2Tf
From figures
(4.13)
gr
4.3 through 4 11, if a, h, r and 8 are known the total 0 com-
ponent of the electric
butions of ~;(e)
e-~or
field can be easily
and ~~( 6J)can be neglected
In a similar
visualized.
to varying
If r >> ~ , the contridegrees.
fashion the total radial component of the electric
field can
be written as
(4. 15)
These can also be visualized
from figures
4.3 through 4.11 given a, h, r
and O. ln using I~1 1, \~~ I and I?’~ I graphs shown earlier
exercised
because they should be added with the proper
In time domain the 6 component of the far e~ectric
as
care should be
phase factor.
.
field can be written
5
(4. 16)
16
o
1
I
1
I
I I I I I I
I
I
I
I I
I II
I
I
1 I
1
I
I I I I i I
I
I
I
I
I
I
1
g=7r/2
. 01 I
1
i
I
I I I I I I
I
1 1 I I
\
1
k
1
1
I
1
I I
I
I
I
1
I
I
I
I
I
I
1
I
I
I
I
1
I
I
I
1
f3=7r/2%
.
4
1
.001
-!
.0001 I
I
I
I
1
I
I
[
I
I
I
I
I
I
I
1
1
.1
1
I
I
I
I
I
I
I
t
I
1
I
1u
100
10
‘h
Figure 4.4.
● &’;(e)j
Effect of @
CY= 1
0
.
10
1
.1
.01
—“
CD
22”
w
.001
.0001
L
.00001
I
.000001 I
●
I
1
I
I 1
I
I I I
1
I
I
1 I I I I I I
10
1
‘h
Figure 4.5.
Effect of e on ~~(e),
“
a = 1
I
I
I
I I I I 1,n J.Wu
10
~-”’
‘
‘‘
I
I
I
I
I I
1
.1
.01
001
I
.1
1
1
Figure 4.6.
I
I
I I I I I
1
Comparison
I
I
of
!Ii,, q
!
I [ I I I
100
10
=1
o
i,,
I
10
I
I
I
i
I
I
I I
I
I
I
1
I
I
I
I
I
1
1
I
I I I
I
I
I I I II
1
I
I
I
I
I
I I 1-
1
,,
I
.1
K!
.
001
.0001
1
I
I
I
I
I
100
=1
10
1
.1
I .01 –-
.001
●
I
0001
.
1
I
I I I I I II
I
1
!
‘h
Figure 4, 8.
Comparison
of
I 1 1 I I II
10
i
100
1
1’
I
I
I I I I I I
I
1
I
I
I
I t I I I 1I
I
I
I I I I I II
10
I I I I I
I
I
I
I I I I I
I
I
I
---
‘N
GJ
. 01 1
.1
1
Figure
4.9.
Effect
of generator
capacitance
on 1~}1,
I I I I
100
(3 = ~/2
1
CY=l
@=l.5
0=2
.
.00
\
.000
—
.1
100
10
1
‘h
Figure 4.10.
Effect of generator
o
capacitance
on lr~l,
e=~/2
10
12
I
I
I
I
I
i
1 I
I
1
I
I
1
1 I 1I I1
I
I I f I 1
I
1
ck’=2.
57\\S\
.1
.01
b’
rJ-
IL*
—
.001
●
0001
.00001
.000001
b
I
\
I
I
I
I 1 1 1 1 II
I
I
I
I
‘h
Figure 4.11.
Effect
of generator
capacitance
I
I I I 11
100
10
1
. 1
I
1 I I I 1 I
4
on lgJ
..J
f)=7f/2
with
<T
?’;(0)
= sin($)
-m
h
e
sin2
(0)
[
IJ(rh)
-
2
sin4 (0)
l-e
{1
c1
-a{7h-(1-cos(e))}
26
l-e
+ 2 Cos
( T )/
h
u(Th)
\
j( Urh-
(1 - Cos (0)))
+ { ~:-(l-cos(e))}~
2~
+ 2 sin
()(2
{ l-e
a
j(
u Tll- (~+ COSMJ)))
“’
1’.
(4. 17)
and
‘h=
et-r
h
()
Using (3. 13) we can write the l/r2 part of the 6 component of the electric
field as
o
(4. 18)
where
26
r
= sin (e)
-(IT
1
{1
1 -e
sin2 (0)
L.
h
c1
u(7h)
2
sin4 (6)
+{~h-(l-cos(e))}
l-e
u (Th- (1 - CclS(e)))
~2
)
20
+ 2 sin
(z
a
1
‘h
- (1 + Cos(e))
-a
-a{7h-(l+cos(e))}
1 -e
(4. 19)
while the 1/r 3 part of the @ component of the electric
2t
t
E3 (;$t)
e
= $
E2 (;, t)dt
f
-w
e
u (Th -(l+ccls(e)))”
~2
= ~
r
dT
If-m
field as
‘T
Ef (;, t)dt
e
-m
(4. 20)
where
2’7
1
‘
2
‘h
‘h:
E-CY
si~(,j){
, { II
26
1
+ 2 Cos –
2~Th
‘h
4 ‘h
l-e
u(Th)
2
a
‘
(Th -(l
2
- (1 - CoS(e))z
- (1 - CoS(@))
a
1
- (1 - Cos(e))
u (Th - (1 - cow))
~2
\
213
2 sin ~ &
01{
‘h
7~-
‘h
- (1 + CoS(o))
(1 + COS(6))2
1
- (1 + Cos(e))
c?
I
●
-Czph-(l+cos(e))}
- (1 + Cos(e))
~2
I
‘a{7h-(1-cos(@)}
+l-e
2
CZ
+
- Cos(e))
+’-e
~z
Uph
- (1 + Cos(e)))
‘1
1
(4.21)
Using (4. 16 through 4.2 I ) the total time domain 6 component of the electric
field can be written
as
(4.22)
In figures
4.12 through 4.20 ~;(6)$
angles and a.
late tfies.
5~(0),
and ~~(6) are plotted for various
As can be seen ~fi(e) and ~ ;(6-) become more important
u a, r, h and 6 are known, one can reconstruct
at
the total ~
component at the given point.
The total radial component of the electric
field can be obtained to be
28
..
1.9
I
I
I
1
I
I
I
I
I
1.5
#I=7T/6
1.1
\
!9=7r/3
,,
.7
.
(3=7i/2
F
a
-1-1
.3
I
-.1
-.5
I
1
I
I
I
I
I
I
I
.4
-
03
-ml
w
.2
(
1
3
2
4
5
‘h
●
‘1,,
‘1
1
[
)
I
\
1-
1
I
I
.4
1’
‘,
\
.
,2
(1
-0
3
1
‘h
Figure
4.14.
Effect of @ on $;(e)
using Q = 2
4
5
1.1
.9
.7
.1
-.1
-.
3
1
o
I
1
1
I
I
2
I
I
3
1
4
‘h
4.15.
Comparison
of $\(@), ~#0) and ~~(0) for e = 7r/2$a = 1
0
.
I
I
5
o
*
1.3
1.1
.9
e)
.7
.5
co
GJ
.3
‘ye)
.1
‘.
-.
1
3
o
I
I
I
1
I
I
2
Comparison
of~~(0),
1
I
4
‘h
4.16.
I
~~(0),
—
I
5
I
I
I
1
I
I
I
I
I
1,
1.
-
ccl 1.(
.03
w
.
.*
W
.2
-.
2
‘E;(e)
E;(f))
1
iLI
I
1
I
2
1
3
1
1
4
‘h
Figure
4.17.
I
5
Comparison
=1
I
1.1
I
I
I
I
I
1
I
I
.9
.7
.5
co
CJl
m
.4
w
.3
.1
-* 1
-.
3
0
1
Figure 4.18.
.
.
t
4
h
Effect of generator
capacitance
on~~(o),
0 = ~/2
I
.4
,
w
01
-a
,2
:&l
w
o
1
2
3
4
‘h
Figure 4.19,
.
Effect of generator
capacitance cm&~(6),
.4
0 = 7r/2
5
o
.4
I
n
co
-.l
.2
0
0
1
Figure
2
4.20.
+
‘h
Effect of generator
3
capacitance”on
4
~;(e),
o = w/2
5
o
(4. 23)
As should be expected,
the radial component becomes
In a similar
late times.
more important
fashion the total @ component of the magnetic
at
field
is given by
v
H(;,t)=~~
#
o [][
–~ ‘i($)+ $ ~~(e)
(4. 24)
1
~
Both Er(;, i ) and Hd(;, t ) at a given point can easily be obtained if h, r, e
and a are known.
As an example of the procedure
discussed
above, let us consider
an
impedance loaded dipole antenna having the characteristics
(large
proposed Vm%i.cal electric
s 3.8 nF, the generator
of ATHAMAS 11
8,9
The antenna capacitance
is
dipole).
capacitance
s 4 nF, the charge equivalent height
of the antenna s 50 m while the half angle of the bicone = 40. 4~. Since the
antenna is assumed to be over a perfectly
generator
voltage is taken as 10 MV to include the effect of perfectly
ducting ground.
the electric
figures
conducting ground plane,
Using these characteristics,
4.21 through 4.26 in both time and frequency
field are plotted in
domains.
Since the
pulser is assumed to have a step function input, the high frequency
reach a steady state value.
A similar
field components in cylindrical
the shadowing,
the diffraction
the above condition the fields
the measured
results
quantities.
fields
while the late time domain fields
procedure
coordinates.
- 6) <6 ~ the formulae
e<olor(n
con-
the @ and r components of
field and the #Jcomponent of the magnetic
behave as 1/f, f being the frequency,
the
Ii should be noted that if
for the fields
from the edges,
can be used to obtain the
are not valid because of
etc.
If r >> h and o satisfies
as calculated here should compare well with
For low frequencies
are valid for all @.
38
or late times if r >> h the
9
I
i
I
1
I
I
I
2X104
1 5X104
●
1X104
~
ccl
●
5X104
o
1
f3=50”/
I
-. 5X104
I
I
.fj
0
10X1O
I
I
–c
2OX1O “
I
1
-6
3OX1O
Time (seconds)
Figure
4.21.
Ee at r=300m using an ideal. puls er and the antenna on a ground plane
40X10-6
0
loxlo
-6
-6
2OX1O
Time (seconds)
-6
3OX1O
-6
4OX1O
Er at r=300m using an ideal pulser and the antenna on a ground plane
Figure 4.22.
o
●
0
.
.
2 5X104
●
I
1
I
I
I
I
I
1
I
1. 5X104
.
5X104
o
-. 5X104
o
P
loxlo-”
I
*
2-X10-D
3oxlo-”
4OX1O
-6
-2
10
I
I
1
1
I I I III
I
I
I 1I I II
1 I I I I I 1I
I
I
1 1 I I I II
I
1 i 1I
I
I
I I I I I
1
I
I I 1 1J
L
.
N
-z
2
10
-3
U)
2!3
.
10-4
10
-5
I
104
0
i,,,,,,,,,
1 I I 11 I
105
Figure 4.24.
1
I
106
Frequency
E. at r=300m using an i
I
III
107
(hertz)
pulser and the antenna on a ground plane
w
I
108
a
0
-2
10
E
I I I I 1I I
I
I
I
1 I I I i
I
I
I I I I
I
I
1 I I I 11 I
I
I
I
I
I
I I I I III
I
I
I I ! I
I
I
I I I I 1I I
I
I
I 1 I I II,
1 I
“3
10
10-7
10
-8
104
1
II
105
Figure
4.25.
106
Frequency (hertz)
107
Er at r=300m using an ideal pulser and the antenna on a ground plane
108
10-3
I
I
I
1 I IIII
I
1 1 I 1 1i I 1
1
.’-””
I
‘+
I I 1 1I I I
1
-‘
I
I 1
I
I
I
“
9=900
,6=70”
r\x
6=50°
-4
10
10-5
o
!)~1
[
1
104
1 1 I I I 1I I
105
1
I
I I 1 I 1I I
106
Frequency
Figure
4.26.
Zofi@ at r=300m using a .
.
I
1 I I I I I 1I
107
I
I
I 1 I II
1
1
(hertz)
deal pulser and the antenna on a ground plane
●
*
v.
Conclusions
A procedure
and magnetic
has been developed
components
of an axially
which yields the near field electric
and lengthwise
symmetric
dipole if the far field components
of the same are known.
has been shown that if Ef6,
the @ component of the far field is kno~n>
all other components
fields
and magnetic
This procedure
can be determined.
components
i. e.,
of the electric
both in time and frequency
fields
can simply be obtained by frequency
with respect
including their near
domain the near field
scaling the far field com-
is equally applicable
ponents of an electric
magnetic
clear that if Hf6 , i. e.,
field terms
If the far field com-
discussed
dipole,
the
can still be used by noting that a
of an electric
dipole.
Immediately
the 6 component of the far magnetic
of the electric
can be
here.
dipole instead of an electric
in this report
dipole is a complement
all other components
data.
calculation,
dipole type source are known, the near fields
If the antenna is a magnetic
developed
the case of analytical
to measured
obtained easily by using the procedures
procedures
the far
to time.
Although we have only discussed
this procedure
it
is shown to have been applicable
In frequency
domains.
fields
In particular,
ponents while in time domain they can be obtained by integrating
*
electric
and magnetic
can be obtained by using the principle
45
fields
it is
field is know n,,
including the near
of duality.
References
1.
C. E. Baum, “Some Characteristics
of Electric and Magnetic Dipole
Antennas for Radiating Transient Pulses, 1‘ Sensor and Simulation
Notes, Note 125, January 1969.
2.
J. Van Bladel,
3.
T. T. Wu, R.W. l?. King, “The Cylindrical Antenna with Nonreflecting Resistive Loading, “ IEEE Trans. G-AP, AP-13, May 1965,
pp. 369-373.
4.
L. C. Shen, R. W. P. King, I‘The Cylindrical Antenna with Nonreflecting Resistive Loading, “ IEEE Trans. G-AP, AP-13,
November 1965, p. 998.
5.
Loaded Radiating Dipole Based on a
C. E. Baum, “Resistively
Transmission-Line
Model for the Antenna, !’ Sensor and Simulation
Notes, Note 81, April 7, 1969.
6.
Y. P. Liu, D. L. Sengupta, C. T. Tai, “On the Transient Waveforms Radiated by a Resistively
Loaded Linear Antenna, ‘1 Sensor
and Simulation Notes, Note 178, February 1973.
Electromagnetic
Fields,
McGraw
Hill,
1964.
I
D. L. Wright and J. F. Prewitt,
“Transmission
Line Model of
Radiating Dipole with Special Form of Impedance Loading, “ Sensor
and Sir.nulation Notes, Note 185, September 1973.
8.
B. K. Singaraju, C. E. Baum, J. H. Darrah, !’Design Improvements
Incorporated in ATHANIAS H (Larger VPD), “ ATHAMAS Memos,
Memo 11, January 1976.
9.
B i K. Singaraju, C. E. Baum, J. H. ?arrah,
and D. 130ssbach,
‘fUse of ATHAMAS II (Larger WF13) for Testing Aircraft in Flight, ‘~
A.THAMAS Memos, Memo 12, April 1976.
46
o