This document analyzes a circular cylindrical dipole antenna using Fourier transforms and mode matching. It presents: 1) A rigorous solution for the input impedance and current distribution of a finite circular cylindrical dipole antenna in rapidly convergent series. 2) Numerical results showing good agreement between the presented solution and experimental data for input admittance and current distribution. 3) Analysis of the effect of cylinder radius on the angular radiation pattern, which varies less than 1dB for most angles as radius increases.

1. A Circular Cylindrical Dipole Antenna
Hyo J. Eom, Jong K. Park, and Yong H. Cho
Department of Electrical Engineering
Korea Advanced Institute of Science and Technology
373-1, Kusong Dong, Yusung Gu, Taejon, Korea
Phone +82-42-869-3436 Fax +82-42-869-8036
E-mail : hjeom@ee.kaist.ac.kr
Abstract A problem of circular cylindrical dipole antenna is revisited. The Fourier
transform and mode matching is used to obtain its rigorous solution in convergent
series. Our solution is compared with other results in terms of antenna admittance
and current distribution. The angular radiation patterns of circular cylinder antenna
are shown for di erent circular cylinder radius of a dipole antenna.
Key words : Fourier-transform, dipole antenna, input impedance, radiation pattern
1 Analysis and Numerical Results
A dipole antenna is a very basic radiating element and has been extensively studied.
An in nite circular cylindrical dipole antenna was considered in 1] and their ad-
mittance characteristics were studied using a numerical approach. An in nite/ nite
cylindrical dipole antenna was also considered by using the traveling wave of current
2] and the Fourier-transform approach 3]. The purpose of present work is to revisit
a problem of a nite-length circular cylindrical dipole antenna and to obtain its rigor-
ous solution in rapidly-convergent series. We will utilize the Fourier transform/mode
1

2. matching approach which was used in analyzing other circular cylindrical-type anten-
nas 3,4]. Fig. 1 shows a center-fed dipole antenna consisting of 2h-long conducting
circular cylinders. For analytic convenience, we place two semi-in nite circular cylin-
ders at z = b1 and b3 + d3. We suppress an e i!t time factor throughout. In region
(I) (r > a), the scattered eld is
EI
z(r;z) = 1
2
Z 1
1
~Ez( )H(1)
0 ( r)e i zd (1)
where =
q
k2
0
2
; k0 = !p
0 = 2
0
, and H(1)
n (:) is the nth order Hankel function
of the rst kind. In region (II) (r < a), the applied and scattered elds are
EII
z (r;z) =
3X
n=1
1X
m=0
pn
mJ0( nmr)cosdnm(z bn) u(z bn) u(z bn dn)] (2)
where p2
0(= V
d2
) is an excitation, u( ) is a unit step function, dnm = m
dn ; nm =
q
k2
n d2
nm; kn = !p
n, and Jn(:) is the nth order Bessel function. Applying the
Fourier transform to the Ez- eld continuity, EI
z(a;z) = EII
z (a;z); gives
~Ez( )H(1)
0 ( a) =
3X
n=1
1X
m=0
pn
mJ0( nma)Gn
m( ) (3)
where
Gn
m( ) = i ( 1)mei dn 1]
2
d2
nm
ei bn (4)
Multiplying the H - eld continuity, HI(a;z) = HII(a;z), by cos l
dp (z bp) and inte-
grating, we obtain
3X
n=1
1X
m=0
h
J0( nma)I1
n
0
dn
2
J1( nma)
nm
m np ml
i
pn
m = 0 (5)
where ml is the Kronecker delta, 0 = 2, m = 1 (m = 1;2; ),
I1 = 1
2
Z 1
1
H(1)
1 ( a)
H(1)
0 ( a)
Gn
m( )Gp
l ( )d
= dn
2
H(1)
1 ( a) m np ml
H(1)
0 ( a)
j =dnm
2k0
2
a
Z 1
0
2
vf1( v) dv
2
v( 2
v d2
nm)( 2
v d2
pl)(J2
0 ( va) + N2
0 ( va)) (6)
f1( ) = ( 1)m+leijbn+dn bp dpj ( 1)meijbn+dn bpj
( 1)leijbn bp dpj + eijbn bpj (7)
2

3. v = k0(1 + iv); and v =
q
k2
0
2
v: For an in nitely-long dipole antenna (h = 1),
our solution (5) reduces to (16) in 3]. The current on a circular cylinder Iz(z) is
Iz(z) = 2 a HI(a;z)
= 4k2
0
3X
n=1
1X
m=0
pn
mJ0( nma)
sgn(z bn)
Z 1
0
v eijz bnj v ( 1)meijz bn dnj v]dv
2
v( 2
v d2
nm) J2
0 ( va) + N2
0 ( va)]
(8)
where
sgn(z) =
8
<
:
1 (z 0)
1 (z > 0)
(9)
and =
q
= 0. The far-zone radiation pattern is
HI( )
3X
n=1
1X
m=0
pn
mJ0( nma) Gn
m( k0 cos )
sin H(1)
0 (k0asin )
(10)
where z = Rcos ; r = Rsin . Fig. 2 shows the input admittance versus the normal-
ized antenna length, con rming that our solution agrees well with the experimental
data in 2]. We use m = 15 for n = 1 and 3 in (5) and d3 = d1 = 0 to achieve
numerical convergence. We also con rmed that our solution (8) agreed with Fig. 4 in
2]. It is interesting to check the e ect of two semi-in nite circular cylinders lying over
z > b3 + d3 and z < b1 on antenna parameters. When d3(= d1) varies from 0:5 0 to
2 0, the input admittance remains almost unchanged, while the current distribution
near the end of dipole antenna (z b3;b1 +d1) increases by 5%. Our additional com-
putation reveals that the current distribution over the semi-in nite cylinder (z < b1)
is less than 1% of that over the antenna (b1 + d1 < z < 0). Fig. 3 illustrates the
behaviors of the antenna radiation pattern given by (10) for di erent cylinder radius.
As the radius increases from 0:007 0 to 0:07 0, a variation in the main beam pattern
is within 1dB for 63 < < 117 . Near = 0 and 180 , the radiation pattern blows
up due to the presence of two semi-in nite cylinders placed in the end- re direction.
In order to eliminate the e ect of two semi-circular cylinders on the radiation pattern,
3

4. we approximately evaluate the far-zone eld by taking the Fourier transform of the
current distribution over 2h-long dipole antenna.
HI( )
hZ 0
b1+d1
Iz(z)e ik0zcos
dz +
Z b3
d2
Iz(z)e ik0zcos
dz
i
sin (11)
Fig. 3 illustrates that the radiation power based on (11) reduces to zero at = 0
and 180 . Note that the di erence between (10) and (11) is very little except for
near end- re direction. In conclusion, our rigorous solution (5) is simple to use and
accurate enough in most practical cases dealing with a nite dipole antenna.
2 Acknowledgment
This work was supported by grant No. 1999-1-302-011-3 from the interdisciplinary
research program of KOSEF.
4

5. 3 Figure Captions
Figure 1 : Geometry of the dipole antenna.
Figure 2 : Input admittance versus antenna length h (a = 100d2 = 0:007 0;d1 =
d3 = 0).
Figure 3 : Angular radiation pattern versus cylinder radius a (d2 = 0:00007 0;d1 =
d3 = 0;h = 0:5 0).
5

6. References
1] E.K. Miller, "Admittance dependance of the in nite cylindrical antennas upon
exciting gap thickness", Radio Sci., vol. 2 (New Series), no. 12, pp. 1431-1435,
Dec. 1967
2] L. Shen, T.T. Wu, and R.W.P. King, "A simple formula of current in dipole
antennas" IEEE Trans. Antennas Propagat., vol. 16, no. 5, pp. 542-547, Sept. 1968
3] S.A. Saoudy and M. Hamid "Analysis of an arbitrarily excited-loaded dipole an-
tenna with a derived expression for the eld in the feed gap," Can. J. Phys., vol.
66, pp. 680-691, 1988
4] J.K. Park and H.J. Eom, Fourier transform analysis of dielectric- lled edge-slot
antenna," Radio Sci., vol. 32, no. 6, pp. 2149-2154, Nov./Dec. 1997, Correction to
Fourier transform analysis of dielectric- lled edge-slot antenna," vol. 33, no. 3, p.
631, May-June 1998
6

7. b = 02
b1
Region (I)
z
r
µ, ε0
r
b +d1 1
b +d2 2
b +d3 3
b3
Region (II)
µ, ε3
Region (II)
µ, ε2
Region (II)
µ, ε1
PEC
PEC
PEC
PEC
2ah
h
Figure 1: Geometry of the dipole antenna.
7

8. inputadmittance[m]
Ω
antenna length, λ0h/
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
−6
−4
−2
0
2
4
6
8
10
12
14
16
18
-6
0
6
12
18
0.3 0.5 0.70.1
susceptance
conductance
experiment [2]o
theory [2]x
Figure 2: Input admittance versus antenna length h (a = 100d2 = 0:007 0;d1 = d3 =
0).
8

9. normalizedradiationpower
[ degree ]θ
0 20 40 60 80 100 120 140 160 180
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 20 60 100 140 180
0.2
0.4
0.6
0.8
1
a = 0.07
a = 0.007
power by (10)
λ0
λ0
a = 0.07
a = 0.007
power by (11)
λ0
λ0
x
o
Figure 3: Angular radiation pattern versus cylinder radius a (d2 = 0:00007 0;d1 =
d3 = 0;h = 0:5 0).
9