DIPOLE ANTENNAS

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radiation is independent of  (rotationally symmetric about
the z axis). Dipole antennas and arrays of dipoles are commonly
used for high-frequency (HF) and ultrahigh-frequency
(UHF) communications, TV, and FM broadcasting, and as
electric field probes. This article will describe the basic nature
and applications of dipole antennas and some of their variations
such as biconical and bowtie antennas, slot dipoles,
folded dipoles, sleeve dipoles, and shunt-fed dipoles. The commonly
used broadband log-periodic and Yagi–Uda dipole
arrays are also discussed.
INFINITESIMAL DIPOLE (HERTZIAN DIPOLE)
An infinitesimal dipole (L  ) is a small element of a linear
dipole that is assumed to be short enough that the current
(I) can be assumed to be constant along its length L. It is also
called a Hertzian dipole. The electric and magnetic field components
of this dipole are (1)
H = 1
4π
IL sin θ e−jβ0 r
jβ0
r
+ 1
r 2 φ (1)
E = jη0IL
2πβ0
cos θ
jβ0
r 2
+ 1
r 3 e−jβ0 rr
− jη0IL
4πβ0
sin θ −β2
0
r
+ jβ0
r 2
+ 1
r 3 e−jβ0 rθ
(2)
where
0
(0/0)1/2 is the intrinsic impedance (
377 )
for free space, and
0
(00)1/2 is the propagation constant
(
/c, where c is the speed of light). The fields
decay rapidly (1/r3 variation) very near the antenna, and
less rapidly (1/r variation) farther away. The fields with
terms 1/r2 and 1/r3 (the induction terms) provide energy
that is stored near the antenna. The fields with 1/r variation
(the radiation terms) represent actual energy propagation
away from the antenna. The distance away from the
DIPOLE ANTENNAS
antenna where the induction and radiation terms are equal
is d
/2. When d  /2, one is in the near field of
A dipole antenna is most commonly a linear metallic wire or the antenna, and the induction terms dominate. When d

rod with a feed point at the center as shown in Fig. 1. Most /2, one is in the far field, and the radiation terms domioften,
this type of antenna has two symmetrical, aligned, ra- nate. In the far field, the wave propagation is in the transdiating
arms. Because of the symmetry of the antenna rela- verse electromagnetic (TEM) mode, which is characteristic
tive to the xy plane containing the feed point, the resultant of far-field radiation from finite structures.
J. Webster (ed.), Wiley Encyclopedia of Electrical and Electronics Engineering. Copyright # 1999 John Wiley & Sons, Inc.
576 DIPOLE ANTENNAS
these elements. The resultant fields far from the antenna at
a distance r0 are
E = jηI(0)
2πr sin kh
F(θ )e j(ωt−kr)θ (6)
and
H = jI(0)
2πr sin kh
F(θ )e j(ωt−kr)φ (7)
x
y
z
where

(/)1/2, and where the  dependence F() of the
Figure 2. Radiation pattern for an infinitesimal (or Hertzian) dipole. radiated fields is called the pattern factor and is given by the
following:
The far-zone radiated fields of the Hertzian dipole follow
from (1) and (2) by retaining the 1/r varying terms:
F(θ ) = cos(kh cos θ) − cos kh
sin θ
(8)
H = The radiated power density P() is given by j
4πr
IL sin θ e−jβ0 rφ (3)
P(θ ) = E ·E∗
2η
= ηI 2(0)
8π2r2 sin2 kh
F2E = (θ ) (9) jη0
4πr
IL sin θ e−jβ0 rθ (4)
As expected for TEM wave propagation, the E and H fields Using


0
120, this can also be expressed in terms of
are perpendicular to each other and to the outward propaga- the total radiated power W [
I2(0)Ra/2] and the feedpoint
tion in the r direction. Also, the ratio E resistance Ra as follows:  /H

0
(0/0)1/2,
which is the intrinsic impedance of free space.
The radiation pattern of this Hertzian dipole is shown in
Fig. 2, and exhibits the classical symmetry expected of dipole P(θ ) = 30
πr2
W
Ra
F2(θ )
sin2 kh
(10)
antennas, being both independent of  and symmetric about
the xy plane through the center (feedpoint) of the dipole. The
magnitude of the total radiated power is Prad
40 2I2
0 (L/ )2.
From Eqs. (3) and (4) it is interesting to note that even for
this constant-current infinitesimal dipole, the radiated power
density is proportional to sin2 . Hence, it is maximum for

90 (i.e. in the xy plane normal to the orientation of the
dipole) and zero for the directions along the length of the dipole
(
0 and 180). The latter property for zero radiation
along the length of the dipole will be seen for all linear dipoles
regardless of length. It follows from the fact that a linear antenna
may be considered as composed of infinitesimal dipoles
do not create E and H fields or radiated power density for the

0 and 180 directions.
LINEAR DIPOLE ANTENNAS
The geometry of a linear dipole antenna of length 2h is shown
in Fig. 1. The current distribution is sinusoidal and is approximately
given by
I(z

) = I(0)
sin kh
sin k(h − |z
|) for − h < z

< h (5)
where I(0) is the current at the feedpoint of the antenna,
h
L/2 is the half length of the antenna, and k
()1/2 is
the propagation constant in the material surrounding the dipole.
The current distributions for several lengths of dipole
antennas are shown in Fig. 3.
h = 3 /4
h = λ /2
h = λ /4
λ
The electric and magnetic fields around the dipole are calculated
by modeling the antenna as a series of Hertzian or Figure 3. Current distributions and associated radiation patterns
elemental dipoles and integrating the fields from each of for several different lengths of dipole antennas.
DIPOLE ANTENNAS 577
Table 1. Wire Lengths Required to Produce a Resonant
Half-Wave Dipole for a Wire Diameter of 2a and a Length L
Shortening Resonant Dipole
Length-to-Diameter Required Length, Thickness
Ratio, L/(2a) (%) L Class
5000 2 0.49 Very thin
50 5 0.475 Thin
10 9 0.455 Thick
1
3
5
7
9
11
13
15
330 350
a = 0.0001 m
a = 0.005 m
310
Z0 = 72 Ω
2a
290
f (MHz)
250 270
VSWR
0.5 m
The normalized radiation patterns are shown in Fig. 3(b) for
several different lengths of dipoles. Figure 4. VSWR of a dipole antenna as a function of frequency and
The directivity of a dipole antenna related to the maximum wire thickness (from Ref. 5).
power density that an antenna can create at a distance r0 is
given by
D = the linear dipole of the same length (see Fig. 3) except that Pmax
P0
= F2(θ )max
12

π
0 F2(θ ) sin θ dθ
= 120
Ra
F2(θ )max
sin2 kh
(11)
the orientations of E and H are interchanged. Also, the feedpoint
impedance Zs of a slot antenna is related to that of the
where P0
W/(4r2
0) is the isotropic power density that would dual linear antenna by the following equation:
have been created at the field point if the antenna had a directivity
of one and radiated isotropically for all angles
(clearly a mathematical possibility though not physically realizable).
Zs = η2
4Za
(12)
The input resistance Ra of a center-fed dipole antenna of
length L
2h is twice that of an end-fed monopole antenna
of length h. This may therefore be obtained by using the where Za is the impedance of the dual linear antenna.
graphs given in the related encyclopedia article on MONOPOLE
ANTENNAS.
The ohmic losses of a dipole antenna [given by
BICONICAL DIPOLES
I2(0)Rohmic/2] are quite small, particularly for h/
0.1. The
resultant antenna radiation efficiencies [given by Ra/(Ra  A biconical dipole, as shown in Fig. 5(a) is commonly used for
Rohmic)] are on the order of 90% to 99%. broadband applications when the flare angle  is between 30
Two effects make physical dipoles act slightly different and 60. The exact flare angle is not critical, so it is generally
than ideal dipoles. The first is that realistic antennas have chosen so that the impedance of the dipole nearly matches
some finite thickness, and the second is that the ends of the the impedance of the feeder line to which it is connected. The
dipole couple capacitively to air, effectively making the dipole impedance of the biconical dipole varies as a function of waveelectrically
longer by 2% to 9% than its physical length. For length and flare angle, with a relatively flat impedance rea
half-wave dipole (L
2h
/2), for instance, the physical sponse for wide flare angles. Hence the broadband nature of
length must be slightly shortened in order to create a reso- this antenna.
nant-length antenna (Xa
0). Table 1 shows the wire lengths Some variations of this method of using flaring to increase
required to produce a resonant half-wave dipole. This short- bandwidth are the flat bowtie antenna (which may be built on
ening varies from 2% to 9%, depending on the thickness of a printed circuit board) and the wire version of the biconical
the dipole. antenna shown in Figs. 5(b) and ©, respectively.
Since a dipole antenna is a physically resonant structure,
its feedpoint impedance (particularly the reactance Xa) varies
greatly with frequency. Thus, these antennas have a fairly
narrow bandwidth. The voltage standing-wave ratio (VSWR)
of a dipole antenna as a function of frequency and wire thickness
is shown in Fig. 4 for an antenna that would be halfwave
resonant at 300 MHz. Using a criterion for ‘‘usable
bandwidth’’ that the measured VSWR should be less than
2 : 1, this antenna has bandwidths of 310  262
48 MHz for
the thicker wire and 304  280
24 MHz for the thinner
wire. As fractions of the design frequency (300 MHz), the
bandwidths are 16% and 8%, respectively (2).
SLOT DIPOLE
(a) (b) ©
The slot dipole antenna is dual to the linear dipole antenna. Figure 5. Biconical dipole antenna and variations: (a) biconical diThe
radiation pattern of a slot antenna is identical to that of pole, (b) flat bowtie, © wire version of biconical dipole.
578 DIPOLE ANTENNAS
Figure 6. Folded dipole antenna.
FOLDED DIPOLE ANTENNAS
A folded dipole antenna is shown in Fig. 6. The dipole is created
by joining two cylindrical dipoles at the ends and driving
the entire structure by a transmission line (often a two-wire
transmission line) at the center of one arm as shown. The
feedpoint impedance of a folded dipole of two identical-diameter
arms is four times as large as for an unfolded dipole of
the same length. This can actually be advantageous, since the (a) (b)
feedpoint resistance may now be comparable to the character- Figure 8. Collinearly mounted vertical dipoles for VHF and UHF
istic impedance Z0 of the transmission or feeder line. The re- radio and TV broadcasting: (a) pole-mounted array of collinear diactance
of the antenna may easily be compensated by using a poles, (b) vertical dipoles spaced around a pole.
lumped element with a reactance that is the negative of the
reactance at the terminals of the folded dipole antenna or else
by using a foreshortened antenna length to resonant length
arms so that Xa
0 (see Table 1).