Download The Dipole

The Dipole
A dipole can be thought of as a two wire transmission line in which the two
conductors are folded out at right angles to each other.
Dipole
Length, l
Transmission line (feed)
match
Free space
This is a useful way to view the dipole, as the theory of transmission lines can
be applied to understand how it works. The dipole section provides a ‘match’
between the ‘feed’ line and ‘free space’.
For any antenna to launch a signal, the field must be made to ‘fringe’ from the
feed line into the space around the antenna.
Considering how the field associated with the feed behaves at the dipole will
show that as charges move on the surface, the field fringes into the space
around the dipole.
+
-
Then looking at the way the field fringes from the dipole, and thinking of it as a
section of transmission line, shows that there will be no radiation along the
axis of the structure. This is because the tips of the dipole represent an open
circuit. Picturing the dipole folded back to be part of the feed line will make
this idea clearer.
The current and voltage distribution along the dipole are similar to those for a
section of transmission line terminated in an open circuit, where power is
reflected. The resulting standing wave pattern on the dipole puts a voltage
maximum at the tips, where the current is close to zero. The impedance at the
feed point will depend upon the distance from the open circuit (ie the dipole
half-length). The main difference between the impedance seen at the feed
point of the dipole and that which would be seen on a section of line
terminated in an open circuit is that power is radiated from the dipole and
hence there will be an associated ‘real’ part of the impedance.
Open circuit
In general, this real part, or resistance, consists of the RADIATION
RESISTANCE (Rrad) and the LOSS RESISTANCE (Rloss). The radiation
resistance is a ‘fictitious’ resistance that would dissipate the same power as
the antenna radiates.
When the dipole is half a wavelength long electrically, the input impedance
will be purely real and equal to 73 (if there are no losses). The feed point is
then at a ‘series resonance’ in the transmission line equivalent circuit, a
quarter of a wavelength back from the open circuit termination. The equivalent
circuit is:
L
C
RLoss Rrad
Prad=I2Rrad
In this model, the inductance and capacitance are determined by the dipole
length and radius. The longer the dipole, the larger the values of L and C
resulting in a lower resonant frequency. The conductor radius controls the Q
and hence the ratio of L to C, larger radius giving lower Q. The loss resistance
is primarily due to the resistance of the conductor, which will reduce as the
radius increases.
In practice, the physical length of the dipole must be reduced to approximately
95% of half a wavelength to appear electrically half a wavelength long.
The radiation pattern is ‘OMNIDIRECTIONAL’, in other words the gain is
constant throughout one of the principal planes. For the dipole, the gain is
constant throughout the H-plane, which is perpendicular to the dipole axis.
The gain in the E-Plane varies according to a ‘figure of eight’ pattern.
E-plane
H-plane
E-Plane
H-Plane
G=2.1dB
G=2.1dB
The radiation pattern for the dipole is of a similar form for lengths from close
to zero up to one wavelength, when the three dimensional ‘doughnut’ pattern
begins to break into extra lobes. This can be investigated using AERIAL1.
The input impedance of the dipole changes dramatically over this range, from
a high capacitive reactance, through resonance to an inductive reactance and
through resonance again.
The Hertzian Dipole
A Hertzian dipole is a vanishingly short dipole. In practice, a dipole which is
very short (length</50) is a good approximation to this. Referring to the
transmission line analogy will show that the input impedance of a very short
dipole has a high capacitive reactance and a small radiation resistance. For
the Hertzian dipole, these are given by:
 l 
Rrad  80 2  
 
2
where l = length
and
and
  l  
ln  2a   1
  
X a  120 
 l 
tan  

a = radius.
directivity = 1.5 (compared to 1.643 for a half wave dipole)
effective aperture = 0.122 (compared to 0.132 for half wave)
General Dipole far field components
In the far field for a dipole of length l, the electric and magnetic field
components are given by:
H  j
jt
j
I oe e
2r
E  H
2r

  l

 l  
 cos  cos   cos   

 
 
sin 



