Full resolution (JPEG) - On this page / på denna sida - 1958, H. 7 - The Quarter-Wave Dipole, by Bengt Josephson
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Fig. 7.
Twin-line shortened
dipole.
r- v
z*
h - kit
V’lZi,
(to)
(11)
where
Zfi = radiation impedance of the antenna conductors
connected in parallel
Zs — input impedance between the antenna
conductors
Equations (8) — (11) give the antenna impedance
4 Zi, Zg + Zs, (4 Zd + k Zb)
4 Zb + 4 Zd + (2 - k)Z., { ~>
lf Zi, or Zs have resistance components this results
in a power loss. It is then of interest to determine the
efficiency of the antenna. The input power is
P.n=~’Rc{z}
and the power loss
l/’2 11/ _
Pf= wRc[ i + Hcw
AV = JZJi
Pin Rc{Z}
1 V
T
Re[Zb)
Zb"’
+
V - V’ - Re[Zs)
W -
V
(15)
(14)
(15)
Hence the efficiency
n = 1 - pft Pin (lti)
The voltage ratios in (15) arc calculated from
equations (8)—(11).
The formulas (12) and (15) allow an investigation
of the possibilities of broadbanding a folded dipole
with the aid of load impedances located as in
figure 12.
Symmetrical Antenna
In the case examined below the antenna consists
of two equal wires, and thus k = 1. The general and
rather complicated formulas may then be simplified
with the aid of the following substitutions:
in = 2 Zb + Zs{1
ii =■ |2 Zb + 4 Zd\
j) = |4 Za — Z, |s
(17)
(18)
(19)
I sing the notations Z = R + jX, Z[> = Ru + jXt,, and
so on, the following expressions for impedance and
efficiency of the symmetrical antenna have been
deduced:
R
4 in Ih + ii R, + p R/,
2 in ’+ 2 ii — i>
4 ni Xd + ii + p Xb
2 ni + 2 ii — p
1
, ~n R~s~+P Rh
(20)
(21)
(22)
4 ni Rd
These formulas are suitable for numerical
calculations.
To determine the radiation impedance Zj, the
radius of a round wire is calculated, which is
equivalent to the two antenna wires connected in parallel.
According to Sclielkunoff this radius is I ad, where
(I is the centre distance and a the radius of the wires.
Then Zj as a function of frequency is given in the
curves of Hallen1 or Brown and Woodward’.
Resistance-loaded Short-wave Antenna
There are great difficulties in designing broadband
antennas for the short-wave range, which do not
take up excessive space. An antenna which seems
attractive is described by Williams3. It is a folded
dipole loaded with a resistance 2 Z^ = GOO ohms, and
Fig. 8. Impedance of the antenna in figure 7, normalized
to 300 ohms. A capacitance of 15 pF is placed over
the feeding line 1.7 m from the feed point.
1 98 ELTEKN I K 1958
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