Dipole field strength in free space , in telecommunications , is the electric field strength caused by a half wave dipole under ideal conditions. The actual field strength in terrestrial environments is calculated by empirical formulas based on this field strength.
Power density [ edit ]
Let N be the effective power radiated from an isotropic antenna and p be the power density at a distance d from this source[1]
p
=
N
4
⋅
π
⋅
d
2
{\displaystyle {\mbox{p}}={\frac {N}{4\cdot \pi \cdot d^{2}}}}
Power density is also defined in terms of electrical field strength;
Let E be the electrical field and Z be the impedance of the free space
p
=
E
2
Z
{\displaystyle {\mbox{p}}={\frac {E^{2}}{Z}}}
The following relation is obtained by equating the two,
N
4
⋅
π
⋅
d
2
=
E
2
Z
{\displaystyle {\frac {N}{4\cdot \pi \cdot d^{2}}}={\frac {E^{2}}{Z}}}
or by rearranging the terms
E
=
N
⋅
Z
2
⋅
π
⋅
d
{\displaystyle {\mbox{E}}={\frac {{\sqrt {N}}\cdot {\sqrt {Z}}}{2\cdot {\sqrt {\pi }}\cdot d}}}
Numerical values [ edit ]
Impedance of free space is roughly
120
⋅
π
{\displaystyle 120\cdot \pi }
Since a half wave dipole is used, its gain over an isotropic antenna (
2.15 dBi
=
1.64
{\displaystyle {\mbox{2.15 dBi}}=1.64}
) should also be taken into consideration,
E
=
1.64
⋅
N
⋅
120
⋅
π
2
⋅
π
⋅
d
≈
7
⋅
N
d
{\displaystyle {\mbox{E}}={\frac {{\sqrt {1.64\cdot N}}\cdot {\sqrt {120\cdot \pi }}}{2\cdot {\sqrt {\pi }}\cdot d}}\approx 7\cdot {\frac {\sqrt {N}}{d}}}
In this equation SI units are used.
Expressing the same equation in:
kW instead of W in power ,
km instead of m in distance and
mV/m instead of V/m in electric field
is equivalent to multiplying the expression on the right by
1000
{\displaystyle {\sqrt {1000}}}
.[2] In this case,
E
≈
222
⋅
N
d
{\displaystyle {\mbox{E}}\approx 222\cdot {\frac {\sqrt {N}}{d}}}
See also [ edit ]
References [ edit ]
^ Reference data for radio Engineers , Howard W.Sams co,Indianapolis, 1956, 27-7
^ K.H.Kaltbeitzer: Site selection , EBU Techhnical Monograph 3104,Bruxelles,1965, p 30
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