Dipole field strength in free space explained

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

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 ⋅ \pi ⋅ 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)

The following relation is obtained by equating the two,

(N)/(4 ⋅ \pi ⋅ d ^{2}) = (E ^{2})/(Z)

or by rearranging the terms

E = (\sqrt{N)/(⋅ \sqrt{Z}}{ 2 ⋅) \sqrt{\pi} ⋅ d}

Numerical values

Impedance of free space is roughly

120 \pi ~ \Omega

Since a half wave dipole is used, its gain over an isotropic antenna (

2.15dBi = 1 . 64 ) should also be taken into consideration,E = (\sqrt{ 1 . 64 ⋅ N)/(⋅) \sqrt{ 120 ⋅ \pi}}{ 2 ⋅ \sqrt{\pi} ⋅ d} ≈ 7 ⋅ (\sqrt{N)/() }

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

\sqrt{ 1000 } .^[2] In this case,E ≈ 222 ⋅ (\sqrt{N)/() }

See also

• Antenna (radio)
• Effective radiated power
• Electric field
• Field strength meter
• Radio propagation model

References

1. Reference data for radio Engineers, Howard W.Sams co, Indianapolis, 1956, 27-7
2. K.H.Kaltbeitzer: Site selection, EBU Techhnical Monograph 3104, Bruxelles, 1965, p 30