Английская Википедия:Dipole field strength in free space

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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

<math>\mbox{p} = \frac{N}{4\cdot \pi \cdot d^2}</math>

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

<math>\mbox{p} = \frac{E^2}{Z}</math>

The following relation is obtained by equating the two,

<math> \frac{N}{4\cdot \pi \cdot d^2}= \frac{E^2}{Z}</math>

or by rearranging the terms

<math> \mbox{E} =\frac{\sqrt{N} \cdot\sqrt{Z}}{2\cdot \sqrt{\pi}\cdot d}</math>

Numerical values

Impedance of free space is roughly <math> 120 \cdot \pi</math>

Since a half wave dipole is used, its gain over an isotropic antenna (<math>\mbox{2.15 dBi} = 1.64</math> ) should also be taken into consideration,

<math> \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}</math> 

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 <math> \sqrt{1000}</math>. In this case,

<math>\mbox{E} \approx 222\cdot\frac{\sqrt{N}}{d} </math>

See also

• Antennas
• Effective radiated power
• Electric field
• Field strength meter
• Radio propagation model