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# Field strength in free space

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 Title: Field strength in free space Author: World Heritage Encyclopedia Language: English Subject: Line-of-sight propagation Collection: Publisher: World Heritage Encyclopedia Publication Date:

### Field strength in free space

Field strength in free space, in telecommunications, is the 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]

\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 R be the impedance of the free space

\mbox{p} = \frac{E^2}{R}

The following relation is obtained by equating the two,

\frac{N}{4\cdot \pi \cdot d^2}= \frac{E^2}{R}

or by rearranging the terms

\mbox{E} =\frac{\sqrt{N} \cdot\sqrt{R}}{2\cdot \sqrt{\pi}\cdot d}

## Numerical values

Impedance of free space is 120 \cdot \pi

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

\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

is equivalent to multiplying the expression on the right by \sqrt{1000}.[2] In this case,

\mbox{E} \approx 222\cdot\frac{\sqrt{N}}{d}

## References and notes

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
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