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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 is a term in telecommunications. It 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]

$\mbox\left\{p\right\} = \frac\left\{N\right\}\left\{4\cdot \pi \cdot d^2\right\}$

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

$\mbox\left\{p\right\} = \frac\left\{E^2\right\}\left\{R\right\}$

The following relation is obtained by equating the two,

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

or by rearranging the terms

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

## Numerical values

Impedance of free space is $120 \cdot \pi$

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

$\mbox\left\{E\right\} =\frac\left\{\sqrt\left\{1.64 \cdot N\right\} \cdot \sqrt\left\{ 120\cdot \pi\right\}\right\}\left\{2\cdot \sqrt\left\{\pi\right\}\cdot d\right\}$
\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 $\sqrt\left\{1000\right\}$.[2] In this case,

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

## References and notes

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