Dipole field strength in free space

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]\displaystyle{ \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]\displaystyle{ \mbox{p} = \frac{E^2}{Z} }[/math]

The following relation is obtained by equating the two,

[math]\displaystyle{ \frac{N}{4\cdot \pi \cdot d^2}= \frac{E^2}{Z} }[/math]

or by rearranging the terms

[math]\displaystyle{ \mbox{E} =\frac{\sqrt{N} \cdot\sqrt{Z}}{2\cdot \sqrt{\pi}\cdot d} }[/math]

Numerical values

Impedance of free space is roughly [math]\displaystyle{ 120 \cdot \pi }[/math]

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

[math]\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} }[/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]\displaystyle{ \sqrt{1000} }[/math]. In this case,

[math]\displaystyle{ \mbox{E} \approx 222\cdot\frac{\sqrt{N}}{d} }[/math]

See also

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