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

$\text{p}=\frac{N}{4\cdot \pi \cdot d^2}$

Power density is also defined in terms of electrical field strength;

Let E be the electrical field and Z be the impedance of the free space

$\text{p}=\frac{E^2}{Z}$

The following relation is obtained by equating the two,

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

or by rearranging the terms

$\text{E}=\frac{\sqrt{N}\cdot \sqrt{Z}}{2\cdot \sqrt{\pi }\cdot d}$

Numerical values

Impedance of free space is roughly $120\pi \Omega$

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

$\text{E}=\frac{\sqrt{1.64\cdot N}\cdot \sqrt{120\cdot \pi }}{2\cdot \sqrt{\pi }\cdot d}\approx 7\cdot \frac{\sqrt{N}}{d}$

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

mV/m instead of V/m in electric field

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

$\text{E}\approx 222\cdot \frac{\sqrt{N}}{d}$

See also

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