Field strength formula

July 24, 2017

Magnetic Field Strength

When a transmitter is connected to an antenna and radiates power, it's often interesting to know what is the electromagnetic field strength at a given distance. The following diagram summarizes the problem:

A transmitter of power Pt is connected to an antenna of gain that radiates in the surrounding space. We are interested to know the intensity of the field , and at the distance from the transmitting antenna.

This measurement must be done in the far field region, otherwise the formula used here are not valid. This means that the measurement must be taken at an adequate minimum distance from the transmitting antenna, so that we can neglect its shape and suppose that we have a nice and spherical wave. This calculator is not intended for near field analysis.

Some theory

The power provided by the transmitter is radiated by the antenna. As the waves leave the antenna, they spread on the surface of spheres of increasing radius as they travel away. In a very similar way, when dropping a stone in a pond, circular ripples leave the point of impact and become larger and larger in diameter as they travel away.

Wave-fronts can be approximated with spheres only if we are far enough from the antenna that originated them, so that its shape can be neglected and considered a point source. For this reason, we can only consider the far field region.

As the spheres become bigger and bigger, their surface increases with the square of the distance d2. The total amount of power carried by the wave doesn't change (without losses), so the same power spreads on a larger and larger surface, explaining the 1/d2 dependence of the power density of the wave and finally of the received power.

Furthermore, this simple model doesn't take into account any effect of the ground: the transmitting antenna needs to radiate in free space and to have line of sight with the measuring point. Antennas that use the ground as part of them, like vertical monopoles, cannot be calculated reliably. Ground can also reflect waves and reflections are not take into account, only the straight path is considered. The effect of the ground is less important at microwave frequencies, since it tends to absorb energy instead of reflecting it back and since the distance to the ground in terms of wavelength is much larger. In other words, in most cases, the model is ok for wavelengths shorter than a few meters, say frequencies from the VHF band and up.

This being said, with our simple spherical waves model, calculating the power density at a given distance is quite straightforward and depends mainly on the geometrical considerations above, as stated by the following equation:

Calculating the Magnetic Field Strength on the Axis of a
Calculating the Magnetic Field Strength on the Axis of a ...
Magnetic Field Strength Equation
Magnetic Field Strength Equation

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