Power levels and density

All electronic devices have some RF emissions. The measure of the strength of these signals is the power density, which is the amount of RF power (measured in milliwatts (mW)) hitting a particular surface area (measured in square centimeters (cm2)). The power density of a signal can be calculated using the output power level (for example, 250 mW), and the distance from the transmitter. Higher power density numbers equate to stronger signals, a closer proximity to the signal, or a combination of these two factors.

Calculate the power density using the following formula:

Power density = (TxPwr ∙ AntGain) ∕ (4∙π∙Distance²) mW/cm² where:
TxPwr = The radio frequency transmits power input to the antenna (in milliwatts)
AntGain = The power gain of the antenna (unit less)
π = 3.1417 (unit less)
Distance = Distance from the transmitter (in centimeters)

Honeywell smart electricity meters use radios that operate in the 900-MHz ISM band using Frequency Hopping Spread Spectrum (FHSS) technology and they have a maximum transmit power (TxPwr) of 250 mW (EnergyAxis Gatekeeper) and 1000 mW (SynergyNet Router).  The radiation pattern of a device depends on the antenna and on surrounding objects. When installed in an electrical socket, the energy radiated backwards through the socket into the home would be significantly less due to the metal socket.

The metal socket reduces the energy transmitted into the residence but redirects the energy out the front of the meter. As measured as part of the FCC certification process, the maximum antenna gain for a meter in a metal socket was 5.64 dBi, which equates to a gain of 3.66. For calculation purposes, we will use a distance of two feet (61 cm). However, typically, the distance between an electricity meter and a person would be far greater than two feet.

Using the numbers in the previous paragraph, we can calculate a worst-case theoretical power density for our 250-mW smart meter.

Power density = (250∙3.66) / (4∙π∙(61)2) = 0.02 mW/cm²

More typical numbers, especially for someone in the residence of the meter in question, would be an antenna gain of 0.5 and a distance of more than 10 feet. Using these numbers, a more realistic power density value would be:

Power density = (250∙0.5) / (4∙π∙(305) 2) = 0.0001 mW/cm²