How to Calculate Antenna Power Density (Poynting vector)

The calculation of Poynting vector (energy flux density of an EM field) is the finest example of a practical application of Maxwell's equations, and is often performed by RF / EMC engineers to calculate the magnetic field strength (H), the electric field strength (E), and the magnetic flux density (B) of active antennas. This type of analysis is necessary for evaluation of EM Field (EMF) exposure from IoT products that use radio access technologies such as 5G, LTE, Bluetooth, etc. The ICNIRP guidelines provide the limits for EMF exposure in public areas as well as in areas with restricted access. When the user head or body is not expected to be within 20cm from the transmitting antenna during its operational use (i.e. for longer than 6 minutes as per EN 50665), then a simple calculation based on Maxwell's equations is sufficient to demostrate the product compliance. In other cases (i.e. when the user is expected to be within 20cm from the transmitting antenna), a Specific Absporption Rate (SAR) or Absorbed Power Density (APD) testing will apply instead, depending on operational frequency.
In this video, I demonstrate how to perform the calculation of antenna power densitiy with a conventional LTE transmitter (Telit modem LE910C4) and a low gain LTE antenna (Abracon 698-960/1710-2690). As will be shown in the video, the calculation results are significantly below the ICNIRP limits, and therefore, the product compliance has been successfully proven.

ps. The conversion to dBW from dBm is rather unneccessary on the second look and can be skipped, however, I decided to keep it for completeness.

The LTE (4G) modem used in this video:
https://www.telit.com/devices/le910cx...

Antenna datasheet:
https://abracon.com/datasheets/AFAC58...