Shortest range length to measure the total radiated power

Total radiated power (TRP) is a key performance metric in over‐the‐air (OTA) testing of wireless devices. The TRP is evaluated by integration of the power density over a surface enclosing the device under test (DUT). In principle, this total power flow shall be independent from the surface. However, the power received at the instrumentation in a given polarisation typically relates to the intensity of the corresponding component of the impinging E ‐field. In the far‐field, the E ‐field magnitude and power density are straightforwardly related, but not in the near‐field. Therefore, the measured TRP generally depends on the scanned surface and test distance. This study introduces a closed‐form expression for the measured power integrated over a surface surrounding the DUT, including the influence of the probe. The formulas are first applied to simulated spherical testing systems, where three different measurement probes coupled to a DUT model radiating at 28 GHz. Results are then validated experimentally in two spherical scanners, using physical samples of one of the modelled probes and the DUT. Both numerical and experimental results confirm the Fraunhofer distance as a lower bound range length for OTA TRP evaluation with negligible influence from the measurement probe.