# On the measurement errors in SAR supervision introduced by directional couplers

## TL;DR

This paper introduces a framework to calculate errors in SAR supervision caused by directional couplers.

## Contribution

A novel mathematical framework is proposed to quantify SAR calculation errors due to directional couplers.

## Key findings

- SAR calculation errors depend on directional coupler reference plane position and array S-parameters.
- Directional couplers with over 40 dB directivity are needed to keep SAR errors below 5%.
- The framework can calculate a safety factor for SAR inaccuracies and adapt to other measurements.

## Abstract

This study proposes a framework for determining the calculation error in online SAR supervision introduced by directional couplers.

A mathematical framework is introduced showing how the error in the measured excitation vector compared to the actual excitation vector can be rewritten as a new set of virtual observation points (VOPs). By comparing the new set of VOPs to the original VOPs through an optimization, the maximum underestimation of SAR can be calculated. The framework is then applied to five different RF arrays.

The results show that the error in SAR calculation is very dependent on the position of the reference plane of the directional coupler measurements and the S-parameters of the array. To have an error of less than 5%, directional couplers with a directivity better than 40 dB are necessary for the worst case of the investigated arrays.

The framework presented in this paper provides an approach for calculating a safety factor to account for the inaccuracies introduced by directional coupler measurements in online SAR supervision. The framework can also be adapted to other types of measurements.