Closed-Form Expressions of Electric and Magnetic Near-Fields for the Calibration of Near-Field Probes

Near-field scan (NFS) is a powerful method to diagnose electromagnetic compatibility (EMC) issues. Some of the related applications require quantitative measurement of near-field, which relies on calibrated near-field probes (NFPs). A typical and convenient structure to calibrate them is the microstrip line. Although this structure seems simple, determining near-field distribution is not straightforward and 3-D electromagnetic (EM) simulation is usually preferred. Because of the complexity of EM solvers and the dependence of results on their configuration which requires a solid expertise, this approach introduces an additional difficulty in the calibration process and a source of uncertainty. This article proposes closed-form expressions based on quasi-static approximation to calculate near-field distribution over microstrip line and simple calibration structures. This article specifies the frequency limits of this method, which can reach several gigahertz, covering most of the needs in EMC diagnosis at printed circuit board (PCB) and integrated circuit (IC) levels. Several probes are calibrated with these formulations, which are validated through comparison of the near-field measurements above the same case study. A special care is also provided during the calibration process to ensure that the probe characteristics remain independent of the probe height.