Field Coupling Mechanism Investigation of mm-Wave Magnetic Near-Field Probe Based on a Generalized Equivalent Circuit

Abstract

A field-response-equivalent circuit is advantageous for explaining the field coupling mechanism of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H$ </tex-math></inline-formula> -field probes. Previous works have primarily explained the coupling between a field probe and the calibration kit. In this article, a field coupling circuit model is proposed in a generalized form to directly predict the voltage induced by the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H$ </tex-math></inline-formula> -field and the unwanted <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$E$ </tex-math></inline-formula> -field in the probe for the millimeter-wave (mm-wave) range. The field response circuit model is based on the loop impedance model and incident field response of a loop antenna in the form of a series expansion. This article reveals that the zero-mode response corresponds to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H$ </tex-math></inline-formula> -field coupling, whereas the first mode corresponds to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$E$ </tex-math></inline-formula> -field coupling and is validated through the numerical simulation based on the circular loop antenna. The coupling of the fabricated <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H$ </tex-math></inline-formula> -field probe is predicted based on the equivalent circuit model and the prediction matches numerical simulation and measurement results from 1 to 40 GHz. The equivalent circuit can be used to predict the probe field coupling with an error less than 4 dB. Finally, this article provides a generalized equivalent circuit as a tool to analyze and understand the probe field coupling quantitively. This article reuses some content from a thesis (Liu, 2021) in <xref ref-type="sec" rid="sec1" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Sections I</xref> <xref ref-type="sec" rid="sec2" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"/> – <xref ref-type="sec" rid="sec3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">III</xref> with permission.