Multi-Ports ($2^{n}$) 2×-Thru De-Embedding: Theory, Validation, and Mode Conversion Characterization

Because of the simplicity of design and measurement, as well as the accuracy of results, the 2×-thru de-embedding has replaced the traditional de-embedding algorithms such as thru-reflect-line and short-open-load-thru for printed circuit board (PCB) characterization. In this paper, the theory of [$2^{n}$ -port 2×-Thru de-embedding is derived first. The self-error reduction schemes are introduced to mitigate the de-embedding errors due to non-ideal manufacturing effects that make mode conversion terms non-zero. Both the theory and the self-error reduction schemes are fully validated through simulation and measurement cases.