Assessing Vulnerabilities in Line Length Parameterization and the Per-Unit-Length Paradigm for Phase Modulation and Figure-of-Merit Evaluation in 60 GHz Liquid Crystal Phase Shifters

The figure-of-merit (FoM) is a crucial metric in evaluating liquid crystal (LC) phase shifters, significantly influencing the selection of superior device candidates. This paper identifies, for the first time, a fundamental limitation in the widely-used High-Frequency Structure Simulator (HFSS), a closed-source commercial tool, when modeling reconfigurable delay line phase shifters (RDLPS) based on LC at millimeter-wave (mmW) frequencies for Beyond 5G (B5G) and Sixth-Generation (6G) applications. Specifically, the study reveals unreliable predictions of differential phase shifts (DPS) when using the line length parameterization (LLP) approach, with an accuracy of only 47.22%. These LLP-induced inaccuracies lead to misleading FoM calculations, potentially skewing comparative analyses against phase shifters implemented with different geometries or advanced technologies. Additionally, the per-unit-length (PUL) paradigm, commonly employed by microwave circuit engineers for evaluating and optimizing microwave transmission line designs, is also found to have limitations in the context of mmW RDLPS based on LC. The PUL methodology underestimates the FoM by 1.38206°/dB for an LC coaxial RDLPS at 60 GHz. These findings underscore a critical symmetry implication, where the assumed symmetry in phase shift response is violated, resulting in inconsistent performance assessments. To address these challenges, a remediation strategy based on a scenario-based “Length-for-π” (LFP) framework is proposed, offering more accurate performance characterization and enabling better-informed decision-making in mmW phase shifter design.