The Choice of Line Lengths in Multiline Thru-Reflect-Line Calibration

Electrical Engineering and Systems Science > Signal Processing [Submitted on 21 Dec 2025 (v1), last revised 31 May 2026 (this version, v3)] Title:The Choice of Line Lengths in Multiline Thru-Reflect-Line Calibration View PDF HTML (experimental)Abstract:This paper presents an analysis and rigorous procedure for determining the optimal lengths of line standards in multiline thru-reflect-line (TRL) calibration of vector network analyzers (VNAs). The solution is obtained through nonlinear constrained optimization of the eigenvalue problem in multiline TRL calibration. Additionally, we propose a simplified approach for near-optimal length selection based on predefined sparse rulers. Alongside the length calculation, we discuss the required number of lines to meet bandwidth requirements. The proposed methods are validated through measurements of multiple multiline TRL calibration kits on printed circuit boards of different materials and stackups, covering frequencies up to 150 GHz. A measurement-based Monte Carlo uncertainty analysis, using error boxes derived from impedance standard substrate measurements, demonstrates that the proposed line lengths distribute calibration uncertainty more evenly across lines compared to a commercial calibration kit. Practical examples are provided for various applications, including lossy and dispersive lines, as well as banded solutions for waveguides. Submission history From: Ziad Hatab [view email][v1] Sun, 21 Dec 2025 08:31:08 UTC (967 KB) [v2] Tue, 28 Apr 2026 06:05:16 UTC (11,098 KB) [v3] Sun, 31 May 2026 21:11:37 UTC (11,611 KB) Current browse context: eess.SP Change to browse by: References & Citations Loading... Bibliographic and Citation Tools Bibliographic Explorer (What is the Explorer?) Connected Papers (What is Connected Papers?) Litmaps (What is Litmaps?) scite Smart Citations (What are Smart Citations?) Code, Data and Media Associated with this Article alphaXiv (What is alphaXiv?) CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub (What is DagsHub?) Gotit.pub (What is GotitPub?) Hugging Face (What is Huggingface?) ScienceCast (What is ScienceCast?) Demos Recommenders and Search Tools Influence Flower (What are Influence Flowers?) CORE Recommender (What is CORE?) arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.