A Material Characteristic Measurement System for HTWT Support Rods Based on SLSP Resonator and Simulation-Driven Calibration

This article presents a system for measurement of the distribution of complex permittivity (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\varepsilon $ </tex-math></inline-formula>) and attenuation of support rods employed in helix traveling-wave tubes (HTWTs). By leveraging the spoof localized surface plasmon (SLSP) structure as a miniaturized resonator, a compression size of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\lambda _{0}$ </tex-math></inline-formula>/19 (where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\lambda _{0}$ </tex-math></inline-formula> represents the free-space wavelength) is attained, featuring six resonant modes within the bandwidth, each with a quality factor (Q-factor) exceeding 80. Grounded on the design of the resonator, a low-cost planar microwave sensor is developed. Through the simulation-driven calibration method, the dielectric constant (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\varepsilon _{r}'$ </tex-math></inline-formula>), loss tangent (tan<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\delta $ </tex-math></inline-formula>), and attenuation coefficient (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$A_{\text {loss}}$ </tex-math></inline-formula>) at various positions of the support rod are obtained by measuring and converting the S-parameters. A flexible hardware system is currently being established, incorporating replaceable fixtures, transmission devices, and a vector network analyzer (VNA). Additionally, a control software is under development to facilitate the control of the measurement system and data processing. The measurement system is utilized for measuring the characteristics of the S-band HTWT support rod within an 80 mm range.