Susceptibility to Low-Frequency Breakdown in Full-Wave Models of Liquid Crystal-Coaxially-Filled Noise-Shielded Analog Phase Shifters

Building on the fully encapsulated architecture of liquid crystal (LC) coaxial phase shifters, which leverages noise-shielding advantages for millimeter-wave wideband reconfigurable applications, this study addresses the less-explored issue of low-frequency breakdown (LFB) susceptibility in modern full-wave solvers. Specifically, it identifies the vulnerability nexus between the tuning states (driven by low-frequency bias voltages) and the constitutive elements of LC-filled coaxial phase shifters—namely, the core line, housing grounding, and radially sandwiched tunable dielectrics—operating at millimeter-wave frequencies (60 GHz WiGig), microwave (1 GHz), and far lower frequency regimes (down to 1 MHz, 1 kHz, and 1 Hz) for long-wavelength or quasi-static conditions, with specialized applications in submarine communications and geophysical exploration. For completeness, the study also investigates the device state prior to LC injection, when the cavity is air-filled. Key computational metrics, such as effective permittivity and characteristic impedance, are analyzed. The results show that at 1 kHz, deviations in effective permittivity exceed four orders of magnitude compared to 1 GHz, while characteristic impedance exhibits deviations of three orders of magnitude. More critically, in the LFB regime, theoretical benchmarks from 1 MHz to 1 kHz and 1 Hz demonstrate an exponential increase in prediction error for both effective permittivity, rising from 16.8% to 1.5 × 104% and 1.5 × 107%, and for characteristic impedance, escalating from 8.1% to 1.15 × 103% and 3.9 × 104%, respectively. Consequently, the prediction error of the differential phase shift, minimal at 60 GHz (0.16%), becomes noticeable at 1 MHz (4.39%), increases sharply to 743.88% at 1 kHz, and escalates dramatically to 2.18 × 1010% at 1 Hz. The findings reveal a pronounced frequency asymmetry in LFB susceptibility for the LC coaxial phase shifter biased at extremely low frequencies.