Closed‐form analytical formulas are presented to calculate a figure of merit (FoM) of a liquid crystal (LC) phase shifter (PS) based on microstrip transmission line (MS TL). New expressions are derived to account for anisotropic loss of LC and loss in the superstrate. Although approximate, the presented framework provides a useful insight into the effect of numerous design parameters of the LC PS, such as geometric dimensions of TL or complex permittivity of LC and the superstrate. Comparison with the full‐wave numerical analysis of Maxwell's equations showed good agreement in the calculated effective permittivity, dielectric and conductor losses and the FoM for operating frequencies up to 12 to 15 GHz. Furthermore, reasonable quantitative agreement for the FoM is maintained for geometries of interest even at millimeter wave frequencies, up to 30 GHz.

中文翻译：

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基于微带传输线的液晶移相器设计公式

提出了封闭形式的分析公式，用于基于微带传输线（MS TL）计算液晶（LC）移相器（PS）的品质因数（FoM）。得出新的表达式以说明LC的各向异性损失和上层板的损失。尽管是近似的，但本文提出的框架可帮助您深入了解LC PS的众多设计参数的效果，例如TL的几何尺寸或LC和覆层的复介电常数。与Maxwell方程的全波数值分析进行比较，结果表明，在高达12至15 GHz的工作频率下，计算出的有效介电常数，介电和导体损耗以及FoM均具有良好的一致性。此外，即使在毫米波频率下，对于感兴趣的几何形状，也可以保持FoM的合理定量协议，