Design and Optimization of Highly Miniaturized Liquid Crystal Phase Shifters Based on Defected Ground Structures

This paper presents a fast and compact design method for planar liquid crystal (LC) phase shifters, using circuit models based on filter design principles. By applying equivalent circuit optimization to phase shifters utilizing defected ground structure inverted microstrip lines (DGS-IMSL), an efficient optimization framework is developed. This framework enables a fast and comprehensive phase shifter optimization regarding compactness, bandwidth, and impedance matching, all while enabling millisecond-range response times. To validate the optimization framework, two phase shifters based on 23rd-order filters are designed and experimentally verified at center frequencies around 28 GHz and 60 GHz. The 28 GHz prototype achieves a high compactness exceeding <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$1250^{\circ }/\lambda _{0}$</tex-math></inline-formula> and a figure of merit (FoM) above <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$65^{\circ }$</tex-math></inline-formula>/dB with an LC layer thickness of 4.6 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mu$</tex-math></inline-formula>m. The 60 GHz prototype features sub-25 ms response times enabled by a thin 2 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mu$</tex-math></inline-formula>m LC layer, compactness over <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$650^{\circ }/\lambda _{0}$</tex-math></inline-formula>, and an FoM greater than <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$65^{\circ }$</tex-math></inline-formula>/dB. Altogether, the proposed design framework enables the realization of fast, application-specific LC phase shifters with highly optimized performance.