## 6 Conclusions  
This paper has presented a novel method to increase \(\Delta\phi\) by inserting IPs into an LC-based SIW phase for the first time. Inserted IPs increase \(\Delta\phi\) by generating different phase advances based on the \(\varepsilon_{r}\) of the LC. Furthermore, the amount of \(\Delta\phi\) increase can be adjusted by manipulating the \(r\) and \(p\) of the IPs. Simulation results at an operating frequency of 28 GHz showed \(\Delta\phi\) = 58.1\({}^{\circ}\) and \(IL\) = 1.1 dB, with FoM1 (ratio of maximum \(\Delta\phi_{max}\) and the insertion loss) = 52.82 \({}^{\circ}\)/dB and FoM2 (\(\Delta\phi_{max}\) per length) = 2.62 \({}^{\circ}\)/mm. Compared with the conventional LC-based SIW phase shifter that uses the same amount of LC, FoM1 increased by 16.06% and FoM2 increased by 55.03%. In addition, compared to the conventional, LC-based SIW phase shifter, which uses additional LC instead of IP insertion, FoM1 was reduced by 6.94%, and FoM2 was increased by 21.3%. The proposed design with additional IPs has a higher \(\Delta\phi\) per length than the conventional structure that uses additional LCs instead of IPs. Inserting inductive posts can enhance the phase shifting range without increasing the dimension or the amount of LCs of the LC-based SIW phase shifter. Therefore, the proposed design can reduce the size of the phase shifter or the amount of LCs required to achieve the desired differential phase shift. We believe this work will contribute to developing a compact and cost-effective LC-based SIW phase shifter for building future telecommunication systems. However, further studies, including parameter studies and investigations into dispersion characterization and implementation with regards to the LC filling process, are necessary to reach the commercialization level of LC-based SIW structures. Conceptualization, H.-J.S. and [PERSON]-Y.C. ; Validation, J.-S.M. ; Formal analysis, H.-J.S., J.-S.M. and J.-Y.C. ; Writing--original draft, H.-J.S. and J.-S.M. ; Writing--review & editing, J.-S.M. ; Project administration, W.-S.K. All authors have read and agreed to the published version of the manuscript. This work was supported by Nepes in South Korea, and the liquid crystal ZOC-A001 was supplied from JNC Corporation in Japan. This work was also supported by the Samsung Research Funding Center of Samsung Electronics under Project Number SRFC-TE2103-01. Not applicable. * _[PERSON]_ (1997) [PERSON] Liquid crystal materials and liquid crystal displays. _Annu. Rev. Mater. Sci._**1997**, _27_, 305-379. [CrossRef]
* _[PERSON] et al. (2009)_ [PERSON]; [PERSON]; [PERSON] [PERSON]; [PERSON] [PERSON]; [PERSON] [PERSON]; [PERSON] [PERSON] Tunable liquid crystal phase shifter for microwave frequencies. _Electron. Lett._**2009**, _45_, 686-687. [CrossRef]
* _[PERSON] et al. (2002)_ [PERSON]; [PERSON]; [PERSON] Tunable inverted-microstrip phase shifter device using nematic liquid crystals. In Proceedings of the 2002 IEEE MTT-S International Microwave Symposium Digest, Seattle, WA, USA, 2-7 June 2002; pp. 367-371. [CrossRef]
* _[PERSON] and [PERSON] (2019)_ [PERSON]; [PERSON] Liquid Crystal-Based Enclosed Coplanar Waveguide Phase Shifter for 54-66 GHz Applications. _Crystals_**2019**, \(9\), 650. [CrossRef]
* _[PERSON] et al. (2014)_ [PERSON]; [PERSON] [PERSON]; [PERSON]; [PERSON] [PERSON]; [PERSON]; [PERSON]; [PERSON] [PERSON]; [PERSON] [PERSON]; [PERSON] [PERSON]; [PERSON] [PERSON]; et al. Reliability study of a tunable Ka-band SIW-phase shifter based on liquid crystal in LTCC-technology. _Int. J. Microw. Wirel. Technol._**2014**, \(7\), 521-527. [CrossRef]
* _[PERSON] et al. (2013)_ [PERSON]; [PERSON]; [PERSON] _Microstrip Lines and Slotlines_, 3 rd ed. ; Artech House: Boston, MA, USA, 2013; pp. 497-498. * _[PERSON] et al. (2015)_ [PERSON]; [PERSON] Liquid crystal enabled substrate integrated waveguide variable phase shifter for millimeter-wave application at 60 ghz and beyond. In Proceedings of the 2015 IEEE MTT-S International Microwave Symposium, Phoenix, AZ, USA, 17-22 May 2015; pp. 1-4.