## 1 Introduction  
The liquid crystal (LC) based reflectarray antenna is a common reconfigurable reflectarray antenna type [1; 2; 3; 4]. This antenna type is widely used, especially at frequencies over 60 GHz [5; 6; 7]. Due to the advantages of a low profile, simple structure, and easy fabrication, the liquid crystal based reflectarray antennas have been discussed by many researchers, especially for the applications in the millimeter-wave and THz frequency ranges [8; 9]. [PERSON] et al., proposed a single resonant square patch reflectarray antenna, which had the capability of a phase shift of 180\({}^{\circ}\)[10]. To improve the phase and bandwidth capability, [PERSON] et al., proposed the multi-resonant unit cells for a reconfigurable reflectarray antenna [11]. This antenna uses triple rectangular dipole patches placed in a parallel to achieve a large bandwidth while achieving a phase shift of more than 360\({}^{\circ}\). [PERSON] et al., proposed rectangular elements achieved a phase shift of 546\({}^{\circ}\) at 77 GHz [12]. In [9], a tunable 2\(\pi\) LC phase shifter was reported at 357 GHz by using 40 V driving voltage. However, due to the small size of a dipole antenna, the coverage of the metal is insufficient. When a bias voltage is applied to a dipole, the orientation of the liquid crystal is uneven which compromises the accuracy. This problem exists in a series of the LC-based electrically tunable devices, including the absorbers, phase shifters, filters, etc., where the uneven liquid crystal layer is usually replaced by the equivalent dielectric constant, but that causes the difference between the actual and simulation values. Many methods were reported to improve accuracy. A block separately module was proposed in [13], to improve the design accuracy by dividing different copper layers of the liquid crystal layer into several regions, achieving the sub-regional simulation, but such a design requires a more complex design process. Graphene material was also used to reduce the inhomogeneity of the static electric field [14]. [PERSON] et al. used the few-layer porous graphene to generate the uniform static field and achieve a THz absorber [15]. However, the disadvantage is that it is impossible to control the voltage of each line.  
Motivated by the previous works, we propose an LC-based electrically tunable slot phase shifter. The proposed slot unit cell phase shifter for the reflectarray system is designed, fabricated and tested. The electromagnetic reflecting characteristics of the reflectarray system are simulated and analyzed. It is proven that the proposed structure has the advantage of providing a more homogeneous static electric field. The comparison of the proposed phase shifter performances with the mentioned phase shifter are tabulated in Table 1. Due to the large patch area, the achieved saturation reduced the bias voltage by 50% compared with the previously reported ones. The performance of the proposed phase shifter is validated by the array consisting of 30 \(\times\) 30 unit cells. In the experiments, a liquid crystal is employed to provide the tunable phase-shifting unit cells in the F frequency band. The results show that the proposed spatial phase shifter provides the phase shift and continuous tunability over a broad frequency range.