Electromagnetic Properties of Liquid Crystal Materials
LC material is a kind of material between liquid and solid, which has both liquid flow characteristics and crystal anisotropy. It can be seen from Fig. 1 that under the control of different external control voltages, the director of the LC molecule determines the dielectric constant tensor in different deflection states14,15.
The relationship between the tensor and the director is as follows16:
$$\begin{gathered} \overleftrightarrow \varepsilon ={\varepsilon _ \bot } \cdot \overleftrightarrow 1+\Delta \varepsilon \left( {\overrightarrow n \otimes \overrightarrow n } \right) \hfill \\ ={\varepsilon _ \bot }\left[ {\begin{array}{*{20}{c}} 1&0&0 \\ 0&1&0 \\ 0&0&1 \end{array}} \right]+\Delta \varepsilon \cdot \left[ {\begin{array}{*{20}{c}} {n_{x}^{2}}&{{n_x}{n_y}}&{{n_x}{n_z}} \\ {{n_x}{n_y}}&{n_{y}^{2}}&{{n_y}{n_z}} \\ {{n_x}{n_z}}&{{n_y}{n_z}}&{n_{z}^{2}} \end{array}} \right] \hfill \\ \end{gathered}$$
1
Formula (1), represents the tensor product between the pointing vectors, where \(\overrightarrow{n}=\left({cos}\theta ,0,{sin}\theta \right)\) ,which can be further simplified as:
$$\overleftrightarrow \varepsilon =\left[ {\begin{array}{*{20}{c}} {{\varepsilon _ \bot }+\Delta \varepsilon {{\cos }^2}\theta }&0&{\Delta \varepsilon \sin \theta \cos \theta } \\ 0&{{\varepsilon _ \bot }}&0 \\ {\Delta \varepsilon \sin \theta \cos \theta }&0&{{\varepsilon _ \bot }+\Delta \varepsilon {{\sin }^2}\theta } \end{array}} \right]$$
2
When the applied voltage is 0V, does not deflect, and the dielectric constant tensor can be expressed as follows:
\({\overleftrightarrow \varepsilon _ \bot }=\left[ {\begin{array}{*{20}{c}} {{\varepsilon _ \bot }}&0&0 \\ 0&{{\varepsilon _\parallel }}&0 \\ 0&0&{{\varepsilon _ \bot }} \end{array}} \right]\) \({\overleftrightarrow \varepsilon _\parallel }=\left[ {\begin{array}{*{20}{c}} {{\varepsilon _ \bot }}&0&0 \\ 0&{{\varepsilon _ \bot }}&0 \\ 0&0&{{\varepsilon _\parallel }} \end{array}} \right]\) (3)
When the applied voltage reaches saturation, the deflection angle becomes 90°. At this point, the LC molecule aligns parallel to the electric field direction, as depicted in Fig. 1(c), and its dielectric constant tensor can be simplified to the following formula.
Figure 2 visually demonstrates the change of relative dielectric constant (\({\epsilon }_{r}\)) and loss tangent angle (tanδ) of LC materials with voltage. It can be observed that when the voltage changes within the range of threshold voltage and saturation voltage, the \({\epsilon }_{r}\) and tanδ will also change within the corresponding extreme value.
It can be seen from the figure that the LC molecule will produce elastic deformation in the process of deflection, and the change of energy will deflect the director, thus realizing the frequency switching function. The tunability of general tunable materials is usually expressed by \({\epsilon }_{r}\) of LC materials. The following formula is the expression of the tuning ability of nematic LC17:
$${\tau _{LC}}=\frac{{{\varepsilon _{r,\parallel }} - {\varepsilon _{r, \bot }}}}{{{\varepsilon _{r,\parallel }}}}$$
4
In the optical field, the anisotropy can be represented by the following formula when LC materials are used in the microwave field because the refractive index can replace the dielectric constant:
$$\Delta n={n_\parallel } - {n_ \bot }=\sqrt {{\varepsilon _{r,\parallel }}} - \sqrt {{\varepsilon _{r, \bot }}}$$
5
According to the Oseen Frank Energy and electromagnetic characteristics related to LC molecules, the famous Freedericksz transition voltage (Vth) is a voltage with no molecular reorientation can be reduced derived18. The threshold voltage can be defined as:
$${V_{th}}=\pi \sqrt {\frac{{2{k_{11}}}}{{{\varepsilon _0}\Delta {\varepsilon _r}}}}$$
6
Antenna Design
Figure 3 shows the structure diagram and side view of each layer of the frequency reconfigurable antenna. The overall dimensions of the antenna is 20×25×7.635mm3, and the layered structure is adopted. The antenna is mainly composed of three layers, and the specific parameters of each layer are shown in Table 1.
Table 1
| |
Front Dielectric
|
LC layer
|
Back Dielectric
|
|
Material
|
Taconic-TLY5(TM)
|
Rogers5880
LC- BYIPS-P01
|
Aluminum
|
|
Thickness
(mm)
|
0.381
|
0.254
|
7
|
|
εr
|
2.2
|
2.2
2.74 to 5.4
|
1
|
|
tanδ
|
0.0009
|
0.0009/-
|
0
|
|
Substrate Size(mm3)
|
17×25×0.381
|
25×25×0.254
|
25×25×7
|
The top layer is the Taconic TLY5 (TM) dielectric substrate with a thickness of 0.381mm, its dielectric constant is 2.2, and the loss tangent angle is 0.0009. The upper surface of the first layer of the dielectric substrate is etched with a parasitic patch element of 5.5×5.2 mm2, and its lower surface is a radiation patch and part of the feeding structure. The four cylindrical through holes with a diameter of 1mm at the center of the dielectric substrate facilitate the injection of LC and the discharge of air during the physical test. The middle layer is a high-frequency dielectric plate with the same \({\epsilon }_{r}\)and tanδ as the former, and its thickness is 0.254 mm. The 7×7×0.254 mm3 cavity in the center of the dielectric substrate of this layer is used for storing LCs, and two electromagnetic band gap structures of the same size and the same distance are placed on both sides of a part of the microstrip structure. The bottom layer is made of a metal aluminum block with a flange through the hole on the side for fixing 2.4 mm RF connector. The cylindrical through-hole with a diameter of 1mm on both sides of the whole structure is used to fix the multi-layer dielectric substrate. When an external control voltage is applied, an electric field can be formed between the inverted microstrip structure and the aluminum block to control the molecular deflection of the LC.
To further broaden the impedance bandwidth of the antenna, this design uses the principle that parasitic patches can generate new resonance points near the original frequency points and load parasitic patches on the upper part of the upper dielectric substrate. The impact of parasitic patch units on antenna performance is demonstrated in Fig. 4 (a). Additionally, the return loss has been effectively widened. To further understand the working principle of the parasitic patch, the parameters of the parasitic patch are analyzed. Figure 4 (b) illustrates that a new resonant point can only be generated near the resonant frequency point when the size of the parasitic unit closely matches that of the radiation patch, thereby facilitating spread spectrum effects.
The original microstrip patch antenna and the parasitic patch placed above the main patch form two RLC parallel resonant circuits with the ground, respectively. These two resonant circuits are capacitively coupled through the radiation field of the main patch. Figure 4(c) demonstrates the equivalent circuit of the additional antenna parasitic patch. By modifying the shape, size, and quantity of parasitic elements based on the principle of parasitic elements and equivalent circuits, it is possible to enhance the antenna bandwidth.