A liquid crystal phased array continuous beam scanning method based on non-zero switching

Abstract

This invention provides a continuous beam scanning method for liquid crystal phased arrays based on non-return-to-zero switching, belonging to the field of phased array antenna technology. The method involves obtaining the correspondence between the driving voltage and the steady-state liquid crystal molecule orientation angle, the driving voltage and the steady-state effective dielectric constant, and a microstrip transmission line model, thus establishing the relationship between the driving voltage and the phase difference. Based on the target beam pointing angle and the phased array antenna parameters, the target phase compensation value is obtained. Based on the correspondence between the driving voltage and the phase difference and the target phase compensation value, array-level dynamic simulation is performed to obtain a fixed driving voltage and a dynamic response curve. Based on the dynamic response curve and the fixed driving voltage, the driving voltage is adjusted using a unidirectional progressive control strategy, and under the constraint that no phase loopback occurs in any radiating element, continuous beam scanning results are obtained. This invention solves the bottleneck problems of rapid continuous scanning and system-level simulation optimization in liquid crystal phased arrays.

Description

Technical Field

[0001] This invention relates to the field of phased array antenna technology, and in particular to a continuous beam scanning method for liquid crystal phased arrays based on non-return-to-zero switching. Background Technology

[0002] With the rapid development of satellite communication and 6G networks, next-generation mobile communication and satellite internet systems have created an urgent need for low-cost and miniaturized phased array antennas. Traditional active phased arrays are limited by their high cost and large size. In contrast, liquid crystal phased array antennas, based on liquid crystal materials with tunable dielectric constant, low loss, and low cost, achieve beam scanning through electronic control and also feature compact structure and easy integration, gradually becoming an ideal choice to solve this problem.

[0003] However, the inherent relaxation characteristics of liquid crystal materials result in slow response speeds, severely limiting the application of antennas in dynamic beam scanning. Currently, to overcome the bistable nature of liquid crystals, traditional phase switching schemes generally employ a "zero-reset switching" strategy, where the voltage is first removed to restore the liquid crystal molecules to their initial state, and then a new voltage is applied to deflect them to the next target state. This process leads to significant beam switching delays and causes scanning link interruptions during scanning, making continuous scanning difficult. Secondly, existing research focuses primarily on the electrical control characteristics analysis and optimization of single phase shifter units, lacking modeling and simulation methods from the perspective of the array system level. As a multi-unit collaborative system, the beam scanning performance of a liquid crystal phased array depends not only on the performance of individual phase shifters but also on factors such as array structure, inter-unit coupling, and drive coordination. Currently, there is a lack of systematic design methods that can effectively combine liquid crystal physical models and microwave circuit models to perform array-level dynamic response simulations, making it difficult to accurately predict and optimize the phase transient behavior during beam switching.

[0004] In summary, existing liquid crystal phased array technology faces two major bottlenecks: First, due to the limitations of material properties and the "zeroing and switching" strategy, there is an inherent delay in beam switching, and the zeroing process will interrupt the scanning link, which cannot meet the requirements of rapid continuous scanning in dynamic communication scenarios; Second, there is a lack of efficient array-level dynamic simulation and optimization tools, making it difficult to improve scanning performance and reliability at the system level. Summary of the Invention

[0005] To address the aforementioned shortcomings in existing technologies, this invention provides a continuous beam scanning method for liquid crystal phased arrays based on non-return-to-zero switching, which solves the bottleneck problems in rapid continuous scanning and system-level simulation optimization of liquid crystal phased arrays.

[0006] To achieve the aforementioned objectives, the technical solution adopted by this invention is: a continuous beam scanning method for a liquid crystal phased array based on non-return-to-zero switching, comprising: S1: Based on the continuous medium theory of liquid crystal molecular dynamics, the dynamic response process of liquid crystal materials under the action of an external electric field is accurately modeled to obtain the mapping relationship between the driving voltage and the orientation angle of liquid crystal molecules in steady state. S2: The dielectric constant of each layer of liquid crystal molecules is calculated based on the mapping relationship between the driving voltage and the steady-state orientation angle of the liquid crystal molecules using the liquid crystal dielectric anisotropy tensor model. The mapping relationship between the driving voltage and the steady-state effective dielectric constant is obtained using the spatial averaging method. S3: Based on the mapping relationship between driving voltage and steady-state effective dielectric constant and the microstrip line transmission line model, the correspondence between driving voltage and phase difference is obtained by using the transmission phase calculation method; S4: Based on the target beam pointing angle and phased array antenna array parameters, the target phase compensation value is obtained using the geometric phase compensation calculation method; S5: Based on the correspondence between driving voltage and phase difference and the target phase compensation value, array-level dynamic simulation is performed using inverse interpolation and numerical solution of dynamic equations to obtain fixed driving voltage and dynamic response curves. S6: Based on the dynamic response curve and fixed driving voltage, the driving voltage is adjusted using a unidirectional progressive control strategy. Under the constraint that no phase folding occurs in any of the radiating elements, continuous beam scanning results are obtained, and continuous beam scanning of the liquid crystal phased array is completed.

[0007] Further, S1 includes: Based on the continuous medium theory of liquid crystal molecular dynamics, this paper addresses the contradiction between the complexity of liquid crystal molecular dynamics equation calculation and the high real-time requirements of array-level multi-element calculation and simulation. The liquid crystal dynamics equation is simplified for engineering applications by ignoring its inertia term and Leslie coefficient term, discretizing the liquid crystal layer into multiple sub-layers along the thickness direction, and constructing a set of ordinary differential equations. The ordinary differential equations are numerically solved to simulate the change of the orientation angle of liquid crystal molecules in each layer with time under a given driving voltage. Based on the aforementioned change process, a mapping relationship between the driving voltage and the steady-state orientation angle of the liquid crystal molecules is established.

[0008] Furthermore, the expression for the liquid crystal dynamics equation is: ; The expression for the i-th ordinary differential equation in the system of ordinary differential equations is: ; ; in, Represents the elastic constant of the development curve. Indicates the orientation angle of liquid crystal molecules. Represents the bending elastic constant. This represents the spatial coordinates of the liquid crystal layer along its thickness direction. Represents the vacuum dielectric constant. Indicates electric field strength. Indicates the driving voltage. Indicates the thickness of the liquid crystal layer. Indicates low-frequency dielectric anisotropy. Indicates the rotational viscosity of the liquid crystal. Indicates time, This represents the orientation angle of the liquid crystal molecules in the i-th layer. This represents the orientation angle of the liquid crystal molecules in the (i+1)th layer. This represents the orientation angle of the liquid crystal molecules in the (i-1)th layer. The step size represents the spatial discreteness, and i represents the layer index after discreteness in the thickness direction of the liquid crystal layer.

[0009] Further, S2 includes: Based on the dielectric anisotropy tensor model of liquid crystal, the dielectric constant components of each liquid crystal layer under fixed orientation are calculated by utilizing the geometric relationship between the liquid crystal molecule director and the orientation angle of each liquid crystal molecule in steady state. The dielectric constant components of each liquid crystal layer are spatially averaged using the spatial averaging method. Combined with the mapping relationship between the driving voltage and the steady-state liquid crystal molecule orientation angle, a mapping relationship between the driving voltage and the steady-state effective dielectric constant is established.

[0010] Further, S3 includes: Based on the mapping relationship between the driving voltage and the steady-state effective dielectric constant, the range of variation of the effective dielectric constant of the liquid crystal layer under different driving states is determined; Based on the microstrip transmission line model and the effective dielectric constant variation range, the microstrip line length is determined by the maximum phase difference requirement, and a dielectric constant correction factor is introduced to calibrate the theoretical phase difference, resulting in a calibrated method for calculating the transmission phase. Based on the calibrated transmission phase calculation method, a correspondence between the driving voltage and the output phase difference of the phase shifter under steady state is established.

[0011] Furthermore, the expression for the phase difference output by the phase shifter is: ; in, Indicates the phase difference at the output of the phase shifter. This represents the multiplication correction factor related to the dielectric constant. Indicates the operating frequency. Indicates the length of the microstrip line. Represents the speed of light in a vacuum. This represents the macroscopically effective dielectric constant of the liquid crystal layer at time t, corresponding to the driving voltage V. This represents the macroscopic effective dielectric constant of the liquid crystal layer when the driving voltage is 0.

[0012] Further, S4 includes: Based on the target beam pointing angle and phased array antenna array parameters, a phase change model is constructed using the geometric phase compensation calculation method. Using the phase change model, the target phase compensation value required for each radiating element in the antenna array is obtained.

[0013] Further, S5 includes: Based on the correspondence between driving voltage and phase difference, the fixed driving voltage corresponding to the target phase compensation value of each radiating element is found by inverse interpolation. The fixed driving voltage is substituted as an input parameter into the liquid crystal molecule dynamics model; Array-level dynamic simulation is performed using inverse interpolation and numerical solution of the dynamic equations to calculate the transient process of the output phase change of each radiating element over time and generate dynamic response curves.

[0014] Further, S6 includes: Based on the dynamic response curve, the increasing relationship of the phase of each radiating element during continuous beam scanning is obtained; Based on the fixed driving voltage and the increasing relationship, the driving voltage is adjusted using a unidirectional progressive control strategy. During the adjustment process, the applicable array size and scanning range are determined with the constraint that no phase wrap-around occurs in any of the radiating elements. Based on the array size and scanning range, under the constraints, the antenna array is driven to switch beam pointing according to a preset scanning angle sequence, and the overall time is evaluated by combining the rise time and fall time to obtain the continuous beam scanning result, thus completing the continuous beam scanning of the liquid crystal phased array.

[0015] The beneficial effects of this invention are as follows: This invention provides a continuous beam scanning scheme and implementation method for millimeter-wave liquid crystal phased arrays. For the first time, it integrates modeling of the dynamic response process of liquid crystal molecules based on continuous medium theory, the liquid crystal dielectric anisotropy tensor model, the microstrip line transmission line model, and the geometric phase compensation calculation method to construct a complete and quantifiable technology mapping chain. Based on this technology mapping chain, the driving voltage required for each antenna radiating element and the dynamic response curve of the liquid crystal phase shifter during liquid crystal phased array driving are obtained. Furthermore, this invention utilizes a co-directional progressive control strategy to adjust the driving voltage. Under the constraint that no phase lag occurs in any radiating element, it completely avoids the delay introduced by the traditional zero-reset switching method, achieving rapid continuous beam scanning results. Attached Figure Description

[0016] This specification will be further described by way of exemplary embodiments, which will be described in detail with reference to the accompanying drawings. These embodiments are not limiting; in these embodiments, the same reference numerals denote the same structures, wherein: Figure 1 This is an exemplary flowchart of a liquid crystal phased array continuous beam scanning method based on non-return-to-zero switching, according to some embodiments of this specification.

[0017] Figure 2 The figures are simulation results of the steady-state changes in the orientation angle of liquid crystal molecules with the position of the liquid crystal layer under different driving voltages, as shown in some embodiments of this specification.

[0018] Figure 3 The figures show simulation results of the change of liquid crystal dielectric constant with liquid crystal layer position under different driving voltages in steady state, based on some embodiments of this specification.

[0019] Figure 4 This is a simulation diagram showing the relationship between the steady-state driving voltage and the effective dielectric constant of the liquid crystal layer, based on some embodiments of this specification.

[0020] Figure 5 This is a simulation diagram showing the relationship between the steady-state driving voltage and the output phase difference of the liquid crystal phase shifter, based on some embodiments of this specification.

[0021] Figure 6 This is a simulation diagram of the dynamic phase response and final beamforming effect of a liquid crystal phased array unit under the action of a driving voltage, as shown in some embodiments of this specification.

[0022] Figure 7 These are simulation diagrams of the phased array scanning process shown in some embodiments of this specification.

[0023] Figure 8 This is a simulation diagram showing the phase change of liquid crystal phased array elements over time under a conventional scanning method as illustrated in some embodiments of this specification.

[0024] Figure 9 This is a simulation diagram showing the phase change of liquid crystal phased array elements over time under a scanning method based on non-return-to-zero switching, as illustrated in some embodiments of this specification. Detailed Implementation

[0025] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.

[0026] Example Figure 1 This is an exemplary flowchart illustrating a continuous beam scanning method for a liquid crystal phased array based on non-return-to-zero switching, according to some embodiments of this specification. Figure 1 As shown, the process includes the following steps. In some embodiments, the process may be executed by a processor.

[0027] S1: Based on the continuous medium theory of liquid crystal molecular dynamics, the dynamic response process of liquid crystal materials under the action of an external electric field is accurately modeled to obtain the mapping relationship between the driving voltage and the orientation angle of liquid crystal molecules in steady state.

[0028] The continuous medium theory is a theoretical framework for describing the macroscopic physical properties of liquid crystal materials. For example, the theory can include parameters such as elastic constants (bending and bending elastic constants) and rotational viscosity.

[0029] In some embodiments, the processor can obtain the theory of continuous medium by analyzing the physical properties of liquid crystal materials.

[0030] The mapping relationship between driving voltage and steady-state liquid crystal molecule orientation angle, for example, can include data on the change of orientation angle of liquid crystal molecules in each layer over time under a given driving voltage.

[0031] In some embodiments, the processor can obtain the mapping relationship between the driving voltage and the steady-state orientation angle of liquid crystal molecules by numerically solving the liquid crystal dynamics equation.

[0032] In some embodiments, the processor can simplify the liquid crystal dynamics equations based on the continuous medium theory of liquid crystal molecular dynamics, addressing the contradiction between the complexity of calculating the liquid crystal molecular dynamics equations and the high real-time requirements of array-level multi-element calculations and simulations. This simplification is done to accommodate engineering applications, ignoring inertia and Leslie coefficient terms, discretizing the liquid crystal layer into multiple sub-layers along the thickness direction, and constructing a set of ordinary differential equations. The set of ordinary differential equations is then numerically solved to simulate the change in the orientation angle of liquid crystal molecules in each layer over time under a given driving voltage. Based on this change, a mapping relationship between the driving voltage and the steady-state orientation angle of the liquid crystal molecules is established.

[0033] The liquid crystal dynamics equation is a mathematical model that describes the dynamic behavior of the director of a nematic liquid crystal under the action of an external electric field. For example, the equation can include data such as the orientation angle of liquid crystal molecules, spatial coordinates, time, and electric field strength.

[0034] In some embodiments, the processor can obtain the liquid crystal dynamics equation by simplifying the vector theory (Ericksen-Leslie) equations for engineering applications (ignoring inertia and Leslie coefficient terms).

[0035] A set of ordinary differential equations refers to a set of time evolution equations obtained by discretizing the partial differential equations of liquid crystal dynamics in space. For example, the set of equations may include the derivative data of the molecular orientation angle of each of the N sub-layers of the liquid crystal layer along the thickness direction as a function of time.

[0036] In some embodiments, the processor can obtain a system of ordinary differential equations by approximating the spatial derivatives using the central difference method.

[0037] In some embodiments, the expression for the liquid crystal dynamics equation is: ; The expression for the i-th ordinary differential equation in the system of ordinary differential equations is: ; ; in, Represents the elastic constant of the development curve. Indicates the orientation angle of liquid crystal molecules. Represents the bending elastic constant. This represents the spatial coordinates of the liquid crystal layer along its thickness direction. Represents the vacuum dielectric constant. Indicates electric field strength. Indicates the driving voltage. Indicates the thickness of the liquid crystal layer. Indicates low-frequency dielectric anisotropy. Indicates the rotational viscosity of the liquid crystal. Indicates time, This represents the orientation angle of the liquid crystal molecules in the i-th layer. This represents the orientation angle of the liquid crystal molecules in the (i+1)th layer. This represents the orientation angle of the liquid crystal molecules in the (i-1)th layer. The step size represents the spatial discreteness, and i represents the layer index after discreteness in the thickness direction of the liquid crystal layer.

[0038] In some embodiments, the ordinary differential equation is at the left and right boundaries, i.e. and From time to time and ,and , ,in This is the pretilt angle of the liquid crystal molecules. At non-boundary locations, i.e. When the central difference method is used to approximate the spatial derivative, that is... , ,in The step size is used for spatial discretization. Each equation describes the state of a spatial point over time. This set of equations can be numerically integrated using an ordinary differential equation solver to obtain the time evolution of the entire system. To accurately analyze the boundary layer, the coherence length of the liquid crystal during spatial discretization is used. There need to be at least 10 spatial points, that is ,in On the basis of meeting this condition, further balance between simulation accuracy and speed is required. The setting. Finally, consider the pretilt angle of the liquid crystal molecules. The effect, in the initial state, hour and in driving voltage hour Based on this, by solving the above equations, simulations are performed under a given driving voltage. The process of changing the orientation angle of liquid crystal molecules in each layer over time is analyzed to obtain the driving voltage, the distribution of liquid crystal molecule orientation angles, and the time required to reach steady state. The dynamic relationship.

[0039] like Figure 2 As shown, this illustrates the steady-state distribution of the orientation angle of liquid crystal molecules along the thickness direction of the liquid crystal layer under different driving voltages in an optional embodiment of the present invention. When the driving voltage... At 0.0V, the molecular orientation angle at each position remains at the preset pretilt angle. The voltage starts from 0.0. When the voltage is increased to 4.0 V and exceeds its threshold voltage, the molecular orientation angle within the liquid crystal layer increases significantly overall, except at the boundaries, and exhibits a non-uniform distribution along the thickness direction, gradually increasing from the substrate interface towards the center. The figure also indicates the time required to reach steady state at each voltage. .

[0040] S2: The dielectric constant of each layer of liquid crystal molecules is calculated based on the mapping relationship between the driving voltage and the steady-state orientation angle of the liquid crystal molecules using the liquid crystal dielectric anisotropy tensor model. The mapping relationship between the driving voltage and the steady-state effective dielectric constant is obtained using the spatial averaging method.

[0041] The liquid crystal dielectric anisotropy tensor model is a mathematical model that describes the anisotropic properties of the dielectric constant of liquid crystal in different spatial directions. For example, the model may include a relative permittivity component parallel to the direction of the liquid crystal molecule pointing vector and a relative permittivity component perpendicular to the direction of the pointing vector.

[0042] In some embodiments, the processor can obtain the liquid crystal dielectric anisotropy tensor model by testing the electromagnetic properties of the liquid crystal material.

[0043] The mapping relationship between driving voltage and steady-state effective dielectric constant, for example, may include the driving voltage value at steady-state time and the corresponding overall effective dielectric constant value of the liquid crystal layer.

[0044] In some embodiments, the processor can obtain the mapping relationship between the driving voltage and the steady-state effective dielectric constant by combining the liquid crystal layer dynamic response model and spatial averaging calculation.

[0045] In some embodiments, the processor can calculate the dielectric constant components of each liquid crystal layer under a fixed orientation based on the liquid crystal dielectric anisotropy tensor model and the geometric relationship between the liquid crystal molecule director and the orientation angle of each liquid crystal molecule in steady state; it can also perform spatial averaging of the dielectric constant components of each liquid crystal layer using a spatial averaging method, and establish a mapping relationship between the driving voltage and the steady-state effective dielectric constant by combining the mapping relationship between the driving voltage and the orientation angle of the liquid crystal molecule in steady state.

[0046] The dielectric constant component refers to the fundamental relative dielectric constant that constitutes the dielectric anisotropy tensor model of liquid crystal. For example, this component may include a relative dielectric constant component parallel to the direction of the liquid crystal molecule pointing vector and a component perpendicular to the direction.

[0047] In some embodiments, the processor can obtain dielectric constant component data through material electromagnetic property testing.

[0048] The steady-state effective dielectric constant refers to the equivalent dielectric constant of the entire liquid crystal layer under a fixed electric field and orientation state. For example, this parameter can include the spatial average value of the dielectric constant of each liquid crystal layer.

[0049] In some embodiments, the processor can obtain the macroscopic effective dielectric constant by calculating the dielectric constant of N layers of liquid crystal under a fixed orientation and performing spatial averaging.

[0050] In some embodiments, the anisotropic tensor model of the dielectric constant of the liquid crystal is: ; in, The dielectric anisotropy of liquid crystal at its operating frequency is defined as follows: , This refers to the relative permittivity component parallel to the direction of the liquid crystal molecule's orientation vector at the operating frequency. This represents the relative permittivity component perpendicular to the direction of the liquid crystal molecule's orientation vector at the operating frequency. 3 3 identity matrices ,in This is a pointer vector, representing the local orientation of liquid crystal molecules. (Symbol) Represents the tensor product (external product). Let be the position vector, where , , This represents the coordinates of different points inside the liquid crystal cell. For time.

[0051] When liquid crystal molecules are When the plane is rotated, its molecular orientation vector can be expressed as: ; At this point, the anisotropic tensor model of the liquid crystal dielectric constant can be expressed as: ; For a liquid crystal phase shifter, when driven by voltage, its electric field direction is fixed along the thickness direction of the liquid crystal layer. In the axial direction, the dielectric constant of each layer can be expressed as: ; Based on the liquid crystal layering model and the molecular orientation angle distribution in each layer, the anisotropic tensor model of the liquid crystal dielectric constant is used to calculate... The dielectric constant of a liquid crystal layer under a fixed orientation is: ; in By spatial averaging, the value at a given driving voltage is obtained. Macroscopic effective dielectric constant of the lower liquid crystal layer for: ; This allows the orientation state of liquid crystal micromolecules to be equated to the macroscopic microwave transmission medium characteristics.

[0052] In some embodiments, such as Figure 3 As shown, this illustrates the steady-state distribution of the liquid crystal dielectric constant with respect to the thickness direction of the liquid crystal layer under different driving voltages in an optional embodiment of the present invention. Based on Figure 2 The steady-state distribution of the orientation angle of liquid crystal molecules under various voltages was calculated using the aforementioned dielectric constant model, resulting in the figure shown. Distribution curves along the thickness direction. Macroscopic effective dielectric constant corresponding to the increase in driving voltage from 0.0V to 4.0V and exceeding its threshold voltage. (Note in the figure) It increases from 2.809 to 3.068. At the same time, the dielectric constant exhibits a non-uniform distribution in the thickness direction, and its profile is consistent with the distribution pattern of molecular orientation angle.

[0053] In some embodiments, in order to achieve a balance between mapping accuracy and simulation calculation efficiency and to ensure the overall practicality of the array-level dynamic simulation model, 0.1V can be used as the scanning step size of the driving voltage.

[0054] In some embodiments, such as Figure 4 As shown, it illustrates the driving voltage in an alternative embodiment of the invention. With the effective dielectric constant of liquid crystal The quantitative mapping relationship under steady state is: Figure 3 The dielectric constant distributed along the thickness is directly reflected by spatial averaging. As the driving voltage increases from 0.0V to 5.0V, the corresponding steady-state effective dielectric constant increases from 2.809 to 3.074. The data shows that... When the voltage is below its threshold voltage of 0.3V, the change is slow as the voltage increases. After the voltage exceeds its threshold voltage, the growth characteristic is saturated as the voltage increases: the growth is significant in the low voltage range, and the growth rate gradually slows down as the voltage continues to increase.

[0055] S3: Based on the mapping relationship between driving voltage and steady-state effective dielectric constant and the microstrip line transmission line model, the correspondence between driving voltage and phase difference is obtained using the transmission phase calculation method.

[0056] A microstrip transmission line model is a physical model used to calculate the phase of a microwave signal transmitted in a microstrip phase shifter. For example, the model may include parameters such as the phase difference of the phase shifter output, the operating frequency, and the length of the microstrip line.

[0057] In some embodiments, the processor can establish a microstrip line transmission line model using microwave transmission line theory. In the microstrip line transmission line model, the phase difference at the output of the phase shifter under ideal conditions... The microstrip line length l and the operating frequency And the phase velocity of the microwave in the transmission line is determined. According to transmission line theory, the expression for the microstrip line transmission line model is: .

[0058] The relationship between driving voltage and phase difference refers to the regulation relationship between control voltage and phase shifter output phase in a phased array system. For example, this relationship can include the driving voltage value under steady state and the corresponding phase shifter output phase difference value.

[0059] In some embodiments, the processor can calculate the correspondence between the driving voltage and the phase difference by combining the mapping relationship between the driving voltage and the steady-state effective dielectric constant with the microstrip line transmission line model.

[0060] In some embodiments, the processor can determine the range of effective dielectric constant variation of the liquid crystal layer under different driving states based on the mapping relationship between the driving voltage and the steady-state effective dielectric constant; based on the microstrip line transmission line model and the range of effective dielectric constant variation, the microstrip line length is determined according to the maximum phase difference requirement, and a dielectric constant correction factor is introduced to calibrate the theoretical phase difference to obtain a calibrated transmission phase calculation method; based on the calibrated transmission phase calculation method, a correspondence between the driving voltage and the steady-state phase shifter output phase difference is established.

[0061] The effective dielectric constant variation range refers to the extreme range of dielectric constant that the liquid crystal layer can achieve within the operating voltage range. For example, this range can include the data of the macroscopic effective dielectric constant from minimum to maximum value when the driving voltage changes from 0V to the maximum operating voltage.

[0062] In some embodiments, the processor can obtain the effective dielectric constant variation range by performing step scan calculations on the driving voltage.

[0063] The dielectric constant correction factor is a multiplicative coefficient used to calibrate the phase response deviation between the ideal microstrip line model and the actual device. For example, the factor may include a fitted curve or discrete data points that vary with the effective dielectric constant.

[0064] In some embodiments, the processor can obtain the dielectric constant correction factor by measuring the actual output phase difference and calculating the theoretical phase difference and then fitting the ratio of the two.

[0065] The calibrated transmission phase calculation method refers to a more accurate phase difference calculation formula after introducing a correction factor. For example, the method may include the corrected phase shifter output phase difference data.

[0066] In some embodiments, the processor can obtain a calibrated transmission phase calculation method by multiplying a dielectric constant correction factor into the basic microstrip line transmission phase theoretical expression.

[0067] In some embodiments, the expression for the phase difference output by the phase shifter is: ; in, Indicates the phase difference at the output of the phase shifter. This represents the multiplication correction factor related to the dielectric constant. Indicates the operating frequency. Indicates the length of the microstrip line. Represents the speed of light in a vacuum. This represents the macroscopically effective dielectric constant of the liquid crystal layer at time t, corresponding to the driving voltage V. This represents the macroscopic effective dielectric constant of the liquid crystal layer when the driving voltage is 0.

[0068] In some embodiments, the maximum phase difference output by the microstrip line model liquid crystal phase shifter is ,in The speed of light in a vacuum The effective macroscopic dielectric constant of the liquid crystal layer when the driving voltage is 0 is determined by the pretilt angle of the liquid crystal molecules. The decision is as follows: ; Based on this, let Thus, the microstrip line length is determined. At this time, in the driving voltage The basic theoretical expression for the output phase difference of the liquid crystal phase shifter is: ; in, For driving voltage Corresponding to The effective dielectric constant of the liquid crystal layer at any given time.

[0069] The fundamental theoretical formula describes the proportional relationship between phase difference and the square root of the dielectric constant. However, in practical systems, due to factors such as edge field effects and non-uniform material distribution, this theoretical relationship often deviates from measured results, rendering the fundamental formula no longer entirely applicable. This deviation essentially alters the propagation behavior of electromagnetic waves in composite media, which can be equivalent to a systematic scaling of the propagation path or phase velocity, its effect manifested primarily as an overall proportional adjustment to the theoretical phase change. Therefore, a multiplicative correction factor related to the dielectric constant is introduced. It is the most direct and essential mathematical description of such physical deviations, and can effectively calibrate the ideal model to the actual device response.

[0070] In some embodiments, the processor can measure a set of... by fabricating a test liquid crystal phase shifter unit. The macroscopic effective dielectric constant ,this Each data point needs to cover the entire effective dielectric constant range, and the corresponding actual output phase difference needs to be measured. The measured Substituting into the basic theoretical formula, calculate the corresponding theoretical phase difference: .

[0071] In some embodiments, the multiplication correction factor is calculated for each data point: ; This quantifies the degree of deviation between the actual phase response and the prediction of the ideal transmission line model under this fixed dielectric constant. Based on this, [further details are needed]. Group data with effective dielectric constant As the independent variable, the calculated As the dependent variable, numerical spline interpolation was used for curve fitting to obtain a continuous correction factor function. Drive voltage The corresponding steady-state phase shifter output phase difference can be expressed by the mapping relationship as follows: .

[0072] In some embodiments, the driving voltage is scanned in 0.1V steps to obtain the steady-state effective dielectric constant corresponding to the range from 0V to 5V. It is assumed that under ideal simulation conditions, the effects of edge field effects, non-uniform material distribution, etc., do not exist; that is, a correction factor is set. Based on this, a set of discrete voltage-phase data pairs is further obtained through the aforementioned mapping relationship. To construct a continuous voltage-to-phase modulation function. This invention employs spline interpolation. First, the discrete voltage-phase data is sorted and preprocessed to ensure its monotonicity; then, cubic spline interpolation is used to establish a piecewise polynomial function. This allows the function to have a second-order continuous derivative at the interpolation nodes, thus enabling high-precision fitting of complex nonlinear relationships between voltage and phase.

[0073] In some embodiments, such as Figure 5 As shown, it illustrates the direct control relationship between the driving voltage and the phase difference of the liquid crystal phase shifter output in a steady state in an optional embodiment of the present invention. This relationship is based on Figure 4 The established voltage-effective dielectric constant mapping and the phase model derivation are used to demonstrate that as the driving voltage increases from 0.0V to 5.0V, the steady-state phase difference provided by the phase shifter increases from 0° to 400°, covering a 360° phase difference output range. Furthermore, when the driving voltage exceeds the threshold voltage, the phase difference output by the phase shifter is proportional to the driving voltage.

[0074] S4: Based on the target beam pointing angle and phased array antenna array parameters, the target phase compensation value is obtained using the geometric phase compensation calculation method.

[0075] The target beam pointing angle refers to the spatial orientation of the main lobe that the phased array antenna is expected to radiate. For example, this angle can include the spatial angle value under fixed scanning requirements.

[0076] In some embodiments, the processor can obtain the target beam pointing angle by setting the beam scanning requirements of the system.

[0077] Phased array antenna parameters refer to parameters that describe the physical and geometric characteristics of the antenna array. For example, these parameters may include the number of array elements and the spacing between array elements.

[0078] In some embodiments, the processor can obtain phased array antenna array parameters through the hardware structure design of the antenna array.

[0079] The target phase compensation value refers to the phase difference value that each element of the antenna array needs to be configured in order to form the main lobe at the target beam pointing angle. For example, the compensation value may include the specific phase degree corresponding to each radiating element in the antenna array.

[0080] In some embodiments, the processor can obtain the target phase compensation value by performing geometric calculations combining the target beam pointing angle and the phased array antenna array parameters.

[0081] In some embodiments, the processor can construct a phase change model based on the target beam pointing angle and phased array antenna array parameters using a geometric phase compensation calculation method; and use the phase change model to obtain the target phase compensation value required for each radiating element in the antenna array.

[0082] A phase change model is a mathematical model that describes the phase difference variation between elements in a phased array system. For example, in a uniform linear array, this model can include linear progressive relationship data between element indices and target phase compensation values.

[0083] In some embodiments, the processor can establish a phase change acquisition model based on the principle of phased array antenna array.

[0084] In some embodiments, the liquid crystal phase shifter-based phased array system employs an analog architecture for beamforming, with all antennas linked to a single radio frequency chain. Beamforming with a fixed pointing angle is achieved through phase modulation of the liquid crystal phase shifter. The antennas used are omnidirectional radiating antennas. The liquid crystal phased array is configured as a uniform linear array, and the antenna element spacing is set to... ,in, wavelength of the emitted wave .

[0085] For a uniform linear array at the target angle The required phase compensation value for each unit below is ; The array antenna pattern can be obtained by setting the phase compensation value of this unit, at a scanning angle of... Sometimes: ; in, The power of the omnidirectional radiating liquid crystal antenna.

[0086] As shown in Table 2, it illustrates the antenna phase compensation values ​​required for each radiating element of the phased array system under different target beam pointing angles, calculated based on the method described above.

[0087] Specifically, a 6-element uniform linear phased array was used. Array element spacing half wavelength According to the method described above, the pointing angle of the target beam was calculated. The required phase compensation value for each element when varying in 10° intervals within the range of -50° to +50° For ease of calculation, the phase has been modulo 360°.

[0088] S5: Based on the correspondence between driving voltage and phase difference and the target phase compensation value, array-level dynamic simulation is performed using inverse interpolation and numerical solution of dynamic equations to obtain fixed driving voltage and dynamic response curve.

[0089] Fixed driving voltage refers to the specific voltage required for a fixed radiating element in a phased array system to reach its target phase compensation value. For example, this voltage may include the input voltage value required for each phase-shifting element in the array to reach its corresponding target steady-state phase.

[0090] In some embodiments, the processor can obtain fixed drive voltage data by using inverse interpolation in the correspondence between drive voltage and phase difference.

[0091] The dynamic response curve refers to the transient process trajectory of the output phase of each element in a phased array system as time changes. For example, the curve may include a time node sequence and the phase value of each element corresponding to each time node.

[0092] In some embodiments, the processor can obtain dynamic response curve data by inputting a fixed driving voltage into the liquid crystal molecular dynamics model and performing numerical solutions.

[0093] In some embodiments, the processor can use inverse interpolation to find the fixed driving voltage corresponding to the target phase compensation value of each radiating unit based on the correspondence between the driving voltage and the phase difference; substitute the fixed driving voltage as an input parameter into the liquid crystal molecule dynamics model; perform array-level dynamic simulation using inverse interpolation and numerical solution of the dynamic equations, calculate the transient process of the output phase of each radiating unit changing with time, and generate a dynamic response curve.

[0094] A liquid crystal molecular dynamics model is a computational framework for simulating the dynamic behavior of molecules, consisting of liquid crystal dynamics equations and their spatial discretization. For example, the model may include dynamic evolution data such as driving voltage and macroscopic electrical parameters of the liquid crystal.

[0095] In some embodiments, the processor can obtain a liquid crystal molecule dynamics model through continuous medium theory modeling.

[0096] In some embodiments, driving voltage With output phase Steady-state correspondence between For any target phase Solve for the required driving voltage. Equivalent to solving the equation .Depend on Figure 5 It can be seen that when the driving voltage exceeds the threshold voltage, the phase changes monotonically with the voltage. Therefore, it can be accurately obtained by inverse interpolation. The driving voltage required for each phase-shifting unit to reach the corresponding target steady-state phase .

[0097] like Figure 6 As shown, it illustrates the dynamic phase response and final beamforming effect of a liquid crystal phased array unit under the action of a driving voltage in an alternative embodiment of the present invention.

[0098] Figure 6 a (Dynamic response curve of output phase difference of each array element): Records the calculation of the compensated phase of each unit based on the target angle using the geometric phase compensation calculation method described in S4 when the target beam pointing angle is 10°. Then, the required driving voltage of each unit is found in reverse using the inverse interpolation method described in S5. Finally, the liquid crystal molecule dynamics model described in S1 is used for simulation. Finally, the output molecular turning angle is mapped to the output phase difference of the phase shifter using the mapping methods described in S2 and S3 to obtain the output phase difference of each phase shifting unit in the array. Over time The transient process of change. The curves show that after the corresponding driving voltage determined by the inverse interpolation method is applied, the phase value of each element starts from the initial state (0°), follows the dynamic response law of the liquid crystal material, gradually changes, and finally converges to the target steady-state phase value listed in Table 2 (element 1 remains at 0°, element 2 converges to 31.26°, element 3 converges to 62.51°, element 4 converges to 93.77°, and element 5 converges to 125.03°).

[0099] Figure 6 b (Array pattern with beam pointing at 10°): Shows the array pattern when all elements are in phase. Figure 6 After reaching the steady-state value shown in figure a, the radiation pattern of the entire phased array in space The directional pattern is in A distinct peak value for the main lobe appears at this point.

[0100] Figure 6 The effectiveness of the constructed array-level liquid crystal phased array simulation model was directly verified, and key dynamic response data were provided for subsequent evaluation of beam switching speed and optimization of continuous scanning strategy.

[0101] S6: Based on the dynamic response curve and fixed driving voltage, the driving voltage is adjusted using a unidirectional progressive control strategy. Under the constraint that no phase folding occurs in any of the radiating elements, continuous beam scanning results are obtained, and continuous beam scanning of the liquid crystal phased array is completed.

[0102] Constraints refer to the system limitations that must be met when implementing a non-return-to-zero continuous beam scanning strategy. For example, such conditions may include the determination data that the actual phase change path of all radiating elements is strictly monotonic and does not experience phase wrap-around (i.e., the maximum phase does not exceed 2π).

[0103] In some embodiments, the processor can obtain the constraint by analyzing the theoretical phase increment of each array element during beam scanning.

[0104] Continuous beam scanning results refer to the state in which the spatial beam pointing of a phased array system changes continuously after executing a fixed drive strategy. For example, the results may include array radiation pattern data corresponding to different scanning time nodes.

[0105] In some embodiments, the processor can obtain continuous beam scanning results by driving the entire array to switch according to a preset scanning angle sequence and evaluating the overall time.

[0106] In some embodiments, the processor can obtain the increasing relationship of the phase of each radiating element during continuous beam scanning based on the dynamic response curve; based on the fixed driving voltage and the increasing relationship, the driving voltage is adjusted using a unidirectional progressive control strategy. During the adjustment process, the applicable array size and scanning range are determined with the constraint that no phase folding occurs in any of the radiating elements; based on the array size and scanning range, under the constraint, the antenna array is driven to switch beam pointing according to a preset scanning angle sequence, and the overall time is evaluated by combining the rise time and fall time to obtain the continuous beam scanning result, thus completing the continuous beam scanning of the liquid crystal phased array.

[0107] The incremental relationship refers to the characteristic that the theoretical phase of each array element increases monotonically with the scanning angle during continuous beam scanning in a fixed direction. For example, this relationship can include comparison data where the phase at the next target angle is greater than the current phase.

[0108] In some embodiments, the processor can obtain an increasing relationship by calculating and comparing the theoretical phase values ​​of each array element at adjacent scanning angles.

[0109] The array size refers to the total number of radiating elements contained in a phased array antenna that performs a non-return-to-zero continuous scanning scheme. For example, the size may include the specific number of antenna elements that meet the constraints (such as 5).

[0110] In some embodiments, the processor can obtain the array size data by evaluating constraints within a fixed scan range.

[0111] The scanning range refers to the spatial angle range in which a phased array antenna can achieve continuous non-return-to-zero beam scanning under fixed constraints. For example, the range may include the start angle and end angle of continuous scanning (such as 0° to 30°).

[0112] In some embodiments, the processor can calculate and obtain the scan range data by combining array size parameters and constraints.

[0113] In some embodiments, the phase of the phase shifter is proportional to the driving voltage when the driving voltage is greater than a threshold voltage. For a A uniform linear array scanned from 0° to a positive angle (e.g., from 0° to 90°), its... The theoretical phase of each element is given by the formula Decide.

[0114] Within this range, due to Monotonically increasing, therefore the theoretical phase of each array element... It also increases monotonically with the scanning angle. At this point, the current phase of each array element in any scanning step... Phase with the next target angle The driving voltage corresponding to the bit and All satisfy: ; By progressively adjusting the driving voltages of each element in the same direction, continuous and rapid beam scanning can be achieved without intermediate zeroing. Similarly, for negative angle scanning, converting the phase of each element from negative to positive also satisfies this progressive relationship and is applicable to non-zero switching schemes. However, the effective phase adjustment range of the liquid crystal phase shifter is limited to 0° to 360°. When the theoretical phase increment of a certain element exceeds 360°, the system will perform phase wrap-around (i.e., modulo 360° operation), causing a discontinuous jump in its actual phase value (for example, when jumping from 360° to 370°, 370° is wrapped around to 10°, which numerically appears as a decrease). This wrap-around process disrupts the continuity of phase change, making the ideal premise of "monotonically increasing" continuous switching no longer valid. In this case, it is not possible to achieve overall phase array beam adjustment by progressively adjusting the driving voltages of each element in the same direction. Similarly, non-zero switching under negative angle scanning also needs to satisfy this constraint. Therefore, the non-zero switching needs to be performed when no phase wrap-around of any array element occurs within the current scan angle step.

[0115] In some embodiments, for an array element number of A uniform linear array, its first Phase of each element This is the maximum value among all array elements. According to the phase increment relationship, if at the maximum scanning angle... At that point, the maximum phase It satisfies the constraint that phase wrap-around does not occur, i.e., its value is no greater than This ensures that all array elements are in a state from 0° to The phase progression condition is satisfied throughout the entire scanning process. Therefore, the applicability constraint of the non-return-to-zero switching scheme can be quantified as the following inequality: .

[0116] Based on this constraint, a balance needs to be struck when determining the number of array elements and the maximum scanning angle. In the beamforming calculation formula, j represents the imaginary unit; in the constraint inequality, 2π represents a complete phase period, used to determine whether phase wrapping occurs in the radiating element.

[0117] In some embodiments, to meet actual beam scanning requirements, if the positive angle scanning range is set to 0° to 30°, substituting into the constraint inequality yields a maximum allowable number of array elements of 5. Observing the data in Table 2, in a step of 20° to 30°, the phase of array element 6 jumps from 307.28° to 90.00°. This looping phenomenon causes it to fail to meet the phase progression condition, confirming the conclusion that the number of array elements is at most 5. If the scanning range is extended to 0° to 40°, the constraint condition requires the maximum number of array elements to decrease to 4. The data in Table 2 shows that in a step of 30° to 40°, the phase of array element 5 jumps from 360.00° to 102.81°, also failing to meet the direct progression condition. Although the phase change of array element 4 in this process, from 270.00° to 347.11°, satisfies the increasing relationship, to ensure that all array elements meet the non-return-to-zero switching requirement throughout the entire scan, the number of array elements still needs to be limited to 4. Ultimately, taking into account beam scanning requirements, phase constraints of non-return-to-zero switching, and the impact of the number of array elements on beam pattern performance, this embodiment determines to use an array size of 5 elements and limits its effective non-return-to-zero continuous scanning range to 0° to 30°.

[0118] In traditional zero-switching liquid crystal phased array scanning schemes This refers to the time required for a liquid crystal phase shifter to reach 90% of its steady-state phase when switching from zero phase to the next non-zero phase. This refers to the time required for the liquid crystal phase shifter to reach 10% of its current phase when switching from a non-zero phase to a zero phase. This is relevant to the proposed non-return-to-zero switching liquid crystal phased array scanning strategy. This is the time required for a liquid crystal phase shifter to reach 90% of its steady-state phase when switching from the current phase to the next phase that is greater than the current phase.

[0119] In some embodiments, to compare and verify the performance difference between the proposed non-return-to-zero switching array continuous scanning scheme and the traditional return-to-zero switching scheme, Figure 7 The phased array scanning process shown is used to simulate the object. The scanning process sequentially sets the target angle to 0°, 10°, 20° and 30°, and the switching performance of the two schemes is compared and analyzed under these conditions.

[0120] like Figure 8 As shown, this illustrates the simulation results of the phase difference of each element output by a liquid crystal phased array changing over time when using a conventional zero-switching scanning scheme in some embodiments. During the simulation, the target angle of the phased array is deflected from 0° to 10° (corresponding to the rise time) from 0s to 50s. The phased array target angle will be deflected from 10° to 0° in 50s-75s (corresponding to a decrease in time). The phased array target angle will be deflected from 0° to 20° in 75s-125s (corresponding to the rise time). The phased array target angle will be deflected from 20° to 0° in 125s-150s (corresponding to a decrease in time). The phased array target angle will be deflected from 0° to 30° in 150s-200s (corresponding to the rise time). ).

[0121] Figure 8 The specific response times are shown in Table 3. Considering that each array element is driven in parallel, the overall scan time of the system depends on the array element with the slowest response. Based on the data in the table, the response time can be obtained from the second array element. The result is 40.47 s. This result highlights the fundamental shortcomings of traditional switching strategies: when performing beam switching at arbitrary angles, the driving voltages of all phase shifters must first be reset to zero to restore the liquid crystal molecules to their initial state before the voltage is reapplied to deflect them to the new state. It is this "reset to zero and then rebuild" process that leads to the significant switching delay.

[0122] like Figure 9 As shown, this illustrates the simulation results of the phase difference output by each element of the liquid crystal phased array changing over time when employing the proposed non-return-to-zero switching scanning scheme in some embodiments. During the simulation, the target angle of the phased array is deflected from 0° to 10° (corresponding to the rise time) from 0s to 50s. The phased array target angle will be deflected from 10° to 20° in 50s-100s (corresponding to the rise time). The phased array target angle will be deflected from 20° to 30° in 100-150 seconds (corresponding to the rise time). ).

[0123] Figure 9The specific response times are shown in Table 4. Considering that each array element is driven in parallel, the overall scan time of the system depends on the array element with the slowest response. Based on the data in the table, the response time can be obtained from the second array element. The scan time is 25.11s. Compared to the 40.47s required by the traditional zero-reset switching scheme, the total time is reduced by 15.36s, and the scan speed is improved by 37.9%. This significant improvement is mainly due to two aspects: First, the non-zero-reset strategy completely avoids the relaxation time required for voltage zeroing and molecular reset before each switch. This reduces the time required for each angle switch from the traditional Simplify to a single Second, the time from the non-zero phase to the next target phase (as shown in Table 4). and The time to rise from zero phase to the same phase is generally shorter than that from zero phase, indicating that the strategy further optimizes the dynamic response of the rise process. Therefore, the proposed scheme not only eliminates the inherent delay of the zeroing stage, but also improves the switching efficiency of the phase establishment stage.

[0124] By employing a synergistic design of array-level phase progression and non-return-to-zero voltage switching, the beam switching speed of the liquid crystal phased array is significantly improved while maintaining beam pointing accuracy. The feasibility and reliability of this non-return-to-zero switching strategy rely entirely on the precise voltage-transient phase mapping model established in steps S1 to S5, which maps from microscopic molecular dynamics to macroscopic array phase. It is precisely based on the high-precision prediction capability provided by this model that the system can safely eliminate the traditional "return-to-zero" step, directly achieving rapid and continuous beam scanning, thus forming a complete and reliable system-level solution, provided that phase lag is certain to not occur. See Table 1, which shows the operating parameters of the liquid crystal phased array system simulated in this embodiment of the invention.

[0125] Table 1 Operating parameters of the liquid crystal phased array system

[0126] Table 2. Phase of each antenna element in the phased array system at various target angles.

[0127] Table 3. Response times of each array element in the traditional zero-switching liquid crystal phased array scanning scheme.

[0128] Table 4. Response times of each array element in the non-return-to-zero switching liquid crystal phased array scanning scheme.

Claims

1. A continuous beam scanning method for a liquid crystal phased array based on non-return-to-zero switching, characterized in that, include: S1: Based on the continuous medium theory of liquid crystal molecular dynamics, the dynamic response process of liquid crystal materials under the action of an external electric field is accurately modeled to obtain the mapping relationship between the driving voltage and the orientation angle of liquid crystal molecules in steady state. S2: The dielectric constant of each layer of liquid crystal molecules is calculated based on the mapping relationship between the driving voltage and the steady-state orientation angle of the liquid crystal molecules using the liquid crystal dielectric anisotropy tensor model. The mapping relationship between the driving voltage and the steady-state effective dielectric constant is obtained using the spatial averaging method. S3: Based on the mapping relationship between driving voltage and steady-state effective dielectric constant and the microstrip line transmission line model, the correspondence between driving voltage and phase difference is obtained by using the transmission phase calculation method; S4: Based on the target beam pointing angle and phased array antenna array parameters, the target phase compensation value is obtained using the geometric phase compensation calculation method; S5: Based on the correspondence between driving voltage and phase difference and the target phase compensation value, array-level dynamic simulation is performed using inverse interpolation and numerical solution of dynamic equations to obtain fixed driving voltage and dynamic response curves. S6: Based on the dynamic response curve and fixed driving voltage, the driving voltage is adjusted using a unidirectional progressive control strategy. Under the constraint that no phase folding occurs in any of the radiating elements, continuous beam scanning results are obtained, and continuous beam scanning of the liquid crystal phased array is completed.

2. The continuous beam scanning method for a liquid crystal phased array based on non-return-to-zero switching according to claim 1, characterized in that, S1 includes: Based on the continuous medium theory of liquid crystal molecular dynamics, the liquid crystal dynamic equations are simplified for engineering applications. The inertial term and Leslie coefficient term are ignored, and the liquid crystal layer is discretized into multiple sub-layers along the thickness direction to construct a system of ordinary differential equations. The ordinary differential equations are numerically solved to simulate the change of the orientation angle of liquid crystal molecules in each layer with time under a given driving voltage. Based on the aforementioned change process, a mapping relationship between the driving voltage and the steady-state orientation angle of the liquid crystal molecules is established.

3. The continuous beam scanning method for a liquid crystal phased array based on non-return-to-zero switching according to claim 2, characterized in that, The expression for the liquid crystal dynamics equation is: ； The expression for the i-th ordinary differential equation in the system of ordinary differential equations is: ； ； in, Represents the elastic constant of the development curve. Indicates the orientation angle of liquid crystal molecules. Represents the bending elastic constant. This represents the spatial coordinates of the liquid crystal layer along its thickness direction. Represents the vacuum dielectric constant. Indicates electric field strength. Indicates the driving voltage. Indicates the thickness of the liquid crystal layer. Indicates low-frequency dielectric anisotropy. Indicates the rotational viscosity of the liquid crystal. Indicates time, This represents the orientation angle of the liquid crystal molecules in the i-th layer. This represents the orientation angle of the liquid crystal molecules in the (i+1)th layer. This represents the orientation angle of the liquid crystal molecules in the (i-1)th layer. The step size represents the spatial discreteness, and i represents the layer index after discreteness in the thickness direction of the liquid crystal layer.

4. The continuous beam scanning method for a liquid crystal phased array based on non-return-to-zero switching according to claim 1, characterized in that, S2 includes: Based on the dielectric anisotropy tensor model of liquid crystal, the dielectric constant components of each liquid crystal layer under fixed orientation are calculated by utilizing the geometric relationship between the liquid crystal molecule director and the orientation angle of each liquid crystal molecule in steady state. The dielectric constant components of each liquid crystal layer are spatially averaged using the spatial averaging method. Combined with the mapping relationship between the driving voltage and the steady-state liquid crystal molecule orientation angle, a mapping relationship between the driving voltage and the steady-state effective dielectric constant is established.

5. The continuous beam scanning method for a liquid crystal phased array based on non-return-to-zero switching according to claim 1, characterized in that, S3 includes: Based on the mapping relationship between the driving voltage and the steady-state effective dielectric constant, the range of variation of the effective dielectric constant of the liquid crystal layer under different driving states is determined; Based on the microstrip transmission line model and the effective dielectric constant variation range, the microstrip line length is determined by the maximum phase difference requirement, and a dielectric constant correction factor is introduced to calibrate the theoretical phase difference, resulting in a calibrated method for calculating the transmission phase. Based on the calibrated transmission phase calculation method, a correspondence between the driving voltage and the output phase difference of the phase shifter under steady state is established.

6. The continuous beam scanning method for a liquid crystal phased array based on non-return-to-zero switching according to claim 5, characterized in that, The expression for the output phase difference of the phase shifter is: ； in, Indicates the phase difference at the output of the phase shifter. This represents the multiplication correction factor related to the dielectric constant. Indicates the operating frequency. Indicates the length of the microstrip line. Represents the speed of light in a vacuum. This represents the macroscopically effective dielectric constant of the liquid crystal layer at time t, corresponding to the driving voltage V. This represents the macroscopic effective dielectric constant of the liquid crystal layer when the driving voltage is 0.

7. The continuous beam scanning method for a liquid crystal phased array based on non-return-to-zero switching according to claim 1, characterized in that, S4 includes: Based on the target beam pointing angle and phased array antenna array parameters, a phase change model is constructed using the geometric phase compensation calculation method. Using the phase change model, the target phase compensation value required for each radiating element in the antenna array is obtained.

8. The continuous beam scanning method for a liquid crystal phased array based on non-return-to-zero switching according to claim 1, characterized in that, S5 includes: Based on the correspondence between driving voltage and phase difference, the fixed driving voltage corresponding to the target phase compensation value of each radiating element is found by inverse interpolation. The fixed driving voltage is substituted as an input parameter into the liquid crystal molecule dynamics model; Array-level dynamic simulation is performed using inverse interpolation and numerical solution of the dynamic equations to calculate the transient process of the output phase change of each radiating element over time and generate dynamic response curves.

9. The continuous beam scanning method for a liquid crystal phased array based on non-return-to-zero switching according to claim 1, characterized in that, S6 includes: Based on the dynamic response curve, the increasing relationship of the phase of each radiating element during continuous beam scanning is obtained; Based on the fixed driving voltage and the increasing relationship, the driving voltage is adjusted using a unidirectional progressive control strategy. During the adjustment process, the applicable array size and scanning range are determined with the constraint that no phase wrap-around occurs in any of the radiating elements. Based on the array size and scanning range, under the constraints, the antenna array is driven to switch beam pointing according to a preset scanning angle sequence, and the overall time is evaluated by combining the rise time and fall time to obtain the continuous beam scanning result, thus completing the continuous beam scanning of the liquid crystal phased array.

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