CN113849962A - Liquid crystal holographic phased array antenna beam synthesis method for correcting reference wave model - Google Patents
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Abstract
The invention discloses a liquid crystal holographic phased array antenna beam synthesis method for correcting a reference wave model, and belongs to the technical field of holographic antennas. The method is based on the electromagnetic radiation and scattering theory, establishes a high-precision electromagnetic model considering the scattering effect of each radiation unit on guided waves through a semi-analytic method, modifies a reference wave model in the holographic principle, improves the amplitude and phase precision of each unit excitation signal, finally improves the antenna beam forming performance, and solves the problem of low precision of the conventional beam synthesis method based on the holographic principle.
Description
Technical Field
The invention belongs to the technical field of holographic antennas, and particularly relates to a liquid crystal holographic phased array antenna beam synthesis method for correcting a reference wave model.
Background
The current method of implementing holographic antennas is to apply the holographic principle in optics to the microwave band. The holographic principle is originated from optics at first, and is to interfere reference light with object light scattered by an object, record interference fringes, and recover a three-dimensional image of the object when the interference fringes are irradiated by the same reference light, wherein the interference fringes contain all amplitude and phase information of the scattered light of the object. Since then, the idea of the holographic principle is applied to the field of microwave antennas, and the concept of holographic antennas has been brought forth. Early holographic antennas utilized curved metal strip patterns on printed circuit boards in place of the alternating bright and dark fringes of interfering field strength. Theoretically, the changes of the bright and dark fringes of the interference field are continuous, and the metal strip pattern can only realize two states of 'existence' and 'nonexistence' of metal, belongs to binary quantization, has poor quantization precision, and causes the limitation of radiation performance. Later, scalar and tensor holographic super-surface antennas are proposed, and by means of the change of the size or the rotation angle of each sub-wavelength unit, more states are introduced to simulate holographic interference fringes, so that the beam forming precision of the holographic antenna is improved to a certain extent, but performances such as the aperture efficiency and the sidelobe level of the antenna are different from practical requirements, and dynamic regulation and control cannot be achieved.
In recent years, liquid crystal materials have attracted great research interest because of their dielectric continuously tunable properties, which are helpful for realizing dynamic control of devices. The liquid crystal material is fused with the holographic super-surface antenna, so that the liquid crystal holographic phased array antenna with dynamic beam forming and beam scanning capabilities can be realized. Compared with the traditional half-wavelength spacing phased array antenna, the liquid crystal holographic phased array antenna has the characteristic of sub-wavelength unit spacing of the super-surface antenna, so that the antenna has higher regulation and control flexibility.
However, the current holographic principle beam synthesis method has low precision and limited beam forming performance, which is characterized by low antenna aperture efficiency, large side lobe and premature grating lobe in the scanning process. The reason is that, when the holographic principle is used, the excitation signal (i.e. the reference wave) of each unit needs to be known, the main mode field of the standard waveguide is used as the reference wave at present, the scattering effect of each radiation unit on the main mode field is not considered, and the actual guided wave necessarily contains higher-order modes caused by the scattering of the radiation unit. Therefore, the actual guided wave is not completely consistent with the reference wave model, which means that the amplitude and phase information of the excitation signal of each radiation unit is inaccurate, and the difference between the physical radiation front obtained after synthesis and the theoretical interference pattern is large, resulting in poor beam forming effect.
Therefore, the error of the beam synthesis algorithm is a key factor for restricting the beam forming performance of the holographic antenna, and the accurate calculation and regulation of the amplitude and the phase of the excitation signal of each unit are crucial to improving the beam forming performance of the holographic antenna. The more accurate the reference wave model is, the closer the antenna array surface state approaches the theoretical interference pattern, and the higher the beamforming accuracy is. The current reference wave model simply adopts a guided wave main mode field model, which can cause a series of problems of poor beam forming precision, low aperture efficiency, main beam pointing deviation, unsatisfactory gain, larger side lobe, grating lobe appearing too early in the scanning process, limited scanning angle range and the like due to unit amplitude and phase error.
Disclosure of Invention
The invention aims to solve the problem that the shaping performance of an antenna beam is limited due to inaccuracy of a reference wave model in the prior art, and provides a liquid crystal holographic phased array antenna beam comprehensive method for correcting the reference wave model, which takes the scattering effect of each radiation unit on a guided wave into account, corrects the reference wave model and improves the amplitude and phase precision of unit excitation signals; the continuous adjustable characteristic of the liquid crystal material is utilized to introduce multi-bit quantization coding, so that the physically realized antenna array surface is closer to the interference pattern calculated by theory, and the beam forming and beam scanning performances of the holographic antenna are finally improved.
The technical problem proposed by the invention is solved as follows:
a liquid crystal holographic phased array antenna beam synthesis method for correcting a reference wave model comprises the following steps:
step 1. extraction of Unit polarizability
Each sub-wavelength radiation unit in the liquid crystal holographic phased array antenna is equivalent to a magnetic dipole, and the whole liquid crystal holographic phased array antenna is equivalent to a coupling magnetic dipole array; simulating a single radiation unit by utilizing full-wave electromagnetic simulation software, extracting electric field and magnetic field distribution, and calculating the equivalent magnetic polarizability of the radiation unit:
wherein alpha ism,xxIs the equivalent magnetic polarizability of the components of the electric and magnetic fields in the x-direction, j is the imaginary unit, ω is the angular frequency, μ is the permeability, H0xIs the component of the magnetic field in the x-direction, S is the surface area of the radiating element, ExComponent of the electric field in the x-direction, EyComponent of the electric field in the y-direction, αm,xyEquivalent magnetic polarizability, α, for the components of the electric and magnetic fields in the x and y directions, respectivelym,yxEquivalent magnetic polarizability, H, of the components of the electric and magnetic fields in the y-and x-directions, respectively0yComponent of the magnetic field in the y-direction, αm,yyEquivalent magnetic polarizability which is the component of the electric and magnetic fields in the y-direction;
equivalent magnetic polarizability in tensor form
Comprises the following steps:
wherein,
a unit vector representing the x-direction,
a unit vector representing the y direction;
step 2. expression of dyadic Green function
Within waveguide dyadic Green function
Comprises the following steps:
wherein,
is the position of the ith radiation unit,
the j is the position of the jth radiation unit, i and j are positive integers, and i is not equal to j; gxx＝Hx x-pol/mx，Gxy＝Hy x-pol/mx，Gyx＝Hx y-pol/my，Gyy＝Hy y-pol/my；GxxFor the component of the dyadic Green function in the waveguide in the xx direction, Hx x-polComponent of the magnetic field in the x-direction, m, produced by an x-polarized magnetic dipolexIs the size of the x-polarized magnetic dipole source, GxyAs a component of the dyadic Green function in the xy direction, H, within the waveguidey x-polComponent of the magnetic field in the y-direction, G, generated by an x-polarized magnetic dipoleyxIs the component of the dyadic Green function in the waveguide in the yx direction, Hx y-polMagnetic field generated for y-polarized magnetic dipole in x-directionComponent of direction, myIs the size of the y-polarized magnetic dipole source, GyyIs the component of the dyy direction of the dyadic Green function in the waveguide, Hy y-polThe component of the magnetic field in the y-direction that is generated by the y-polarized magnetic dipole;
outside waveguide dyadic Green function
Comprises the following steps:
wherein,
is a unit dyadic, k02 pi/lambda, lambda is the wavelength corresponding to the working frequency,
total dyadic Green function
Expressed as:
step 3, solving the equivalent magnetic dipole moment of the radiation unit
Magnetic dipole moment of radiating element
Comprises the following steps:
wherein，
And
an incident wave magnetic field and a scattered wave magnetic field respectively;
wherein ε is a dielectric constant;
the two formulas are combined to obtain:
wherein,
and
the equivalent magnetic dipole moment of the radiating element can be solved reversely by the above formula for known quantity
Step 4, solving the holographic formula after the modified reference wave
Writing the equivalent magnetic dipole moment of the radiating element in complex form as the multiplication of the amplitude term and the phase:
wherein, | | represents modulus taking, and angle represents phase taking;
and multiplying the above formula into a standard waveguide main mode field expression to correct the amplitude and the phase of the reference wave, wherein the holographic formula after the reference wave is corrected is as follows:
wherein psiintf，iIn order to interfere with the field intensity distribution,
is the number of waves in space and,
is the pointing direction of the target wave,
is the wave number in the waveguide; superscript denotes conjugation;
step 5. amplitude modulation
Further obtaining an amplitude modulation formula based on the holographic interference field intensity distribution:
wherein M (i, theta) is the amplitude modulation value of the ith radiation unit at the desired beam pointing angle theta, MmaxFor a maximum value of the set amplitude modulation value, MminRe represents a real part for the minimum value of the set amplitude modulation value;
the method comprises the steps of obtaining the relation between radiation power and liquid crystal dielectric constant by performing electromagnetic simulation on a radiation unit, obtaining the relation between liquid crystal bias voltage and the liquid crystal dielectric constant by testing, obtaining the relation between the radiation power of the radiation unit and the liquid crystal dielectric constant, establishing a mapping table, and reading the liquid crystal bias voltage corresponding to the amplitude modulation value of the radiation unit by searching the mapping table, so that the amplitude modulation of the radiation unit is realized.
And traversing all the values of i to obtain the liquid crystal bias voltage in all the radiation units in the liquid crystal holographic phased array antenna.
Preferably, in the method of the present invention
Is replaced by
Indicating the position of the radiation element in the ith row and the jth column in the two-dimensional holographic phased array antenna,
is replaced by
The method is applicable to the synthesis of the two-dimensional holographic antenna array.
Further, the liquid crystal holographic phased-array antenna is composed of a radiation structure, a feed structure and a liquid crystal layer, wherein the radiation structure comprises a micro-strip patch array which is periodically arranged according to a sub-wavelength interval, the feed structure is composed of a waveguide with a slot array, the liquid crystal layer is packaged between the feed structure and the radiation structure layer, and the micro-strip patch array and the waveguide with the slot array are respectively used as a positive electrode and a negative electrode for applying external bias voltage. Microstrip patch, corresponding bitThe liquid crystal layer and the feed structure constitute a radiating element. The dielectric constant of the liquid crystal material is changed by regulating the bias voltage of each radiating unit, so that the radiation intensity of the radiating units is changed. By utilizing the method, the known reference wave expression and the expected target wave expression are mathematically calculated to obtain the theoretical interference field intensity spatial distribution, the interference field intensity spatial distribution is subjected to discretization and quantization processing to obtain the state required by each radiation unit of the antenna array, and the bias voltage signal is applied to the liquid crystal of each radiation unit to enable the physical phased array antenna array surface to simulate the theoretical interference pattern, thereby realizing beam shaping. And the bias voltage distribution pattern of each radiation unit is changed, so that dynamic beam forming and beam scanning can be realized. Because the dielectric constant of the liquid crystal is continuously adjustable, each liquid crystal antenna unit can realize a plurality of quantization states through the bias voltage control of multi-bit digital coding, for example, 2 can be realized through 3-bit coding3The antenna array surface realized in physics can be more approximate to the interference pattern in theory by using the multi-bit coding, which is beneficial to improving the beam forming precision.
The invention has the beneficial effects that:
the method of the invention modifies the reference wave and the multi-bit code, so that the amplitude and phase precision of the reference wave at each unit are improved, the physically realized antenna array surface is closer to the theoretical interference pattern, the target wave characteristic can be restored more accurately, the beam pointing precision is improved, the side lobe is reduced, the grid lobe is prevented from appearing too early, and the antenna beam shaping performance is finally and effectively improved.
Drawings
FIG. 1 is a schematic flow diagram of the process of the present invention;
FIG. 2 is a schematic structural diagram of a rectangular waveguide fed one-dimensional liquid crystal holographic phased array antenna unit according to an embodiment;
fig. 3 is a schematic diagram of an antenna array structure of a rectangular waveguide fed one-dimensional liquid crystal holographic phased array according to an embodiment;
FIG. 4 is a schematic structural diagram of a parallel plate waveguide fed two-dimensional liquid crystal holographic phased array antenna unit according to the second embodiment;
fig. 5 is a schematic diagram of a two-dimensional liquid crystal holographic phased array antenna array structure fed by a parallel plate waveguide according to the second embodiment.
Detailed Description
The invention is further described below with reference to the figures and examples.
Example one
The present embodiment provides a method for synthesizing a liquid crystal holographic phased array antenna beam for correcting a reference wave model, a flow diagram of which is shown in fig. 1, and the method includes the following steps:
step 1. extraction of Unit polarizability
Each sub-wavelength radiation unit in the liquid crystal holographic phased array antenna is equivalent to a magnetic dipole, and the whole liquid crystal holographic phased array antenna is equivalent to a coupling magnetic dipole array;
the liquid crystal holographic phased-array antenna of this embodiment is a one-dimensional liquid crystal holographic phased-array antenna based on rectangular waveguide feed, and a schematic structural diagram of a radiation unit is shown in fig. 2, and includes a first dielectric plate 101, a radiation patch 102 located below the first dielectric plate 101, a second dielectric plate 103 located below the radiation patch 102, a rectangular waveguide 105 located below the second dielectric plate 103, a slot 104 located on the upper surface of the rectangular waveguide 105, and an excitation port 106 located on an opening surface of the rectangular waveguide 105. In this embodiment, the material of the first dielectric plate 101 is glass, and the material of the second dielectric plate 103 is liquid crystal.
Radio frequency signals are excited through the port 106, the other end of the opening face is provided with a matching port, and the radio frequency signals are coupled to the patch 102 through the gap 104 to be radiated. Modeling and simulating in a CST microwave working chamber, extracting electric field and magnetic field distribution, and calculating the equivalent magnetic polarizability of a radiation unit:
wherein alpha ism,xxIs the equivalent magnetic polarizability of the components of the electric and magnetic fields in the x-direction, j is the imaginary unit, ω is the angular frequency, μ is the permeability, H0xIs the component of the magnetic field in the x-direction, S is the surface area of the radiating element, ExComponent of the electric field in the x-direction, EyComponent of the electric field in the y-direction, αm,xyEquivalent magnetic polarizability, α, for the components of the electric and magnetic fields in the x and y directions, respectivelym,yxEquivalent magnetic polarizability, H, of the components of the electric and magnetic fields in the y-and x-directions, respectively0yComponent of the magnetic field in the y-direction, αm,yyEquivalent magnetic polarizability which is the component of the electric and magnetic fields in the y-direction;
equivalent magnetic polarizability in tensor form
Comprises the following steps:
wherein,
a unit vector representing the x-direction,
a unit vector representing the y direction;
the resulting polarizability parameter depends only on the structure and material of the cell, and is independent of the incident field and the location of the cell in the array. All cells in the array that are in the same state can be represented by the same polarizability parameter.
The schematic structural diagram of the phased array antenna array is shown in fig. 3, and the phased array antenna array comprises a radiation structure and a feed structure, wherein the radiation structure comprises a dielectric slab 201, a one-dimensional microstrip patch array 202, a liquid crystal layer 204, and an adhesive 203 for packaging liquid crystal, and the feed structure comprises a rectangular waveguide 206, a one-dimensional slot array 205 located on the upper surface of the rectangular waveguide 206, and a feed port 207 located on one opening surface of the rectangular waveguide 206.
When a radio frequency signal is fed through the port 207, the guided wave in the waveguide will propagate toward the other opening surface of the rectangular waveguide 206, and couple to the radiating patch array 202 through the slot array 205, and radiate upward in a leaky-wave manner in a half-space. The radiation power of each unit can be regulated by regulating the liquid crystal dielectric constant of each unit by utilizing the holographic principle, and finally the expected radiation pattern is realized.
Step 2. expression of dyadic Green function
And the dyadic Green function is divided into two areas, namely the inside of the waveguide and the outside of the waveguide, which are respectively deduced.
In the waveguide, the position of the ith radiation unit is considered
For the position of the jth radiation unit
The scattering effect is obtained, i and j are positive integers, i is not equal to j, and the solution is carried out by adopting a multiple mirror image method and an electromagnetic superposition principle aiming at the influence of an upper waveguide surface and a lower waveguide surface
Magnetically polarized dipole and multiple mirror images at observation point
The radiation field, dividing the radiation field by the magnitude of the source, yields an expression for the green function, namely:
Gxx＝Hx x-pol/mx
Gxy＝Hy x-pol/mx
Gyx＝Hx y-pol/my
Gyy＝Hy y-pol/my
wherein G isxxFor the component of the dyadic Green function in the waveguide in the xx direction, Hx x-polComponent of the magnetic field in the x-direction, m, produced by an x-polarized magnetic dipolexIs the size of the x-polarized magnetic dipole source, GxyAs a component of the dyadic Green function in the xy direction, H, within the waveguidey x-polComponent of the magnetic field in the y-direction, G, generated by an x-polarized magnetic dipoleyxIs the component of the dyadic Green function in the waveguide in the yx direction, Hx y-polComponent of the magnetic field in the x-direction, m, produced by a y-polarized magnetic dipoleyIs the size of the y-polarized magnetic dipole source, GyyIs the component of the dyy direction of the dyadic Green function in the waveguide, Hy y-polThe component of the magnetic field in the y-direction that is generated by the y-polarized magnetic dipole;
within waveguide dyadic Green function
Comprises the following steps:
outside waveguide dyadic Green function
Adopting a free space dyadic Green function:
wherein,
is a unit dyadic, k02 pi/lambda, lambda being the operating frequencyThe wavelength corresponding to the wavelength of the light,
total dyadic Green function
Expressed as:
step 3 of solving equivalent magnetic dipole moment of radiation unit
Magnetic dipole moment of radiating element
Comprises the following steps:
wherein,
and
the electromagnetic wave scattering device is characterized by comprising an incident wave magnetic field and a scattered wave magnetic field respectively, wherein the incident wave refers to a field where a waveguide main mode works, and the scattered wave is reflected by scattering effect of each antenna unit on feed traveling wave;
wherein ε is a dielectric constant;
the two formulas are combined to obtain:
wherein,
and
the equivalent magnetic dipole moment of the radiating element can be solved reversely by the above formula for known quantity
Step 4, solving the holographic formula after the modified reference wave
Writing the equivalent magnetic dipole moment of the radiating element in complex form as the multiplication of the amplitude term and the phase:
wherein, | | represents modulus taking, and angle represents phase taking;
and multiplying the above formula into a standard waveguide main mode field expression to correct the amplitude and the phase of the reference wave, wherein the holographic formula after the reference wave is corrected is as follows:
wherein psiintf，iFor the interference field intensity distribution (interference pattern),
is the number of waves in space and,
is the pointing direction of the target wave,
is the wave number in the waveguide; superscript denotes conjugation;
in the above formula, the first and second carbon atoms are,
is a target wave, and is a target wave,
is a reference wave; the conventional holographic formula is:
is a target wave, and is a target wave,
is a reference wave; by contrast, the modified reference wave of the present invention is multiplied by an amplitude and phase associated with the location of the element at each radiating element (denoted by the i-subscript), where the amplitude and phase modification factors are mathematical models reflecting the scattering effect of each radiating element on the reference wave;
step 6. amplitude modulation
Further obtaining an amplitude modulation formula based on the holographic interference field intensity distribution:
wherein M (i, theta) is the amplitude modulation value of the ith radiation unit at the desired beam pointing angle theta, MmaxFor a set widthMaximum value of degree modulation value, MminRe represents the real part for the minimum value of the set amplitude modulation value.
The method comprises the steps of obtaining the relation between radiation power and liquid crystal dielectric constant by performing electromagnetic simulation on a radiation unit, obtaining the relation between liquid crystal bias voltage and the liquid crystal dielectric constant by testing, obtaining the relation between the radiation power (namely the square of modulation amplitude) of the radiation unit and the liquid crystal dielectric constant, establishing a mapping table, and reading the liquid crystal bias voltage corresponding to the amplitude modulation value of the radiation unit by searching the mapping table, thereby realizing amplitude modulation of the radiation unit.
And traversing all the values of i to obtain the liquid crystal bias voltage in all the radiation units in the liquid crystal holographic phased array antenna.
Example two
The present embodiment provides a method for synthesizing a liquid crystal holographic phased array antenna beam for correcting a reference wave model, a flow diagram of which is shown in fig. 1, and the method includes the following steps:
step 1. extraction of Unit polarizability
Each sub-wavelength radiation unit in the liquid crystal holographic phased array antenna is equivalent to a magnetic dipole, and the whole liquid crystal holographic phased array antenna is equivalent to a coupling magnetic dipole array;
the liquid crystal holographic phased-array antenna described in this embodiment is a two-dimensional liquid crystal holographic phased-array antenna based on parallel plate waveguide feed, and a schematic structural diagram of a radiation unit is shown in fig. 4, and includes a dielectric plate 301, a radiation patch 302, a dielectric plate 303, a metal plate 304 with a slit in the center, a dielectric plate 305, a metal plate 306, and a dipole antenna 307. The dielectric plates 301 and 305 are made of glass, and the dielectric plate 303 is made of liquid crystal.
The structure shown in fig. 4 is built in a CST microwave operating room, and a radiation boundary condition is applied, and a dipole antenna 307 generates a cylindrical wave, which is coupled to the radiation patch 302 through a gap at the center of the upper metal plate 304 to further radiate to the upper half space. Extracting the distribution of the electric field and the magnetic field through CST simulation, calculating equivalent magnetic polarizability parameters by the same method as the step 1 in the first embodiment, and expressing the magnetic polarizability in a tensor form
Changing the dielectric constant of the liquid crystal, simulating and calculating the equivalent magnetic polarizability again, and establishing an equivalent magnetic polarizability model library of the unit under all possible states.
The array structure diagram of the two-dimensional liquid crystal phased-array antenna fed by the parallel plate waveguide is shown in fig. 5, and comprises a radiation structure and a feed structure, wherein the radiation structure comprises a dielectric plate 401, a two-dimensional microstrip patch array 402 and a liquid crystal layer 403, the feed structure comprises a parallel plate waveguide and a coaxial connector 407, and the parallel plate waveguide comprises an upper metal plate 404, a dielectric plate 405 and a lower metal plate 406 which are provided with slot arrays. The microstrip patch array 402 is aligned with the slot array on the metal plate 404 one by one. The coaxial connector 407 is located at the very center of the parallel plate waveguide for feeding the rf signal. The guided wave in the parallel plate waveguide will propagate outwards and couple to the radiating patch array 402 through the slot array, radiating upwards in half-space in the form of a leaky wave. The radiation power of each unit can be regulated by regulating the bias voltage of the liquid crystal of each unit by utilizing the holographic principle, and finally the expected radiation directional diagram is realized.
Step 2. expression of dyadic Green function
And the dyadic Green function is divided into two areas, namely the inside of the waveguide and the outside of the waveguide, which are respectively deduced.
In the waveguide, the position of the radiation unit in the ith row and the jth column is considered
For the radiation unit of the p row and the q column
The scattering effect of the position, i is not equal to p or j is not equal to q, aiming at the influence of the upper waveguide surface and the lower waveguide surface, a multiple mirror image method and an electromagnetic superposition principle are adopted to solve
Magnetically polarized dipole and multiple mirror images at observation point
The radiation field, dividing the radiation field by the magnitude of the source, yields an expression for the green function, namely: gxx＝Hx x-pol/mx，Gxy＝Hy x-pol/mx，Gyx＝Hx y-pol/my，Gyy＝Hy y-pol/my；
Within waveguide dyadic Green function
Comprises the following steps:
outside waveguide dyadic Green function
Adopting a free space dyadic Green function:
wherein,
is a unit dyadic, k02 pi/lambda, lambda is the wavelength corresponding to the working frequency,
total dyadic Green function
Expressed as:
step 3, solving the equivalent magnetic dipole moment of the radiation unit
Magnetic dipole moment of radiating element
Comprises the following steps:
wherein,
and
the electromagnetic wave scattering device is characterized by comprising an incident wave magnetic field and a scattered wave magnetic field respectively, wherein the incident wave refers to a field where a waveguide main mode works, and the scattered wave is reflected by scattering effect of each antenna unit on feed traveling wave;
wherein ε is a dielectric constant;
the two formulas are combined to obtain:
wherein,
and
the equivalent magnetic dipole moment of the radiating element can be solved reversely by the above formula for known quantity
Step 4, solving the holographic formula after the modified reference wave
Writing the equivalent magnetic dipole moment of the radiating element in complex form as the multiplication of the amplitude term and the phase:
wherein, | | represents modulus taking, and angle represents phase taking;
and multiplying the above formula into a standard waveguide main mode field expression to correct the amplitude and the phase of the reference wave, wherein the holographic formula after the reference wave is corrected is as follows:
wherein psiintf，ijFor the interference field intensity distribution (interference pattern),
is the number of waves in space and,
is the pointing direction of the target wave,
is the wave number in the waveguide; superscript denotes conjugation;
in the above formula, the first and second carbon atoms are,
is a target wave, and is a target wave,
is a reference wave; the conventional holographic formula is:
is a target wave, and is a target wave,
is a reference wave; by contrast, the modified reference wave of the present embodiment is multiplied by an amplitude and a phase related to the position of each radiation element (represented by subscript ij), where the amplitude and phase modification factors are mathematical models reflecting the scattering effect of each radiation element on the reference wave;
step 5. amplitude modulation
Further obtaining an amplitude modulation formula based on the holographic interference field intensity distribution:
wherein M (i, j, theta, phi) is an amplitude modulation value of the ith row and jth column radiation unit when the azimuth angle and the pitch angle of the expected beam direction are phi and theta respectively, MmaxFor a maximum value of the set amplitude modulation value, MminRe represents the real part for the minimum value of the set amplitude modulation value.
The method comprises the steps of obtaining the relation between radiation power and liquid crystal dielectric constant by performing electromagnetic simulation on a radiation unit, obtaining the relation between liquid crystal bias voltage and the liquid crystal dielectric constant by testing, obtaining the relation between the radiation power (namely the square of modulation amplitude) of the radiation unit and the liquid crystal dielectric constant, establishing a mapping table, and reading the liquid crystal bias voltage corresponding to the amplitude modulation value of the radiation unit by searching the mapping table, thereby realizing amplitude modulation of the radiation unit.
And traversing all the values of i and j to obtain the states required by all the radiation units in the liquid crystal holographic phased array antenna.
It is foreseeable that because the amplitude and phase precision of the reference wave at each unit is improved, a more accurate holographic interference pattern can be obtained by using the holographic formula after the reference wave model is corrected, and the multi-bit high-precision quantization of the liquid crystal is combined, so that the liquid crystal super-surface structure which is physically realized can be more approximate to the theoretical interference field intensity distribution, thereby more accurately restoring the target wave characteristic, improving the beam pointing precision, reducing the side lobe, avoiding the premature occurrence of the grating lobe, and finally greatly improving the antenna performance.
As the holographic principle is an analytic comprehensive method, the method has extremely high comprehensive efficiency and can meet the requirement of real-time regulation and control. In addition, the holographic principle is also suitable for multi-beam synthesis, and only the target wave needs to be replaced by an expected multi-beam directional pattern function.
The present invention has been described in connection with the accompanying drawings, but the specific implementation of the present invention is not limited by the above-described manner, and it is within the scope of the present invention to employ various insubstantial modifications of the inventive method concept and solution, or to directly apply the inventive concept and solution to other applications without modification.
Claims (4)
1. A liquid crystal holographic phased array antenna beam synthesis method for correcting a reference wave model is characterized by comprising the following steps:
step 1. extraction of Unit polarizability
Each sub-wavelength radiation unit in the liquid crystal holographic phased array antenna is equivalent to a magnetic dipole, and the whole liquid crystal holographic phased array antenna is equivalent to a coupling magnetic dipole array; simulating a single radiation unit by utilizing full-wave electromagnetic simulation software, extracting electric field and magnetic field distribution, and calculating the equivalent magnetic polarizability of the radiation unit:
wherein alpha ism,xxIs the equivalent magnetic polarizability of the components of the electric and magnetic fields in the x-direction, j is the imaginary unit, ω is the angular frequency, μ is the permeability, H0xIs the component of the magnetic field in the x-direction, S is the surface area of the radiating element, ExComponent of the electric field in the x-direction, EyComponent of the electric field in the y-direction, αm,xyEquivalent magnetic polarizability, α, for the components of the electric and magnetic fields in the x and y directions, respectivelym,yxEquivalent magnetic polarizability, H, of the components of the electric and magnetic fields in the y-and x-directions, respectively0yComponent of the magnetic field in the y-direction, αm,yyEquivalent magnetic polarizability which is the component of the electric and magnetic fields in the y-direction;
equivalent magnetic polarizability in tensor form
Comprises the following steps:
wherein,
a unit vector representing the x-direction,
a unit vector representing the y direction;
step 2. expression of dyadic Green function
Within waveguide dyadic Green function
Comprises the following steps:
wherein,
is the position of the ith radiation unit,
the j is the position of the jth radiation unit, i and j are positive integers, and i is not equal to j; gxx＝Hx x-pol/mx，Gxy＝Hy x-pol/mx，Gyx＝Hx y-pol/my，Gyy＝Hy y-pol/my；GxxFor the component of the dyadic Green function in the waveguide in the xx direction, Hx x-polComponent of the magnetic field in the x-direction, m, produced by an x-polarized magnetic dipolexIs the size of the x-polarized magnetic dipole source, GxyAs a component of the dyadic Green function in the xy direction, H, within the waveguidey x-polComponent of the magnetic field in the y-direction, G, generated by an x-polarized magnetic dipoleyxIs the component of the dyadic Green function in the waveguide in the yx direction, Hx y-polComponent of the magnetic field in the x-direction, m, produced by a y-polarized magnetic dipoleyIs the size of the y-polarized magnetic dipole source, GyyIs the component of the dyy direction of the dyadic Green function in the waveguide, Hy y-polThe component of the magnetic field in the y-direction that is generated by the y-polarized magnetic dipole;
outside waveguide dyadic Green function
Comprises the following steps:
wherein,
is a unit dyadic, k02 pi/lambda, lambda is the wavelength corresponding to the working frequency,
total dyadic Green function
Expressed as:
step 3, solving the equivalent magnetic dipole moment of the radiation unit
Magnetic dipole moment of radiating element
Comprises the following steps:
wherein,
and
an incident wave magnetic field and a scattered wave magnetic field respectively;
wherein ε is a dielectric constant;
the two formulas are combined to obtain:
wherein,
and
the equivalent magnetic dipole moment of the radiating element can be solved reversely by the above formula for known quantity
Step 4, solving the holographic formula after the modified reference wave
Writing the equivalent magnetic dipole moment of the radiating element in complex form as the multiplication of the amplitude term and the phase:
wherein, | | represents modulus taking, and angle represents phase taking;
and multiplying the above formula into a standard waveguide main mode field expression to correct the amplitude and the phase of the reference wave, wherein the holographic formula after the reference wave is corrected is as follows:
wherein, yintf，iIn order to interfere with the field intensity distribution,
is the number of waves in space and,
is the pointing direction of the target wave,
is the wave number in the waveguide; superscript denotes conjugation;
step 5. amplitude modulation
Further obtaining an amplitude modulation formula based on the holographic interference field intensity distribution:
wherein M (i, theta) is the amplitude modulation value of the ith radiation unit at the desired beam pointing angle theta, MmaxFor a maximum value of the set amplitude modulation value, MminRe represents a real part for the minimum value of the set amplitude modulation value;
the method comprises the steps of obtaining the relation between radiation power and liquid crystal dielectric constant by performing electromagnetic simulation on a radiation unit, obtaining the relation between liquid crystal bias voltage and liquid crystal dielectric constant by testing, thus obtaining the relation between the radiation power of the radiation unit and the liquid crystal dielectric constant, establishing a mapping table, and reading the liquid crystal bias voltage corresponding to the amplitude modulation value of the radiation unit by searching the mapping table, thereby realizing amplitude modulation on the radiation unit;
and traversing all the values of i to obtain the liquid crystal bias voltage in all the radiation units in the liquid crystal holographic phased array antenna.
2. The method for beam synthesis of a liquid crystal holographic phased array antenna with modified reference wave model as claimed in claim 1, wherein the method of claim 1
Is replaced by
Indicating the position of the radiation element in the ith row and the jth column in the two-dimensional holographic phased array antenna,
is replaced by
The position of a radiation unit in a p-th row and a q-th column in the two-dimensional holographic phased array antenna is represented, i is not equal to p or j is not equal to q, a beam pointing angle theta is replaced by (theta, phi), and phi and theta after replacement represent the azimuth angle and the pitch angle of beam pointing, so that the two-dimensional holographic phased array antenna is suitable for synthesis of the two-dimensional holographic antenna array.
3. The wave beam synthesis method for the liquid crystal holographic phased array antenna with the modified reference wave model as claimed in claim 1 or claim 2, wherein the liquid crystal holographic phased array antenna is composed of a radiation structure, a feed structure and a liquid crystal layer, the radiation structure comprises a microstrip patch array which is periodically arranged according to a sub-wavelength interval, the feed structure is composed of a waveguide with a slot array, the liquid crystal layer is packaged between the feed structure and the radiation structure layer, and the microstrip patch array and the waveguide with the slot array are respectively used as a positive electrode and a negative electrode for applying an external bias voltage; the microstrip patch, the liquid crystal layer at the corresponding position and the feed structure form a radiation unit; the dielectric constant of the liquid crystal material is changed by regulating the bias voltage of each radiation unit, so that the radiation intensity of the radiation units is changed; performing mathematical calculation on a known reference wave expression and an expected target wave expression to obtain theoretical interference field intensity spatial distribution, performing dispersion and quantization processing on the interference field intensity spatial distribution to obtain bias voltage required by each radiation unit in the phased array antenna, and applying a bias voltage signal to liquid crystal of each radiation unit to enable a physical phased array antenna array surface to simulate a theoretical interference pattern so as to realize beam shaping; and the bias voltage distribution pattern of each radiation unit is changed, and dynamic beam forming and beam scanning are realized.
4. The method of claim 3, wherein the dielectric constant of the liquid crystal is controlled by a multi-bit digitally encoded bias voltage, each liquid crystal antenna element achieving multiple quantization states.
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