A linear polarization dispersion compensation method and unit based on equivalent circuit model

Abstract

The present invention provides a linear polarization dispersion compensation method and unit based on an equivalent circuit model. Based on ADS and HFSS simulation software, the phase distribution of the non-diffracting beam is adjusted through the equivalent circuit model to obtain the resonant frequency required for each region; the equivalent circuit analysis method of the frequency selective surface FSS of the multilayer medium is adopted to correspond the above equivalent circuit model to the actual physical parameters one by one, and the actual physical parameters obtained are put into HFSS for simulation verification to obtain results that are basically consistent with the expected effect; the function of dispersion compensation for linear polarization electromagnetic waves is realized. The present invention constructs a non-diffracting beam by modulating the phase distribution of the non-diffracting beam, and controls the phase change and the basic phase at the same time, providing theoretical guidance for the precise design of the linear polarization dispersion compensation unit. The working bandwidth of the super atom for dispersion compensation of the present invention reaches 40%, and the working principle of the super atom is better explained.

Description

Technical Field

[0001] The invention belongs to the field of electromagnetic microwave radio frequency technology, and in particular relates to a linear polarization dispersion compensation method and unit based on an equivalent circuit model. Background Art

[0002] Metasurface is a surface composed of artificially designed meta-atoms. It is used in various fields due to its powerful ability to control the phase, amplitude, frequency and polarization of electromagnetic waves, such as multi-beamforming, stealth cloaks, radar cross-section reduction and holographic imaging. However, due to the material dispersion relationship of meta-atoms themselves, most of these meta-atoms are designed at a single frequency point, that is, as the frequency of the incident electromagnetic wave changes, the designed function will change; for example, a beam deflection metasurface with a center frequency of 75GHz, when the frequency of the incident electromagnetic wave is 75GHz, the deflection angle of its output beam is 45 degrees; but when the frequency of the incident electromagnetic wave is 60GHz, its beam deflection angle will become 25 degrees.

[0003] Although this dispersion phenomenon has a wide range of applications, there is also an urgent need for dispersion-compensating metasurfaces in the fields of communication, detection, imaging, and display. Wang et al. proposed a principle for compensating dispersion in 2017. They designed a reflective meta-atom, adjusted the slope of the phase by adjusting the geometric parameters of the meta-atom, and adjusted the basic phase by rotating the meta-atom. Since the basic phase is adjusted by rotating the meta-atom, the method of compensating dispersion here is only applicable to circularly polarized incident electromagnetic waves. There are also some reports on dispersion compensation for linearly polarized electromagnetic waves, but these works lack theoretical guidance. Therefore, it is very meaningful to efficiently and accurately design linear polarization dispersion compensation units. Summary of the invention

[0004] The technical problem to be solved by the present invention is to provide a linear polarization dispersion compensation method and unit based on an equivalent circuit model, which are used to perform dispersion compensation on linear polarization electromagnetic waves.

[0005] The technical solution adopted by the present invention to solve the above technical problems is: a linear polarization dispersion compensation method based on an equivalent circuit model, comprising the following steps:

[0006] S1: Adjust the phase distribution of the undiffracted beam through the equivalent circuit model to obtain the required resonant frequency of each area of ​​the metasurface to generate a broadband achromatic quasi-diffracted beam;

[0007] S2: Perform equivalent circuit analysis on the multilayer dielectric frequency selective surface, and correspond the equivalent circuit model to the actual physical parameters one by one; verify the actual physical parameters obtained by simulation until the results consistent with the expected effect are obtained;

[0008] S3: Re-extract the equivalent circuit of the multilayer dielectric frequency selective surface.

[0009] According to the above scheme, in step S1, the specific steps are:

[0010] S11: Phase distribution using zero-order Bessel metasurface;

[0011] S12: Selecting the central metal region as the phase reference to adjust the relative phase distribution of each region;

[0012] S13: Adjust the phase distribution of each region of the metasurface so that the metaatom resonates within or near the working frequency band. Further, in the step S11, let L be the array period and D be the maximum non-diffraction distance, then the axicon angle θ is:

[0013]

[0014] Let f be the frequency of the beam in free space, c be the speed of light in free space, and (x, y) be the position of each region of the metasurface. Then the phase distribution of the zero-order Bessel metasurface is adopted. for:

[0015]

[0016] Furthermore, in the step S12, taking the first region of pure metal as a reference, the relative phase distribution of each region is adjusted to:

[0017]

[0018] Furthermore, in step S13, the phase resonance frequency f0 is set to the frequency when the phase is π; let m be an integer, and adjust the phase distribution so that the meta-atom resonates within or near the working frequency band:

[0019]

[0020] Furthermore, in step S2, the specific steps are:

[0021] S21: The equivalent circuit of the frequency selective surface is a capacitor and an inductor connected in series, and a low-pass circuit model is obtained, which is converted into a band-pass circuit model;

[0022] S22: Convert the bandpass circuit model into an equivalent bandpass circuit model using multi-layer structure physical implementation.

[0023] Furthermore, in step S22, the equivalent bandpass circuit model includes capacitors and inductors connected in series on the parallel branches, and a parallel admittance inverter; the capacitors and inductors connected in series are realized by selecting a suitable frequency selective surface, and the admittance inverter is realized by a 1 / 4 wavelength converter, and the operating frequency is the center of the designed operating bandwidth;

[0024] Let T0 be the group delay of each area, f c is the cutoff frequency of the low-pass circuit, Z0 is the wave impedance of free space, B is the working bandwidth of the band-pass circuit, n is the number of layers where the frequency selective surface is located, then the inductance L n,d and capacitor C n,d The calculation formulas are as follows:

[0025]

[0026] Furthermore, the order of the frequency selective surface required to realize the reflective array in each area of ​​the metasurface depends on the phase variation capability of the frequency selective surface in the operating frequency band, that is, the range of the group delay; the larger the range of the group delay variation, the greater the order of the frequency selective surface required.

[0027] Furthermore, in step S3, the specific steps are:

[0028] S31: According to the transmission line theory, the dielectric layer is equivalent to a series transmission line, and the frequency selective surface is equivalent to a parallel admittance. The network T is a cascade of the left transmission line, the frequency selective surface network and the right transmission line. Since a dielectric layer is added on both sides of the frequency selective surface, let A1 be the transmission matrix of the dielectric layer. is the transmission matrix of the frequency selective surface; then the overall transmission matrix A is written as:

[0029] A=A1A FSS A1;

[0030] set up is the inverse matrix of A1, then the transmission matrix A of the frequency selective surface FSS It is expressed as:

[0031]

[0032] S32: According to the transmission matrix A FSS With the impedance matrix Z FSS The impedance matrix Z FSS It is expressed as:

[0033]

[0034] According to the definition of microwave network theoretical impedance and each element, the impedance matrix Z FSSThe four elements of are equal and are equivalent impedances of the frequency selective surface;

[0035] S33: According to the above equivalent circuit model, the equivalent circuit of the frequency selective surface is a series capacitor and inductor, so the series impedance of the frequency selective surface is:

[0036]

[0037] The capacitance and inductance within the frequency band are averaged, and then optimized using a genetic algorithm to ultimately extract the corresponding capacitance and inductance.

[0038] A linear polarization dispersion compensation unit based on an equivalent circuit model, the system comprises a processor and a memory, the memory stores computer instructions, the processor is used to execute the computer instructions stored in the memory, and when the computer instructions are executed by the processor, the system implements the steps of a linear polarization dispersion compensation method based on an equivalent circuit model.

[0039] The beneficial effects of the present invention are:

[0040] 1. The present invention discloses a linear polarization dispersion compensation method and unit based on an equivalent circuit model. Based on ADS and HFSS simulation software, the phase distribution of the undiffracted beam is adjusted through the equivalent circuit model to obtain the resonant frequency required in each area. The equivalent circuit analysis method of the frequency selective surface FSS of a multilayer medium is adopted to correspond the above-mentioned equivalent circuit model to the actual physical parameters one by one, and the obtained actual physical parameters are put into HFSS for simulation verification to obtain results that are basically consistent with the expected effect. The function of dispersion compensation for linearly polarized electromagnetic waves is realized.

[0041] 2. The present invention constructs a diffraction-free beam by modulating the phase distribution of the diffraction-free beam and simultaneously controls the phase change and the basic phase, providing theoretical guidance for the precise design of a linear polarization dispersion compensation unit.

[0042] 3. The working bandwidth of the super-atom for dispersion compensation of the present invention reaches 40%, which provides a better explanation of the working principle of the super-atom. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 is a flow chart of an embodiment of the present invention.

[0044] Figure 2 It is a graph showing the change in phase of the reflection coefficient of each region of the adjusted metasurface with frequency according to an embodiment of the present invention.

[0045] Figure 3 It is a low-pass equivalent circuit model diagram of an embodiment of the present invention.

[0046] Figure 4It is a bandpass equivalent circuit model diagram of an embodiment of the present invention.

[0047] Figure 5 It is a bandpass equivalent circuit model diagram of the physical implementation of the embodiment of the present invention.

[0048] Figure 6 3 is a trend diagram of the reflection phase of the super-atom in the three regions of the ADS according to the embodiment of the present invention changing with the frequency.

[0049] Figure 7 FIG. 4 is a front view of an I-shaped FSS embedded in a multi-layer medium according to an embodiment of the present invention.

[0050] Figure 8 FIG. 4 is a top view of an I-shaped FSS embedded in a multi-layer medium according to an embodiment of the present invention.

[0051] Fig. 9 FIG. 4 is an equivalent circuit diagram of an I-shaped FSS embedded in a multilayer medium according to an embodiment of the present invention.

[0052] Fig.10 4 is a graph showing the variation trend of the extracted capacitance with the W parameter according to an embodiment of the present invention.

[0053] Fig.11 4 is a graph showing the variation trend of the extracted inductance with the L2 parameter according to an embodiment of the present invention.

[0054] Fig.12 It is a diagram of a superatomic structure model of an embodiment of the present invention.

[0055] Fig.13 4 is an equivalent circuit diagram of the superatom structure model of the embodiment of the present invention.

[0056] Fig.14 It is a trend diagram of the phase of the super-atom in three regions changing with frequency in HFSS according to an embodiment of the present invention. DETAILED DESCRIPTION

[0057] The present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0058] See also Figure 1 , an embodiment of the present invention comprises the following steps:

[0059] S1: The phase distribution of the undiffracted beam is adjusted through the equivalent circuit model to obtain the resonant frequency required for each area of ​​the metasurface to generate a broadband achromatic quasi-diffracted beam; S11: Let L be the array period and D be the maximum undiffracted distance, then the axicon angle θ is:

[0060]

[0061] Assuming f is the frequency of the beam in free space, c is the speed of light in free space, and (x, y) is the position of each area of ​​the metasurface, the phase distribution of the zero-order Bessel metasurface is:

[0062]

[0063] S12: Taking the first region of pure metal as a reference, the relative phase distribution of each region is adjusted to:

[0064]

[0065] S13: Figure 2 The phase variation of the reflection coefficient of each region of the metasurface in the E band with frequency is given, from top to bottom, it is region 1 to region 10. Since the central metal region is selected as the phase reference, the resonant frequency f0 of the phase is set to the frequency when the phase is π; the element with f0 within the working bandwidth is called the resonant element, and the element with f0 not within the working bandwidth is called the non-resonant element. Figure 2 In the example, only the meta-atoms in the first region belong to the resonant elements. Then the phase distribution is adjusted to make the meta-atoms resonate within or near the working frequency band:

[0066]

[0067] Here, m is an integer, so it does not affect the phase distribution of each region.

[0068] Table 1 gives the resonant frequencies f of components in different regions. r1 、f r2 、f r3 , corresponding to -π, -3π, and -5π, respectively. The resonant frequencies shown in bold in Table 1 are ultimately used in the precise design of the reflective element.

[0069] Table 1 Resonant frequencies corresponding to different regions of the reflectarray antenna

[0070] area Fr1 Fr2 Fr3 2 87.7 3 73.1 4 62.6 5 54.8 6 43.8 87.7 7 36.5 73.0 8 33.7 67.4 9 30.2 60.5 90.7 10 27.4 54.8 82.2

[0071] S2: The equivalent circuit analysis method of multilayer dielectric frequency selective surface is used to correspond the equivalent circuit model with the actual physical parameters one by one; the equivalent circuit model is as follows Figure 3 , 4 , as shown in 5;

[0072] S21: converting the low-pass circuit model into a band-pass circuit model;

[0073] S22: converting the bandpass circuit model into an equivalent bandpass circuit model using multilayer structure physical implementation;

[0074] Let T0 be the group delay of each area, f c for Figure 3 The cut-off frequency of the low-pass circuit shown in the figure, Z0 is the wave impedance of free space, B is the working bandwidth of the designed band-pass circuit, n is the number of layers where the frequency selective surface is located, according to the derivation of the above equivalent circuit, the final inductance L n,d and capacitance C n,d They are shown as follows:

[0075]

[0076] from Figure 5 It can be seen that the final equivalent circuit model includes capacitors and inductors in series on the parallel branches, and a parallel admittance inverter. The series capacitors and inductors are realized by selecting appropriate FSS. The admittance inverter is realized by a 1 / 4 wavelength converter, and its operating frequency is the center of the designed operating bandwidth, that is, 75GHz. The order of FSS required to realize the reflective array depends on its phase change capability in the operating frequency band, that is, the range of group delay. The larger the group delay change range, the greater the order of FSS required. According to the formula, the capacitance and inductance values ​​of the circuit model required for the four-layer reflective elements in the three regions are given in Table 2. In order to verify the accuracy of the equivalent circuit, the equivalent capacitance and inductance given in Table 2 are verified in ADS, and the trend of its phase change with frequency is shown in the following figure. Figure 6 .

[0077] Table 2 Capacitance and inductance values ​​of the equivalent circuit model of meta-atoms in three regions

[0078]

[0079]

[0080] S3: Re-extract the equivalent circuit of the I-shaped patch wrapped in a multilayer dielectric. According to the transmission line theory, the dielectric layer can be equivalent to a series transmission line, and the FSS can be equivalent to a parallel admittance, such as Figure 7 , 8 , 9. The network T is the cascade of the transmission line on the left, the FSS network and the transmission line on the right. Since a dielectric layer is added on both sides of the FSS, its transmission matrix can be written as:

[0081] A=A1A FSS A1

[0082] Here A is the overall transmission matrix, A1 is the transmission matrix of the dielectric layer, is the transmission matrix of FSS. Then the transmission matrix of FSS is expressed as:

[0083]

[0084] here Refers to the inverse matrix of A1. According to the conversion relationship between the transmission matrix and the impedance matrix, Z FSS It is expressed as:

[0085]

[0086] According to the impedance of microwave network theory and the definition of each element, Z FSS The four elements are equal and are the equivalent impedance of FSS. According to the above equivalent circuit model, the equivalent circuit of FSS is a series capacitor and inductor, so its series impedance is:

[0087]

[0088] Since the equivalent capacitance and inductance are not particularly stable within the frequency range to be solved, in order to reduce the error, the capacitance and inductance within the frequency band to be solved are averaged, and then optimized using a genetic algorithm to finally extract the corresponding capacitance and inductance.

[0089] Fig.10 , 11 The variation trend of capacitance and inductance with l2 and w is given. Table 3 gives the values ​​of l1, l2 and w corresponding to the three regions. In order to verify the accuracy of the physical parameters in Table 3, HFSS is used for full-wave simulation. The model structure and equivalent circuit are shown in Fig.12 , 13 shown. Fig.14 The trends of phase variation with frequency in different regions are given.

[0090] Table 3 Key physical parameters of the three regions

[0091]

[0092] The results show that:

[0093] observe Figure 4 and with Figure 2 Compared with the ideal phase change trend, the slope of the designed phase curve is basically the same, and the resonance points of regions 2, 3, and 9 are 87.7, 73, and 60.4 GHz, respectively, which are consistent with the resonance frequencies given in Table 1, indicating the accuracy of the circuit used. Figure 8 and with Figure 4 A comparison of the phase change trends in ADS shows that the phase change trends are consistent, and the resonance points are shifted to low frequencies, but the magnitude of the shift is small and basically consistent, so it is believed that the extracted physical parameters are accurate.

[0094] It should be understood that the size of the serial numbers of the steps in the above embodiments does not mean the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the present application.

[0095] The above embodiments are only used to illustrate the design ideas and features of the present invention, and their purpose is to enable those skilled in the art to understand the content of the present invention and implement it accordingly. The protection scope of the present invention is not limited to the above embodiments. Therefore, any equivalent changes or modifications made based on the principles and design ideas disclosed by the present invention are within the protection scope of the present invention.

Claims

1. A linear polarization dispersion compensation method based on an equivalent circuit model, characterized in that: The following steps are involved: S1: Adjust the phase distribution of the undiffracted beam through the equivalent circuit model to obtain the required resonant frequency of each area of ​​the metasurface to generate a broadband achromatic quasi-diffracted beam; S2: Perform equivalent circuit analysis on the multilayer dielectric frequency selective surface, and correspond the equivalent circuit model to the actual physical parameters one by one; verify the actual physical parameters obtained by simulation until the results consistent with the expected effect are obtained; the specific steps are: S21: The equivalent circuit of the frequency selective surface is a capacitor and an inductor connected in series, and a low-pass circuit model is obtained, which is converted into a band-pass circuit model; S22: converting the bandpass circuit model into an equivalent bandpass circuit model using multilayer structure physical implementation; The equivalent bandpass circuit model includes capacitors and inductors connected in series on the parallel branches, and a parallel admittance inverter. The series capacitors and inductors are realized by selecting a suitable frequency selective surface, and the admittance inverter is realized by a 1 / 4 wavelength converter. The operating frequency is the center of the designed working bandwidth. Let T0 be the group delay of each area, f c is the cutoff frequency of the low-pass circuit, Z0 is the wave impedance of free space, B is the working bandwidth of the band-pass circuit, n is the number of layers where the frequency selective surface is located, then the inductance L n,d and capacitor C n,d The calculation formulas are as follows: S3: Re-extract the equivalent circuit of the multilayer dielectric frequency selective surface; the specific steps are: S31: According to the transmission line theory, the dielectric layer is equivalent to a series transmission line, and the frequency selective surface is equivalent to a parallel admittance. The network T is a cascade of the left transmission line, the frequency selective surface network and the right transmission line. Since a dielectric layer is added on both sides of the frequency selective surface, let A1 be the transmission matrix of the dielectric layer. is the transmission matrix of the frequency selective surface; then the overall transmission matrix A is written as: A=A1A FSS A1; Let A1 - is the inverse matrix of A1, then the transmission matrix A of the frequency selective surface FSS It is expressed as: S32: According to the transmission matrix A FSS With the impedance matrix Z FSS The impedance matrix Z FSS It is expressed as: According to the definition of microwave network theoretical impedance and each element, the impedance matrix Z FSS The four elements of are equal and are equivalent impedances of the frequency selective surface; S33: According to the above equivalent circuit model, the equivalent circuit of the frequency selective surface is a series capacitor and inductor, so the series impedance of the frequency selective surface is: The capacitance and inductance within the frequency band are averaged, and then optimized using a genetic algorithm to ultimately extract the corresponding capacitance and inductance.

2. The linear polarization dispersion compensation method based on an equivalent circuit model according to claim 1, characterized in that: In the step S1, the specific steps are: S11: Phase distribution using zero-order Bessel metasurface; S12: Selecting the central metal region as the phase reference to adjust the relative phase distribution of each region; S13: Adjusting the phase distribution of each region of the metasurface so that the meta-atom resonates within or near an operating frequency band.

3. The linear polarization dispersion compensation method based on an equivalent circuit model according to claim 2, characterized in that: In the step S11, assuming that L is the array period and D is the maximum non-diffraction distance, the axicon angle θ is: Let f be the frequency of the beam in free space, c be the speed of light in free space, and (x, y) be the position of each region of the metasurface. The phase distribution φ(f) of the zero-order Bessel metasurface is:

4. The linear polarization dispersion compensation method based on an equivalent circuit model according to claim 3, characterized in that: In the step S12, taking the first region of pure metal as a reference, the relative phase distribution of each region is adjusted to:

5. The linear polarization dispersion compensation method based on an equivalent circuit model according to claim 3, characterized in that: In the step S13, the phase resonance frequency f0 is set to the frequency when the phase is π; let m be an integer, and adjust the phase distribution so that the meta-atom resonates within or near the working frequency band:

6. The linear polarization dispersion compensation method based on an equivalent circuit model according to claim 1, characterized in that: The order of the frequency selective surface required to realize the reflective array in each area of ​​the metasurface depends on the phase variation capability of the frequency selective surface in the operating frequency band, that is, the range of the group delay; the larger the range of the group delay variation, the greater the order of the frequency selective surface required.

7. A linear polarization dispersion compensation unit based on an equivalent circuit model, comprising a processor and a memory, characterized in that: The memory stores computer instructions, and the processor is used to execute the computer instructions stored in the memory. When the computer instructions are executed by the processor, the steps of a linear polarization dispersion compensation method based on an equivalent circuit model as described in any one of claims 1 to 6 are implemented.

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