A method for calculating the nonlinear target scattering cross-section of harmonic radar

Abstract

The present invention provides a method for calculating the scattering cross-sectional area of ​​a nonlinear target by a harmonic radar, comprising the following steps: establishing a nonlinear target harmonic scattering surface current element model; obtaining harmonic radar incident electromagnetic wave parameters and parameters of the nonlinear target to be determined; using the nonlinear target parameters to be determined and the incident electromagnetic wave parameters, combined with the nonlinear target harmonic scattering surface current element model, calculating the induced current density of third harmonic scattering excited by the surface of the nonlinear target to be determined; using a panel element method to establish the surface model of the nonlinear target to be determined, using triangular panels to mesh the surface of the nonlinear target to be determined, integrating each triangular panel using a numerical method to calculate the third harmonic scattering electric field intensity of the nonlinear target to be determined; and calculating the harmonic scattering area of ​​the nonlinear target. By considering the microscopic nonlinear volt-ampere characteristics to establish the nonlinear target scattering surface current element model, the present invention provides an effective method for calculating the scattering characteristics of nonlinear targets in harmonic radars.

Description

Technical Field

[0001] The present invention relates to the technical field of harmonic radar, and in particular to a method for calculating the nonlinear target scattering cross-section of a harmonic radar. Background Art

[0002] Harmonic radar exploits the nonlinear characteristics of the target and detects the harmonic components scattered by the target. Unlike fundamental radar, which only receives the reflected signal of the fundamental wave, harmonic radar receives the second and third harmonics excited by the target. This allows harmonic radar to effectively search for and identify nonlinear targets. Compared with fundamental radar, harmonic radar features a novel detection mechanism and strong anti-clutter performance, making it a new radar technology with significant application value. Its outstanding advantages include strong anti-clutter performance, strong anti-stealth capabilities, and excellent recognition performance. Harmonic radar has broad application prospects in fields such as national economic development and national defense.

[0003] However, the research on the scattering cross section of nonlinear scattering targets is still unclear, and there is no method to calculate the scattering cross section of nonlinear targets, which seriously restricts the design and application promotion of harmonic radar systems. Summary of the Invention

[0004] The technical problem solved by the present invention is to overcome the deficiencies of the prior art and provide a method for calculating the scattering cross-section of a nonlinear target by a harmonic radar, thereby solving the problem that the nonlinear target characteristics cannot be calculated.

[0005] The technical solution of the present invention is:

[0006] A method for calculating the nonlinear target scattering cross-sectional area of ​​a harmonic radar comprises the following steps:

[0007] (1) Establish a nonlinear target third harmonic scattering surface current element model;

[0008] (2) obtaining harmonic radar incident electromagnetic wave parameters and nonlinear target parameters to be determined, wherein the incident electromagnetic wave parameters include the incident electromagnetic wave angular frequency and the incident electromagnetic wave electric field intensity;

[0009] (3) Using the parameters of the incident electromagnetic wave and the parameters of the nonlinear target to be determined, combined with the nonlinear target third harmonic scattering surface current element model, calculate the induced current density of the nonlinear target surface that excites the third harmonic scattering;

[0010] (4) Using the surface element method to establish the nonlinear target surface model to be solved, and using regular shape surface elements to mesh the nonlinear target surface to be solved;

[0011] (5) Setting a reference point, integrating each element using a numerical method based on the incident electromagnetic wave parameters and the induced current density of the third harmonic scattering excited by the nonlinear target to be determined, and calculating the electric field intensity of the third harmonic scattering electric field of the nonlinear target to be determined at the reference point;

[0012] (6) Calculate the third harmonic scattering area of ​​the nonlinear target based on the electric field intensity of the third harmonic scattering electric field of the nonlinear target to be determined at the reference point and the electric field intensity of the incident electromagnetic wave.

[0013] Preferably, the nonlinear target is a metal target, including metal 1 and metal 2, with an insulating layer between metal 1 and metal 2.

[0014] Preferably, the nonlinear target parameters to be determined include metal 1 barrier height, metal 2 barrier height and insulating layer thickness.

[0015] Preferably, in step (1), the nonlinear target third harmonic scattering surface current element model is specifically:

[0016]

[0017] D=4πs(2m) 0.5 / h

[0018] V0=E i Δl

[0019]

[0020] Where J3 is the surface current density of the nonlinear target surface that excites the third harmonic scattering, m is the electron mass, e0 is the electron charge, and h is the Planck constant. is the barrier height of metal 1, is the metal 2 barrier height, s is the thickness of the insulating layer, K is the temperature coefficient of conductivity, Δl is the skin depth, ω0 is the angular frequency of the incident electromagnetic wave, μ is the magnetic permeability of the metal target, γ is the conductivity of the metal target, E i is the electric field strength of the incident electromagnetic wave reaching the metal target surface.

[0021] Preferably, in step (5), the electric field intensity of the third harmonic scattered electric field of the nonlinear target to be determined at the reference point is calculated, specifically by the following expression:

[0022]

[0023] in, is the electric field intensity of the third harmonic scattered electric field of the nonlinear target to be determined at the reference point, j is the imaginary unit, k is the wave number of the incident electromagnetic wave, Z is the impedance of the electromagnetic wave in vacuum, e is the natural logarithm, r is the distance from the surface of the nonlinear target to be determined to the reference point, π is the pi constant, |E i | is the modulus of the electric field intensity of the incident electromagnetic wave reaching the metal target surface, S is the surface area of ​​the nonlinear target to be determined, J m3 is the surface current density of the target surface m-th element that excites the third harmonic scattering, k3 is the wave number of the third harmonic, is the wave vector of the third harmonic scattered by the mth surface element, is the position vector from the mth surface element to the reference point.

[0024] Preferably, in step (6), the third harmonic scattering area of ​​the nonlinear target to be determined is calculated based on the electric field intensity of the third harmonic scattering electric field of the nonlinear target to be determined at the reference point and the electric field intensity of the incident electromagnetic wave, specifically by the following expression:

[0025]

[0026] Where σ3 is the third harmonic scattering area of ​​the nonlinear target to be determined.

[0027] Preferably, the regularly shaped surface element is a triangular surface element.

[0028] The advantages of the present invention compared with the prior art are:

[0029] Based on the relationship between microscopic nonlinear volt-ampere characteristics and nonlinear scattering, the present invention establishes a surface current element model for harmonic scattering of nonlinear targets. On this basis, the surface element method is used to model the nonlinear target surface. The intensity of the harmonic scattering electric field of the nonlinear target surface is calculated by discrete nonlinear integration, thereby realizing a method for calculating the harmonic scattering characteristics of a macroscopic structure. The method also comprehensively considers the response of harmonic radar scattering targets, scattering field boundary constraints, and surface current processing, thereby realizing the calculation of the scattering cross-sectional area of ​​nonlinear targets detected by harmonic radar. The method has important value for the design and application of harmonic radar systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 This is a flow chart of the method for calculating the nonlinear target scattering cross-sectional area of ​​harmonic radar according to the present invention;

[0031] Figure 2 This is the simulation result of the third harmonic RCS of a metal target in an embodiment of the present invention. DETAILED DESCRIPTION

[0032] The following detailed description of the present invention will make the features and advantages of the present invention more clear and explicit.

[0033] The nonlinear target receives the incident electromagnetic wave from the harmonic radar, generates harmonic components through nonlinearity, and then radiates the harmonic components of various frequencies outward;

[0034] When an electromagnetic wave with an angular frequency of ω0 and an electric field strength amplitude of E0 is incident on a nonlinear target surface, the harmonic components of various frequencies in the electric field scattered by the nonlinear target surface are expressed as follows:

[0035]

[0036] Where n is the number of harmonics scattered by the nonlinear target under the action of the incident electromagnetic wave, a n is the complex energy series coefficient, a1 is the linear response of the nonlinear target to the incident electromagnetic wave, {a2, a3, ...} represents the nonlinear response characteristics of the nonlinear target to the incident electromagnetic wave, E S (t) is the total scattered electric field of the nonlinear target under the action of the incident electromagnetic wave.

[0037] The above formula describes a series of harmonics with an angular frequency of nω0, from which the nonlinear response of harmonic scattering of different orders can be obtained.

[0038] A microscopic nonlinear harmonic scattering surface current element model is established based on the microscopic material volt-ampere characteristics of the nonlinear target.

[0039] Specifically, the study of harmonic radar nonlinear cross sections essentially examines the nonlinear phenomena that occur when an incident wave strikes a boundary. Based on the physical inference that electric charges cannot be created or extinguished, and that electromagnetic fields are excited by charge and current distributions, the electromagnetic field must satisfy boundary conditions at the interface between two media. Reflection and transmission of electromagnetic waves occur due to the current induced by the incident wave at the material interface. This induced current radiates a scattered field, the source of which must satisfy boundary conditions. Therefore, surface currents and surface magnetic fluxes can be explained by the total tangential field at the surface.

[0040]

[0041] in, To cause the induced current of the nth harmonic component, is the unit normal vector of the nonlinear target surface, The magnetic field intensity of the scattered field formed by all harmonic components, n = 1, 2, 3..., n is a positive integer.

[0042] The corresponding charge densities are then related to the respective currents via the law of charge conservation:

[0043]

[0044] ω0 is the angular frequency of the incident wave, μ is the magnetic permeability, and i is the imaginary part.

[0045] Different currents correspond to harmonics of different frequencies. For harmonic components, the scattered field includes all harmonic components such as fundamental, secondary, and tertiary.

[0046] Nonlinear targets can reradiate harmonics when exposed to an external excitation field. These targets are typically man-made, with typical examples including PN junctions and metals. A harmonic scattering surface current element model is developed using the third harmonic scattering of a metal target as an example.

[0047] Starting from the material properties of the nonlinear node, the nonlinear volt-ampere characteristic is established, and based on it, the re-radiation characteristics of the node under the irradiation of an external excitation field are analyzed, and the nonlinear target harmonic radiation surface current element expression is established.

[0048] The harmonic components in step 1 can be scattered by different frequencies, and the surface current element expression for exciting the third harmonic can be obtained as follows:

[0049]

[0050] in,

[0051]

[0052] D=4πs(2m) 0.5 / h

[0053] Where J3 is the surface current density of the nonlinear target surface that excites the third harmonic scattering, m is the electron mass, e0 is the electron charge, and h is the Planck constant. is the barrier height of metal 1, is the metal 2 barrier height, s is the thickness of the insulating layer, and K is the temperature coefficient of conductivity.

[0054] The surface current element is concentrated on the nonlinear target surface and within the surface skin depth, so: V0 = E i Δl,

[0055]

[0056] Where Δl is the skin depth, ω0 is the angular frequency of the incident electromagnetic wave, μ is the magnetic permeability of the metal target, γ is the electrical conductivity of the metal target, and E i is the electric field strength of the incident electromagnetic wave reaching the metal target surface.

[0057] A nonlinear target scattering element simulation model is established, and the induced current on the nonlinear target surface is calculated by combining it with the microscopic nonlinear harmonic scattering current element model.

[0058] The nonlinear target surface is divided into Region 1 and Region 2. Assume that each region has current, magnetic current, and charge. The field at any point in Region 1 is equal to the sum of the volume integral of each source in Region 1 and the surface integral of the field on the surface formed by the sources in Region 2.

[0059] When solving the induced current on the surface of an object, the following assumptions are made: (1) The radius of curvature of the target surface must be much larger than the wavelength; (2) Only those areas on the surface of the object that are directly illuminated by the incident wave will generate induced current, that is, only the bright area of ​​the target will generate induced current; (3) The wave number of the electromagnetic wave should tend to infinity; (4) The characteristics of the induced current on the bright area of ​​the target are the same as the current characteristics on the infinite plane tangent to the surface at the incident point.

[0060] When solving the scattered field of a nonlinear target, it is assumed that the electric and magnetic fields in each discrete unit are constant. The surface of the nonlinear target is divided into several triangular grids, and the integral is solved using numerical methods.

[0061] Assume that the target object is divided into m small triangles Tm, where 1, 2, ..., m. For the illuminated triangular mesh, the surface of the triangular mesh will generate an induced current, while for the unilluminated triangular mesh, the surface of the mesh will not generate an induced current. The panel method can be used to obtain:

[0062]

[0063] in, The induced current of the mth triangle causes the nth harmonic. is the unit normal vector of the mth triangle surface element, The mth triangle is incident with the nth harmonic electromagnetic wave magnetic field. If a triangular surface element is irradiated by the electromagnetic wave, an induced current will be generated on the surface of the surface element. If a triangular surface element is not irradiated by the electromagnetic wave, no induced current will be generated on the target surface.

[0064] On this basis, for the third harmonic, the electric field intensity of the third harmonic scattered electric field of the nonlinear target to be determined at the reference point is calculated by the following expression:

[0065]

[0066] in, is the electric field intensity of the third harmonic scattered electric field of the nonlinear target to be determined at the reference point, j is the imaginary unit, k is the wave number of the incident electromagnetic wave, Z is the impedance of the electromagnetic wave in vacuum, e is the natural logarithm, r is the distance from the surface of the nonlinear target to be determined to the reference point, π is the pi constant, |E i | is the modulus of the electric field intensity of the incident electromagnetic wave reaching the metal target surface, S is the surface area of ​​the nonlinear target to be determined, J m3is the surface current density of the target surface m-th element that excites the third harmonic scattering, k3 is the wave number of the third harmonic, is the wave vector of the third harmonic scattered by the mth surface element, is the position vector from the mth surface element to the reference point.

[0067] The third harmonic scattering area of ​​the nonlinear target to be determined is calculated using the following expression:

[0068]

[0069] Where σ3 is the third harmonic scattering area of ​​the nonlinear target to be determined.

[0070] The above expression can be extended to the calculation of the nth harmonic scattering area of ​​a nonlinear target by replacing the part of the expression corresponding to the third harmonic component with the nth harmonic.

[0071] In a specific embodiment, the nonlinear target is a square metal plate, the side length of the square is 20 times the incident wavelength, the incident wave frequency is 3GHz, the electromagnetic wave is vertically incident along the z-axis, and the observation angle is from 0° to 180°. Using the harmonic radar nonlinear target scattering cross-sectional area calculation method of the present invention, the harmonic

[0072] The three-scattering cross section, such as Figure 2 shown.

[0073] The contents not described in detail in the specification of the present invention belong to the common knowledge of those skilled in the art.

Claims

1. A method for calculating the nonlinear target scattering cross-section of a harmonic radar, characterized in that: The following steps are involved: (1) Establish a nonlinear target third harmonic scattering surface current element model; (2) obtaining harmonic radar incident electromagnetic wave parameters and nonlinear target parameters to be determined, wherein the incident electromagnetic wave parameters include the incident electromagnetic wave angular frequency and the incident electromagnetic wave electric field intensity; (3) Using the parameters of the incident electromagnetic wave and the parameters of the nonlinear target to be determined, combined with the nonlinear target third harmonic scattering surface current element model, calculate the induced current density of the nonlinear target surface that excites the third harmonic scattering; (4) Using the surface element method to establish the nonlinear target surface model to be solved, and using regular shape surface elements to mesh the nonlinear target surface to be solved; (5) Setting a reference point, integrating each element using a numerical method based on the incident electromagnetic wave parameters and the induced current density of the third harmonic scattering excited by the nonlinear target to be determined, and calculating the electric field intensity of the third harmonic scattering electric field of the nonlinear target to be determined at the reference point; (6) Calculating the third harmonic scattering area of ​​the nonlinear target based on the electric field intensity of the third harmonic scattering electric field of the nonlinear target to be determined at the reference point and the electric field intensity of the incident electromagnetic wave; It is calculated by the following expression: Among them, σ3 is the third harmonic scattering area of ​​the nonlinear target to be determined; is the electric field intensity of the third harmonic scattered electric field of the nonlinear target to be determined at the reference point, r is the distance from the surface of the nonlinear target to be determined to the reference point, π is the pi constant, E i is the electric field strength of the incident electromagnetic wave reaching the metal target surface.

2. The method for calculating the nonlinear target scattering cross-section of a harmonic radar according to claim 1, wherein: The nonlinear target is a metal target, including metal 1 and metal 2, with an insulating layer between metal 1 and metal 2.

3. The method for calculating the nonlinear target scattering cross-section of a harmonic radar according to claim 2, wherein: The nonlinear target parameters to be determined include the metal 1 barrier height, the metal 2 barrier height and the insulation layer thickness.

4. The method for calculating the nonlinear target scattering cross-section of a harmonic radar according to claim 3, wherein: In step (1), the nonlinear target third harmonic scattering surface current element model is specifically: D=4πs(2m) 0.5 / h V0=E i Δl Where J3 is the surface current density of the nonlinear target surface that excites the third harmonic scattering, m is the electron mass, e0 is the electron charge, and h is the Planck constant. is the barrier height of metal 1, is the metal 2 barrier height, s is the thickness of the insulating layer, K is the temperature coefficient of conductivity, Δl is the skin depth, ω0 is the angular frequency of the incident electromagnetic wave, μ is the magnetic permeability of the metal target, γ is the conductivity of the metal target, E i is the electric field strength of the incident electromagnetic wave reaching the metal target surface.

5. The method for calculating the nonlinear target scattering cross-section of a harmonic radar according to claim 4, characterized in that: In step (5), the electric field intensity of the third harmonic scattered electric field of the nonlinear target to be determined at the reference point is calculated, specifically by the following expression: in, is the electric field intensity of the third harmonic scattered electric field of the nonlinear target to be determined at the reference point, j is the imaginary unit, k is the wave number of the incident electromagnetic wave, Z is the impedance of the electromagnetic wave in vacuum, e is the natural logarithm, r is the distance from the surface of the nonlinear target to be determined to the reference point, π is the pi constant, |E i | is the modulus of the electric field intensity of the incident electromagnetic wave reaching the metal target surface, S is the surface area of ​​the nonlinear target to be determined, J m3 is the surface current density of the target surface m-th element that excites the third harmonic scattering, k3 is the wave number of the third harmonic, is the wave vector of the third harmonic scattered by the mth surface element, is the position vector from the mth surface element to the reference point.

6. A method for calculating the nonlinear target scattering cross-section of a harmonic radar according to any one of claims 1 to 5, characterized in that: The regular-shaped surface element is a triangular surface element.

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