CN112462153B - Fresnel coefficient-based method for estimating radiation characteristics of antennas in dielectric plate - Google Patents
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Abstract
The invention discloses a Fresnel coefficient-based method for estimating radiation characteristics of an antenna in a dielectric slab, which comprises the following steps of: (1) mesh subdivision is carried out on the antenna model in the dielectric plate; (2) calculating the mirror image position of the antenna model in the dielectric plate; (3) calculating an electric field generated by the surface current of the antenna model in the dielectric plate; (4) calculating a mirror current; (5) calculating a Fresnel coefficient; (6) calculating an electric field generated by the mirror current; (7) establishing a surface electric field integral equation of an antenna model in a dielectric plate; (8) solving the integral equation of the surface electric field by a moment method; (9) electromagnetic radiation characteristics of the antenna in the dielectric plate are estimated. The method and the device describe the influence of the dielectric plate on the internal antenna by utilizing the Fresnel coefficient, realize the estimation of the radiation characteristic of the antenna in the dielectric plate, provide guidance for the subsequent antenna design and accelerate the design process.
Description
Technical Field
The invention belongs to the technical field of communication, and further relates to a Fresnel coefficient-based method for estimating radiation characteristics of an antenna in a dielectric slab in the technical field of antennas. The invention can analyze the radiation characteristic of the antenna in the dielectric plate and accelerate the design process of the antenna.
Background
In the field of antenna technology, in order to ensure that the performance of an antenna is not interfered by the external environment, the antenna is generally protected by using antenna covers, medium filling and the like. It is also common for the antenna to be embedded in a dielectric plate, such as an antenna in automotive glass. These means of protecting the antenna also introduce new problems: the additional devices have an effect on the radiation characteristics of the antenna. The influence of the dielectric plate on the radiation characteristic of the antenna can be analyzed by a moment method.
Bogdano et al, in their published paper "significance of Hybrid MoM Scheme for Composite geometry with Layered Structures" (International Serial/work on Direct and Inverse schemes of Electromagnetic and economic Wave Theory (DIED), conference paper 2016[ D ]), propose an Electromagnetic estimation method based on quasi-electrostatic field analysis modified lattice functions. The method comprises the following implementation steps: (1) and (3) mirroring the surface current of the antenna by taking the upper surface and the lower surface of the dielectric plate as a symmetrical plane, and calculating the current coefficient of the mirrored current through quasi-electrostatic field analysis. (2) And constructing a matrix equation of a moment method by using the current correction Green function of the antenna and the mirror image. (3) And solving an equation to obtain the surface current of the antenna, and analyzing the radiation characteristic of the antenna. The method realizes the analysis of the radiation characteristic of the antenna in the dielectric plate. However, the method still has the following defects: because quasi-electrostatic field analysis is adopted when the current coefficient of the mirror image antenna is calculated, the surface current coefficient of the mirror image antenna is corrected by using the mirror image coefficient of the electrostatic field. However, when the difference between the dielectric constant of the dielectric plate and the dielectric constant outside the dielectric plate is small, even when the dielectric constant of the dielectric plate is smaller than the dielectric constant outside the dielectric plate, the accuracy of quasi-electrostatic field analysis may be reduced, thereby affecting the analysis accuracy of the antenna radiation characteristic.
Disclosure of Invention
The invention aims to provide a Fresnel coefficient-based method for estimating radiation characteristics of an antenna in a dielectric slab, aiming at overcoming the defects of the prior art, and solving the problem that the estimation of the radiation characteristics of an electromagnetic field of the antenna in the dielectric slab is inaccurate by using quasi-electrostatic field analysis when the dielectric constant of the dielectric slab is smaller than the dielectric constant outside the dielectric slab, even the dielectric constant of the dielectric slab is smaller than the dielectric constant outside the dielectric slab.
The idea of the invention for achieving the above purpose is to calculate the electric field generated by the antenna in the dielectric plate by utilizing the Fresnel coefficient, construct the integral equation of the surface electric field of the antenna in the dielectric plate, obtain the surface current of the antenna in the dielectric plate by the equation, and estimate the radiation characteristic of the antenna in the dielectric plate by utilizing the surface current of the antenna in the dielectric plate.
The method comprises the following specific steps:
(1) and (3) carrying out mesh subdivision on the antenna model in the dielectric plate:
within the range of [ lambda/12, lambda/8 ] wavelength, dividing an antenna model in the dielectric slab into a plurality of triangular meshes, setting the number of sampling points according to the requirement of integration precision, and calculating the position of each triangular mesh Gaussian sampling point corresponding to each triangular mesh by using a Gaussian numerical integration formula;
(2) calculating the mirror image position of the antenna model in the dielectric plate:
(2a) calculating the 1 st mirror image of each Gaussian sampling point in each triangular grid on the antenna model in the dielectric slab by using a 1 st mirror image formula;
(2b) calculating the 2 nd time mirror image of each Gaussian sampling point in each triangular grid on the antenna model in the dielectric slab by using a 2-time mirror image formula;
(2c) calculating the mth mirror image of each Gaussian sampling point in each triangular grid on the antenna model in the dielectric slab by using an m-order mirror image formula, wherein m represents a positive integer which is more than 2 and less than 20;
(3) calculating an electric field generated by each Gaussian sampling point current in each triangular grid on the antenna model in the dielectric plate by using a field solving formula:
(4) calculating each mirror current of each Gaussian sampling point current in each triangular grid in the antenna model in the dielectric plate by using a mirror current formula;
(5) calculating the Fresnel coefficient after each mirror image of each Gaussian sampling point in each triangular grid on the antenna model in the dielectric slab by using a Fresnel formula:
(6) calculating the electric field generated by each mirror current of each Gaussian sampling point in each triangular grid on the antenna model in the dielectric plate by using the following formula:
wherein,
representing the electric field generated by the pth image current of the jth Gaussian sampling point in the ith triangular grid on the antenna model in the dielectric plate at the ith Gaussian sampling point on the kth triangular gridP represents the number of mirror images, p is 1,2, and m, η represents the wave impedance of the dielectric slab model,
respectively showing the reflection coefficient of a Fresnel vertical incidence surface and the reflection coefficient of a Fresnel parallel incidence surface between the p-th mirror image of the jth Gaussian sampling point in the ith triangular grid and the ith Gaussian sampling point on the kth triangular grid, L (-) shows an electric field integral operator,
representing the p-th image current of the j-th Gaussian sampling point in the ith triangular grid;
(7) establishing a surface electric field integral equation of an antenna model in a dielectric plate:
establishing a surface electric field integral equation at each Gaussian sampling point in each triangular grid on the antenna model in the dielectric plate according to the boundary condition of the dielectric plate antenna model;
(8) solving the integral equation of the surface electric field by a moment method:
solving a surface electric field integral equation of the antenna in the dielectric plate by a moment method to obtain the surface current of the antenna model in the dielectric plate;
(9) estimating the electromagnetic radiation characteristic of the antenna in the dielectric plate:
and solving related parameters of the antenna radiation problem by the antenna surface current, and estimating the electromagnetic radiation characteristic of the antenna in the dielectric plate.
Compared with the prior art, the invention has the following advantages:
because the Fresnel coefficient is utilized to calculate the electric field generated by the antenna in the dielectric plate, the problem that the radiation characteristic of the antenna in the dielectric plate is not accurately described through quasi-electrostatic field analysis when the difference between the dielectric constant of the dielectric plate and the dielectric constant outside the dielectric plate is small, even the dielectric constant of the dielectric plate is smaller than the dielectric constant outside the dielectric plate is solved, so that the propagation rule of electromagnetic waves in the dielectric plate can be more accurately described through the quasi-electrostatic field analysis, and the electromagnetic radiation characteristic of the antenna in the dielectric plate can be more accurately estimated.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a schematic diagram of a current at a point on an antenna within a dielectric slab and a partial mirror image of the current;
FIG. 3 is a schematic diagram of an antenna model in a dielectric board in a simulation experiment according to the present invention;
fig. 4 is a graph showing the impedance comparison of the antenna in the dielectric plate obtained by the simulation experiment of the present invention: wherein, fig. 4(a) is a comparative curve diagram of the real part of the impedance of the antenna in the dielectric plate obtained by the simulation experiment of the present invention; fig. 4(b) is a comparison graph of imaginary parts of the antenna impedance in the dielectric plate obtained by the simulation experiment of the present invention.
Detailed Description
The present invention will be described in further detail below with reference to the accompanying drawings.
The steps of the present invention will be described in further detail with reference to fig. 1.
Step 1, mesh subdivision is carried out on an antenna model in a dielectric plate.
Within the range of [ lambda/12, lambda/8 ] wavelength, dividing an antenna model in the dielectric slab into a plurality of triangular meshes, setting the number of sampling points according to the requirement of integration precision, and calculating the position of each triangular mesh Gaussian sampling point corresponding to each triangular mesh by using a Gaussian numerical integration formula;
and 2, calculating the mirror image position of the antenna model in the dielectric plate.
Calculating the 1 st mirror image of each Gaussian sampling point in each triangular grid on the antenna model in the dielectric slab by using the following 1 st mirror image formula:
wherein,
representing the 1 st mirror image of the jth Gaussian sampling point in the ith triangular grid on the antenna model in the dielectric platei,jRepresenting ith triangular mesh on antenna model in dielectric plateJ-th Gaussian sampling point, di,jRepresents a point ri,jThe vertical distance to the upper surface of the dielectric slab model,
which represents the unit normal direction of the upper surface of the dielectric slab model.
Calculating the 2 nd order mirror image of each Gaussian sampling point in each triangular grid on the antenna model in the dielectric slab by using the following 2 order mirror image formula:
wherein,
and (4) representing the 2 nd mirror image of the jth Gaussian sampling point in the ith triangular grid, and h represents the thickness of the dielectric slab model.
Calculating the mth mirror image of each Gaussian sampling point in each triangular grid on the antenna model in the dielectric slab by using the following mth mirror image formula, wherein m represents a positive integer which is more than 2 and less than 20:
wherein,
representing the m-th mirror image of the j-th Gaussian sampling point in the ith triangular grid on the antenna model in the dielectric slab,
representing the m-2 th mirror image of the jth Gaussian sampling point in the ith triangular grid on the antenna model in the dielectric slab; when m-2 is an odd number,
indicating points
When the vertical distance from the lower surface of the dielectric slab model is m-2 is an even number,
indicating points
The vertical distance to the upper surface of the dielectric slab model.
FIG. 2 is a schematic diagram of a current at a point on an antenna in a dielectric plate and a partial mirror image of the current, wherein the square frame is a longitudinal section of the dielectric plate, ri,jIs the jth Gaussian sampling point in the ith triangular grid on the antenna model in the dielectric plate,
are respectively a point ri,jThe 1 st, 2 nd, 3 rd and 4 th mirror images, and the arrow is the current corresponding to each point and mirror image.
And 3, calculating an electric field generated by the current of each Gaussian sampling point in each triangular grid on the antenna model in the dielectric plate by using the following field solving formula:
Ei,j、k,l＝ηL(Ji,j)
wherein E isi,j、k,lThe electric field generated by the current of the jth Gaussian sampling point in the ith triangular grid on the antenna model in the dielectric plate at the ith Gaussian sampling point on the kth triangular grid is represented, Ji,jRepresenting the current at the jth gaussian sample point in the ith triangular grid.
wherein,
represents the current Ji,jCurrent J obtained by projecting to the outside of the upper surface of the dielectric slab model in the normal directioni,jThe vertical component.
And 5, calculating the Fresnel coefficient of each mirrored Gaussian sampling point in each triangular grid on the antenna model in the dielectric slab by using the following Fresnel formula:
wherein,
respectively representing the reflection coefficient of a Fresnel vertical incidence surface and the reflection coefficient of a Fresnel parallel incidence surface between the p-th mirror image of the jth Gaussian sampling point in the ith triangular grid and the ith Gaussian sampling point on the kth triangular grid; epsilonr1Represents the relative dielectric constant, ε, in a dielectric slab modelr2Representing the relative permittivity of the free space outside the dielectric slab model, sin represents the sine operation, cos represents the cosine operation,
and representing the included angle between the unit vector of the connecting line of the p-th mirror image of the jth Gaussian sampling point in the ith triangular grid and the ith Gaussian sampling point on the kth triangular grid and the normal direction of the upper surface of the dielectric slab model.
Step 6, calculating an electric field generated by each mirror current of each Gaussian sampling point in each triangular grid on the antenna model in the dielectric plate by using the following formula:
wherein,
an electric field generated by the p-th image-reflecting current of the j-th Gaussian sampling point in the ith triangular grid on the antenna model in the dielectric slab at the ith Gaussian sampling point on the kth triangular grid is represented, p represents the serial number of image times, p is 1,2, the.
Respectively showing the reflection coefficient of a Fresnel vertical incidence surface and the reflection coefficient of a Fresnel parallel incidence surface between the p-th mirror image of the jth Gaussian sampling point in the ith triangular grid and the ith Gaussian sampling point on the kth triangular grid, L (-) shows an electric field integral operator,
representing the p-th mirrored current of the j-th gaussian sampling point in the ith triangular grid.
And 7, establishing a surface electric field integral equation of the antenna model in the dielectric plate.
According to the boundary conditions of the dielectric plate antenna model, establishing a surface electric field integral equation at each Gaussian sampling point in each triangular grid on the antenna model in the dielectric plate as follows:
wherein,
representing the kth triangle on the antenna model in the dielectric plateThe method comprises the following steps that (1) the external normal direction of a grid is formed, i represents the sequence number of a triangular grid split by an antenna model in a dielectric plate, alpha represents the total number of the triangular grid split by the antenna model in the dielectric plate, j represents the sequence number of Gaussian sampling points on the triangular grid, and beta represents the total number of the Gaussian sampling points on the triangular grid;
the applied excitation field of the ith Gaussian sample point on the kth triangular mesh is shown.
And 8, solving a surface electric field integral equation by using a moment method.
And (3) solving a surface electric field integral equation of the antenna in the dielectric plate by using a moment method to obtain the surface current of the antenna model in the dielectric plate.
And 9, estimating the electromagnetic radiation characteristic of the antenna in the dielectric plate.
And solving related parameters of the antenna radiation problem by the antenna surface current, and estimating the electromagnetic radiation characteristic of the antenna in the dielectric plate.
The effect of the present invention will be further explained with the simulation experiment.
1. Simulation conditions are as follows:
the simulation experiment conditions of the invention are as follows: the processor model is Intel (R) core (TM) i5-8250U 1.6GHz CPU, 8GB RAM; the programming language is Fortran.
2. Simulation content and result analysis:
the model of the simulation experiment of the invention is an antenna model in a dielectric plate, which consists of a dielectric plate model and a dipole antenna model. As shown in FIG. 3, the rectangular parallelepiped is a dielectric slab model, and has a length of 1.2m, a width of 1m, a height of 0.3m, and a relative dielectric constant of 2.0. Two same long and narrow rectangles in the cuboid form the dipole antenna, the joint of the two rectangles is an external excitation position, the center of the dipole antenna is superposed with the center of the dielectric plate, and each rectangle is 0.5m long and 0.02m wide. The relative dielectric constant of the free space of the dielectric plate in the simulation experiment is 6.0.
The simulation experiment of the present invention is to use the Electromagnetic estimation method based on quasi-electrostatic field analysis and correction of Green function in the present invention and the prior art (see the paper "variance of Hybrid MoM Scheme for Composite geometry with Layered Structures" (International semi-conductor/works on Direct and Inverse documents of Electromagnetic and Acoustic Wave Theory (DIED), conference paper 2016[ D ]) published by Faik G. Bogdano mentioned in the background art) to respectively simulate the antenna model in the dielectric plate and calculate the antenna impedance of the antenna model in the dielectric plate. The excitation voltage of the dipole antenna is 1V, the sweep frequency range is 100 MHz-700 MHz, the frequency interval is 12MHz, and a curve of the impedance of the dipole antenna in the dielectric plate changing along with the frequency is obtained.
In order to verify the simulation effect of the method and the prior art, the simulation experiment model is simulated under the simulation conditions by using a Windscreen electromagnetic simulation method of commercial software FEKO, the antenna impedance of the antenna in the dielectric plate is calculated, the sweep frequency range is 100 MHz-700 MHz, and the frequency interval is 12MHz, so that the curve of the impedance of the dipole antenna in the dielectric plate changing along with the frequency is obtained.
Fig. 4(a) is a comparison graph of a real part of the impedance of the antenna in the dielectric plate obtained by the simulation experiment of the present invention, and fig. 4(b) is a comparison graph of an imaginary part of the impedance of the antenna in the dielectric plate obtained by the simulation experiment of the present invention. In fig. 4(a) and 4(b), the abscissa represents frequency in MHz, and the ordinate represents impedance in Ohm. The curves marked with squares in fig. 4(a) and 4(b) respectively represent the real part and imaginary part curves of the antenna impedance simulated by the method of the present invention. The curves marked with circles in fig. 4(a) and 4(b) represent the real part and imaginary part curves of the antenna impedance, respectively, obtained by FEKO simulation in commercial software; the curves marked with triangles in fig. 4(a) and 4(b) represent the real part and imaginary part curves of the antenna impedance, respectively, obtained by simulation in the prior art. As can be seen from the graph of FIG. 4(a), the simulation results of the method of the present invention are better matched with the FEKO simulation results of the commercial software in the frequency ranges of 150MHz to 180MHz and 340MHz to 370 MHz; as can be seen from the graph of FIG. 4(b), the simulation results of the method of the present invention are better matched with the FEKO simulation results of the commercial software in the frequency ranges of 150MHz to 220MHz and 320MHz to 380 MHz. Therefore, the simulation result of the method is higher in precision.
Claims (8)
1. A Fresnel coefficient-based method for estimating radiation characteristics of an antenna in a dielectric slab is characterized in that an electric field generated by the antenna in the dielectric slab is calculated by utilizing the Fresnel coefficient, a surface electric field integral equation of the antenna in the dielectric slab is constructed, surface currents of the antenna in the dielectric slab are obtained by the equation, and the radiation characteristics of the antenna in the dielectric slab are estimated by utilizing the surface currents of the antenna in the dielectric slab; the method comprises the following specific steps:
(1) and (3) carrying out mesh subdivision on the antenna model in the dielectric plate:
within the range of [ lambda/12, lambda/8 ] wavelength, dividing an antenna model in the dielectric slab into a plurality of triangular meshes, setting the number of sampling points according to the requirement of integration precision, and calculating the position of each triangular mesh Gaussian sampling point corresponding to each triangular mesh by using a Gaussian numerical integration formula;
(2) calculating the mirror image position of the antenna model in the dielectric plate:
(2a) calculating the 1 st mirror image of each Gaussian sampling point in each triangular grid on the antenna model in the dielectric slab by using a 1 st mirror image formula;
(2b) calculating the 2 nd time mirror image of each Gaussian sampling point in each triangular grid on the antenna model in the dielectric slab by using a 2-time mirror image formula;
(2c) calculating the mth mirror image of each Gaussian sampling point in each triangular grid on the antenna model in the dielectric slab by using an m-order mirror image formula, wherein m represents a positive integer which is more than 2 and less than 20;
(3) calculating an electric field generated by the surface current of the antenna model in the dielectric plate:
calculating an electric field generated by each Gaussian sampling point current in each triangular grid on the antenna model in the dielectric plate by using a field solving formula:
(4) calculating each mirror current of each Gaussian sampling point current in each triangular grid in the antenna model in the dielectric plate by using a mirror current formula;
(5) calculating the Fresnel coefficient after each mirror image of each Gaussian sampling point in each triangular grid on the antenna model in the dielectric slab by using a Fresnel formula:
(6) calculating the electric field generated by each mirror current of each Gaussian sampling point in each triangular grid on the antenna model in the dielectric plate by using the following formula:
wherein,
an electric field generated by the p-th image-reflecting current of the j-th Gaussian sampling point in the ith triangular grid on the antenna model in the dielectric slab at the ith Gaussian sampling point on the kth triangular grid is represented, p represents the sequence number of image times, p is 1,2, the.
Respectively showing the reflection coefficient of a Fresnel vertical incidence surface and the reflection coefficient of a Fresnel parallel incidence surface between the p-th mirror image of the jth Gaussian sampling point in the ith triangular grid and the ith Gaussian sampling point on the kth triangular grid, L (-) shows an electric field integral operator,
representing the p-th image current of the j-th Gaussian sampling point in the ith triangular grid;
(7) establishing a surface electric field integral equation of an antenna model in a dielectric plate:
establishing a surface electric field integral equation at each Gaussian sampling point in each triangular grid on the antenna model in the dielectric plate according to the boundary condition of the dielectric plate antenna model;
(8) solving the integral equation of the surface electric field by a moment method:
solving a surface electric field integral equation of the antenna model in the dielectric plate by a moment method to obtain the surface current of the antenna model in the dielectric plate;
(9) estimating the electromagnetic radiation characteristic of the antenna in the dielectric plate:
and solving related parameters of the antenna radiation problem by the antenna surface current, and estimating the electromagnetic radiation characteristic of the antenna in the dielectric plate.
2. The method for estimating radiation characteristics of an antenna in a dielectric slab based on fresnel coefficients as defined in claim 1, wherein the 1-time mirror image formula in step (2a) is as follows:
wherein,
representing the 1 st mirror image of the jth Gaussian sampling point in the ith triangular grid on the antenna model in the dielectric platei,jRepresents the j-th Gaussian sampling point in the ith triangular grid on the antenna model in the dielectric plate, di,jRepresents a point ri,jThe vertical distance to the upper surface of the dielectric slab model,
which represents the unit normal direction of the upper surface of the dielectric slab model.
3. The fresnel-coefficient-based method for estimating radiation characteristics of an antenna in a dielectric slab according to claim 2, wherein the 2-time mirror equation in step (2b) is as follows:
wherein,
and (4) representing the 2 nd mirror image of the jth Gaussian sampling point in the ith triangular grid, and h represents the thickness of the dielectric slab model.
4. The fresnel-coefficient-based method for estimating radiation characteristics of an antenna in a dielectric slab according to claim 2, wherein the m-order mirror image formula in step (2c) is as follows:
wherein,
representing the m-th mirror image of the j-th Gaussian sampling point in the ith triangular grid on the antenna model in the dielectric slab,
representing the m-2 th mirror image of the jth Gaussian sampling point in the ith triangular grid on the antenna model in the dielectric slab; when m-2 is an odd number,
indicating points
When the vertical distance from the lower surface of the dielectric slab model is m-2 is an even number,
indicating points
The vertical distance to the upper surface of the dielectric slab model.
5. The method for estimating radiation characteristics of an antenna in a dielectric slab based on fresnel coefficients as defined in claim 1, wherein the field-finding formula in step (3) is as follows:
Ei,j、k,l＝ηL(Ji,j)
wherein E isi,j、k,lThe electric field generated by the current of the jth Gaussian sampling point in the ith triangular grid on the antenna model in the dielectric plate at the ith Gaussian sampling point on the kth triangular grid is represented, Ji,jRepresenting the current at the jth gaussian sample point in the ith triangular grid.
6. The method for estimating radiation characteristics of an antenna in a dielectric slab based on fresnel coefficients as defined in claim 5, wherein the mirror current formula in step (4) is as follows:
wherein,
represents the current Ji,jCurrent J obtained by projecting to the outside of the upper surface of the dielectric slab model in the normal directioni,jThe vertical component.
7. The method for estimating radiation characteristics of an antenna in a dielectric slab based on fresnel coefficients according to claim 1, wherein the fresnel formula in step (5) is as follows:
wherein,
respectively representing the reflection coefficient of a Fresnel vertical incidence surface and the reflection coefficient of a Fresnel parallel incidence surface between the p-th mirror image of the jth Gaussian sampling point in the ith triangular grid and the ith Gaussian sampling point on the kth triangular grid; epsilonr1Represents the relative dielectric constant, ε, in a dielectric slab modelr2Representing the relative permittivity of the free space outside the dielectric slab model, sin represents the sine operation, cos represents the cosine operation,
and representing the included angle between the unit vector of the connecting line of the p-th mirror image of the jth Gaussian sampling point in the ith triangular grid and the ith Gaussian sampling point on the kth triangular grid and the normal direction of the upper surface of the dielectric slab model.
8. The fresnel-coefficient-based method for estimating radiation characteristics of an antenna in a dielectric slab according to claim 5, wherein the surface electric field integral equation in step (7) is as follows:
wherein,
the external normal direction of the kth triangular grid on the antenna model in the dielectric plate is represented, i represents the serial number of the triangular grid split by the antenna model in the dielectric plate, alpha represents the total number of the triangular grids split by the antenna model in the dielectric plate, j represents the serial number of Gaussian sampling points on the triangular grid, and beta represents the total number of the Gaussian sampling points on the triangular grid;
the applied excitation field of the ith Gaussian sample point on the kth triangular mesh is shown.
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