CN106709150A - Fine simulation-based current distribution and near-field electromagnetic distribution three-dimensional visual method - Google Patents

Abstract

The three-dimensional visualization method of current distribution and near-field electromagnetic distribution based on fine simulation of the present invention includes: a). Judging the data type, if it is electromagnetic field data, perform step b); if it is current field data, perform step d); b ). First obtain the frequency value, the name of the electromagnetic field and the number of points it contains from the electromagnetic field data; c). Count the number of points and triangles contained in the electromagnetic field data; d). First obtain the frequency value and the number of points it contains from the current field data Number of points; e). Statistics of the number of points, lines, triangles, and quadrilaterals contained in the current field data; f). Calculation of the amplitude and phase angle of the complex component; g). Visual display of the amplitude and phase angle; g) . Conversion from frequency domain to time domain. The visualization method of the invention can test the rationality of the design without processing the actual object, and can analyze the electromagnetic compatibility problem; it can reduce the product design cost and shorten the product development cycle.

Description

A detailed simulation-based 3D visualization of current distribution and near-field electromagnetic distribution method

technical field

The invention relates to a three-dimensional visualization method of current distribution and near-field electromagnetic distribution, more specifically, a three-dimensional visualization method of current distribution and near-field electromagnetic distribution based on fine simulation.

Background technique

The numerical simulation of electromagnetic field is based on the theory of electromagnetic field and uses high-performance computer technology as a tool to solve complex electromagnetic field and microwave engineering problems. With the rapid development of computer hardware and software, various electromagnetic field numerical calculation methods have been able to successfully solve a large number of engineering problems after a long period of development. Electromagnetic field numerical simulation is widely used in microwave and millimeter wave communications, radar, precision guidance, electromagnetic compatibility, Electromagnetic fields such as medical diagnosis, navigation and geological exploration have become a modern necessary means for the analysis and design of electromagnetic characteristics of equipment, and have great practical value.

In recent years, with the complexity of modern electromagnetic engineering problems, we often encounter some problems with a huge amount of calculation, such as the analysis of electromagnetic scattering characteristics of antennas near complex electric large-scale platforms such as aircrafts and warships, the analysis and synthesis of large array antennas, and the Platform electromagnetic compatibility issues, etc. These issues put forward more accurate and more efficient urgent requirements for electromagnetic simulation calculations, often requiring large-scale parallel fine electromagnetic simulation calculations with tens of thousands of cores or even hundreds of thousands of cores in parallel. Traditional FEKO, HFSS Due to the limitation of the number of parallel cores, the commercial software can no longer meet the needs of large-scale parallel simulation calculations. Detailed electromagnetic simulation enables accurate simulation of electromagnetic problems such as antennas and microwave systems.

After the fine electromagnetic simulation is completed, it is necessary to research and analyze the generated simulation result data to obtain a series of simulation results, and intuitively display the near-field electromagnetic distribution diagram and current distribution cloud diagram. Fine electromagnetic simulation engineering is generally calculated on a supercomputer, which will generate a large amount of complex data. If these data are directly studied, it will not only be time-consuming, but also prone to deviation. With the improvement of computer performance, the scale and complexity of solving problems continue to increase, and the amount of data that needs to be processed and calculated is increasing. The analysis and interpretation of calculation results are becoming more and more difficult, which seriously affects the visualization of scientific computing. efficiency and quality.

The physical meaning of the electromagnetic near field is to set a surface near the object and investigate the electromagnetic field characteristics on the surface. The simulation calculation results involve the components of the electric field and magnetic field parameters in the x, y, and z directions. Each component contains real and imaginary parts. , as well as physical quantity information such as amplitude, phase, db value and absolute value. The current distribution refers to the current distribution on the surface of the object. The simulation calculation results involve the real and imaginary parts of the current and magnetic current parameters, as well as information such as amplitude, phase, db value, and normalization. Therefore, when constructing display graphics, it is necessary to read the relevant data in the result file accurately and quickly. .

Contents of the invention

In order to overcome the shortcomings of the above-mentioned technical problems, the present invention provides a three-dimensional visualization method for current distribution and near-field electromagnetic distribution based on fine simulation.

The three-dimensional visualization method of current distribution and near-field electromagnetic distribution based on fine simulation of the present invention is special in that it is realized through the following steps:

a). Judging the data type, judging whether the data to be processed is current field data or electromagnetic field data, if it is electromagnetic field data, then perform step b); if it is current field data, perform step d);

b). First obtain the frequency value, the name of the electromagnetic field and the number of points it contains from the electromagnetic field data, and store the electric field strength corresponding to each point in the following format: Ex real part, Ex imaginary part, Ey real part, Ey imaginary part , Ez real part, Ez imaginary part, the magnetic field strength is stored in the following format: Hx real part, Hx imaginary part, Hy real part, Hy imaginary part, Hz real part, Hz imaginary part;

The complex number Ex real part+iEx imaginary part, Ey real part+iEy imaginary part, Ez real part+iEz imaginary part respectively represent the components of the electric field intensity of the electromagnetic field in the x, y, z directions, and the complex number Hx real part+iHx imaginary part, Hy real part+iHy imaginary part, Hz real part+iHz imaginary part respectively represent the component of the magnetic field intensity of electromagnetic field on x, y, z direction; Execute step c);

c). Count the number of points and triangles contained in the electromagnetic field data, and number all points in the data according to the form of p1, p2, ..., pn1, n1 is the number of points contained in the electromagnetic field, and the three points corresponding to each point Coordinate components are stored in the form of (x, y, z); all triangles are numbered in the form of t1, t2, ..., tn2, n2 is the number of triangles contained in the electromagnetic field, and the three points involved in each triangle are stored serial number; perform step f);

d). First obtain the frequency value and the number of points it contains from the current field data, and store the current density corresponding to each point in the following format: ex real part, ex imaginary part, ey real part, ey imaginary part, ey Real part, ey imaginary part, complex number ex real part+iex imaginary part, ey real part+iey imaginary part, ey real part+iey imaginary part represent the components of the current density of the current field in the x, y, z directions respectively; execute step e);

e). Count the number of points, lines, triangles, and quadrilaterals contained in the current field data, number all points in the form of P1, P2, ..., Pn3, and store the three coordinate components corresponding to each point It is in the form of (x, y, z); number all lines in the form of L1, L2, ..., Ln4, and store the serial numbers of the two points involved in each line; store all triangles in the form of T1, T2, ... , Tn5 in the form of numbering, and store the serial numbers of the three points involved in each triangle; number all quadrilaterals in the form of T1, T2, ..., Tn6, and store the serial numbers of the four points involved in each quadrilateral; n3 , n4, n5, n6 are the points, lines, triangles and quadrilaterals contained in the current field respectively; Execute step f);

f). The calculation of the amplitude and phase angle of the complex number component, the complex number component of the midpoint of the electromagnetic field or the current field is uniformly expressed as the complex number expression form of Z=Re+iIm, Re represents the real part of the complex number, Im represents the imaginary part, and the complex number The real and imaginary parts of the components are brought into the formula (1) to obtain the corresponding included angle jm:

jm=arctan(Im/Re)*57.2957795 (1)

Then calculate the phase angle of the corresponding complex component according to formula (2):

The unit of phase angle is degree;

Then the magnitude of the corresponding complex number component is obtained by formula (3):

g).Visual display of amplitude and phase angle, if the data to be visualized is an electromagnetic field, then perform step g-1); if the data to be visualized is a current field, then perform step g-2);

g-1). According to the coordinates of the points, all points of the electromagnetic field are displayed in space, and the magnitude of the electric field intensity is calculated according to formula (4) and formula (5):

Different colors are used to represent the size of the physical values |E|, |Ex|, |Ey|, |Ez|, in order to realize the electric field strength values |E|, |Ex|, |Ey|, |Ez| in the three-dimensional space Visualize separately; use different colors to represent the size of the physical values |H|, |Hx|, |Hy|, |Hz|, in order to realize the magnetic field strength values |H|, |Hx|, |Hy|, |Hz| Separate visualization of three-dimensional space;

g-2). According to the coordinates of the points, all the points of the current field are displayed in space, and the size of the current field is obtained according to the formula (6):

Different colors are used to represent the size of the physical values |e|, |ex|, |ey|, |ez|, in order to realize the current density values |e|, |ex|, |ey|, |ez| in the three-dimensional space Visualize separately;

g). The conversion from the frequency domain to the time domain, the three complex components contained in the electric field strength, magnetic field strength, and current density are defined as X, Y, and Z, respectively, which can be expressed by formula (7):

In the formula, represent the unit vectors in the x, y, and z directions, respectively;

Then, use calculation formula (8) to convert:

Let ωt=θ, formula (8) is transformed into the expression form such as formula (9):

The magnitude of the electric field strength, magnetic field strength and current density is calculated by the formula (10):

Let ωt=θ=0,10,20,...,360, each θ corresponds to a frame of data, so that the 4 time domain results J _x (t), J _y (t), J _z (t) can be displayed dynamically , J(t).

The beneficial effects of the present invention are: through the post-processing display of fine electromagnetic numerical simulation, the size |E| of the electric field strength in the electromagnetic field and its components |Ex|, |Ey|, |Ez| The changes in the electromagnetic field can display the electromagnetic intensity |H| and the components |Hx|, |Hy|, |Hz| in the three directions in the electromagnetic field; for the current field, it can display the current The variation of the density |e| and its three-direction components |ex|, |ey|, |ez| in space. At the same time, it can dynamically display the dynamic results of electromagnetic field and current field.

Designers can test the rationality of the design without processing the actual product, and can analyze its electromagnetic compatibility problems; it can reduce product design costs and shorten the product development cycle. At the same time, it can reduce the requirements for the professional skills of R&D personnel, making the design of antennas and microwave systems more simple and popular.

Description of drawings

Fig. 1 is the storage form of the electric field of the frequency of electromagnetic field, name, point number and point and the magnetic field strength among the present invention;

Fig. 2 is the storage form of the point number, triangle number and the coordinate of point of electromagnetic field among the present invention;

Fig. 3 is the storage form of the triangle of electromagnetic field among the present invention;

Fig. 4 is the storage form of frequency, number of points and current density of current field among the present invention;

Fig. 5 is the storage form of the point number, line number, triangle number, quadrilateral number and point coordinates of electric current field among the present invention;

Fig. 6 is the triangular storage form of the current field in the present invention.

detailed description

The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

The three-dimensional visualization method of current distribution and near-field electromagnetic distribution based on fine simulation of the present invention is realized by the following steps:

a). Judging the data type, judging whether the data to be processed is current field data or electromagnetic field data, if it is electromagnetic field data, then perform step b); if it is current field data, perform step d);

b). First obtain the frequency value, the name of the electromagnetic field and the number of points it contains from the electromagnetic field data, and store the electric field strength corresponding to each point in the following format: Ex real part, Ex imaginary part, Ey real part, Ey imaginary part , Ez real part, Ez imaginary part, the magnetic field strength is stored in the following format: Hx real part, Hx imaginary part, Hy real part, Hy imaginary part, Hz real part, Hz imaginary part;

The complex number Ex real part+iEx imaginary part, Ey real part+iEy imaginary part, Ez real part+iEz imaginary part respectively represent the components of the electric field intensity of the electromagnetic field in the x, y, z directions, and the complex number Hx real part+iHx imaginary part, Hy real part+iHy imaginary part, Hz real part+iHz imaginary part respectively represent the component of the magnetic field intensity of electromagnetic field on x, y, z direction; Execute step c);

As shown in Figure 1, the storage form of the electric field and the magnetic field strength of frequency, name, number of points and points of the electromagnetic field in the present invention are provided, the first row data 8000.000 shown is the frequency, the near1 electromagnetic field name in the second row, 4276 is the number of points contained in the electromagnetic field, 0.3218716971E-03, 0.5891410262E-03, -0.1465537402E-02, -0.1925838724E-02, 0.5001709048E+00, 0.1244888338E+00 in the third line are expressed in scientific notation Ex real part, Ex imaginary part, Ey real part, Ey imaginary part, Ez real part, Ez imaginary part of the first point; -0.1441311550E-03, 0.2616475876E-03, 0.1323058472E-02 0.4121834747E of the fourth line -03, 0.3766323009E-05, and 0.5852417167E-05 are the Hx real part, Hx imaginary part, Hy real part, Hy imaginary part, Hz real part, and Hz imaginary part expressed in scientific notation, respectively. The following are the electric field strength and magnetic field strength data of the 2nd point, 3rd point, 4th point, and 5th point in turn, and the subsequent points are not given.

c). Count the number of points and triangles contained in the electromagnetic field data, and number all points in the data according to the form of p1, p2, ..., pn1, n1 is the number of points contained in the electromagnetic field, and the three points corresponding to each point Coordinate components are stored in the form of (x, y, z); all triangles are numbered in the form of t1, t2, ..., tn2, n2 is the number of triangles contained in the electromagnetic field, and the three points involved in each triangle are stored serial number; perform step f);

As shown in Figure 2, the storage form of the points, triangle numbers and point coordinates of the electromagnetic field is provided in the present invention, the 4267 of the first row is the points included in the electromagnetic field, and the 8187 triangle numbers; 1 of the second row is the points Number, -0.137556757, -0.2, 0 are the coordinates of the first point, the third line is the number and coordinates of the second point, and so on, the coordinates of the first 30 points are given in Figure 2, and the subsequent points The coordinates of are not given.

As shown in Figure 3, the storage form of the triangle of the electromagnetic field in the present invention is given. The first column is the number of the triangle, which is sequentially numbered 1, 2, ..., 8187, and 2000, 2018, and 1953 in the first row are The numbers of the 3 points involved in the triangle numbered 1.

d). First obtain the frequency value and the number of points it contains from the current field data, and store the current density corresponding to each point in the following format: ex real part, ex imaginary part, ey real part, ey imaginary part, ey Real part, ey imaginary part, complex number ex real part+iex imaginary part, ey real part+iey imaginary part, ey real part+iey imaginary part represent the components of the current density of the current field in the x, y, z directions respectively; execute step e);

As shown in Figure 4, the storage form of the frequency, number of points and current density of the current field in the present invention is given; 8000.000 in the first row is frequency, 4342 is the number of points contained in the current field, 0.13283302E+00, 0.13283302E+00 in the second row, -0.13872743E+00, -0.57846857E-02, -0.35265610E-01, 0.63445792E-0, -0.62157389E-01 represent the ex real part, ex imaginary part, ey real part, ey of the current density of the first point Imaginary part, ey real part, ey imaginary part, the third line represents the current density of the second point, and so on.

e). Count the number of points, lines, triangles, and quadrilaterals contained in the current field data, number all points in the form of P1, P2, ..., Pn3, and store the three coordinate components corresponding to each point It is in the form of (x, y, z); number all lines in the form of L1, L2, ..., Ln4, and store the serial numbers of the two points involved in each line; store all triangles in the form of T1, T2, ... , Tn5 in the form of numbering, and store the serial numbers of the three points involved in each triangle; number all quadrilaterals in the form of T1, T2, ..., Tn6, and store the serial numbers of the four points involved in each quadrilateral; n3 , n4, n5, n6 are the points, lines, triangles and quadrilaterals contained in the current field respectively; Execute step f);

As shown in Figure 5, the storage form of the point number, line number, triangle number, quadrilateral number and point coordinates of the current field in the present invention is given, 4342 is the point number in the first row, 0 is the line number, and 8446 is the triangle number , 0-bit quadrilateral number. The 1 in the second line is the number of the point, the following 1.396077961000000E-002, 1.906514836000000E-003, 1.864936505000000E-002 are the coordinates of the point numbered 1 expressed in scientific notation, and the third line is the point numbered 2 and its coordinates.

As shown in Figure 6, the triangular storage form of the current field in the present invention is given, in the first row, 1 is the number of the triangle, and the following 22, 256, 221 are the three points involved in the triangle numbered 1 in the second row, 2 is the number of the triangle, 221, 23, 22 are the numbers of the three points involved in the triangle numbered 2, and so on.

f). The calculation of the amplitude and phase angle of the complex number component, the complex number component of the midpoint of the electromagnetic field or the current field is uniformly expressed as the complex number expression form of Z=Re+iIm, Re represents the real part of the complex number, Im represents the imaginary part, and the complex number The real and imaginary parts of the components are brought into the formula (1) to obtain the corresponding included angle jm:

jm=arctan(Im/Re)*57.2957795 (1)

Then calculate the phase angle of the corresponding complex component according to formula (2):

The unit of phase angle is degree;

Then the magnitude of the corresponding complex number component is obtained by formula (3):

g).Visual display of amplitude and phase angle, if the data to be visualized is an electromagnetic field, then perform step g-1); if the data to be visualized is a current field, then perform step g-2);

g-1). According to the coordinates of the points, all points of the electromagnetic field are displayed in space, and the magnitude of the electric field intensity is calculated according to formula (4) and formula (5):

Different colors are used to represent the size of the physical values |E|, |Ex|, |Ey|, |Ez|, in order to realize the electric field strength values |E|, |Ex|, |Ey|, |Ez| in the three-dimensional space Visualize separately; use different colors to represent the size of the physical values |H|, |Hx|, |Hy|, |Hz|, in order to realize the magnetic field strength values |H|, |Hx|, |Hy|, |Hz| Separate visualization of three-dimensional space;

In the process of displaying the electric field strength, |E|, |Ex|, |Ey|, |Ez| are displayed separately, that is, in a display process, different colors are used to represent the size of |E| It is displayed in the space; according to the selection requirements, different colors are used to indicate the size of |Ex|, and it will be displayed. Similarly, |Ey|, |Ez|, |H|, |Hx|, |Hy|, |Hz| are individually displayed.

g-2). According to the coordinates of the points, all the points of the current field are displayed in space, and the size of the current field is obtained according to the formula (6):

Different colors are used to represent the size of the physical values |e|, |ex|, |ey|, |ez|, in order to realize the current density values |e|, |ex|, |ey|, |ez| in the three-dimensional space Visualize separately;

g). The conversion from the frequency domain to the time domain, the three complex components contained in the electric field strength, magnetic field strength, and current density are defined as X, Y, and Z, respectively, which can be expressed by formula (7):

In the formula, represent the unit vectors in the x, y, and z directions, respectively;

Then, use calculation formula (8) to convert:

Let ωt=θ, formula (8) is transformed into the expression form such as formula (9):

The magnitude of the electric field strength, magnetic field strength and current density is calculated by the formula (10):

Let ωt=θ=0,10,20,...,360, each θ corresponds to a frame of data, so that the 4 time domain results J _x (t), J _y (t), J _z (t) can be displayed dynamically , J(t).

Claims (1)

1. a kind of CURRENT DISTRIBUTION and near field electromagnetic based on fine emulation are distributed three-dimensional visualization method, it is characterised in that pass through Following steps are realized：

A) judges data type, judges that pending data are electric current field data or electromagnetic field data, if electromagnetism number of fields According to then performing step b)；If electric current field data, step d) is performed；

B) obtains frequency values, electromagnetic field title and its points for containing first from electromagnetic field data, and each point is corresponding Electric-field intensity be stored as following form：Ex real parts, Ex imaginary parts, Ey real parts, Ey imaginary parts, Ez real parts, Ez imaginary parts, magnetic field intensity are deposited It is following form to store up：Hx real parts, Hx imaginary parts, Hy real parts, Hy imaginary parts, Hz real parts, Hz imaginary parts；

Plural Ex real parts+iEx imaginary parts, Ey real part+iEy imaginary parts, Ez real part+iEz imaginary parts represent the electric-field intensity of electromagnetic field respectively Component in the x, y, z-directions, plural Hx real parts+iHx imaginary parts, Hy real part+iHy imaginary parts, Hz real part+iHz imaginary parts are represented respectively The magnetic field intensity of electromagnetic field component in the x, y, z-directions；Perform step c)；

C) points, the triangle number included in statistics electromagnetic field data, by all points in data according to p1, p2 ..., pn1 Form is numbered, and n1 contains number a little for electromagnetic field, and each corresponding three coordinate components of point is stored as (x, y, z) Form；By all triangles according to t1, t2 ..., the form of tn2 be numbered, n2 is the triangle number contained by electromagnetic field, And store three sequence numbers of point that each triangle is related to；Perform step f)；

D) obtains frequency values and its points for containing first from electric current field data, and each is put into corresponding current density It is stored as following form：Ex real parts, ex imaginary parts, ey real parts, ey imaginary parts, ey real parts, ey imaginary parts, plural ex real parts+iex imaginary parts, Ey real part+iey imaginary parts, ey real part+iey imaginary parts represent the current density of current field component in the x, y, z-directions respectively；Perform Step e)；

E) statistics electric current field data included in points, line number, triangle number, quadrangle number, by all points according to P1, P2 ..., the form of Pn3 is numbered, and each corresponding three coordinate components of point is stored as the form of (x, y, z)；By institute It is wired according to L1, L2 ..., the form of Ln4 is numbered, and stores two sequence numbers of point involved by each line；By all three It is angular according to T1, T2 ..., the form of Tn5 is numbered, and stores three sequence numbers of point that each triangle is related to；Will be all Quadrangle according to T1, T2 ..., the form of Tn6 is numbered, and stores four sequence numbers of point that each quadrangle is related to；n3、 N4, n5, n6 are respectively contained points, line number, triangle number, quadrangle number in current field；Perform step f)；

F) complex number components of electromagnetic field or current field midpoint are collectively expressed as Z by the calculating of the amplitude, phase angle of complex number components The plural number expression form of=Re+iIm, Re represents real, and Im represents imaginary part, and the real part and imaginary part of complex number components are brought into Formula (1) asks for corresponding angle jm：

Jm=arctan (Im/Re) * 57.2957795 (1)

Then the phase angle of corresponding complex number components is asked for according to formula (2)：

Phase angular unit is degree；

Then the amplitude of corresponding complex number components is asked for by formula (3)：

$\left|Z\right|=\sqrt{{\mathrm{Re}}^2+{\mathrm{Im}}^2}---\left(3\right);$

G) amplitudes, the visualization at phase angle shows, if treating that visual data, for electromagnetic field, perform step g-1)；If Treat that visual data for current field, then perform step g-2)；

G-1) according to point coordinate by electromagnetic field institute a little show in space, according to formula (4), formula (5) respectively Ask for the size of electric-field intensity：

$\left|E\right|=\sqrt{|Ex{|}^2+|Ey{|}^2+|Ez{|}^2}---\left(4\right)$

$\left|H\right|=\sqrt{|Hx{|}^2+|Hy{|}^2+|Hz{|}^2}---\left(5\right)$

The size of physical quantity | E |, | Ex |, | Ey |, | Ez | is represented using different colors, to realize electric-field intensity numerical value | E |, | Ex |, | Ey |, | Ez | solid space visualization respectively；Represented using different colors physical quantity | H |, | Hx |, | Hy |, the size of | Hz |, to realize the visualization respectively of field strength value | H |, | Hx |, | Hy |, | Hz | in solid space；

G-2) according to point coordinate by current field institute a little show in space, current field is asked for according to formula (6) Size：

$\left|e\right|=\sqrt{|ex{|}^2+|ey{|}^2+|ez{|}^2}---\left(6\right)$

The size of physical quantity | e |, | ex |, | ey |, | ez | is represented using different colors, to realize current density numerical value | e |, | ex |, | ey |, | ez | solid space visualization respectively；

G) frequency domains to time domain conversion, 3 complex number components that electric-field intensity, magnetic field intensity, current density are included are fixed respectively Justice be X, Y, Z, then its can be indicated by formula (7)：

$\begin{array}{c}J=J_x{\hat{a}}_x+J_y{\hat{a}}_y+J_z{\hat{a}}_z\\ J_x=\mathrm{Re}\left(X\right)+j\·\mathrm{Im}\left(X\right)\\ J_y=\mathrm{Re}\left(Y\right)+j\·\mathrm{Im}\left(Y\right)\\ J_z=\mathrm{Re}\left(Z\right)+j\·\mathrm{Im}\left(Z\right)\end{array}---\left(7\right)$

In formula,The unit vector on x, y, z direction is represented respectively；

Then, changed using computing formula (8)：

$\begin{array}{c}\begin{array}{c}{J}_x\left(t\right)=\mathrm{Re}\left(J_x{e}^{j\mathrm{\ω}t}\right)=\mathrm{Re}(\[\mathrm{Re}(x)+j\·\mathrm{Im}\left(x\right)\]\[\cos \mathrm{\ω}t+j\·\sin \mathrm{\ω}t\])\\ =\mathrm{Re}\left(x\right)\cos \mathrm{\ω}t-\mathrm{Im}\left(x\right)\sin \mathrm{\ω}t\end{array}\\ \begin{array}{c}{J}_y\left(t\right)=\mathrm{Re}\left(J_y{e}^{j\mathrm{\ω}t}\right)=\mathrm{Re}(\[\mathrm{Re}(y)+j\·\mathrm{Im}\left(y\right)\]\[\cos \mathrm{\ω}t+j\·\sin \mathrm{\ω}t\])\\ =\mathrm{Re}\left(y\right)\cos \mathrm{\ω}t-\mathrm{Im}\left(y\right)\sin \mathrm{\ω}t\end{array}\\ \begin{array}{c}{J}_z\left(t\right)=\mathrm{Re}\left(J_z{e}^{j\mathrm{\ω}t}\right)=\mathrm{Re}(\[\mathrm{Re}(z)+j\·\mathrm{Im}\left(z\right)\]\[\cos \mathrm{\ω}t+j\·\sin \mathrm{\ω}t\])\\ =\mathrm{Re}\left(z\right)\cos \mathrm{\ω}t-\mathrm{Im}\left(z\right)\sin \mathrm{\ω}t\end{array}\end{array}---\left(8\right)$

ω t=θ, formula (8) is made to be converted into such as the expression-form of formula (9)：

$\begin{array}{c}{J}_x\left(t\right)=\mathrm{Re}\left(x\right)cos\mathrm{\θ}-\mathrm{Im}\left(x\right)\sin \mathrm{\θ}\\ J_y\left(t\right)=\mathrm{Re}\left(y\right)cos\mathrm{\θ}-\mathrm{Im}\left(y\right)\sin \mathrm{\θ}\\ J_z\left(t\right)=\mathrm{Re}\left(z\right)cos\mathrm{\θ}-\mathrm{Im}\left(z\right)\sin \mathrm{\θ}\end{array}---\left(9\right)$

Electric-field intensity, magnetic field intensity, the size of current density are asked for by formula (10)：

$J\left(t\right)=\sqrt{J_x{\left(t\right)}^2+J_y{\left(t\right)}^2+J_z{\left(t\right)}^2}$

Make ω t=θ=0,10,20 ..., 360, each θ one frame data of correspondence, so by 4 result in time domain J of Dynamic Display_x (t)、J_y(t)、J_z(t)、J(t)。