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

Abstract

The invention discloses a fine simulation-based current distribution and near-field electromagnetic distribution three-dimensional visual method. The method comprises the steps of a), judging a data type, and if the data type is electromagnetic field data, executing the step b); if the data type is current field data, executing the step d); b), firstly obtaining a frequency value, an electromagnetic field name and a contained point number from the electromagnetic field data; c), performing statistics on the point number and a triangle number contained in the electromagnetic field data; d), firstly obtaining a frequency value and a contained point number from the current field data; e), performing statistics on the point number, a line number, a triangle number and a quadrangle number contained in the current field data; f), calculating amplitudes and phase angles of multiple components; g), visually displaying the amplitudes and the phase angles; and h), performing conversion from a frequency domain to a time domain. According to the visual method, the reasonability of design can be tested without processing a real object, and the electromagnetic compatibility problem of the design can be analyzed; and, the product design cost can be reduced and the product research and development cycle can be shortened.

Description

A kind of CURRENT DISTRIBUTION and near field electromagnetic distribution three-dimensional visualization based on fine emulation Method

Technical field

The present invention relates to a kind of CURRENT DISTRIBUTION and near field electromagnetic distribution three-dimensional visualization method, in particular, especially relate to And a kind of CURRENT DISTRIBUTION and near field electromagnetic distribution three-dimensional visualization method based on fine emulation.

Background technology

Electromagnetic field numerical simulation is built upon on the basis of Theory of Electromagnetic Field, is solved with high-performance computer technology as instrument Certainly complex electromagnetic fields and microwave engineering problem.With developing rapidly for computer hardware and software, various electromagnetism Flow Field Numerical meters Calculation method can successfully solve large quantities of engineering problems by prolonged development, and electromagnetic field numerical simulation is widely used in The electromagnetic arts such as microwave and millimetre-wave attenuator, radar, precise guidance, electromagnetic compatibility, medical diagnosis, navigation and geological prospecting, into It is installation electromagnetical specificity analysis and the modernization necessary means of design, with huge practical value.

In recent years, with the complication of modern Electromagnetic Engineering problem, the huge problem of some amounts of calculation is frequently encountered, such as The Electromagnetic Scattering of the neighbouring antenna of the complexity such as aircraft, warship electrically large sizes platform, the analysis of large-scale array antenna and comprehensive Close and electrically large platform electromagnetic compatibility problem etc., these problems Electromagnetic Simulation is calculated propose it is more accurate, more efficient urgent Demand, the fine Electromagnetic Simulation for generally requiring the large-scale parallel of cores up to ten thousand or even hundreds of thousands core parallel scale is calculated, traditional The business softwares such as FEKO, HFSS are limited by parallel check figure cannot meet the demand of large-scale parallel simulation calculation.Finely Electromagnetic Simulation can carry out accurate simulation to electromagnetic problems such as antenna and microwave systems.

, it is necessary to the Simulation result data to producing is researched and analysed to know emulation after fine Electromagnetic Simulation is completed Series of results, intuitively the electromagnetism distribution map and CURRENT DISTRIBUTION cloud atlas in graphical representation near field etc..Fine Electromagnetic Simulation engineering Typically calculated on supercomputer, a large amount of, complicated data can be produced, if directly studying these data, not only taken When, and easily produce deviation.With the raising of computing power, the scale of Solve problems is continued to increase, and complexity is constantly carried High all to increase, it is necessary to process and calculate the data volume for producing, the analysis and explanation of result of calculation are more and more difficult, have a strong impact on The efficiency and quality of visualization in scientific computing.

The physical significance of electromagnetic near field is to set a face, the electromagnetic nature on investigation face, emulation meter in its near vicinity The result of calculation is related to three components in direction of electric field magnetic field parameter x, y, z, and each component includes real part, imaginary part, also amplitude, The physical quantity informations such as phase, db values and absolute value.CURRENT DISTRIBUTION refers to the current distributions of body surface, the knot of simulation calculation Fruit is related to real part, the imaginary part of electric current magnetic current parameter, also there is the information such as amplitude, phase, db values and normalization.Therefore, construct aobvious During diagram shape, it is necessary to quickly and accurately read the related data in destination file..

The content of the invention

Shortcoming in order to overcome above-mentioned technical problem of the invention, there is provided a kind of based on the fine CURRENT DISTRIBUTION for emulating and near Field electromagnetism distribution three-dimensional visualization method.

CURRENT DISTRIBUTION and near field electromagnetic distribution three-dimensional visualization method based on fine emulation of the invention, its special feature It is to be realized by following steps：

A) judges data type, judges that pending data are electric current field data or electromagnetic field data, if electromagnetism Field data, then perform 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 is put into institute Corresponding electric-field intensity is stored as following form：Ex real parts, Ex imaginary parts, Ey real parts, Ey imaginary parts, Ez real parts, Ez imaginary parts, magnetic field are strong Degree is stored as following form：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 of electromagnetic field respectively Intensity 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 difference The magnetic field intensity of expression electromagnetic field component in the x, y, z-directions；Perform step c)；

C) statistics electromagnetic field data included in points, triangle number, by all points in data according to p1, p2 ..., The form of pn1 is numbered, and n1 contains number a little for electromagnetic field, and each corresponding three coordinate components of point is stored as The form of (x, y, z)；By all triangles according to t1, t2 ..., the form of tn2 be numbered, n2 is three contained by electromagnetic field Angular number, 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 electric current Density 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 are empty Portion, 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)；Will It is wired according to L1, L2 ..., the form of Ln4 is numbered, and stores two sequence numbers of point involved by each line；Will be all Triangle according to T1, T2 ..., the form of Tn5 is numbered, and stores three sequence numbers of point that each triangle is related to；By institute Have 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) calculating of the amplitude, phase angle of complex number components, by electromagnetic field or the complex number components unified representation at current field midpoint It is the plural number expression form of Z=Re+iIm, Re represents real, and Im represents imaginary part, by the real part and imaginary part of complex number components Bring formula (1) into and ask 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)：

G) amplitudes, the visualization at phase angle shows, if treating that visual data, for electromagnetic field, perform step g-1)； If treating that visual data, for current field, 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) The size of electric-field intensity is asked for respectively：

The size of physical quantity | E |, | Ex |, | Ey |, | Ez | is represented using different colors, to realize the electric-field strength number of degrees The visualization respectively of value | E |, | Ex |, | Ey |, | Ez | in solid space；Represented using different colors physical quantity | H |, | Hx |, the size of | Hy |, | Hz |, to realize that field strength value | H |, | Hx |, | Hy |, | Hz | are visual in the difference of solid space Change；

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

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

G) frequency domains to time domain conversion, 3 complex number components that electric-field intensity, magnetic field intensity, current density are included point X, Y, Z are not defined as, then it can be indicated by formula (7)：

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

Then, changed using computing formula (8)：

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

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

Make ω t=θ=0,10,20 ..., 360, each θ one frame data of correspondence, so by 4 time domains of Dynamic Display As a result J_x(t)、J_y(t)、J_z(t)、J(t)。

The beneficial effects of the invention are as follows：By fine electromagnetism numerical simulation post processing, electromagnetism can be visually shown Situation of change in space of component | Ex |, | Ey |, | Ez | on size | E | of electric-field intensity and its three directions, can The change feelings of component | Hx |, | Hy |, | Hz | in display electromagnetic field on electromagnetism intensity size | H | and its three directions in space Condition；For current field, component | ex |, | ey |, | the ez | in current density size | e | and its three directions can be shown in sky Interior situation of change.Simultaneously can also Dynamic Display electromagnetic field and current field dynamic result.

Designer can be in the reasonability without processing test design in the case of in kind, it is possible to analyze its electromagnetism simultaneous Appearance problem；Product design costses can be reduced, shortens the research and development of products cycle.Can reduce simultaneously and research staff's professional skill is wanted Ask so that design simplerization of antenna and microwave system, popular.

Brief description of the drawings

Fig. 1 is the electric field and the storage form of magnetic field intensity of frequency, title, points and the point of electromagnetic field in the present invention；

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

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

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

Fig. 5 is the storage form of the coordinate of points, line number, triangle number, quadrangle number and the point of current field in the present invention；

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

Specific embodiment

The invention will be further described with embodiment below in conjunction with the accompanying drawings.

CURRENT DISTRIBUTION and near field electromagnetic distribution three-dimensional visualization method based on fine emulation of the invention, by following step It is rapid to realize：

A) judges data type, judges that pending data are electric current field data or electromagnetic field data, if electromagnetism Field data, then perform 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 is put into institute Corresponding electric-field intensity is stored as following form：Ex real parts, Ex imaginary parts, Ey real parts, Ey imaginary parts, Ez real parts, Ez imaginary parts, magnetic field are strong Degree is stored as following form：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 of electromagnetic field respectively Intensity 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 difference The magnetic field intensity of expression electromagnetic field component in the x, y, z-directions；Perform step c)；

As shown in figure 1, giving the electric field and magnetic field intensity of the frequency of electromagnetic field in the present invention, title, points and point Storage form, shown the first row data 8000.000 are frequency, and near1 electromagnetic fields title in the second row, 4276 are electromagnetism The points that place includes, the 0.3218716971E-03 of the third line, 0.5891410262E-03, -0.1465537402E-02, - 0.1925838724E-02,0.5001709048E+00,0.1244888338E+00 are respectively the 1st that scientific notation is represented Ex real parts, Ex imaginary parts, Ey real parts, Ey imaginary parts, Ez real parts, the Ez imaginary parts of point；- the 0.1441311550E-03 of fourth line, 0.2616475876E-03、0.1323058472E-02 0.4121834747E-03、0.3766323009E-05、 0.5852417167E-05 is respectively Hx real parts, Hx imaginary parts, Hy real parts, Hy imaginary parts, Hz real parts, the Hz void that scientific notation is represented Portion.It is followed successively by,, of electric-field intensity and magnetic field strength date below at the 2nd point at the 3rd point at the 4th point at the 5th point, follow-up point is not given Go out.

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

As shown in Fig. 2 the storage form of the coordinate of the points of electromagnetic field, triangle number and point in the present invention is given, the The 4267 of a line are the points that electromagnetism place includes, 8187 triangle numbers；The 1 of second row is numbered for points ,- 0.137556757th, -0.2,0 is the coordinate of the 1st point, and the third line is the numbering and its coordinate of the 2nd point, the like, figure To the coordinate for giving preceding 30 points in 2, the coordinate of subsequent point is not given.

As shown in figure 3, giving the storage form of the triangle of electromagnetic field in the present invention, first is classified as the volume of triangle Number, its number consecutively be 1,2 ..., 8187, in the first row 2000,2018,1953 for numbering be 1 triangle involved by 3 The numbering of individual point.

D) obtains frequency values and its points for containing first from electric current field data, and each is put into corresponding electric current Density 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 are empty Portion, 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)；

As shown in figure 4, giving the storage form of the frequency of current field in the present invention, points and current density；The first row 8000.000 be frequency, 4342 be current field contained by points, the 0.13283302E+00, -0.13872743E of the second row + 00, -0.57846857E-02, -0.35265610E-01,0.63445792E-0, -0.62157389E-01 represent the 1st point Current density ex real parts, ex imaginary parts, ey real parts, ey imaginary parts, ey real parts, ey imaginary parts, the third line represents second electricity of point Current density, by that analogy.

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)；Will It is wired according to L1, L2 ..., the form of Ln4 is numbered, and stores two sequence numbers of point involved by each line；Will be all Triangle according to T1, T2 ..., the form of Tn5 is numbered, and stores three sequence numbers of point that each triangle is related to；By institute Have 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)；

As shown in figure 5, giving the coordinate of the points of current field in the present invention, line number, triangle number, quadrangle number and point Storage form, in the first row 4342 for points, 0 is line number, and 8446 is triangle number, 0 quadrangle number.In second row 1 Be the numbering of point, 1.396077961000000E-002 below, 1.906514836000000E-003, 1.864936505000000E-002 is the coordinate of point that numbering that scientific notation is represented is 1, and the third line is the point that numbering is 2 And its coordinate.

As shown in fig. 6, giving the storage form of the triangle of current field in the present invention, in the first row, 1 is triangle Numbering, below 22,256,221 for numbering be 1 triangle involved by three numberings of point；In second row, 2 is triangle Numbering, 221,23,22 for numbering be 2 triangle involved by three numberings of point, the like.

F) calculating of the amplitude, phase angle of complex number components, by electromagnetic field or the complex number components unified representation at current field midpoint It is the plural number expression form of Z=Re+iIm, Re represents real, and Im represents imaginary part, by the real part and imaginary part of complex number components Bring formula (1) into and ask 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)：

G) amplitudes, the visualization at phase angle shows, if treating that visual data, for electromagnetic field, perform step g-1)； If treating that visual data, for current field, 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) The size of electric-field intensity is asked for respectively：

The size of physical quantity | E |, | Ex |, | Ey |, | Ez | is represented using different colors, to realize the electric-field strength number of degrees The visualization respectively of value | E |, | Ex |, | Ey |, | Ez | in solid space；Represented using different colors physical quantity | H |, | Hx |, the size of | Hy |, | Hz |, to realize that field strength value | H |, | Hx |, | Hy |, | Hz | are visual in the difference of solid space Change；

During electric-field intensity shows, | E |, | Ex |, | Ey |, | Ez | are individually display, i.e., once showing process In, the size of | E | is represented with different colors, and it is shown in solid space；According to selection demand with different Color represents the size of | Ex |, displays it.Similarly, right | Ey |, | Ez |, | H |, | Hx |, | Hy |, | Hz | are carried out individually Display.

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

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

G) frequency domains to time domain conversion, 3 complex number components that electric-field intensity, magnetic field intensity, current density are included point X, Y, Z are not defined as, then it can be indicated by formula (7)：

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

Then, changed using computing formula (8)：

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

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

Make ω t=θ=0,10,20 ..., 360, each θ one frame data of correspondence, so by 4 time domains of Dynamic Display As a result J_x(t)、J_y(t)、J_z(t)、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)。