JPH05232169A - Method and device for electromagnetic field analysis - Google Patents

Abstract

PURPOSE:To eliminate restrictions on an analysis method and expand the application range by dividing a boundary surface of a space to be analyzed into a plurality of boundary surface elements, providing a surface electric field source and a surface magnetic field source to one reference surface which can be connected to all of the plurality of boundary surface elements with a straight line, and performing calculation by using a specific equation. CONSTITUTION:For example, an area to be analyzed is in a thin and long tubular shape with a curvature and boundary conditions for the area to be analyzed are input to it through a keyboard. A computer performs division processing for dividing the area into sections with a plurality of surfaces P1-P6. Conditions which should be met by the surfaces P1-P6 are to achieve connection with all boundary elements which form a boundary of the area which is divided by two surfaces with a straight line. Then, a surface electric field source Es and a surface magnetic source Hs are given to one reference surface as an energy source and an electric field E and a magnetic field H which exist in or out of the area which is placed on each boundary surface element and is surrounded by each boundary surface element are calculated by equations.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an electromagnetic field analysis method and apparatus, and more particularly to an electromagnetic field analysis method and apparatus used for designing an element or apparatus utilizing an electromagnetic field phenomenon.

[0002]

2. Description of the Related Art Conventionally, in order to efficiently design antennas, waveguides, microstrip circuits, etc., various electromagnetic field analysis methods for numerically analyzing the behavior of electromagnetic fields in these elements and circuits using a computer. Are proposed, and the main ones are the finite element method, the boundary element method and the spatial network method.

As a matter of course, each of these methods has advantages and disadvantages, and they are appropriately used depending on the application. That is, in the finite element method, a steady solution (at a certain frequency) of a closed system can be accurately obtained, but the amount of calculation becomes enormous because the sample points are the entire volume section, and it is difficult to calculate the aperture such as radiation. Is. Further, in the boundary element method, since the sample points are only the surface, the calculation amount is not so large, and the aperture can be calculated, but only a relatively simple shape in which each sample point can be seen is calculated. Further, in the spatial network method, since the Maxwell equation is directly calculated in the time domain, it is possible to faithfully analyze the electromagnetic field phenomenon, but there is a drawback that the sample points are given only to the vertices of the lattice.

[0004]

Here, each of these methods is to investigate the behavior of the electromagnetic field in a predetermined space by solving the Maxwell equation. Charge and current are assumed, and then scalar potential and vector potential are calculated, and electric field and magnetic field are calculated from these potentials.

That is, the Maxwell equation is

[Equation 1]

[Equation 2]

[Equation 3]

[Equation 4] Given in. However, E is an electric field, D is an electric flux density, H is a magnetic field, B is a magnetic flux density, i is a conduction current density, and σ is a charge density. Let A be the vector potential and φ be the scalar potential,

[Equation 5]

[Equation 6] Define as follows.

[0006]

[Equation 7] Holds. Where the identity

[Equation 8] And Lorenz gauge

[Equation 9] Using, the Laplace equation for the vector potential A and the scalar potential φ is

[Equation 10]

[Equation 11] Becomes The vector potential A and the scalar potential φ are calculated from the charge density σ and the current density i given using this Laplace equation, and the electric field and the magnetic field are calculated from the equations (5) and (6).

As described above, in the conventional electromagnetic field analysis method, the electric field and the magnetic field are obtained through the indirect quantity called the potential, so that there is a problem that the structure and the state that can be calculated by the restriction such as the setting of the boundary condition are restricted. ..

The present invention has been made in view of the above problems of the prior art, and an object of the present invention is to provide an electromagnetic field analysis method which can eliminate the restriction of the conventional analysis method and can remarkably expand the applicable range and the applied range. To provide.

[0009]

In order to achieve the above object, an electromagnetic field analysis method according to a first aspect of the present invention comprises a step of dividing a boundary surface of a space to be analyzed into a plurality of boundary surface elements, and a plurality of these boundary surfaces. A step of providing a surface electric field source Es and a surface magnetic field source Hs as an energy source on one reference surface which can be connected to all of the surface elements by a straight line; The external electric field E and magnetic field H are calculated from these surface electric field source Es and surface magnetic field source Hs.

[Equation 12]

[Equation 13] And a step of calculating by

In order to achieve the above object, the electromagnetic field analysis apparatus of claim 2 provides the surface electric field source ES with an electric field source distributed on the surface of a volume section including all driving energy sources, and It is characterized in that the surface magnetic field source Hs is provided by a magnetic field source distributed on the surface of a volume section including all the driving energy sources.

In order to achieve the above-mentioned object, the electromagnetic field analysis apparatus according to a third aspect of the invention has a boundary surface between predetermined regions and a surface electric field source Es.
, An input means for designating the surface magnetic field source Hs, and an electric field and a magnetic field in each element of the predetermined region. And a display means for outputting the calculation result.

In order to achieve the above object, in the electromagnetic field analyzing apparatus of claim 4, the input means is the surface electric field source ES.
Is designated as an electric field source distributed on the surface of the volume section including all the driving energy sources, and the surface magnetic field source Hs is designated as a magnetic field source distributed on the surface of the volume section including all the driving energy sources. Is characterized by.

[0013]

The electromagnetic field analysis method and apparatus of the present invention is based on Ohm's law, which indicates a linear relationship between current and voltage, and Tefnan's theorem, which represents a nonlinear relationship between current and voltage when a source exists inside the system. Introducing the relationship with and into the Maxwell equation, the direct electric field without potential via the boundary element method,
The basic principle is to obtain a magnetic field.

In the conventional Maxwell equation, the current density and the charge density are given without clarifying the term representing the energy source, but in the present invention, an active energy source such as an electric field source or a magnetic field source is given, and the Maxwell equation is given. Include the driving element in itself. As an example of the drive source, the surface electric field source Es and the surface magnetic field source Hs are given to one reference surface overlooking each boundary element in the boundary element method, that is, one reference surface connectable to each boundary element by a straight line. As shown in FIG. 7, the surface electric field source Es is Es = Er.delta. (Z-z0) (where Er is
Is an electric field having only the r component, δ is given by the Dirac delta function), and the surface magnetic field source is Hs as shown in FIG.
= Hαδ (z−z0) (where Hα is a magnetic field having only a component in the α direction orthogonal to the r direction, and δ is a Dirac delta function). The surface electric field source Es and the surface magnetic field source HS generate the pointing vector sources Sas and Sbs as shown in FIGS. 9 and 10, respectively.
Then, when the surface electric field source and the surface magnetic field source are both present as shown in FIG. 11, the pointing vector source Ss is discharged in only one direction as shown in FIG. This pointing vector source serves as a driving source, and the electric field and magnetic field of the boundary element are determined.

That is, new energy sources ES and HS are added to the electric field E and magnetic field H of the above-mentioned Maxwell equation, and defined as Et = E + Es Ht = H + Hs. Similarly, for charge and current, the charge source σ
It is also possible to add s and the current source is to define σt = σ + σs it = i + is Dt = D + Ds Bt = B + Bs. The Maxwell equation at this time is

[Equation 14]

[Equation 15]

[Equation 16]

[Equation 17] Becomes Then, it is clear that such a modified Maxwell equation does not impair the conventional Maxwell equation. That is, if the vector potential A and the scalar potential φ are defined as the quantities representing the total amount of the electric field Et and the magnetic flux density Bt including the energy source,

[Equation 18]

[Formula 19] Becomes These formulas and Lorenz gauge

[Equation 20] Using, the Laplace equation for the vector potential A and the scalar potential φ is

[Equation 21]

[Equation 22] Becomes This expression means that the vector potential and the scalar potential of the modified Maxwell equation in the present invention are defined in the same form as those according to the conventional definition regardless of the presence or absence of the energy source, and therefore the potential of the modified Maxwell equation is It can be seen that the concept does not deny or impair the potential, but also includes the conventional potential.

By using such a modified Maxwell equation, it is possible to directly obtain an electric field and a magnetic field without passing through a potential. That is, (1
Taking rot of 4) and using (15)

[Equation 23] Then, take the rot of (15) again, and further (14)
With

[Equation 24] Becomes A surface electric field source Es and a surface magnetic field source H are provided on one end surface to be analyzed.
Given s, these expressions

[Equation 25]

[Equation 26] Since the right side is the known surface electric field source Es and surface magnetic field source Hs, the electric field E and magnetic field H of arbitrary boundary elements can be obtained. That is, in general, the Laplace equation

[Equation 27] Is the solution

[Equation 28] Therefore, the electric field and the magnetic field are uniquely determined from (26) and (27) (see FIG. 13).

As a more general example of the surface electric field source ES and the surface magnetic field source HS, an electric field source ES = E.delta. (R-r0) distributed on a spherical closed curved surface having a predetermined radius r0 is given. Further, the surface magnetic field source Hs can be given by a magnetic field source HS = H.delta. (R-r0) distributed on a spherical closed curved surface having a predetermined radius r0. In other words, it can be considered that there is a drive source that actively emits energy in a certain space, and as a result, an electric field or magnetic field is generated in the surrounding space, but a spherical volume that completely contains this energy source. A space V is set, its surface is defined as S, and the surface electric field ES is formed on this S (spherical closed curved surface).
, The surface magnetic field HS is set. Naturally, the volume section V may be shaped like a cube or a triangular pyramid depending on the purpose.

Now, in this way, the surface electric field ES, the surface magnetic field HS
The validity of setting A on a spherical closed surface will be explained using a Hertz dipole as an example. As shown in FIG. 14, let us consider a case where a Hertz dipole exists at one point in the space (set as the origin). Conventionally, this Hertz dipole has not been considered as an energy source, but is treated as emitting radio waves. At this time, the electric field E (Er, E
θ, Eα) and the magnetic field H (Hr, Hθ, Hα) are well known, Becomes

On the other hand, a spherical closed surface having a radius r0 is represented by a delta function δ (r-r0). Then, the electric field and the magnetic field are cut out with this closed curved surface. When focusing on the electric field, this spherical closed curved surface is expressed as a delta function weighted by the electric field at that location. That is, ES = E (r, .theta., .Alpha.). Delta. (R-r0). The surface electric field source ES by this weighted delta function is used for the driving term on the right side of the equation (25), and
The left side of the equation shows the state of the electric field generated as a result of the presence of this surface electric field source (current density and charge density do not exist). Then, the electric field at any point in space is Becomes

Therefore, in the far field, Becomes However, the integration range is a hemispherical part that can be seen when looking at the energy source sphere (radius r0) from infinity. Then, it can be confirmed by numerical calculation using a computer or the like that this electric field value matches the theoretical value of the Hertz dipole described above.

What is clear from the above Hertz dipole example is that the electric field and the magnetic field to be formed are
All energy sources that contribute to the formation of the magnetic field are cut out and removed in the volume section containing it, and instead, the electric field, the surface electric field source weighted by the magnetic field, and the surface magnetic field source are called on the surface (closed curved surface) of the volume section. It can be replaced by an energy source. And, this means that if the electric field in a certain closed curved surface is determined, a surface electric field source can be set to the closed curved surface as a driving source, and the electric field in the remaining portion can be determined. On the contrary, when it is desired to set the electric field of a certain portion to a certain value, it means that the electric field in the vicinity of the driving source can be known.

As described above, in the present invention, the electric field and the magnetic field can be directly calculated from the surface electric field source and the electromagnetic field source without passing through the potential, and the initial value is given as the surface electric field source E.
Since it is s and the surface magnetic field source Hs, it is easier than the conventional case where the charge density σ and the current density i are given, and a special space can be analyzed.

Further, the surface electric field E given as an initial value
Since s and the surface magnetic field source Hs give a pointing vector on the surface, it is possible to perform an analysis excellent in conformity with the S parameter well known in circuit design.

[0024]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Preferred embodiments of the electromagnetic field analysis method according to the present invention will be described below with reference to the drawings.

FIG. 1 shows a block diagram of the configuration of the electromagnetic field analysis apparatus of this embodiment. A keyboard 10 is provided as an input means to input a region to be analyzed as a boundary condition, and numerically input a surface electric field source Es and a surface magnetic field source Hs. Input data from the keyboard 10 is supplied to the computer 12 via an input / output port (not shown). The computer 12 is a ROM in which a calculation program is stored, and according to this program, (26),
It has a built-in CPU for calculating the electric field E and the magnetic field H using the equations (27) and (28) and a RAM for storing the calculation results.
Result of calculation stored in RAM, that is, electric field E, magnetic field H
Is supplied to the CRT 14 of the display means and displayed.

FIG. 2 schematically shows an example of a region to be analyzed in this embodiment. This area has an elongated tube shape having a curvature, and the operator uses the keyboard 10 to input the boundary conditions of this analysis area.

When the area is input, the computer 12 performs division processing for dividing the area into a plurality of planes Pi. The condition that this plane Pi must satisfy is the two planes P.
This means that all the boundary elements forming the boundary of the area divided by i and Pi + 1 can be connected by a straight line. FIG. 3 shows an example of a section satisfying such a connectable condition. As is well known, the boundary element method is a method of dividing a boundary region into boundary elements and solving them in a point-selective manner, and it is necessary that two points of interest can be seen, that is, connectable by a straight line. This condition is necessary because the electromagnetic field analysis method of the present invention basically performs calculation using the boundary element method. Therefore, when analyzing a complicated region having a larger curvature, rather than the simple region shown in FIG. 2, the number of surfaces Pi also increases. In this embodiment, for the sake of convenience, the six planes P1, P2, ...
An example of dividing by P6 is shown.

Here, a coefficient as an S parameter is assigned to each of the divided sections. FIG. 4 shows a schematic explanatory diagram of this S parameter, and loads γ1 and γ2 are connected to both end faces 1 and 2 of a system, respectively. Then, assuming that the incident waves of a1 and a2 are respectively incident from the surfaces 1 and 2 and the reflected waves of b1 and b2 are reflected respectively, they depend on the S parameter of the system S and the reflection coefficient of the signal source and the load.

[Equation 29] It is related like. Therefore, both end surfaces (plane Pi in this embodiment) of this system (divided section in this embodiment)
The incident wave and the reflected wave at are determined by the energy drive source as, the signal sources at the input and output ends, the reflection coefficients γ1 and γ2 of the load, and the S parameters of the system. In the numerical calculation method according to the present invention, the S of each divided stage shown in FIG.
It is characterized in that the parameters, the signal sources at both ends of each stage, the reflection coefficient of the load, and the energy driving source at the input end of each stage are sequentially obtained. In FIG. 2, the S parameters in each section are represented by S1, S2, ..., S5.

The purpose of electromagnetic field analysis is to know the values of the electric field and magnetic field at each boundary element in a given region. For this purpose, in this embodiment, the analysis is performed through the following steps. That is, (1) The S parameter Si of each section shown in FIG. 2 is obtained.

For this reason, both end faces Pi and Pi + 1 of each section are non-reflecting end faces, and the input end Pi and the output end Pi + 1 are driven by the reference power wave sources Es0 and Hs0. The S parameter Si is determined from the transmitted wave and the reflected wave in each case.

(2) Next, the equivalent signal source, the load reflection coefficient, and the equivalent energy driving source in each stage in the actual operating state are obtained.

The first surface P1 is driven by a predetermined power source a1,
Using the S parameter Si of each section, the equivalent energy drive source and the equivalent signal source reflection coefficient in the next section are sequentially obtained as shown in FIGS. The equivalent load reflection coefficient is obtained in the same manner. The electric field and magnetic field in that section are obtained from them.

Here, the electromagnetic field analysis method of the present invention is used when obtaining the S parameter Si of each section in (1) and when obtaining the electric field and magnetic field in that section from the equivalent energy driving source ai in (2). Will be

According to the electromagnetic field analysis method of the present invention, a signal source is provided at one end surface, and a surface electric field source Es and a surface magnetic field source Hs, which are power wave sources under the boundary condition corresponding to the reflection coefficient, are applied to drive the boundary, and all boundaries in the section are driven. The feature is that the electric field and magnetic field of the element are directly calculated. Driving both ends with a non-reflective end and driving with a reference drive energy source is equivalent to the operation for obtaining S-parameters, and then replacing both ends with an actual signal source, load reflection coefficient, and equivalent drive energy source. This corresponds to the operation of obtaining the electric field and magnetic field of. Further, the electric field E of these boundary elements, the electric field E of the section other than the end face from the magnetic field, and the surface magnetic field H.
Is calculated.

Specifically, the reference power wave source is input from the keyboard 10, or the reference power wave source stored in advance in the ROM is read and supplied to the CPU, and the ROM or R
The electric field and magnetic field are calculated using the arithmetic expressions (26) and (27) stored in AM, and the S parameter is calculated using (29) and stored in the RAM.

After the S parameter Si in each section is calculated in this way, the process proceeds to step (2).
This step (2) is actually step (2) -A for obtaining the equivalent drive energy source and the equivalent signal source load reflection coefficient as described above, and the equivalent drive energy source and equivalent signal source and the load reflection coefficient from the electric field and the magnetic field. (2) -B is obtained by repeating two steps.

Of these two steps, step (2) -A is based on the characteristic of the S parameter. When a plurality of systems Si are connected as shown in FIG. 5, the systems S1 to Si-1 can be replaced by a single system Wi-1, and at this time, the S parameter Wi of the system Wi is

[Equation 30] It is known that However,

[Equation 31] Is. Therefore, when focusing on a certain system Si, the systems S1 to S5 in the preceding stage are collectively replaced by a single system Wi-1, and the incident energy wave source at that time is given by aqi.

On the other hand, the load γs and the system Wi also have a single load γs.
It can be equivalently displayed with ´, and when replaced as shown in Fig. 6,

[Equation 32]

[Expression 33] It is known that the relationship of Therefore, in order to obtain the electric field and magnetic field in an arbitrary section Si, first, (3
0) and (31) are used to combine the S-parameters of the system, and (32) and (33) are used to calculate the equivalent signal source reflection coefficient and the equivalent drive energy source. (2) according to the present invention as a source Es and a surface magnetic field source Hs.
5) and (26) may be used to find the electric field and magnetic field in the section Si.

As described above, in the present embodiment, an example in which the electric field and magnetic field in the designated region is analyzed by using the S parameter is shown. However, the electromagnetic field analysis method of the present invention gives a surface electric field and a surface magnetic field to directly electromagnetically Since it is a method of knowing the field, it is possible to perform an analysis excellent in consistency with the S parameter.

[0040]

As described above, according to the electromagnetic field analysis method and apparatus of the present invention, it is possible to directly obtain the electric field and magnetic field without using the indirect amount of potential. Further, since the initial values are set in the form of a surface electric field source and a surface magnetic field source, the setting is easier than the conventional setting of the charge density and the current density, and it is possible to set a special condition. Further, since the Laplace equation is used, there is an effect that the method in another electromagnetic field analysis method can be easily applied.

[Brief description of drawings]

FIG. 1 is a configuration block diagram of an embodiment of the present invention.

FIG. 2 is an explanatory diagram of an analysis area of the same embodiment.

FIG. 3 is an explanatory diagram of a section of an analysis area according to the embodiment.

FIG. 4 is an explanatory diagram of S parameters according to the same embodiment.

FIG. 5 is a characteristic explanatory diagram of S parameters in the same example.

FIG. 6 is a characteristic explanatory diagram of S-parameters in the example.

FIG. 7 is an explanatory diagram of a surface electric field source of the present invention.

FIG. 8 is an explanatory diagram of a surface magnetic field source of the present invention.

FIG. 9 is an explanatory diagram of a pointing vector of the surface electric field source of the present invention.

FIG. 10 is an explanatory diagram of a pointing vector of the surface magnetic field source of the present invention.

FIG. 11 is an explanatory diagram of a surface electromagnetic field source of the present invention.

FIG. 12 is an explanatory diagram of a pointing vector of the surface electromagnetic field source of the present invention.

FIG. 13 is an explanatory diagram showing a positional relationship between two points PP ′ of the present invention.

FIG. 14 is an explanatory diagram of a Hertz dipole.

[Explanation of symbols]

 10 keyboard 12 computer 14 CRT

Claims (4)

[Claims] 1. A step of dividing a boundary surface of a region to be analyzed into a plurality of boundary surface elements, and a surface electric field source Es as a driving energy source on one reference surface connectable to all of the plurality of boundary surface elements by a straight line. And a step of providing a surface magnetic field source Hs, and on each boundary surface element and in a region surrounded by each boundary surface element,
Alternatively, the electric field E and the magnetic field H outside the region are calculated from these surface electric field source Es and surface magnetic field source Hs. And an electromagnetic field analysis method comprising: 2. The electromagnetic field analysis method according to claim 1, wherein said surface electric field source ES is given by an electric field source distributed on the surface of a volume section including all drive energy sources, and said surface magnetic field source Hs is driven. An electromagnetic field analysis method, characterized in that a magnetic field source distributed on the surface of a volume section including all energy sources is applied. 3. An electromagnetic field analyzing apparatus for numerically analyzing an electric field and a magnetic field in a predetermined area, comprising: input means for designating a boundary surface, a surface electric field source Es, and a surface magnetic field source Hs of the predetermined area; Electric field and magnetic field in each element of the area An electromagnetic field analysis apparatus comprising: a calculation unit that calculates by means of; and a display unit that outputs a calculation result. 4. The electromagnetic field analysis apparatus according to claim 3, wherein the input means designates the surface electric field source ES as an electric field source distributed on the surface of a volume section including all driving energy sources, and the surface electric field source ES is specified. An electromagnetic field analyzing apparatus characterized in that a magnetic field source Hs is designated as a magnetic field source distributed on the surface of a volume section including all driving energy sources.