JP2017161247A - Electromagnetic field analyzing device, electromagnetic field analyzing method, and computer program - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide an electromagnetic field analyzing device and an electromagnetic field analyzing method that can infer far fields with high precision taking into account the reflections of electromagnetic waves, and a computer program for materializing a computer as an electromagnetic field analyzing device.SOLUTION: On the basis of the result of measuring electromagnetic waves near the radiation source of the electromagnetic waves arranged in an anechoic chamber shielded from the electromagnetic waves, electromagnetic waves in positions away from the radiation source are inferred. The electric field intensity and phase on a cylindrical face at a certain distance away from the radiation source in the horizontal direction are measured, a development point, which is the origin of a basic function at the time of multipolar development, is set in each of a first position where the radiation source is arranged and in a second position symmetric to the first position with the floor face of the anechoic chamber in-between. The coefficient at the time of multipolar development is calculated for each of the development points on the basis of the solution of the Helmholtz equation, and the electromagnetic fields in the area outside the cylindrical face are figured out by multipolar development using coefficients each calculated by superposing one or another of the development points.SELECTED DRAWING: Figure 6

Description

  The present invention relates to an electromagnetic field analyzer that estimates radiated electromagnetic waves in an anechoic chamber, an electromagnetic field analysis method, and a computer program for realizing a computer as an electromagnetic field analyzer.

  All types of electromagnetic waves are emitted from all electronic devices. For example, spark discharge between switch contacts due to opening / closing operation of an electric circuit, electromagnetic interference such as clock frequency and its harmonics indispensable for digital circuit operation, malfunction due to radio or television reception interference, or electromagnetic interference between other external devices Etc. may occur. Therefore, it is an important technique to block unnecessary electromagnetic waves from leaking outside.

  The state of electromagnetic waves actually emitted from electronic devices is measured by a method defined by international standards. Since many of the allowable values of unnecessary radio waves are defined at a measurement distance of 10 m, equipment that can be measured at a distance of 10 m from the radiation source is required.

  In order to reduce the influence of noise in the surrounding environment, it is recently measured in a large anechoic chamber. The anechoic chamber means a dark room that does not emit electromagnetic waves generated in the darkroom to the outside and is not affected by the electromagnetic waves from the outside.

  Since a large anechoic chamber is expensive to use, it is desirable if electromagnetic waves at the design stage can be measured in a small anechoic chamber to estimate the electromagnetic field at a distance of 10 m. For example, Patent Document 1 discloses a far electromagnetic field estimation method for estimating an electromagnetic field by calculating an equivalent current and an equivalent magnetic current from an electromagnetic field measured in the vicinity of a radiation source, and integrating using a Green function. Has been. Non-Patent Document 1 also discloses a method for estimating a radiation electric field intensity using a 10 m method based on a measurement result in an equivalent radiation source model.

Japanese Patent Laying-Open No. 2015-034785

Masato Kawabata and two others, “A Study on Equivalent Radiation Source Modeling of Electronic Equipment for Far Field Estimation”, 2014, The Institute of Electronics, Information and Communication Engineers, EMCJ2013-131, pp. 117

  In the methods disclosed in Patent Literature 1 and Non-Patent Literature 1, a farther solution (hereinafter, far solution) is estimated based on an electromagnetic field measured (measured) in the vicinity of the radiation source. However, none of the methods considers the installation state of the radiation source that is the object of electromagnetic wave measurement.

  That is, ideally, the radiation source only needs to be positioned at the center of the space, but actually electromagnetic waves are reflected by the presence of an installation table, a floor surface, a ceiling surface, or the like on which the radiation source is placed. Therefore, the actual far solution is strongly influenced by the reflected electromagnetic wave, whereas the methods disclosed in Patent Document 1 and Non-Patent Document 1 sufficiently consider the influence of the reflected electromagnetic wave. Difficult to do. Therefore, there is a problem that it is difficult to expect high accuracy in the far-field solution. Here, it is confirmed that the reflected wave from the floor surface has the largest influence on the estimation result among the reflected waves from the floor surface, the installation stand, the ceiling, and the like.

  The present invention has been made in view of such circumstances, and an electromagnetic field analysis apparatus, an electromagnetic field analysis method, and a computer that can estimate a distant solution with high accuracy in consideration of reflected waves of electromagnetic waves. An object of the present invention is to provide a computer program for realizing as a field analysis device.

  In order to achieve the above object, an electromagnetic field analysis apparatus according to a first aspect of the present invention is based on an electromagnetic wave measurement result in the vicinity of an electromagnetic wave radiation source disposed in an anechoic chamber where the electromagnetic wave is shielded. In the electromagnetic field analysis apparatus for estimating electromagnetic waves at a distant position, measurement means for measuring electric field strength and phase on a cylindrical surface that is a certain distance in the horizontal direction from the radiation source, and the radiation source are arranged. An expansion point setting means for setting an expansion point that is an origin of a basis function at the time of multipole expansion at a first position and a second position that is symmetrical with respect to the first position and the floor of the anechoic chamber; In order to calculate the electromagnetic field in the region outside the cylindrical surface based on the measured electric field strength and phase on the cylindrical surface, the coefficient at the time of multipole expansion is calculated based on the solution of the Helmholtz equation. So Coefficient calculation means for calculating each and the electromagnetic field in the region outside the cylindrical surface are estimated by superimposing the electromagnetic fields obtained by multipole expansion using the coefficients calculated for each of the expansion points. And an electromagnetic field estimation means.

  Further, in the electromagnetic field analysis apparatus according to the second invention, in the first invention, the coefficient calculation means preferably calculates the coefficients of the TM wave and the TE wave in the Helmholtz equation by a least square method.

  The electromagnetic field analysis apparatus according to a third aspect of the present invention is the electromagnetic field analyzer according to the first or second aspect, wherein the measuring means measures a phase as an angle at which the electric field is maximum in one period in an electric field pattern that vibrates at a constant frequency. It is preferable.

  Next, in order to achieve the above object, an electromagnetic field analysis apparatus according to a fourth aspect of the present invention is based on the measurement result of the electromagnetic wave in the vicinity of the electromagnetic wave radiation source disposed in the anechoic chamber where the electromagnetic wave is shielded. In an electromagnetic field analyzer for estimating electromagnetic waves at a position away from a radiation source, a measuring means for measuring an electric field strength and a phase on a cylindrical surface that is a certain distance in the horizontal direction from the radiation source, and the radiation source are arranged. Expansion point setting means for setting an expansion point that is the origin of the basis function at the time of multipole expansion at a third position obtained by projecting the first position on the floor surface of the electromagnetic wave anechoic chamber, and the floor surface of the anechoic chamber A mirror copy means for mirror copying the measurement result on the cylindrical surface at a position symmetrical with respect to the electromagnetic field, and an electromagnetic field in a region outside the cylindrical surface based on the measurement result on the cylindrical surface that is mirror-copied In order to calculate, using the coefficient calculation means for calculating the coefficient at the time of multipole expansion based on the solution of the Helmholtz equation, and the electromagnetic field in the region outside the cylindrical surface using the coefficient calculated for the expansion point And an electromagnetic field estimation means for estimating an electromagnetic field by multipole expansion.

  In the electromagnetic field analysis apparatus according to a fifth aspect, in the fourth aspect, the coefficient calculation means preferably calculates the coefficients of the TM wave and the TE wave in the Helmholtz equation by a least square method.

  The electromagnetic field analysis apparatus according to a sixth aspect of the present invention is the electromagnetic field analyzer according to the fourth or fifth aspect, wherein the measuring means measures a phase as an angle at which the electric field becomes maximum in one period in an electric field pattern that vibrates at a constant frequency. It is preferable.

  Next, in order to achieve the above object, an electromagnetic field analysis method according to a seventh aspect of the present invention is based on a measurement result of an electromagnetic wave in the vicinity of an electromagnetic wave radiation source disposed in an anechoic chamber where the electromagnetic wave is shielded. In an electromagnetic field analysis method that can be executed by an electromagnetic field analysis device that estimates an electromagnetic wave at a position away from a radiation source, the electromagnetic field analysis device is a cylindrical surface that is separated from the radiation source by a certain distance in the horizontal direction. Measuring the electric field strength and phase at the first position where the radiation source is disposed, and a second position which is symmetric with respect to the first position and the floor of the anechoic chamber. In order to calculate the electromagnetic field in the region outside the cylindrical surface based on the step of setting the expansion point that is the origin of the basis function at the time of expansion and the measured electric field strength and phase on the cylindrical surface, Calculating a coefficient at the time of multipole expansion for each of the expansion points based on the solution of the two equations, and using the coefficient calculated for each of the expansion points for the electromagnetic field in the region outside the cylindrical surface And superposing and estimating the electromagnetic fields obtained by multipole expansion.

  In the electromagnetic field analysis method according to the eighth aspect of the present invention, preferably, the TM wave and TE wave coefficients in the Helmholtz equation are calculated by the least square method in the seventh aspect.

  In the electromagnetic field analysis method according to the ninth aspect of the present invention, in the seventh or eighth aspect of the invention, it is preferable that the phase is measured as an angle at which the electric field becomes maximum in one period in the electric field pattern that vibrates at a constant frequency.

  Next, in order to achieve the above object, the electromagnetic field analysis method according to the tenth aspect of the present invention is based on the measurement result of the electromagnetic wave in the vicinity of the electromagnetic wave radiation source disposed in the anechoic chamber where the electromagnetic wave is shielded. In an electromagnetic field analysis method that can be executed by an electromagnetic field analysis device that estimates an electromagnetic wave at a position away from a radiation source, the electromagnetic field analysis device is a cylindrical surface that is separated from the radiation source by a certain distance in the horizontal direction. Measuring the electric field strength and phase at the first position where the radiation source is disposed, and a third position projected on the floor of the anechoic chamber, which is the origin of the basis function at the time of multipole expansion A step of setting a development point, a step of mirror-copying the measurement result on the cylindrical surface at a position symmetrical with respect to the floor surface of the anechoic chamber, and a measurement result on the cylindrical surface subjected to mirror-copying To calculate the electromagnetic field in the region outside the cylindrical surface, calculating a coefficient at the time of multipole expansion based on the solution of the Helmholtz equation, and the electromagnetic field in the region outside the cylindrical surface, And estimating an electromagnetic field by multipole expansion using a coefficient calculated for the expansion point.

  Further, in the electromagnetic field analysis method according to the eleventh aspect of the invention, it is preferable that the TM wave and TE wave coefficients in the Helmholtz equation are calculated by the least square method in the tenth aspect of the invention.

  In the electromagnetic field analysis method according to the twelfth aspect of the present invention, in the tenth or eleventh aspect of the present invention, it is preferable that the phase is measured as an angle at which the electric field becomes maximum in one period in the electric field pattern oscillating at a constant frequency.

  Next, in order to achieve the above object, a computer program according to a thirteenth aspect of the present invention is based on a measurement result of an electromagnetic wave in the vicinity of an electromagnetic wave radiation source disposed in an anechoic chamber where the electromagnetic wave is shielded. In a computer program that can be executed by an electromagnetic field analysis device that estimates electromagnetic waves at a position away from the electromagnetic field analysis device, the electromagnetic field analysis device includes an electric field strength on a cylindrical surface that is a certain distance in the horizontal direction from the radiation source, and A measuring means for measuring a phase, a first position where the radiation source is disposed, and a second position which is symmetrical with respect to the first position and the floor surface of the anechoic chamber; An expansion point setting means for setting the expansion point that is the origin of the function, and the electromagnetic field in the region outside the cylindrical surface is calculated based on the measured electric field strength and phase on the cylindrical surface. Therefore, a coefficient calculating means for calculating a coefficient at the time of multipole expansion based on the solution of the Helmholtz equation for each of the expansion points, and an electromagnetic field in the region outside the cylindrical surface for each of the expansion points It is characterized by functioning as an electromagnetic field estimating means for superposing and estimating the electromagnetic fields obtained by multipole expansion using the coefficients calculated in the above.

  In the computer program according to the fourteenth aspect of the present invention, in the thirteenth aspect, the coefficient calculating means preferably functions as means for calculating the coefficients of the TM wave and the TE wave in the Helmholtz equation by a least square method.

  A computer program according to a fifteenth aspect of the invention is the computer program according to the thirteenth or fourteenth aspect, wherein the measuring means is a means for measuring a phase as an angle at which the electric field becomes maximum in one period in an electric field pattern oscillating at a constant frequency. It is preferable to make it function.

  Next, in order to achieve the above object, the computer program according to the sixteenth aspect of the present invention is based on the measurement result of the electromagnetic wave in the vicinity of the electromagnetic wave radiation source disposed in the anechoic chamber where the electromagnetic wave is shielded. In a computer program that can be executed by an electromagnetic field analysis device that estimates electromagnetic waves at a position away from the electromagnetic field analysis device, the electromagnetic field analysis device includes an electric field strength on a cylindrical surface that is a certain distance in the horizontal direction from the radiation source, and Measuring means for measuring the phase, setting the expansion point that is the origin of the basis function for multipole expansion to the third position where the first position where the radiation source is located is projected onto the floor of the anechoic chamber A development point setting means, a mirror copy means for mirror-copying the measurement result on the cylindrical surface at a symmetrical position across the floor surface of the anechoic chamber, Based on the measurement result on the cylindrical surface, in order to calculate the electromagnetic field in the region outside the cylindrical surface, coefficient calculating means for calculating the coefficient at the time of multipole expansion based on the solution of the Helmholtz equation, and the cylindrical surface The electromagnetic field in the outer region is caused to function as electromagnetic field estimation means for estimating the electromagnetic field by multipole expansion using a coefficient calculated with respect to the expansion point.

  In the sixteenth invention, the computer program according to the seventeenth invention preferably causes the coefficient calculating means to function as means for calculating the coefficients of the TM wave and the TE wave in the Helmholtz equation by a least square method.

  The computer program according to an eighteenth aspect of the invention is the computer program according to the sixteenth or seventeenth aspect, wherein the measuring means is a means for measuring the phase as an angle at which the electric field becomes maximum in one period in an electric field pattern that vibrates at a constant frequency. It is preferable to make it function.

  In the first invention, the seventh invention, and the thirteenth invention, the electric field strength and the phase are measured on a cylindrical surface that is a certain distance in the horizontal direction from the radiation source. At the first position where the radiation source is arranged and the second position which is symmetrical with respect to the floor of the anechoic chamber, the expansion point which is the origin of the basis function at the time of multipole expansion is set respectively. Set. Based on the measured electric field strength and phase on the cylindrical surface, calculate the coefficients for the multipole expansion for each expansion point based on the solution of the Helmholtz equation to calculate the electromagnetic field in the region outside the cylindrical surface. To do. The electromagnetic field in the region outside the cylindrical surface is estimated by superimposing the electromagnetic fields obtained by multipole expansion using the coefficients calculated for each of the expansion points. As a result, the first position where the radiation source is arranged and the second position which is symmetric with respect to the first position and the floor surface of the anechoic chamber are expanded as the origin of the basis function at the time of multipole expansion. Each point is set, and the electromagnetic field in the region outside the cylindrical surface is estimated by superimposing the electromagnetic field obtained by multipole expansion using the coefficient calculated for each expansion point. Even when there is a reflected wave on the surface, it is possible to estimate the electromagnetic field in consideration of the influence of the reflected wave when estimating the electromagnetic field in the region outside the cylindrical surface.

  In the second invention, the eighth invention, and the fourteenth invention, the coefficients of the TM wave and the TE wave in the Helmholtz equation are calculated by the least square method, so that the electromagnetic field can be estimated with higher accuracy based on the measurement data. it can.

  In the third invention, the ninth invention, and the fifteenth invention, the phase is measured as the angle at which the electric field is maximized in one period in the electric field pattern oscillating at a constant frequency. It becomes clear that it becomes, and it becomes possible to perform more detailed electromagnetic field analysis.

  In the fourth, tenth, and sixteenth inventions, the electric field strength and phase on a cylindrical surface that is a certain distance in the horizontal direction from the radiation source are measured, and the first position where the radiation source is located is set in the anechoic chamber. The expansion point that is the origin of the basis function at the time of multipole expansion is set at the third position projected onto the floor surface. To mirror-copy the measurement result on the cylindrical surface at a symmetrical position across the floor of the anechoic chamber, and to calculate the electromagnetic field in the area outside the cylindrical surface based on the measurement result on the cylindrical surface that is mirror-copied Next, the coefficient at the time of multipole expansion is calculated based on the solution of the Helmholtz equation, and the electromagnetic field in the region outside the cylindrical surface is estimated by multipole expansion using the coefficient calculated for the expansion point. . As a result, the expansion point that is the origin of the basis function at the time of multipole expansion is set at the third position where the first position where the radiation source is arranged is projected onto the floor of the anechoic chamber. In order to calculate the electromagnetic field in the area outside the cylindrical surface based on the measurement result in the cylindrical surface that is mirror-copied, and the measurement result in the cylindrical surface is mirror-copied to a symmetrical position across the floor of Based on the solution of the Helmholtz equation, the coefficient at the time of multipole expansion is calculated, and the electromagnetic field in the region outside the cylindrical surface is estimated by multipole expansion using the coefficient calculated for the expansion point. Even when there is a reflected wave on the floor surface in the anechoic chamber, it is possible to estimate the electromagnetic field in consideration of the influence of the reflected wave when estimating the electromagnetic field in the region outside the cylindrical surface. In particular, it is possible to estimate the electromagnetic field with high accuracy even in a region where the frequency is relatively low.

  In the fifth invention, the eleventh invention and the seventeenth invention, the coefficients of the TM wave and the TE wave in the Helmholtz equation are calculated by the least square method, so that the electromagnetic field can be estimated with higher accuracy based on the measurement data. it can.

  In the sixth invention, the twelfth invention and the eighteenth invention, the phase is measured as the angle at which the electric field becomes maximum in one period in the electric field pattern oscillating at a constant frequency. It becomes clear that it becomes, and it becomes possible to perform more detailed electromagnetic field analysis.

  According to the above configuration, the origin of the basis function at the time of multipole expansion is set at the first position where the radiation source is disposed and the second position which is symmetrical with respect to the first position and the floor of the anechoic chamber. Are set, and the electromagnetic field in the region outside the cylindrical surface is estimated by superimposing the electromagnetic fields obtained by multipole expansion using the coefficients calculated for each of the expansion points. Even when there is a reflected wave on the floor surface in the dark room, it is possible to estimate the electromagnetic field in consideration of the influence of the reflected wave when estimating the electromagnetic field in the region outside the cylindrical surface.

  In addition, the expansion point, which is the origin of the basis function during multipole expansion, is set at the third position where the first position where the radiation source is located is projected onto the floor of the anechoic chamber. In order to calculate the electromagnetic field in the outer area of the cylindrical surface based on the mirrored copy of the measurement result on the cylindrical surface, the Helmholtz measurement is performed at a symmetrical position across the floor surface. The coefficient for multipole expansion is calculated based on the solution of the equation, and the electromagnetic field in the region outside the cylindrical surface is estimated by multipole expansion using the coefficient calculated for the expansion point. Even when there is a reflected wave on the floor surface in the dark room, it is possible to estimate the electromagnetic field in consideration of the influence of the reflected wave when estimating the electromagnetic field in the region outside the cylindrical surface. In particular, it is possible to estimate the electromagnetic field with high accuracy even in a region where the frequency is relatively low.

It is a block diagram which shows the structure at the time of embodying the electromagnetic field analyzer which concerns on embodiment of this invention using CPU. It is a schematic diagram which shows the structure of the anechoic chamber using the electromagnetic field analyzer which concerns on embodiment of this invention. It is a schematic diagram which shows the structure of the electromagnetic field measurement system using the electromagnetic field analyzer which concerns on embodiment of this invention. It is a functional block diagram of the electromagnetic field analyzer which concerns on Embodiment 1 of this invention. It is a schematic diagram which shows the setting state of the expansion | deployment point of the electromagnetic field analyzer 1 which concerns on Embodiment 1 of this invention. It is a flowchart which shows the process sequence of CPU of the electromagnetic field analyzer which concerns on Embodiment 1 of this invention. It is a functional block diagram of the electromagnetic field analyzer which concerns on Embodiment 2 of this invention. It is a schematic diagram which shows the outline | summary of the mirror surface copy of the electromagnetic field analyzer which concerns on Embodiment 2 of this invention. It is a flowchart which shows the process sequence of CPU of the electromagnetic field analyzer which concerns on Embodiment 2 of this invention. It is the illustration figure which displayed the measurement result in the display apparatus of the electromagnetic field analyzer which concerns on embodiment of this invention. It is the illustration figure which displayed the estimation result in the display apparatus of the electromagnetic field analyzer which concerns on embodiment of this invention.

  Hereinafter, an electromagnetic field analysis apparatus according to an embodiment of the present invention will be specifically described with reference to the drawings. FIG. 1 is a block diagram showing a configuration when an electromagnetic field analysis apparatus 10 according to an embodiment of the present invention is implemented using a CPU. In FIG. 1, an electromagnetic field analysis apparatus 1 includes a CPU (central processing unit) 11 that constitutes a computation unit that performs computation, a memory 12 that stores temporary information generated in accordance with computation, a storage device 13 such as a hard disk, It comprises an I / O interface 14, a video interface 15, a portable disk drive 16, a communication interface 17, and an internal bus 18 for connecting the hardware described above.

  The CPU 11 is connected to the above-described hardware units of the electromagnetic field analysis apparatus 1 via the internal bus 18, and controls the operation of the above-described hardware units and stores the computer program stored in the storage device 13. According to 100, various software functions are performed. The memory 12 is composed of a volatile memory such as SRAM or SDRAM, and a load module is expanded when the computer program 100 is executed, and stores temporary data generated when the computer program 100 is executed.

  The storage device 13 includes a built-in fixed storage device (hard disk), a ROM, and the like. The computer program 100 stored in the storage device 13 is downloaded by the portable disk drive 16 from a portable recording medium 90 such as a DVD or CD-ROM in which information such as programs and data is recorded. To the memory 12 and executed. Of course, it may be a computer program downloaded from a connected external computer via the communication interface 17.

  The storage device 13 includes a measurement information storage unit 131. The measurement information storage unit 131 stores measurement results obtained by measuring the electric field strength and phase on a cylindrical surface that is a certain distance in the horizontal direction from a radiation source such as an electronic component. Here, the phase to be measured means the angle at which the electric field becomes maximum in one period in the electric field pattern that vibrates at a constant frequency.

  The communication interface 17 is connected to an internal bus 18, and is connected to an external network such as the Internet, a LAN, or a WAN, so that data can be transmitted / received to / from an external computer or the like.

  The I / O interface 14 is connected to a data input medium such as a keyboard 21 and a mouse 22 and receives data input. The video interface 15 is connected to a display device 23 such as a CRT monitor or LCD, and displays a predetermined image.

  When estimating an electromagnetic field (electromagnetic wave intensity distribution) on a cylindrical surface 10 m away from the electronic component 2, conventionally, the estimation is based on a measurement result measured at a measurement distance of 3 m. When measuring at a measurement distance of 3 m, it is necessary to change the height of the electronic component 2 in order to supplement the floor reflected wave when it is assumed that measurement is performed at a measurement distance of 10 m. That is, in the present embodiment, the electronic component 2 is placed at a height of, for example, 2 m or higher and measured.

  However, when actually measuring, changing the height at which the electronic component 2 is arranged is not realistic. Therefore, in the present embodiment, the position where the electronic component 2 is arranged is fixed at a height of 0.8 m, and the electromagnetic field on the cylindrical surface at a measurement distance of 5 m from the electronic component 2 is measured. Based on this, an electromagnetic field in a cylindrical surface 10 m away from the electronic component 2 is estimated.

  Hereinafter, based on the measurement result measured on the cylindrical surface 5 m away from the electronic component as a radiation source in a anechoic chamber where electromagnetic waves are shielded, the electromagnetic field on the cylindrical surface 10 m away from the electronic component ( The electromagnetic field analysis method according to the embodiment of the present invention will be described using an example of estimating the electromagnetic wave intensity distribution).

  FIG. 2 is a schematic diagram showing a configuration of an anechoic chamber using the electromagnetic field analysis apparatus 1 according to the embodiment of the present invention. As shown in FIG. 2A, the electromagnetic field analysis apparatus 1 according to the present embodiment is installed outside the anechoic chamber 10, and has an antenna 5 and a turntable 3 that receive an electromagnetic wave that is a main subject of measurement. Is connected to a sensor (such as a rotary encoder) that detects the rotation angle of the motor.

  A turntable 3 that can rotate is provided on the upper surface of the radiation source installation base 4, and an electronic component 2 that is a radiation source is placed on the turntable 3. While rotating the turntable 3, the electromagnetic wave radiated from the electronic component 2 is received by the antenna 5 provided at a position 5 m from the rotation center of the turntable 3. The electromagnetic wave received by the antenna 5 is transmitted to the electromagnetic field analyzer 1 together with the height of the antenna 5 at the time of measurement and the rotation angle (phase) of the turntable 3 at the time of measurement, and the electromagnetic field on a cylindrical surface having a radius of 10 m. Is estimated.

  Specifically, the antenna 5 moves in the height direction along a fixed pole. The antenna 5 is moved up and down while rotating the turntable 3, and electromagnetic waves are measured over a height of 1 to 4 m and 360 degrees. Since the electronic component 2 itself that is a radiation source rotates, an electromagnetic field as shown in FIG. 2B can be obtained by assuming that the electronic component 2 is fixed. That is, the electric field strength of the electromagnetic field can be acquired at each point on the cylindrical surface having a radius of 5 m (in FIG. 2B, a predetermined height interval and a lattice point for each predetermined phase).

  FIG. 3 is a schematic diagram showing a configuration of an electromagnetic field measurement system using the electromagnetic field analysis apparatus according to the embodiment of the present invention. In FIG. 3, the electromagnetic field analyzer controls the operation of a drive unit such as a motor that drives the turntable 3 and the antenna 5. Thereby, the antenna 5 can be moved up and down while rotating the turntable 3, and electromagnetic waves can be measured over a height of 1 m to 4 m and 360 degrees.

  When estimating an electromagnetic field on a cylindrical surface having a radius of 10 m, it is necessary to correctly capture a reflection component on the floor surface. In the present embodiment, the antenna 5 is 5 m away from the electronic component 2 that is a radiation source, and can move up and down between 1 to 4 m in height. Based on the electromagnetic field measured by the antenna 5 at a position 5 m away, the electromagnetic field on the cylindrical surface having a radius of 10 m is estimated with high accuracy in consideration of the effect of the reflected wave reflected by the floor 31.

(Embodiment 1)
FIG. 4 is a functional block diagram of the electromagnetic field analysis apparatus 1 according to Embodiment 1 of the present invention. In FIG. 4, a measurement unit 401 measures the electric field strength and phase on a cylindrical surface that is a certain distance in the horizontal direction from the electronic component 2 that is a radiation source. Here, the phase to be measured means an angle at which the electric field becomes maximum in one period in the electric field pattern that vibrates at a constant frequency.

  The development point setting unit 402 is a position (first position) where the electronic component 2 that is a radiation source is disposed, and a position (second position) that is symmetrical with respect to the first position and the floor of the anechoic chamber. The expansion point that is the origin of the basis function at the time of multipole expansion is set. Here, in the case of multipole expansion, it is necessary to set an origin (hereinafter, expansion point) where the vector sphere function is expanded as a basis function.

  That is, the origin of the basis function vector en (x) for expanding the general function f (x) in (Equation 1) must be set. In the present embodiment, in view of the fact that the influence of the reflected wave cannot be taken into consideration only by using the position (first position) where the electronic component 2 as the radiation source is disposed as the development point, the first Development points are also set at positions (second positions) that are symmetrical with respect to the position and the floor of the anechoic chamber. As a result, by calculating a coefficient to be described later for each of the two development points, it is possible to estimate the electromagnetic field at an arbitrary position in consideration of the influence of the reflected wave.

  The coefficient calculation unit 403 calculates the coefficient at the time of multipole expansion based on the solution of the Helmholtz equation to calculate the electromagnetic field in the region outside the cylindrical surface based on the measured electric field strength and phase on the cylindrical surface. Calculate for each expansion point.

  Here, the electromagnetic wave in the space outside the electromagnetic wave radiation source follows the following Helmholtz equation.

  In (Expression 2), ∇ indicates a Laplacian, and k indicates a wave number (constant). Ψ is a scalar function and satisfies the inner product of the radius vector r and the electric field vector E.

  When the electric field vector E is obtained based on multipole expansion, it can be expressed as (Equation 3).

  In (Equation 3), the first term on the right side represents the TM wave vector, and the second term on the right side represents the TE wave vector, which can be represented by (Equation 4) and (Equation 5), respectively.

  Here, the TM wave is a longitudinal wave in the z direction when the electromagnetic wave travels in the z direction, and the TE wave is a transverse wave in the x direction or the y direction when the electromagnetic wave is assumed to travel in the z direction. , Each mean. In (Expression 4) and (Expression 5), h (kr) indicates a spherical Hankel function, and vector X indicates a vector spherical function. The vector spherical function can be expressed by (Expression 6).

  In the multipole expansion, the electric field vector E is expressed as a complex number. That is, when the real part vector of the electric field vector E is Er and the imaginary part vector is Ei, the time change of the electric field oscillating at a constant frequency ω can be expressed as (Equation 7).

  Here, assuming that the electric field vector measured by the antenna 5 is Ea and the phase is θ, the time change of the electric field can be similarly expressed as (Equation 8).

  Since (Equation 7) and (Equation 8) represent the same thing, the real part vector Er and the imaginary part vector Ei are represented by (Equation 9) using the electric field vector Ea and the phase θ measured by the antenna 5. Can be expressed as:

Thus, the real part vector Er and the imaginary part vector Ei of the electric field vector E are fitted by multipole expansion using (Equation 3) described above. That is, in (Equation 3), the coefficient a _M (l, m) of the TM wave (l, m) component and the coefficient a _E (l, m) of the TE wave (l, m), which are complex scalar quantities, respectively. m) is obtained by linear interpolation. In the present embodiment, the coefficients a _M (l, m) and a _E (l, m) are calculated by the least square method.

Specifically, the evaluation function F is determined as shown in (Expression 10), and the coefficients a _M (l, m) and a _E (l, m) are determined so that the evaluation function F is minimized. That is, the coefficients a _M (l, m) and a _E (l, m) are determined from the simultaneous linear equations obtained from (Equation 11).

  The first term on the right side of (Equation 10) is a multipole expansion formula of the electric field, and the second term means data measured by the 5m method.

The electromagnetic field estimation unit 404 estimates the electromagnetic field in the region outside the cylindrical surface by superimposing the electromagnetic fields obtained by multipole expansion using the coefficients calculated for each of the expansion points. FIG. 5 is a schematic diagram showing a setting state of the development point of the electromagnetic field analysis apparatus 1 according to Embodiment 1 of the present invention. In FIG. 5, the development point is also set at a position (first position) 51 where the radiation source is disposed and a position (second position) 52 that is symmetrical with respect to the floor 31. That is, when z = ± z0 with the height direction as the z-axis, the electric field vector E (overlapping the electric field vector E as shown in (Equation 12) with radius vector r ₁ = radius vector−r ₂ is obtained. r).

In (Equation 12), the electric field vector E (r) on the left side indicates the superposition of the electric field vector E (r−r ₁ ) and the electric field vector E (r + r ₁ ) on the right side. Actually, the condition of reflection on the floor 31, that is, the vector n = (0, 0, 1) is used as the normal vector of the floor, and (Equation 13) needs to be satisfied.

By arranging (Equation 12) in consideration of (Equation 13), the electric field vector E ^new (r) at an arbitrary position in consideration of the reflected wave on the floor 31 can be obtained as in (Equation 14). it can.

Since both the basis vector Z _{l, m} ^new (r) and the basis vector W _{l, m} ^new (r) defined in (Equation 14) satisfy the reflection condition on the floor surface 31, they are cylindrical surfaces at 5 m. The electric field obtained by fitting the measurement data by the least square method satisfies the reflection condition on the floor 31. Thereby, the electromagnetic field in the cylindrical surface with a radius of 10 m can be estimated based on the measurement data on the cylindrical surface at 5 m based on the electric field vector obtained by (Equation 14).

  FIG. 6 is a flowchart showing the processing procedure of the CPU 11 of the electromagnetic field analysis apparatus 1 according to Embodiment 1 of the present invention. In FIG. 6, the CPU 11 of the electromagnetic field analysis apparatus 1 measures the electric field strength and phase on a cylindrical surface that is 5 m away from the electronic component 2 that is a radiation source in the horizontal direction (step S <b> 601).

The CPU 11 has multiple poles at a position (first position) where the electronic component 2 as a radiation source is disposed and a position (second position) that is symmetrical with respect to the first position and the floor of the anechoic chamber. An expansion point that is the origin of the basis function at the time of expansion is set (step S602). Based on the measured electric field intensity and phase on the cylindrical surface, the CPU 11 calculates the electromagnetic field in the region outside the cylindrical surface based on the solution of the Helmholtz equation, that is, the TM wave. The coefficient a _M (l, m) of the (l, m) component and the coefficient a _E (l, m) of the (l, m) component of the TE wave are determined by the least square method (step S603).

The CPU 11 superimposes the electric field vector E (r−r ₀ ) at the expansion point (first position) 51 and the electric field vector E (r + r ₀ ) at the expansion point (second position) 52 (step S604) Based on the condition of reflection on the floor surface 31, an electric field vector E ^new (r) in a cylindrical surface having a radius of 10 m is calculated (step S605).

  As described above, according to the first embodiment, the multipole is provided at the first position where the radiation source is disposed and the second position which is symmetrical with respect to the first position and the floor surface of the anechoic chamber. Set the expansion point that is the origin of the basis function at the time of expansion, and superimpose the electromagnetic field in the area outside the cylindrical surface by the multipole expansion using the coefficient calculated for each of the expansion points. Therefore, even when there is a reflected wave from the floor in an anechoic chamber, when estimating the electromagnetic field in the area outside the cylindrical surface, estimate the electromagnetic field considering the effect of the reflected wave. Is possible.

(Embodiment 2)
FIG. 7 is a functional block diagram of the electromagnetic field analysis apparatus 1 according to Embodiment 2 of the present invention. In FIG. 7, a measurement unit 701 measures the electric field strength and phase on a cylindrical surface that is a certain distance in the horizontal direction from the electronic component 2 that is a radiation source. Here, the phase to be measured means an angle at which the electric field becomes maximum in one period in the electric field pattern that vibrates at a constant frequency.

  The expansion point setting unit 702 is a position at which the electronic component 2 as a radiation source (first position) is projected onto the floor surface 31 of the anechoic chamber (third position) at the time of multipole deployment. Set the expansion point that is the origin of the basis function.

  In the second embodiment, in order to reflect the influence of the reflected wave, a development point for multipole deployment is provided only on the floor surface 31 of the anechoic chamber, and measurement is performed on a cylindrical surface at a distance of 5 m from the radiation source. It is characterized in that the result is mirror copied. That is, the mirror surface copy unit 703 mirror-copies the measurement result on the cylindrical surface at a distance of 5 m from the electronic component 2 that is the radiation source at a position that is symmetrical across the floor surface of the anechoic chamber.

  FIG. 8 is a schematic diagram showing an outline of mirror copy of the electromagnetic field analysis apparatus 1 according to Embodiment 2 of the present invention. In FIG. 8, a pseudo measurement result 82 is obtained by mirror-copying a measurement result 81 measured on a cylindrical surface at a distance of 5 m from the electronic component 2 as a radiation source to a symmetrical position with the floor surface 31 in between.

  Therefore, the measurement result 81 and the pseudo measurement result 82 are collectively considered as one measurement result, and the center point of both, that is, the position (third position) 83 where the radiation source is projected on the floor surface is the origin at the time of multipole deployment, That is, as an expansion point, the electric field vector E is obtained based on multipole expansion according to (Equation 3) of the first embodiment.

  Similar to the first embodiment, the coefficient calculation unit 704 solves the Helmholtz equation in order to calculate the electromagnetic field in the region outside the cylindrical surface based on the measurement result in the cylindrical surface mirror-copied with respect to the development point 83. Based on the above, the coefficient at the time of multipole expansion is calculated.

  The electromagnetic field estimation unit 705 estimates the electromagnetic field in a region outside the cylindrical surface by multipole expansion using a coefficient calculated with respect to the expansion point. In this case, since the measurement result on the cylindrical surface 3 m away from the radiation source is mirror-copied, the electric field strength is the same in the vertical direction and the horizontal direction, and only the direction of the horizontal component is reversed. Thereby, the conditions for reflection on the floor 31 are satisfied.

Therefore, if the vertical component of the measured electric field is E _l (x, y, z) and the horizontal component is E _h (x, y, z), the vertical component of the mirror-copied electric field is E ^cp _l (x, y, z). -Z) and the horizontal component can be expressed as E ^cp _h (x, y, -z), respectively, so (Equation 15) holds.

  By using this in (Equation 3), the electric field vector E can be calculated based on the multipole expansion with the expansion point 83 in FIG. 8 as the origin. By specular copying, it is possible to easily estimate an electric field vector on a cylindrical surface 10 m away from the radiation source in consideration of a reflected wave component that cannot be measured originally.

  FIG. 9 is a flowchart showing a processing procedure of the CPU 11 of the electromagnetic field analysis apparatus 1 according to Embodiment 2 of the present invention. In FIG. 9, the CPU 11 of the electromagnetic field analysis apparatus 1 measures the electric field strength and phase on a cylindrical surface 5 m away from the electronic component 2 that is a radiation source in the horizontal direction (step S <b> 901).

The CPU 11 sets the origin of the basis function at the time of multipole expansion to the position (third position) where the position (first position) where the electronic component 2 as the radiation source is arranged is projected onto the floor 31 of the anechoic chamber. A development point is set (step S902). The CPU 11 makes a mirror copy of the electric field strength and phase on the cylindrical surface as a measurement result (step S903), and calculates the electromagnetic field in the region outside the cylindrical surface at the time of multipole expansion based on the solution of the Helmholtz equation. Of the TM wave, that is, the coefficient a _M (l, m) of the (l, m) component of the TM wave and the coefficient a _E (l, m) of the (l, m) component of the TE wave are determined by the least square method (step S904).

The CPU 11 calculates an electric field vector E ^new (r) on a cylindrical surface having a radius of 10 m based on the condition of reflection on the floor surface 31 (step S905).

  As described above, according to the second embodiment, the origin of the basis function at the time of multipole expansion is the third position obtained by projecting the first position where the radiation source is disposed on the floor surface of the anechoic chamber. Set the development point, mirror-copy the measurement result on the cylindrical surface to a position that is symmetrical across the floor of the anechoic chamber, and based on the measurement result on the mirror-copied cylindrical surface, In order to calculate the electromagnetic field in the region, the coefficient at the time of multipole expansion is calculated based on the solution of the Helmholtz equation, and the electromagnetic field in the region outside the cylindrical surface is multiplexed using the coefficient calculated for the expansion point. Since the electromagnetic field is estimated by polar expansion, even if there is a reflected wave on the floor surface in the anechoic chamber, the electromagnetic field considering the effect of the reflected wave when estimating the electromagnetic field in the area outside the cylindrical surface It is possible to estimate That. In particular, it is possible to estimate the electromagnetic field with high accuracy even in a region where the frequency is relatively low.

  The electric field vector calculated in the first and second embodiments described above is displayed on the display device 23 of the electromagnetic field analysis device 1 as a simulation result, for example. FIG. 10 is an exemplary diagram showing the measurement results on the display device 23 of the electromagnetic field analysis apparatus 1 according to the embodiment of the present invention. As shown in FIG. 10, the magnitude of the electric field is displayed as a color change, and the measurement result is displayed on the lattice points separated by the height and the phase on the cylindrical surface at a position 5 m away from the radiation source. .

  FIG. 11 is an exemplary view showing an estimation result on the display device 23 of the electromagnetic field analysis apparatus 1 according to the embodiment of the present invention. As shown in FIG. 11, the magnitude of the electric field is displayed as a change in color, and the estimated result is displayed on a lattice point separated by height and phase on a cylindrical surface at a position 10 m away from the radiation source. ing.

  In addition, the present invention is not limited to the above-described embodiments, and various modifications and replacements are possible within the scope of the gist of the present invention. For example, the development point is not limited to the first and second embodiments, and a plurality of development points may be set. Therefore, it goes without saying that the first embodiment and the second embodiment may be combined and estimated. In addition, about the distance of the cylindrical surface which measures electromagnetic waves, it is not limited to the Example mentioned above.

1 Electromagnetic field analyzer 2 Electronic component (radiation source)
5 Antenna 11 CPU
12 memory 13 storage device 14 I / O interface 15 video interface 16 portable disk drive 17 communication interface 18 internal bus 31 floor 51 first position (deployment point)
52 Second position (deployment point)
83 Third position (deployment point)
90 portable recording medium 100 computer program

Claims (18)

In the electromagnetic field analysis device for estimating the electromagnetic wave at a position away from the radiation source based on the measurement result of the electromagnetic wave in the vicinity of the radiation source of the electromagnetic wave arranged in the anechoic chamber where the electromagnetic wave is shielded,
Measuring means for measuring the electric field strength and phase in a cylindrical surface at a certain distance in the horizontal direction from the radiation source;
An expansion point that is the origin of the basis function at the time of multipole expansion at a first position where the radiation source is disposed and a second position that is symmetrical with respect to the first position and the floor of the anechoic chamber Expansion point setting means for setting each,
Based on the measured electric field strength and phase on the cylindrical surface, in order to calculate the electromagnetic field in the region outside the cylindrical surface, the coefficient at the time of multipole expansion is calculated for each of the expansion points based on the solution of the Helmholtz equation. Coefficient calculating means for calculating
An electromagnetic field estimation means for estimating an electromagnetic field in a region outside the cylindrical surface by superimposing electromagnetic fields obtained by multipole expansion using coefficients calculated for each of the expansion points. Electromagnetic field analyzer.   2. The electromagnetic field analysis apparatus according to claim 1, wherein the coefficient calculation unit calculates each coefficient of the TM wave and the TE wave in the Helmholtz equation by a least square method.   3. The electromagnetic field analysis apparatus according to claim 1, wherein the measurement unit measures a phase as an angle at which the electric field becomes maximum in one period in an electric field pattern that vibrates at a constant frequency. In the electromagnetic field analysis device for estimating the electromagnetic wave at a position away from the radiation source based on the measurement result of the electromagnetic wave in the vicinity of the radiation source of the electromagnetic wave arranged in the anechoic chamber where the electromagnetic wave is shielded,
Measuring means for measuring the electric field strength and phase in a cylindrical surface at a certain distance in the horizontal direction from the radiation source;
An expansion point setting means for setting an expansion point that is the origin of a basis function at the time of multipole expansion at a third position where the first position where the radiation source is disposed is projected onto the floor surface of the anechoic chamber;
Mirror surface copying means for mirror copying the measurement result on the cylindrical surface at a symmetrical position across the floor surface of the anechoic chamber,
Coefficient calculating means for calculating a coefficient at the time of multipole expansion based on a solution of the Helmholtz equation in order to calculate an electromagnetic field in a region outside the cylindrical surface based on a measurement result on the cylindrical surface copied by mirror surface copying; ,
An electromagnetic field analysis apparatus comprising: an electromagnetic field estimation unit that estimates an electromagnetic field in a region outside the cylindrical surface by multipole expansion using a coefficient calculated with respect to the expansion point.   5. The electromagnetic field analysis apparatus according to claim 4, wherein the coefficient calculating unit calculates each coefficient of the TM wave and the TE wave in the Helmholtz equation by a least square method.   6. The electromagnetic field analysis apparatus according to claim 4, wherein the measuring unit measures a phase as an angle at which the electric field becomes maximum in one period in an electric field pattern that vibrates at a constant frequency. It can be executed by an electromagnetic field analyzer that estimates the electromagnetic wave at a position away from the radiation source based on the measurement result of the electromagnetic wave in the vicinity of the radiation source of the electromagnetic wave disposed in the anechoic chamber where the electromagnetic wave is shielded. In the possible electromagnetic field analysis method,
The electromagnetic field analyzer is
Measuring the electric field strength and phase at a cylindrical surface at a certain distance in the horizontal direction from the radiation source;
An expansion point that is the origin of the basis function at the time of multipole expansion at a first position where the radiation source is disposed and a second position that is symmetrical with respect to the first position and the floor of the anechoic chamber Step for setting each,
Based on the measured electric field strength and phase on the cylindrical surface, in order to calculate the electromagnetic field in the region outside the cylindrical surface, the coefficient at the time of multipole expansion is calculated for each of the expansion points based on the solution of the Helmholtz equation. Calculating with respect to
Estimating the electromagnetic field in the region outside the cylindrical surface by superimposing the electromagnetic fields obtained by multipole expansion using the coefficients calculated for each of the expansion points. Field analysis method.   8. The electromagnetic field analysis method according to claim 7, wherein coefficients of TM wave and TE wave in the Helmholtz equation are calculated by a least square method.   9. The electromagnetic field analysis method according to claim 7, wherein the phase is measured as an angle at which the electric field becomes maximum in one period in the electric field pattern oscillating at a constant frequency. It can be executed by an electromagnetic field analyzer that estimates the electromagnetic wave at a position away from the radiation source based on the measurement result of the electromagnetic wave in the vicinity of the radiation source of the electromagnetic wave disposed in the anechoic chamber where the electromagnetic wave is shielded. In the possible electromagnetic field analysis method,
The electromagnetic field analyzer is
Measuring the electric field strength and phase at a cylindrical surface at a certain distance in the horizontal direction from the radiation source;
Setting a development point, which is the origin of the basis function at the time of multipole development, to a third position where the first position where the radiation source is arranged is projected onto the floor of the anechoic chamber;
Mirror-copying the measurement result on the cylindrical surface at a symmetrical position across the floor of the anechoic chamber;
Calculating a coefficient at the time of multipole expansion based on a solution of the Helmholtz equation in order to calculate an electromagnetic field in a region outside the cylindrical surface, based on a measurement result in the cylindrical surface that has been specularly copied;
Estimating the electromagnetic field in a region outside the cylindrical surface by multipole expansion using a coefficient calculated with respect to the expansion point.   The electromagnetic field analysis method according to claim 10, wherein the coefficients of the TM wave and the TE wave in the Helmholtz equation are calculated by a least square method.   12. The electromagnetic field analysis method according to claim 10, wherein the phase is measured as an angle at which the electric field becomes maximum in one period in the electric field pattern oscillating at a constant frequency. It can be executed by an electromagnetic field analyzer that estimates the electromagnetic wave at a position away from the radiation source based on the measurement result of the electromagnetic wave in the vicinity of the radiation source of the electromagnetic wave disposed in the anechoic chamber where the electromagnetic wave is shielded. In a possible computer program,
The electromagnetic field analysis device
Measuring means for measuring electric field strength and phase on a cylindrical surface at a certain distance in the horizontal direction from the radiation source;
An expansion point that is the origin of the basis function at the time of multipole expansion at a first position where the radiation source is disposed and a second position that is symmetrical with respect to the first position and the floor of the anechoic chamber Expansion point setting means for setting each,
Based on the measured electric field strength and phase on the cylindrical surface, in order to calculate the electromagnetic field in the region outside the cylindrical surface, the coefficient at the time of multipole expansion is calculated for each of the expansion points based on the solution of the Helmholtz equation. And an electromagnetic field for estimating the electromagnetic field in the region outside the cylindrical surface by superimposing the electromagnetic fields obtained by multipole expansion using the coefficients calculated for each of the expansion points. A computer program that functions as an estimation means.   14. The computer program according to claim 13, wherein the coefficient calculation means functions as means for calculating the TM wave and TE wave coefficients in the Helmholtz equation by a least square method.   The computer program according to claim 13 or 14, wherein the computer program causes the measurement unit to function as a unit that measures a phase as an angle at which the electric field becomes maximum in one period in an electric field pattern that vibrates at a constant frequency. It can be executed by an electromagnetic field analyzer that estimates the electromagnetic wave at a position away from the radiation source based on the measurement result of the electromagnetic wave in the vicinity of the radiation source of the electromagnetic wave disposed in the anechoic chamber where the electromagnetic wave is shielded. In a possible computer program,
The electromagnetic field analysis device
Measuring means for measuring electric field strength and phase on a cylindrical surface at a certain distance in the horizontal direction from the radiation source;
An expansion point setting means for setting an expansion point that is the origin of a basis function at the time of multipole expansion at a third position where the first position where the radiation source is disposed is projected onto the floor surface of the anechoic chamber,
Mirror surface copy means for mirror copying the measurement result on the cylindrical surface at a symmetrical position across the floor surface of the anechoic chamber,
Coefficient calculation means for calculating a coefficient at the time of multipole expansion based on a solution of the Helmholtz equation in order to calculate an electromagnetic field in a region outside the cylindrical surface, based on a measurement result in the cylindrical surface that has been mirror-copied, A computer program for causing an electromagnetic field in a region outside the cylindrical surface to function as electromagnetic field estimation means for estimating an electromagnetic field by multipole expansion using a coefficient calculated with respect to the expansion point.   The computer program according to claim 16, wherein the coefficient calculation means functions as means for calculating coefficients of TM waves and TE waves in the Helmholtz equation by a least square method.   18. The computer program according to claim 16, wherein the computer program causes the measurement unit to function as a unit that measures a phase as an angle at which the electric field becomes maximum in one period in an electric field pattern that vibrates at a constant frequency.