1.  Field of the Invention
The present invention relates to an electromagnetic field intensity computing apparatus for computing the intensity of the electromagnetic field of an electric circuit device based on the moment method. 
2.  Description of the Related Art
Since an unnecessary electric wave emitted by an electric circuit device interferes with TV, radio, or other electric waves, various strict restrictions have been put in place in many countries.  For example, Japan has issued the VCCI Standard, the U.S. has issued the FCC Standard, and Germany has issued the VDE Standard. 
To meet such electric wave restrictions, various actions should be taken using shielding technologies, filtering technologies, etc.  Accordingly, it is necessary to quantitatively simulate these actions to determine the extent to which extent the electric wave can be reduced.  Since the simulation of the electromagnetic analysis requires a long process time using a computer, it is necessary to prepare a high-speed and high-precision computing apparatus to compute the intensity of the electromagnetic field of an electric circuit device. 
In a method of computing the electromagnetic field intensity, the electromagnetic field intensity of an object can be easily computed by a well-known logic equation, given a current flowing through each portion of the object.  The current value can be logically obtained by solving the Maxwell equations (electromagnetic wave equations) under given conditions.  However, no exact solution has been obtained by equations under complicated boundary conditions on an object of an optional shape. 
Therefore, any solution for obtaining the current used by the electromagnetic field intensity computing apparatus refers to, more or less, an approximation.  A typical approximate computation can be a small loop antenna approximation, a distributed constant line approximation, or a moment method. 
In the small loop antenna approximation method, the wiring connecting the wave source circuit and the load circuit is treated as a loop antenna.  In this approximation, the current through the loop is assumed to be flat and computed by the method of computing the concentrated constant circuit. 
FIGS.  1A and 1B illustrate the small loop antenna approximation. 
FIG.  1A shows a circuit model comprising a driver 10 that is a wave source circuit; a receiver 11 that is a load circuit; a wiring 14 connecting the driver 10 to the receiver 11, and a dielectric portion 12 inserted between the grounding wire layer 13 and wiring 14. 
In FIG.  1A, the distance between the driver 10 and receiver 11 is l and the distance between the wiring 14 and the grounding wire layer 13 is h.
FIG.  1B is a diagram showing the equalizing circuit of the circuit model shown in FIG.  1A.
In FIG.  1B, the driver 10 is represented by an equalizing circuit comprising a power source V, resistor R.sub.1, and capacitor C.sub.1.  The receiver 11 can be represented by an equalizing circuit comprising a capacitor C.sub.2. 
A line current I flows as a loop as shown in FIG.  1B. The area of the loop is represented by S (=lh).  The straight line below the line current I shown at the upper portion in FIG.  1B indicates that the line current I is constant (flat) regardless of the position of the line. 
The line current I can be computed through a concentrated constant circuit comprising the equalizing circuit of the driver 10 and receiver 11 by the following equation (1). ## EQU1##
Then, using the line current I computed by the above equation (1), a radial electromagnetic field E is computed by the following approximation (2). ## EQU2##
As described above, the computation according to the small loop antenna approximation involves a very simple equation, and the computation can be performed at a high speed. 
However, since the line current I is assumed to be constant on the line, the current distribution on the line varies when the frequency f refers to a high frequency, thereby considerably lowering the precision. 
Thus, the computation using the small loop antenna approximation is the simplest method of all the above listed approximations, but in practice it is not used at all because it is inferior in precision if the size of the loop cannot be ignored when compared with the wave length of the electromagnetic wave. 
The distributed constant circuit approximation refers to a method of considering the current distribution to improve the precision. 
The distributed constant circuit approximation refers to a method of obtaining a current value by applying the equation of the distributed constant line to an object to be represented as a one-dimensional structure by an approximation. 
The computation can be easily done in this method.  The computation time and storage capacity are increased in proportion to the number of analysis elements.  Furthermore, the analysis is made including the reflection and resonance of a line, etc.  Therefore, in the distributed constant circuit approximation, a high-speed and high-precision analysis can be made on an object to which a one-dimensional approximation can be applied. 
FIGS.  2A and 2B show the above described distributed constant line approximation. 
The circuit model shown in FIG.  2A is the same as that shown in FIG.  1A, and the detailed description is omitted here. 
FIG.  2B shows the equalizing circuit of the circuit shown in FIG.  2A.
In FIG.  2B, the equalizing circuit of the driver 10 and receiver 11 is the same as that shown in FIG.  1B.
When the frequency f becomes high and the wave length .lambda.  becomes shorter than the line length l in FIG.  2A, a standing wave current flows through the line and the distribution of the current varies with the line position.  In FIG.  2B, for instance, the value of the line current I is larger on the driver 10 side while the value of the line current I is smaller on the receiver 11 side.  The value of the line current I at a certain point is represented by I(x) while the voltage at a certain point is represented by V(x), where x indicates a variable representing the distance from the receiver 11, that is, the origin (x=0).  The driver 10 refers to (x=L). 
In FIG.  2B, "Zo" indicates a characteristic impedance in a distributed constant line. " Z.sub. L " indicates a characteristic impedance at the receiver 11.  `.beta. ` indicates a wave number and is represented by (.beta.=.omega./c=2.pi./.lambda.).  The wave length .lambda.  is represented by (.lambda.=c/f).  The `c` indicates the velocity of light. 
The current distribution I(x) of the line can be obtained by the following equation (3). ## EQU3##
As described above, the computation done using the distributed constant line approximation allows a high-speed and high-precision analysis to be made on an object to be processed as a one-dimensional structure by an approximation. 
However, some objects that cannot be processed as one-dimensional structures by an approximation are not analyzed. 
The moment method is one of the solutions of an integral equation derived from the Maxwell electromagnetic wave equations, and can process a 3-dimensional object.  In this method, an object is divided into small elements to compute an electric current. 
Thus, since a 3-dimensional object can be processed by the moment method, an electromagnetic field intensity computing apparatus for computing the electromagnetic field intensity of an electric circuit device does computation mainly by the moment method. 
In the computation by the moment method, a metal portion to be analyzed is divided into a mesh form to obtain a mutual impedance Zij among the divided metal portions.  Then, the following moment equation, which governs the mutual impedance Zij, wave source Vi, and electric current Ii flowing through the divided metal portions, is solved to obtain a current value EQU [Zij][Ii]=[Vi] (4)
Using the computation result, the electromagnetic field intensity can be obtained.  The "[ ]" in equation (4) indicates a matrix. 
The following reference 1 describes the above mentioned moment method. 
H. N. Wang, J. H. Richmond and M. C. Giilreath:
"Sinusoidal reaction formulation for radiation and scattering from conducting surface", IEEE TRANSACTIONS ANTENNAS PROPAGATION, vol.  AP-23, 1975
As described above, a current value cannot be obtained in the distributed constant line approximation when an object cannot be processed as a one-dimensional structure.  Therefore, the entire device including the printed board and the housing cannot be analyzed. 
In the moment method, the entire electric circuit device including the printed board and the housing can be analyzed. 
However, the method has the following problems (1) through (5). 
(1) When the size of the device to be analyzed becomes large, the amount of computation also becomes large.  Therefore, the analysis cannot be made within a practical period of time using a current computer. 
(2) The conventional electromagnetic field intensity computing apparatus uses the moment method with dielectric portions on the printed board in the electric circuit device divided into a mesh form to obtain simultaneous equations using, and with the equalizing current and magnetic current flowing on the surface set as unknown values. 
Therefore, a greater number of patches forming a mesh requires a longer time in solving the simultaneous equations in the moment method and also requires a large memory capacity. 
(3) A long time is required in computing the immittance matrix elements among the divided surface patches in a mesh form. 
(4) The above mentioned mutual impedance Zij has been computed using a double-precision real number to perform a high-speed operation.  However, this computation cannot output an exact value of the mutual impedance Zij. 
In detail, in the computation using the double-precision real numbers, lower-order significant numbers are lost when performing multiplication.  Therefore, computing the mutual impedance Zij in this method may result in the loss of digits when the electric length (length in emitted magnetic wave length units) of the metallic mesh becomes short.  As a result, the mutual impedance Zij cannot be obtained exactly. 
(5) The cable pigtail portion (terminating unit of a cable) applicable to the moment method has not been appropriately developed to analyze the electromagnetic radiation from the cable pigtail. 
To solve the above listed problem (1), in the Japanese Patent Application Number 6-27109, the Applicant of the present invention has suggested a method of computing current distribution by dividing an electric circuit device to be analyzed into a portion to which the distributed constant line approximation can be applied and a portion to which the approximation cannot be applied, and by computing the current distribution in the distributed constant line approximation for the applicable portion and computing the current distribution in the moment method for the inapplicable portion. 
To solve the problem (2), in the Japanese Patent Application Number 6-95363, the Applicant of the present invention has suggested a computing method in which a capacitance model of a transmission line is designed and a dielectric portion is converted into a capacitor having the capacity .DELTA.C=C.sub.0 (.epsilon.  eff-1) per unit length.  In this method, C.sub.0 indicates the capacity per unit length, in a vacuum, of the metallic pattern having the dielectric portion inserted. " .epsilon.  eff" indicates an effective dielectric constant. 
The method (Japanese Patent Application Number 6-27109) obtained by combining the above described distributed constant line approximation with the moment method, and the method (Japanese Patent Application Number 6-95363) for the capacitance model of a transmission line have been only effective in a circuit of an electric current through a transmission line. 
As a method of reducing the computation time for immittance matrix elements among the surface patches, the method disclosed by the following reference 2 has been conventionally used. 
E. H. Newman and D. M. Pozar:
"Considerations for Efficient Wire/Surface Modelling" IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION vol.  AP-28, No.1, JANUARY 1980 (reference 2)
In the above mentioned reference 2, if relative positions are equal to each other between the surface patches on a plate to be analyzed, then the mutual impedances are also equal to each other.  Thus, the mutual impedance is computed between the patches having unique relative positions.  The result is used for the matrix elements having similar relative positions. 
However, in the method described by the reference 2, only the relative positions of the patches on a single board are referred to, but this method does not disclose the reduction of the amount of computation by analyzing the relative positional relationships among the patches on a plurality of plates. 
Since the plate to be analyzed can be in various forms, the method of extracting the patches having equal relative positional relationships on one or more plates and then automatically detecting from among them the patches having unique relative positional relationships has not been developed yet.  Therefore, much time and labor have been required to check the relative positional relationships among the patches and extract the relative positions. 
To solve the problem (4), in the Japanese Patent Application Number 6-95362, the Applicant of the present invention has suggested a computing method in which a normal computing unit and high-precision computing unit are provided to compute the mutual impedance to obtain the electromagnetic field intensity.  The high-precision computing unit is used when it is anticipated by checking the wave length, element length, and distance that there is a possibility to lose digits. 
The above described high-precision computation can be done using real numbers of multiple-precision and using multiple-length integers.  In either computation, since the number of digits increases, the computation time is greatly extended. 
Finally, the above described problem (5) is explained in detail. 
An object to be analyzed by the electromagnetic field intensity computing apparatus can be a housing, a printed substrate and a cable of an electric circuit device.  The electric wave radiation from the cable is mainly caused by the pigtail, that is, the terminal processing unit of a cable. 
FIGS.  3A through 3C show the radiation mechanism from the pigtail. 
In FIG.  3A, 20 is a coaxial cable, and 21 is a housing of the electric circuit device. 
When the read wire of a pigtail portion is long and the pigtail portion is not shielded, a common mode current I.sub.3 is induced when the electromagnetic field generated by line currents I.sub.1 and I.sub.2 as shown in FIG.  3A is radiated onto the shielded portion of the coaxial cable 20. 
In this case, the line current I.sub.1 is almost equal to the line current I.sub.2 (I.sub.1.apprxeq. I.sub.2), and the differential mode offsets the electric wave radiation.  However, the common code current I.sub.3 is not offset.  Accordingly, the common code current I.sub.3 causes a serious electric wave. 
In the case shown in FIG.  3A, the conventional method of computing the electromagnetic field intensity is the method shown in FIG.  3B. In this method, the value of the electric wave radiation is computed by equivalently computing the voltage V generated on the lead line of the pigtail portion and designing an antenna to be inserted between the housing 21 and the coaxial cable 20. 
The equivalent circuit is shown in FIG.  3C. In FIG.  3C, Zin indicates an impedance in the coaxial cable 20.  Z1 indicates the impedance in a pigtail lead line.  Ra indicates the radiation resistor from the coaxial cable 20.  An antenna structure is generated using the housing 21 of the electric circuit device as a ground to generate an electric wave. 
FIGS.  4A and 4B show the problems in calculating the electromagnetic field intensity of the pigtail portion. 
As shown in FIG.  4A, when a load Z0 is connected to the tip of the coaxial cable 20 of a device, the device has a pigtail portion also at a load unit.  This may cause further electromagnetic wave radiation.  In this case, no housing is provided at the tip of the coaxial cable 20.  Therefore, no antenna model can be produced. 
Thus, the electric current flowing through the lead line may be analyzed by the moment method without producing an antenna model.  At this time, the following problems (a) through (c) should be solved. 
(a) How is the shield of the thick and cylindrical coaxial cable 20 connected to a thin pigtail lead line 22? 
(b) How is the coaxial cable 20 connected to the housing 21 if the coaxial cable 20 is directly connect ed to the housing? 
(c) The electric current through the shield of the coaxial cable 20 normally flows in parallel with the cable, but flows toward a pigtail lead line 22 when the current approaches the pigtail, and changes its flow from the parallel to vertical direction as shown in FIG.  41.  How is the current represented and processed? 
As described above, the electromagnetic field intensity computing apparatus for computing the electromagnetic field intensity of an electric circuit device according to the moment method conventionally has the above listed problems (1) through (5).  To solve the problems, the Applicant of the present invention has suggested the above described solution. 
However, the suggested solution has been insufficient to precisely compute the electromagnetic field intensity at a high speed.