JP4637799B2 - Electromagnetic circuit cooperation analysis program, recording medium storing electromagnetic circuit cooperation analysis program, and electromagnetic circuit cooperation analysis device - Google Patents

Description

  The present invention relates to a cooperative analysis that combines an electromagnetic field analysis method using a time domain finite difference method and a circuit analysis method using a transient electric circuit analysis.

  In electromagnetic field circuit linkage analysis, analysis is performed while associating an electric field or magnetic field defined in electromagnetic field analysis with a voltage or current defined in circuit analysis. Numerical simulation that combines electromagnetic field analysis and circuit analysis has the characteristic that the characteristics of circuit elements and surrounding electromagnetic field phenomena can be analyzed in a unified manner, which is very useful for analyzing high-frequency signals propagating in a circuit. It is generally known to be useful.

  The time domain finite difference method (hereinafter referred to as “FDTD (Finite Difference Time Domain) method”), which is one method of electromagnetic field analysis as described above, divides the analysis region by a grid, and an unknown electromagnetic field at a grid point. Is to arrange. In the FDTD method, analysis is performed using a structure called a Yee lattice in which a lattice in which an unknown electric field is arranged and a lattice in which an unknown magnetic field is arranged are shifted by half the width of the lattice. The FDTD method derives a relational expression that works between these unknown electric field and magnetic field and the adjacent unknown magnetic field and electric field by differentiating Maxwell's electromagnetic field equation, and based on them, the unknown electric field and magnetic field are converted into a certain time step. This is an analysis method for obtaining the entire electromagnetic field behavior by updating the value in units. According to this analysis method, the electric field and the magnetic field can be obtained alternately by repeatedly updating the electric field at a certain time step, updating the magnetic field after ½ time step, and updating the electric field after one time step. it can.

  Currently, a SPICE (Simulation Program with Integrated Circuit Emphasis) simulator developed by the University of California, Berkeley is known as a transient electrical circuit analysis tool. The tool provides an efficient way to simulate processes in very complex electronic devices.

  In a circuit simulator such as SPICE, first, a current / voltage value at a node of a circuit to be analyzed is used as a variable. Then, a nonlinear simultaneous differential equation is derived by applying the modified nodal analysis method to the net list in which the connection information between the circuit elements and the parameters of the circuit elements are described. Furthermore, this is converted into an algebraic equation using the difference in the time domain and the Newton iteration method. By solving this algebraic equation, the current / voltage value of the circuit at the time of analysis can be obtained. Thereafter, the analysis time is advanced by the difference in the time domain, and the above calculation is repeated to obtain the transient state of the voltage / current of the circuit.

  Non-Patent Document 1 proposes a method combining a FDTD method and a circuit simulator such as SPICE as a method of simulating a circuit such as an integrated circuit. In the electromagnetic field circuit linkage analysis combining the conventional FDTD method and a circuit simulator (SPICE in this case), a circuit element is incorporated in a cell of the FDTD, and a current source is connected between terminals corresponding to one side of the cell. A technique (current source method) that combines the FDTD method and circuit analysis by arranging capacitors is used.

In Patent Document 1, in the current source method described above, a current of a piecewise linear function is obtained by interpolating and extrapolating from a current value calculated from a magnetic field of the FDTD method, instead of a current source having a constant value as a current source. A method of providing a source has been proposed. This improves the accuracy when a non-linear circuit is connected.
JP 2000-330973 A Jun Uno, "Electromagnetic field and antenna analysis by FDTD method", 1st edition, Corona, 1998.

  However, in any of the methods disclosed in Non-Patent Document 1 and Patent Document 1, the function of the current source is calculated based on the current value up to ½ time step before the time when the electric field is derived by circuit analysis. It has established. For this reason, there is a drawback that the time when the current value takes the extreme value is delayed from the time taken by the current value calculated from the magnetic field of the FDTD method.

  Further, in the method disclosed in Patent Document 1, the extreme value itself of the current source function for circuit analysis is larger or smaller than the current value calculated from the magnetic field of the FDTD method. The analysis could be adversely affected.

  The present invention has been made to solve the above-described problems, and an object of the present invention is to provide an electromagnetic field circuit linkage analysis program that performs accurate analysis.

  According to one aspect of the present invention, there is provided a program for causing a computer having an arithmetic processing unit to execute electromagnetic field circuit linkage analysis, wherein the arithmetic processing unit is an analysis target divided into a plurality of cells. A step of performing a first electromagnetic field analysis on one of an electric field or a magnetic field of a cell other than the circuit cell in which the circuit element is inserted among the plurality of cells, and the arithmetic processing unit includes the current time in the circuit cell A step of performing circuit analysis while updating the power supply value at the current time using an interpolation formula based on one of the current value or voltage value of the circuit cell in a predetermined period and a relational formula in electromagnetic field analysis; Based on the results of the first electromagnetic field analysis step and the circuit analysis step, the second electromagnetic field analysis is performed for the other of the magnetic field or electric field of the cell. And a step in which the arithmetic processing unit repeats the step of performing the first electromagnetic field analysis, the step of performing the circuit analysis, and the step of performing the second electromagnetic field analysis until a predetermined condition is satisfied. Prepare.

  Preferably, the power supply value is a current source value, and the arithmetic processing unit further includes a step of obtaining an electric field value and a magnetic field value up to time t−1 / 2Δt in an analysis target region divided into a plurality of cells. The step of performing the first electromagnetic field analysis is a step in which the arithmetic processing unit obtains an electric field value at time t of a cell other than the circuit cell in which the circuit element is inserted among the plurality of cells, and performs the circuit analysis. The arithmetic processing unit initializes the estimated current value at time t + 1 / 2Δt in the circuit cell, the arithmetic processing unit obtains the electric field value of the circuit cell, and the arithmetic processing unit includes the circuit cell. The step of obtaining the electric field value of the circuit cell includes the step of interpolating between the current value calculated from the magnetic field value at time t−1 / 2Δt and the estimated value in the circuit cell by the arithmetic processing unit. By formula The step of setting the value of the current source at time t, and the arithmetic processing unit obtains the voltage value of the circuit cell at time t by performing circuit analysis based on the set value of the current source in the circuit cell. And a step in which the arithmetic processing unit obtains the electric field value of the circuit cell at time t from the voltage value of the circuit cell, and the step of obtaining the current value of the circuit cell calculates the electric field value at time t. And calculating the current value at time t + 1 / 2Δt in the circuit cell and substituting it into the relational expression in the electromagnetic field analysis established between the circuit cell and the cell in the vicinity of the circuit cell. The step of obtaining the electric field value of the circuit cell and the current value of the circuit cell are updated while updating the estimated value until the difference between the current value obtained in the step of obtaining the current value of the circuit cell and the estimated value becomes smaller than a predetermined value. Seeking The circuit at time t is based on the results of the step of repeating the step and the step of repeating the step of obtaining the electric field value of the circuit cell and the step of obtaining the current value of the circuit cell while the arithmetic processing unit updates the estimated value. A step of outputting the electric field value of the cell, and performing the second electromagnetic field analysis, wherein the arithmetic processing unit obtains the magnetic field value of the cell at time t + 1 / 2Δt, and the arithmetic processing unit sets time t to t + Δt. The method further comprises the step of updating to

  Preferably, in the initialization step, the arithmetic processing unit sets an initial value of the estimated value using the current value calculated from the magnetic field value until time t−1 / 2Δt, and updates the estimated value while the circuit cell is updated. In the step of repeating the step of obtaining the electric field value and the step of obtaining the current value of the circuit cell, the arithmetic processing unit updates the current value obtained in the step of obtaining the current value of the circuit cell as an estimated value.

  When the other situation of this invention is followed, the computer-readable recording medium which stored the said electromagnetic field circuit cooperation analysis program is provided.

  According to still another aspect of the present invention, there is provided an electromagnetic field circuit cooperation analysis device for performing a cooperation analysis between an electromagnetic field analysis and a circuit analysis, comprising a circuit analysis unit for performing a circuit analysis, wherein the circuit analysis unit includes a plurality of cells. In the region to be analyzed divided into two, in the circuit cell in which the circuit element is inserted among the plurality of cells, an interpolation formula by one of the current value or the voltage value of the circuit cell in a predetermined period including the current time and A means for performing circuit analysis while updating the power supply value at the current time using a relational expression in electromagnetic field analysis, further comprising an electromagnetic field analysis unit for performing electromagnetic field analysis, wherein the electromagnetic field analysis unit includes a plurality of electromagnetic field analysis units. A first means for performing a first electromagnetic field analysis on one of an electric field or a magnetic field of a cell other than the circuit cell among the cells, and giving a result of the first electromagnetic field analysis to the circuit analysis unit; Based on the result of the path analysis unit, including means for performing a second electromagnetic field analysis on the other of the magnetic field or electric field of the cell, performing the first means, the means for performing circuit analysis, and the second electromagnetic field analysis. And an analysis control unit that repeats the means until a predetermined condition is satisfied.

  According to still another aspect of the present invention, there is provided an electromagnetic field circuit cooperative analysis method for performing cooperative analysis between electromagnetic field analysis and circuit analysis, wherein a plurality of cells are analyzed in a region to be analyzed divided into a plurality of cells. A step of performing a first electromagnetic field analysis on one of an electric field or a magnetic field of a cell other than the circuit cell in which the circuit element is inserted, and a current value of the circuit cell in a predetermined period including the current time in the circuit cell or A circuit analysis step, a first electromagnetic field analysis step, and a circuit analysis are performed while the power supply value at the current time is updated using the interpolation formula based on one of the voltage values and the relational expression in the electromagnetic field analysis. A step of performing a second electromagnetic field analysis on the other of the magnetic field or electric field of the cell based on the result of the step; a step of performing a first electromagnetic field analysis; Performing a analysis, and performing a second electromagnetic field analysis, and a step of repeating until a predetermined condition is satisfied.

  According to the present invention, an accurate analysis using a continuous power supply function can be performed. Thereby, the stability of circuit analysis and the accuracy of electromagnetic field circuit linkage analysis can be improved particularly in a non-linear circuit.

  Hereinafter, embodiments of the present invention will be described with reference to the drawings. In the following description, the same parts are denoted by the same reference numerals. Their names and functions are also the same. Therefore, detailed description thereof will not be repeated.

  As will be apparent from the following description, in the electromagnetic field circuit linkage analysis program of the present invention, when performing electromagnetic field analysis of a circuit board, a continuous power supply function can be set and accurate analysis can be performed. Thereby, the stability of circuit analysis and the accuracy of electromagnetic field circuit linkage analysis can be improved particularly in a non-linear circuit. In the following description, the current source function is set as the power source function. However, even when the voltage source function is set, the electromagnetic field circuit cooperation analysis can be similarly executed.

(1. System configuration of the present invention)
FIG. 1 is a conceptual diagram showing an example of a computer 100 that executes an electromagnetic field circuit cooperation analysis program according to the present invention.

  A computer 100 that executes an electromagnetic field circuit cooperation analysis program will be described with reference to FIG.

  The computer 100 includes a computer main body 102, a display 104 as a display device connected to the computer main body 102, and a keyboard 110 and a mouse 112 as input devices that are also connected to the computer main body 102.

  The computer main body 102 reads and writes information to and from an optical disk drive 108 and a flexible disk (hereinafter referred to as “FD”) 116 for reading information on an optical disk such as a CD-ROM (Compact Disc Read-Only Memory) 118. In addition to the FD drive 106, a CPU (Central Processing Unit) 120 connected to the bus 105, a memory 122 including a ROM (Read Only Memory) and a RAM (Random Access Memory), and a direct access memory device, for example, A hard disk 124 and a communication interface 128 for exchanging data with the outside are included. An optical disk such as a CD-ROM 118 is loaded in the optical disk drive 108. An FD 116 is attached to the FD drive 106.

  In the hard disk 124, circuit board data 134 in which parameters representing physical properties such as the shape of the board, the dielectric constant of the board, analysis conditions, etc. are stored for the circuit board to be analyzed, and the electromagnetic field in the time domain. A program 135 for executing FDTD, which is one of analysis methods, a program 136 for executing circuit analysis, and the like are stored. Here, for example, the circuit board data 134 may be supplied from an external database via the communication interface 128. Each program may be supplied by a recording medium such as the FD 116 or the CD-ROM 118, or may be supplied by another computer via a communication line. The execution of FDTD or circuit analysis may be executed by an external computer via the communication interface 128 and the result may be stored in the hard disk 124.

  In addition, in a storage area of the storage device, for example, the hard disk 124, an electric field value storage area for temporarily storing electric field values and magnetic field values as analysis results during the electromagnetic field analysis, and updating those values in the next step. 137, a magnetic field value storage area 138, and an internal state storage area 139 for storing the internal state in the circuit analysis are provided.

  Here, the program 135 for executing FDTD and the program 136 for executing circuit analysis are collectively referred to as an electromagnetic field circuit cooperation analysis program.

  Therefore, in the following description, it is assumed that time domain electromagnetic field analysis and circuit analysis are executed in cooperation within one computer device. However, the electromagnetic field analysis and the circuit analysis may be executed by separate computer devices, and data may be exchanged between the separate computer devices via the communication interface 128 to perform the cooperative analysis.

  The CPU 120 functioning as an arithmetic processing unit uses the memory 122 as a working memory to execute processing corresponding to the above-described program 135 for executing FDTD and the program 136 for executing circuit analysis.

FIG. 2 is a block diagram illustrating a functional configuration of the CPU 120.
The functional configuration of the CPU 120 will be described with reference to FIG.

  The CPU 120 includes an electromagnetic field analysis unit 202 that executes electromagnetic field analysis according to a program 135 that executes FDTD, and a circuit analysis unit 204 that executes circuit analysis according to a program 136 that executes circuit analysis.

  The electromagnetic field analysis unit 202 acquires the cell size, time step, medium information of the circuit board, and the like from the circuit board data 134. Based on these, the FDTD method is executed, and the electric field value and the magnetic field value are written in the electric field value storage area 137 and the magnetic field value storage area 138.

  The circuit analysis unit 204 acquires a net list and circuit element connection information from the circuit board data 134, and generates a circuit matrix. Further, based on the electric field value derived by the electromagnetic field analysis unit 202, a current source value is set and circuit analysis is executed. Details of this circuit analysis will be described later in (2.2). As a result of the circuit analysis, the obtained electric field value is written in the electric field value storage area 137. Further, when the circuit analysis is performed, the internal state is written into the internal state storage area 139.

  Here, returning to FIG. 1, the CD-ROM 118 may be another medium, such as a DVD-ROM (Digital Versatile Disc), as long as it can record information such as a program installed in the computer main body. In this case, the computer main body 102 is provided with a drive device that can read these media.

  The program 135 for executing FDTD and the program 136 for executing circuit analysis are software executed by the CPU 120 as described above. In general, such software is stored and distributed in a recording medium such as the CD-ROM 118 or the FD 116, read from the recording medium by the optical disk drive 108 or the FD drive 106, and temporarily stored in the hard disk 124. Alternatively, when the computer 100 is connected to the network, it is temporarily copied from the server on the network to the hard disk 124. Then, the data is further read from the hard disk 124 to the RAM in the memory 122 and executed by the CPU 120. In the case of network connection, the program may be directly loaded into the RAM and executed without being stored in the hard disk 124.

  The computer hardware itself shown in FIG. 1 and its operating principle are general. Therefore, an essential part for realizing the functions of the present invention is software stored in a recording medium such as the FD 116, the CD-ROM 118, and the hard disk 124.

  As a general tendency, various program modules are prepared as a part of a computer operating system, and an application program generally calls a module in a predetermined arrangement to advance processing. . In such a case, the software itself does not include such a module, and the electromagnetic field circuit linkage analysis is possible only when the computer cooperates with the operating system. However, as long as a general platform is used, it is not necessary to distribute the software including such modules, and the software itself not including these modules and the recording medium recording the software (and the software distributes on the network). Data signal) can be considered to constitute the embodiment.

(2. Electromagnetic circuit linkage analysis method)
In (2.1), a method of electromagnetic field circuit linkage analysis as shown in Non-Patent Document 1 will be described. Next, in (2.2), the cooperative analysis method according to the present invention will be described.

(2.1 Cooperative analysis method between electromagnetic field analysis and circuit analysis)
First, the FDTD method, which is one of the methods for performing electromagnetic field analysis, will be described, and then the current source method will be described as an example of the analysis method used for cooperative analysis.

  The FDTD method is a numerical calculation method by differentiating Maxwell's electromagnetic field equation. First, an analysis region is divided by a lattice, and an electric field is arranged at the center of each side of the lattice, and a magnetic field is arranged at the center of each surface. When Maxwell's equations are differentiated, the electric and magnetic fields are arranged at positions that are spatially shifted by half cells and temporally by half time steps. Here, the following equation (1) and equation (2) are derived from the Maxwell equation based on electromagnetism: the unknown electric field to be obtained, the known electric field adjacent to the unknown magnetic field and the known electric field one time step before, and the relational expression acting between the known magnetic fields. become that way.

In the formula, bold indicates that the variable is a vector.
Equation (1) is an electric field E (vector) of n time steps, and equation (2) is a relational equation of magnetic field H (vector) of (n + 1/2) time steps. Where Δt _em , μ, ε, and σ are time step, magnetic permeability, dielectric constant, and conductivity, respectively.

By updating the unknown electric field and unknown magnetic field in units of a certain time step Δt _em based on these, the electromagnetic field behavior of the entire analysis area can be obtained in the time domain.

The time step Δt _em in the FDTD method needs to satisfy the Courant stability condition shown in the following formula (3) with respect to the cell size.

Here, c represents the speed of light, and Δx, Δy, and Δz represent the length of each side of the cell.
It is generally known that when the time step Δt _em does not satisfy the equation (3), the calculated value is diverged.

  As described above, in the FDTD method, the time domain electromagnetic field response to be analyzed can be analyzed by sequentially calculating the unknown electric field and the unknown magnetic field in the analysis region by the explicit method.

  Next, the current source method, which is one of the methods for directly combining the FDTD method and the circuit analysis, used for electromagnetic field circuit linkage analysis will be described.

  FIG. 3 is a schematic diagram of cooperative analysis by the current source method. FIG. 3A is a diagram showing an FDTD cell including a circuit element to be subjected to circuit analysis, and FIG. 3B shows an equivalent circuit of the current source method corresponding to the cell of FIG. FIG. 3C is a diagram showing a schematic processing flow of the current source method.

  The current source method will be described with reference to FIG. In FIG. 3A, an electric field is assigned in the direction of the arrow along the side of the lattice cell indicated by the solid line, and a magnetic field is assigned in the direction of the arrow along the side of the lattice cell indicated by the dotted line. Δx, Δy, Δz indicate the length of each side of the FDTD cell, and the solid grid cell and the dotted grid cell are shifted from each other by 1 / 2Δx, 1 / 2Δy, 1 / 2Δz. Here, it is assumed that a circuit element to be subjected to operation analysis by circuit analysis is arranged on the side ab to which the electric field is assigned.

  With reference to FIG. 3C, the flow of processing in the current source method will be described. First, the magnetic field of the cell is calculated by the FDTD method (step S300).

Then, by applying Ampere's law to the cell containing the circuit element and expanding the z component, the following equation (4) is obtained. Furthermore, when ε (ΔxΔy) / Δz in the first term on the left side of Equation (4) is equivalently the capacitance C ₀ of the parallel plate capacitor, and the right side is the total current I flowing through the cell, Equation (4) is It can be rewritten as in 5).

Here, J _L is a conduction current density flowing through the element, V _L is a voltage across the circuit element, and I _L is a total current flowing through the circuit element.

  The total current I flowing in the cell can be obtained by circularly integrating the magnetic field around the element along the surface 31 using Ampere's law. However, since the magnetic field is constant, I can be considered as a constant current source. . Therefore, equation (5) can be considered as an equivalent circuit including a current source 32, a capacitor 33, and a network 34 as shown in FIG.

Returning to FIG. 3C again, the current I is calculated from the magnetic field H obtained by FDTD, and passed to the circuit analysis as the current source value I (step S302), thereby obtaining V _L and I _L by the circuit analysis. Can do. Then, a V _L by a circuit analysis, passes the V _L to calculate the electric field of the cell edges included the circuit elements FDTD method (step S304), in step S306, the electric field E is calculated.

  As described above, the circuit analysis and the FDTD method are directly coupled. Thereby, the coupling with the electromagnetic field can be analyzed considering only the input / output terminals of the circuit.

FIG. 4 is a diagram showing the data flow of the circuit analysis and the FDTD method in time series.
With reference to FIG. 4, the data transfer between the circuit analysis and the FDTD method will be described. In FIG. 4, the time (n-1) field strength at Δt _em E ^n-1 (vector) and the time (n-3/2) the magnetic field strength in the ^{_{Δt em H n-3/2}} ( vector) is known Suppose there is.

The magnetic field strength H ^{n−1 / 2} (vector) at time (n−1 / 2) Δt _em can be obtained by substituting E ⁿ⁻¹ and H ^{n−3 / 2} which are already known into the equation (2). .

However, the electric field strength E ⁿ at time n.DELTA.t _em, the cell including a circuit element (hereinafter, referred to as "circuit cell") calculation method in a cell that does not contain a different.

A cell that does not include a circuit element is obtained by substituting E ⁿ⁻¹ and H ^{n−1 / 2} into equation (1).

The circuit cell is calculated as follows. In the equivalent circuit of FIG. 3B, the initial voltage value of the capacitor 33 is V ⁿ⁻¹ = E _z ⁿ⁻¹ Δz, and the equivalent current source is a constant value I ^{n−1 / 2} = Δx · Δy · ∇ × ^Let H ^{n-1 / 2} . Then, a circuit simulation is performed with a sufficiently small time interval from time (n−1) Δt _em to nΔt _em .

Voltage value V ⁿ of the circuit element at time n.DELTA.t _em is delivered is converted into the electric field strength E ⁿ of the circuit cell to the FDTD method.

At time (n + 1/2) Δt _em , the magnetic field strength H ^{n + 1/2} is obtained by converting E ⁿ converted from the voltage obtained by circuit analysis and H ^{n−1 / 2} obtained by the FDTD method into the equation (2). It can be obtained by substitution.

By updating Δt _em in units as described above, the electromagnetic field behavior of the entire analysis region can be obtained in the time domain.

  Similarly, in the voltage source method, the voltage source value is obtained from the electric field obtained by the FDTD method, the current value at the time of obtaining the magnetic field by the FDTD method is analyzed by a circuit simulator such as SPICE, and converted into a magnetic field to be converted into the FDTD method. To pass the analysis.

(2.2 Electromagnetic field analysis cooperation method of the present invention)
As described above, in the method disclosed in Non-Patent Document 1, in order to derive the electric field of the circuit cell at time nΔt _em , a constant value is obtained based on the current value up to time (n−1 / 2) Δt _em. The current source that takes In the present invention, the current source function i ⁿ (t) from time (n−1 / 2) Δt _em to (n + 1/2) Δt _{em is} expressed as a magnetic field at time (n−1 / 2) Δt _{em in} the FDTD method. This is expressed by an interpolation formula using a current value I ^{n−1 / 2} calculated from the value and a current value I ^{n + 1/2} calculated from the magnetic field value at time (n + 1/2) Δt _em . Here, it defines as a linear function like the following formula | equation (6) as an example.

However, (n−1 / 2) Δt _em <t ≦ (n + 1/2) Δt _em .
Here, I ^{n−1 / 2} is a value obtained from the magnetic field value already calculated by the FDTD method at time nΔt _em , but I ^{n + 1/2} is calculated from time nΔt _{em being} calculated. Is a value obtained from the magnetic field value at a time further advanced by ½Δt _em . For this reason, the value of I ^{n + 1/2} cannot be determined. Therefore, obtaining the relationship to be satisfied by I ^{n + 1/2} from a calculation of the FDTD method. Hereinafter, a specific example will be described.

Consider a case where a circuit element is embedded at the position of the electric field cell E _y (i, j, k). At this time, it is considered that the electric field value E _y ⁿ (i, j, k) at time nΔt _em is obtained by circuit analysis. ^Let the current source function i ⁿ (t) of the equation (6) at the position of the electric field value E _y ⁿ (i, j, k) be i _{y (i, j, k)} ⁿ (t). Then, the equation (6) can be expressed by the following equation (7).

However, (n−1 / 2) Δt _em <t ≦ (n + 1/2) Δt _em .
In addition, the circuit equation formulated by the current source method at the position of the electric field value E _y ⁿ (i, j, k) is a black box having an internal state as in the following equation (8) when viewed from the FDTD method. It can be expressed as a function.

FIG. 5 is a diagram showing the arrangement of the magnetic field variables of the cell.
As shown in FIG. 5, the current value I _y ^{n + 1/2} (i, j, k) can be expressed by the following ampere equation (9) using the magnetic field value near the circuit cell.

Here, the magnetic field value H _x ^{n + 1/2} (i, j, k−1) is calculated by the following equation (10) in the FDTD method.

However, C1 _{hx (i, j, k-1)} and C2 _{hx (i, j, k-1)} are the medium, cell size and time step Δt at the x-direction magnetic field component position (i, j, k-1). It is a constant determined by _em etc.

Similarly, the magnetic field values H _x ^{n + 1/2} (i, j, k), H _z ^{n + 1/2} (i-1, j, k), H _z ^{n + 1/2} (i, j, k) ) Is calculated from the following equations (11), (12), and (13) from the equation (2) in the FDTD method.

Therefore, I _y ^{n + 1/2} (i, j, k) is a known magnetic field before the half time step adjacent to the unknown magnetic field in the FDTD method with respect to the amperage formula using the magnetic field value in the vicinity of the circuit cell. And an expression derived by substituting a relational expression acting between known magnetic fields one time step before. Specifically, equations (10) to (13) are substituted into equation (9), and can be represented by a relational expression in electromagnetic field analysis as in the following equation (14). However, C _{Iy (i, j, k)} in the equation (14) is a constant represented by the equation (15).

FIG. 6 is a diagram showing the arrangement of the electric field variable and magnetic field variable of the cell.
As shown in FIG. 6 and formula (14), the current value I _y ^{n + 1/2} (i, j, k) is determined by the nearby electric field value and I _y ^{n−1 / 2} (i, j, k). It is determined.

Here, among the electromagnetic field variables of Equation (14), the current value calculated from the magnetic field is a known value because the subscript regarding time is n−1 / 2. For the electric field, the time index is ^n. Among these, other circuit elements are embedded for those other than E _yn (i, j, k), which is the electric field value of the circuit cell. Unless otherwise, it is possible to calculate in advance by the FDTD method. In the following, for simplicity, it is assumed that no circuit element is embedded in these electric field cells.

  At this time, Expression (7), Expression (8), and Expression (14) are in the form of simultaneous equations. Therefore, these can be explained by the following procedure, for example.

(Procedure 1) Known I _y ^{n−1 / 2} (i, j, k) is set as an approximate value of I _y ^{n + 1/2} (i, j, k).

(Procedure 2) After the current source function is determined by equation (7), equation (8) is solved to obtain E _y ⁿ (i, j, k). Then, a new approximate value of I _y ^{n + 1/2} (i, j, k) is obtained by substituting the obtained E _y ⁿ (i, j, k) into equation (14).

(Step 3) The current ^{_{I y n + 1/2 (}} i, j, k) and the approximate value of a new approximation of the _{I y} obtained in (Step ^{2) n + 1/2 (} i, j, k) If the difference in values does not satisfy the preset convergence condition, the approximate value of I _y ^{n + 1/2} (i, j, k) is updated from the current value to a new approximate value (procedure Return to 2).

(Procedure 4) If the convergence condition is satisfied, approximate values of I _y ^{n + 1/2} (i, j, k) and E _y ⁿ (i, j, k) are output.

  FIG. 7 is a diagram showing the electromagnetic field analysis and circuit analysis data passing and the current source function according to the above procedure.

  In FIG. 7, the broken line in the circuit analysis graph indicates how the current source function is updated.

  Also, in the case where other circuit elements are incorporated in some of the electric field cells appearing in the expression (14), the expressions (7), (8), and ( It can be solved similarly by deriving 14) and making them simultaneous.

  It is to be noted that the electromagnetic field circuit linkage analysis can be similarly executed even when the voltage source method is used. In this case, first, a voltage source function is set by interpolation from the electric field value obtained by the FDTD method. Then, for Faraday's formula using the electric field value in the vicinity of the circuit cell, a relational expression acting between the unknown electric field and the adjacent known electric field one time step before and the known magnetic field before the half time step in the FDTD method is substituted. The voltage value is updated based on the equation derived from the above. This is repeated until the convergence condition is satisfied.

(3. Implementation on computer 100)
The electromagnetic field circuit linkage analysis according to the above invention can be implemented as computer software by the following procedure.

The procedure is summarized below.
FIG. 8 is a flowchart showing processing of electromagnetic field circuit cooperation analysis according to the present invention.

With reference to FIG. 8, the flow of the cooperative analysis process will be described.
First, in step S800, the CPU 120 reads data such as analysis conditions and circuit information describing analysis settings from the circuit board data 134 stored in the hard disk 124, and performs the following initialization processes 1 to 7: Do.

  1. The CPU 120 initializes the coefficient of the electric field / magnetic field variable of the FDTD method. Here, the coefficient for the update calculation of the electric field and magnetic field variable of the FDTD method is calculated from the medium information and cell size at the position where the electric field and magnetic field variables are described in the analysis conditions, the time step, and the like.

  2. The CPU 120 initializes a matrix necessary for circuit analysis. Here, for a plurality of embedded circuits specified by the analysis conditions, a circuit analysis coefficient matrix is initialized from the read circuit information.

3. The CPU 120 initializes coefficients used when FDTD analysis / circuit analysis is linked. Here, the coefficients necessary for the linkage between the FDTD analysis and the circuit analysis are calculated from the plurality of embedded circuits specified by the analysis conditions and the coefficients for the update calculation of the electric field and magnetic field variables derived in the above 1 in the corresponding circuit cell. Initialize the. For example, for E _y ⁿ (i, j, k), C _{Iy (i, j, k)} is calculated by equation (15).

  4). The CPU 120 sets initial values of electric field / magnetic field variables. Here, each electric field / magnetic field variable is initialized to zero. Alternatively, each electric field and magnetic field variable is initialized based on the initial electromagnetic field distribution information recorded in a file or the like.

  5. The CPU 120 sets an initial value for the internal state of the circuit analysis. Here, an internal state such as a contact potential used in circuit analysis is obtained by operating point analysis or the like and written in the internal state storage area 139.

6). CPU 120 initializes variable i representing the time in units of time step Δt _em . Here, the variable i is initialized with the initial value 0.

7). The CPU 120 initializes variables for circuit analysis cooperation. Here, the variables t1 and t2 that define the analysis time range are set. T1 representing the start time of the analysis time range is set to -1 / 2Δt _em and t2 is set to 1 / 2Δt _em . Further, the current value I ₁ corresponding to each electric field variable at time t1 is calculated by substituting the initial value of the magnetic field into equation (9) and the like.

Next, in step S802, CPU 120 performs electric field calculation processing at time nΔt _em for each electric field variable in the FDTD method. At this time, the calculation of the electric field variable of the circuit cell can be omitted. The CPU 120 writes the calculated electric field value in the electric field value storage area 137.

  In step S804, the CPU 120 calculates the electric field value of the circuit cell by embedded circuit analysis. Details will be described later.

Subsequently, in step S806, CPU 120, in the FDTD method, the magnetic-field calculation processing at time (n + 1/2) Δt em performed for each field variable. Then, the calculated magnetic field value is written in the magnetic field value storage area 138.

Then, in step S808, CPU 120 adds 1 to the variable i representing the time at the time step Delta] t _em units. Also, t1 and t2 defining the analysis time range are updated.

  Finally, in step S810, CPU 120 makes an analysis end determination based on an analysis end condition specified in advance. As an example of the analysis end condition, the number of steps n specified by the analysis condition is compared with i, and when i> n, the end is determined.

  If it is determined that the end condition is not satisfied, the process returns to step S802. Otherwise, the analysis is terminated.

Next, the embedded circuit analysis that is the process of step S804 will be described in detail.
FIG. 9 is a flowchart showing the embedded circuit analysis processing.

The embedded circuit analysis will be described with reference to FIG. In the following, the case where the circuit element is embedded in the electric field cell E _y ⁿ (i, j, k) will be considered.

First, in step S900, CPU 120 sets an initial value to the ^{_{I y n + 1/2 (}} i, j, k) of the estimated value ^{_{I y n + 1/2 (}} i, j, k) _est. Here, the value I1 _y (i, j, k) calculated in advance in step S800 of FIG. 8 is set as the initial value. Note that the initial value may be set by another method such as extrapolation.

  Next, in step S <b> 902, the CPU 120 writes the current internal state of the circuit analysis to the internal state storage area 139 in the hard disk 124 in order to repeatedly execute the circuit analysis.

In step S904, the CPU 120 performs circuit analysis of Expression (8) for the time t (where (n−1 / 2) Δt _em <t ≦ (n + 1/2) Δt _em ). At this time, the current source function of Equation ^{_{(7), I y n-}} 1/2 (i, j, k) as _{I1 y (i, j, k} ) ^{_{a, I y n + 1/2}} (i, j , K) uses I _y ^{n + 1/2} (i, j, k) _est. Further, the CPU 120 obtains the electric field value E _y ⁿ (i from the following equation (16) from the voltage value V _y ⁿ (i, j, k) _est applied to the circuit cell at the time nΔt _em obtained as a result of the circuit analysis. , J, k) _est.

Subsequently, in step S906, the CPU 120 assigns the electric field value E _y ⁿ (i, j, k) _est obtained in step S904 to the equation (14), and I _y ^{n + 1/2} (i, j, k).

Next, in step S908, the CPU 120 indicates that I _y ^{n + 1/2} (i, j, k) and I _y ^{n + 1/2} (i, j, k) _est are expressed by the following equation (17). Determine whether the convergence condition is met.

However, α is a constant set in advance as an analysis condition.
If it is determined that the convergence condition is not satisfied (NO in step S908), in step S916, CPU 120 determines I _y ^{n + 1/2} (i, j, k) _est as I _y obtained in step S906. Update by substituting the value of ^{n + 1/2} (i, j, k).

  Next, in step S918, the CPU 120 reads and restores the current internal state of the circuit analysis. Then, the process of step S904 is performed.

On the other hand, if it is determined that the convergence condition is satisfied (YES in step S908), in step S910, CPU 120 determines that time t (however, nΔt _em <t ≦ (n + 1/2) Δt _em ) of equation (8) Perform circuit analysis. At this time, the current source function of Equation ^{_{(7), I y n-}} 1/2 (i, j, k) as _{I1 y (i, j, k} ) ^{_{a, I y n + 1/2}} (i, j , K) uses I _y ^{n + 1/2} (i, j, k) _est. Thereby, the internal state of the circuit analysis is advanced to the calculation start time (n + 1/2) Δt _em of the next step. Then, the CPU 120 writes the internal state of the circuit analysis in the internal state storage area 139 in the hard disk 124.

Next, in step S912, CPU 120 updates the initial current source value by substituting the value of I _y ^{n + 1/2} (i, j, k) for I1 _y (i, j, k).

Finally, in step S914, the CPU 120 assigns the value of E _y ⁿ (i, j, k) _est obtained in step S904 to the electric field value E _y ⁿ (i, j, k) of the circuit cell, and the electric field value. Write to the storage area 137.

The embedded circuit analysis is performed as described above.
As described above, according to the present invention, circuit analysis is performed by setting a continuous power supply function. Thereby, a highly accurate analysis can be performed. In particular, the stability of circuit analysis and the accuracy of cooperative analysis can be improved in a non-linear circuit.

  In addition, according to the present invention, signal quality, electromagnetic noise, and the like are simulated by a detailed model including non-linear parts at the stage of layout design in the development of electronic equipment products that are required to process a large amount of data at high speed. As a result, the board layout design quality can be improved, and the required number of prototypes can be reduced and the design period can be shortened.

  The embodiment disclosed this time should be considered as illustrative in all points and not restrictive. The scope of the present invention is defined by the terms of the claims, rather than the description above, and is intended to include any modifications within the scope and meaning equivalent to the terms of the claims.

It is a conceptual diagram which shows an example of the computer 100 which performs the electromagnetic field circuit cooperation analysis program which concerns on this invention. 2 is a block diagram showing a functional configuration of a CPU 120. FIG. It is a schematic diagram of the cooperative analysis by the current source method. It is the figure which showed the data flow of a circuit analysis and the FDTD method in time series. It is a figure which shows arrangement | positioning of the magnetic field variable of a cell. It is a figure which shows arrangement | positioning of the electric field variable of a cell, and a magnetic field variable. It is a figure showing the data delivery of the electromagnetic field analysis by the said procedure and circuit analysis, and a current source function. It is the flowchart which showed the process of the electromagnetic field circuit cooperation analysis which concerns on this invention. It is the flowchart which showed the embedded circuit analysis process.

Explanation of symbols

  32 Current source, 33 capacitor, 34 network, 100 computer, 102 computer body, 104 display, 106 FD drive, 108 optical disk drive, 110 keyboard, 112 mouse, 116 FD, 118 CD-ROM, 120 CPU, 122 memory, 124 Hard disk, 128 communication interface, 134 circuit board data, 135 program for executing FDTD, 136 program for executing circuit analysis, 137 electric field value storage area, 138 magnetic field value storage area, 139 internal state storage area.

Claims (5)

A program for causing a computer having an arithmetic processing unit to execute electromagnetic field circuit linkage analysis,
In the region to be analyzed, in which the arithmetic processing unit is divided into a plurality of cells, a first electromagnetic field is applied to one of an electric field or a magnetic field of a cell other than the circuit cell in which the circuit element is inserted among the plurality of cells. Performing the analysis;
In the circuit cell, the arithmetic processing unit uses a current value or a voltage value of the circuit cell in a predetermined period including the current time, and a power supply at the current time using a relational expression in electromagnetic field analysis Performing circuit analysis while updating values;
A step of performing a second electromagnetic field analysis on the other of the magnetic field or electric field of the cell based on the result of the step of performing the first electromagnetic field analysis and the step of performing the circuit analysis,
The arithmetic processing unit repeating the first electromagnetic field analysis step, the circuit analysis step, and the second electromagnetic field analysis step until a predetermined condition is satisfied ;
The arithmetic processing unit, e Bei in the region to be analyzed, which is divided into a plurality of cells, and determining the electric field values and field values from time t-1/2? T,
The step of performing the first electromagnetic field analysis includes:
The arithmetic processing unit includes a step of obtaining an electric field value at a time t of a cell other than the circuit cell in which the circuit element is inserted among the plurality of cells,
The step of performing the circuit analysis includes:
The arithmetic processing unit initializing an estimated value of a current value at time t + 1 / 2Δt in the circuit cell;
The arithmetic processing unit obtaining an electric field value of the circuit cell;
The arithmetic processing unit includes a step of obtaining a current value of the circuit cell;
The step of obtaining the electric field value of the circuit cell includes:
The arithmetic processing unit sets the current source value at the time t in the circuit cell by the interpolation formula between the current value calculated from the magnetic field value at the time t−1 / 2Δt and the estimated value. And steps to
The arithmetic processing unit obtains a voltage value of the circuit cell at the time t by performing a circuit analysis based on the set current source value in the circuit cell;
The arithmetic processing unit has a step of obtaining an electric field value of the circuit cell at the time t from a voltage value of the circuit cell;
The step of obtaining the current value of the circuit cell includes:
Substituting the electric field value at the time t into the relational expression in the electromagnetic field analysis established between the circuit cell and a cell in the vicinity of the circuit cell, the current at the time t + 1 / 2Δt in the circuit cell Determining a value;
The step of performing the second electromagnetic field analysis includes:
An electromagnetic field circuit linkage analysis program for causing a computer to execute an analysis process, wherein the arithmetic processing unit includes a step of obtaining a magnetic field value of the cell at the time t + 1 / 2Δt . The power supply value is a current source value ,
The step of performing a pre-Symbol circuit analysis,
While the arithmetic processing unit updates the estimated value until the difference between the current value obtained in the step of obtaining the current value of the circuit cell and the estimated value becomes smaller than a predetermined value, the electric field of the circuit cell Repeating a step of obtaining a value and a step of obtaining a current value of the circuit cell;
The circuit unit at the time t is based on a result of the step of the step of calculating the electric field value of the circuit cell and the step of determining the current value of the circuit cell while the arithmetic processing unit updates the estimated value. further comprising a step of outputting the electric field value,
Pre Symbol arithmetic processing unit, the time t further comprises the step of updating the t + Delta] t to claim 1, wherein the electromagnetic field circuit linkage analysis program. In the initialization step, the arithmetic processing unit sets an initial value of the estimated value using a current value calculated from a magnetic field value until the time t−1 / 2Δt,
The step of obtaining the electric field value of the circuit cell and the step of obtaining the current value of the circuit cell while updating the estimated value is obtained by the step of the arithmetic processing unit obtaining the current value of the circuit cell. The electromagnetic field circuit cooperation analysis program according to claim 2, wherein the obtained current value is updated as the estimated value. The computer-readable recording medium which stored the electromagnetic field circuit cooperation analysis program of any one of Claims 1-3. An electromagnetic field circuit linkage analysis apparatus for performing linkage analysis between electromagnetic field analysis and circuit analysis,
It has a circuit analysis unit that performs circuit analysis.
In the analysis target area divided into a plurality of cells, the circuit analysis unit includes a circuit cell in which a circuit element is inserted among the plurality of cells, the circuit cell in a predetermined period including a current time. Means for performing circuit analysis while updating the power supply value at the current time using the interpolation formula by one of current value or voltage value and the relational expression in electromagnetic field analysis,
An electromagnetic field analysis unit for performing the electromagnetic field analysis;
The electromagnetic field analysis unit
A first means for performing a first electromagnetic field analysis on one of an electric field or a magnetic field of a cell other than the circuit cell among the plurality of cells and providing a result of the first electromagnetic field analysis to the circuit analysis unit; ,
Means for performing a second electromagnetic field analysis on the other of the magnetic field or electric field of the cell based on the result of the first means and the circuit analysis unit,
An analysis control unit that repeats the first means, the circuit analysis means, and the second electromagnetic field analysis means until a predetermined condition is satisfied ;
In the analysis subject to area divided into a plurality of cells, Bei example a means for obtaining an electric field values and field values from time t-1/2? T,
The first means includes
Obtaining the electric field value at time t of cells other than the circuit cell in which the circuit element is inserted among the plurality of cells,
The means for performing the circuit analysis is:
Means for initializing an estimated value of a current value at time t + 1 / 2Δt in the circuit cell;
Means for determining an electric field value of the circuit cell;
Means for determining a current value of the circuit cell,
Means for obtaining the electric field value of the circuit cell is:
Means for setting a current source value at the time t by the interpolation formula between the current value calculated from the magnetic field value at the time t−1 / 2Δt and the estimated value in the circuit cell;
Means for obtaining a voltage value of the circuit cell at the time t by performing a circuit analysis on the circuit cell based on the set value of the current source;
Means for determining the electric field value of the circuit cell at the time t from the voltage value of the circuit cell;
The means for obtaining the current value of the circuit cell is:
Substituting the electric field value at the time t into the relational expression in the electromagnetic field analysis established between the circuit cell and a cell in the vicinity of the circuit cell, the current at the time t + 1 / 2Δt in the circuit cell Having means for determining the value,
The means for performing the second electromagnetic field analysis includes:
An electromagnetic field circuit cooperative analysis apparatus including means for obtaining a magnetic field value of the cell at the time t + 1 / 2Δt .

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