JP2002197401A - Simulation method and simulator - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a simulation method and a simulator which improves the probability of satisfying the convergence conditions of Newton repetition in the simulation method suited to a simulator for analyzing an event by using Newton's method. SOLUTION: A simultaneous equation is prepared with the node potential of each node of an analyzing object circuit. A circuit simulation method calculates the simultaneous equation by using the Newton's method (step S14) to perform DC operation point analysis. When the convergence condition by Newton repetition is not satisfied (step S15), a random number is multiplied to the value of a node potential which is not convergent to set a new initial value (step S20), to recalculate the simultaneous equation. This series of operation is called a fluctuation method.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

The present invention relates to a simulation method and a simulator, and more particularly, to a simulation method and a simulator suitable for a circuit simulator for performing a DC operating point analysis (hereinafter, referred to as a DC operating point analysis). is there.

[0002]

2. Description of the Related Art Generally, in the design of a semiconductor integrated circuit, a DC operating point analysis is performed using a circuit simulator to analyze characteristics of a circuit to be designed. In the DC operating point analysis, each node potential is obtained by solving a circuit equation of a circuit to be analyzed. In the process of finding each node potential of the circuit equation,
Newton's method is used.

FIG. 5 is a block diagram of a circuit simulator described in Japanese Patent Application Laid-Open No. 5-342294. The analysis condition reading unit 82 reads analysis conditions including element connection information and circuit characteristics from the analysis condition file 81. The operating point analysis unit 83 performs a linear approximation calculation by the Newton method based on the read analysis conditions, and obtains a node potential of each node. The operating point determining unit 84 determines whether or not the obtained node potential has converged.

When the operating point determining section 84 determines that a certain node potential does not converge, it issues a request for reanalysis to the non-convergent node reanalysis control section 90. Non-convergence node re-analysis controller 90
Starts the node initial value setting unit 89, newly sets the initial value of the operating point of the node, changes the analysis condition of the analysis condition file 81, and prepares for the next analysis.

A node initial value setting section 89 sets an operating point for a node whose operating point has converged based on the convergence / non-convergence analysis data 88, and sets this node for a node whose operating point does not converge. The average value of the converging operating points of the surrounding nodes connected across the element is set.

When the analysis condition in the analysis condition file 81 is changed, the non-convergence node re-analysis control unit 90 instructs the analysis condition reading unit 82 to perform the next analysis.

The convergence / non-convergence analysis result output unit 86 stores the operating point of the converged node obtained by the operating point analysis unit 83 and the node name stored in the non-convergence node storage unit 85 in the analysis result file 87. The data is output and recorded as convergence / non-convergence analysis data 88.

[0008]

In the above conventional circuit simulation method, if the operating points of the nodes do not converge,
Some of the nodes that converge are selected from the surrounding nodes that connect the non-converging node and the element. An average value between the selected nodes is obtained, the average value is reset as an initial value of a node that does not converge, and reanalysis is performed.

FIG. 6 shows an example of a circuit to be analyzed in which DC operating point analysis (operating point analysis) is performed by the circuit simulation method of FIG. The circuit to be analyzed is an inverter using p-channel and n-channel transistors.

According to the result of the DC operating point analysis, the node N
The potential of c converges to the power supply voltage VDD, and the potential of the node Nd converges to the ground potential. When the potential of the node Nb is set to the ground potential, the potential of the node Na becomes almost equal to the power supply voltage VD.
Although it converges to D, the potential of the node Nx does not converge.

However, in the conventional circuit simulation method, when resetting the initial value of the potential Vx, the initial value of the potential Vx is determined based on the potential Va and the potential Vb or the potential Vc and the potential Vd. I will ask. In this case, the initial value of the potential Vx is set to approximately VDD / 2.

As an initial value of the potential Vx, a ground potential is almost optimal. Therefore, the initial value (approximately VDD / 2) of the potential Vx adopted above is inappropriate as an approximate value,
It does not converge even with Newton iteration. Under this condition, if the potential Vx does not converge by re-analysis, the same result is obtained no matter how many times it is repeated.

The present invention is effective and is not affected by the surrounding nodes, even if all of the surrounding nodes connected to the non-converging node and the element across the element are non-converging nodes.

SUMMARY OF THE INVENTION The present invention has been made to solve the above-mentioned problems of the prior art, and is a simulation method suitable for a simulator for analyzing an event using the Newton method. It is an object of the present invention to provide a simulation method and a simulator having a high probability of satisfying the convergence condition.

[0015]

In order to achieve the above object, a simulation method according to the present invention is a simulation method for obtaining a solution of a variable from a simultaneous equation having a plurality of variables by using a Newton iteration method. Performing a Newton iteration by giving an initial value to each of the variables, analyzing the solution of each variable obtained by the Newton iteration, and determining whether or not the solution of each variable satisfies a predetermined convergence condition; For the variables determined to satisfy the convergence condition, the solution at that time is given as a new initial value, and for the variables determined not to satisfy the convergence condition, the solution at that time is based on random numbers. Modifying and giving as a new initial value; and
The method further comprises performing Newton iteration based on the new initial value.

According to the simulation method of the present invention, for a variable determined not to satisfy the convergence condition, the solution at that time is corrected based on a random number and given as a new initial value. This is a simulation method suitable for a simulator that analyzes, and can increase the probability of satisfying the convergence condition of Newton iteration.

In the simulation method according to the present invention, it is preferable that the random numbers are generated based on a probability of a uniform distribution. In this case, since the value of the random number is uniformly generated, an optimum initial value can be obtained by repeating the number of times.

When the convergence condition determination step and the new Newton iteration step are performed a predetermined number of times, an error is displayed and the simulation is terminated.
It is also a preferred embodiment of the present invention to display the solution of the variable at that time and the variable that does not satisfy the convergence condition. In this case, it can be determined whether the setting of the initial value is bad or the solution cannot be obtained.

In the simulation method of the present invention, each time a predetermined number of Newton iterations are performed, a step of determining whether or not the convergence condition is satisfied can be performed.

In the simulation method according to the present invention, a variable determined as not satisfying the convergence condition may be set to a new initial value by multiplying the solution at that time by a random number.

Further, in the simulation method of the present invention, each of the variables may be a voltage or a current of a node in a circuit, or a simulator for performing any one of the simulation methods described above.

[0022]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Hereinafter, a simulation method and a simulator according to the present invention will be described based on embodiments of the present invention with reference to the drawings. FIG. 1 is a flowchart illustrating a simulation method according to an embodiment of the present invention.

First, simultaneous equations are created based on the circuit to be analyzed. With the potential of each node of the circuit to be analyzed (hereinafter referred to as a node potential) as a variable, circuit equations are created by the number of variables, and simultaneous equations are created.

The circuit to be analyzed has a non-linear element. The circuit simulator incorporates the simulation method of FIG. 1, calculates simultaneous equations of a circuit to be analyzed using the Newton method, and performs DC operating point analysis.

Here, the principle of the Newton method will be described. The variables are x1 and x2, and the functions are f1 (x) and f2
Assuming (x), the simultaneous equation F (x) is expressed as follows.

(Equation 1)

(Equation 2) Equation (2) is the Jacobian of Equation (1). An iterative formula created based on Newton's method from Formulas (1) and (2) is shown below.

(Equation 3) An appropriate initial value is given to the iterative expression of the expression (3) which is a part of the Newton method. An approximate solution (x) is obtained by calculating and repeating equation (3) starting from the initial value (hereinafter referred to as Newton iteration).

In the Newton iteration, it is determined whether or not a predetermined convergence condition shown below is satisfied with respect to an allowable error ε. | (Xn + 1) − (xn) | <ε (4) When the convergence condition of the equation (4) is satisfied, (xn + 1) is solved.

FIG. 2 shows an application example of the Newton method. 1
The Newton method is applied to a function f (x) having two variables x. As shown in FIG. 7A, f (x) = 0
When a value close to the solution x is set as the initial value x0,
The convergence condition is satisfied by three Newton iterations, and the solution x3 can be obtained.

As shown in FIG. 3B, when a value far from the solution x where f (x) = 0 is set as the initial value x0, 3
The convergence condition is not satisfied even by one Newton iteration. Under this condition, the solution x cannot be obtained even if the number of Newton iterations is increased.

First, an appropriate initial value is given to each node potential, which is a variable of the created simultaneous equations, and a circuit simulation method by the swing method is started. In the circuit simulation method, the process of analyzing the DC operating point in FIG. 1 is executed.

Each node sets an initial value to a node potential when an initial value is given, and sets 0 to a node potential to which no initial value is given (step S11). The counter RN, which is the number of repetitions of the rocking method, is set to 0 (step S12), and the counter N, which is the number of Newton iterations, is set to 0 (step S13).

A simultaneous equation is calculated using the Newton method (step S14), and it is determined whether or not all nodal potentials satisfy the convergence condition of the Newton iteration (step S14).
15). If “YES”, the process ends. If “NO”, it is determined whether the value of the counter N is less than a preset upper limit (step S16).

If "YES", the value of the counter N is set to 1
It increases and the process is continued from step S14. “NO”
If, it is determined whether the value of the counter RN is less than a preset upper limit (step S18).

If "NO", it is recognized that there is a node that cannot satisfy the convergence condition among the node potentials, and error processing is executed (step S21). If "YES", the value of the counter RN is incremented by 1, the process of setting the node potential is executed (step S20), and the process is continued from step S13.

The error processing is classified into a node satisfying the convergence condition and a node not satisfying the convergence condition, displays the node name, the node potential, and the like, and ends the processing.

FIG. 3 is a flowchart of the process of setting the node potential in FIG. Here, let each node potential be XNi. The subscript i of each node potential XNi corresponds to the number of the node to be calculated. The subscript N of each node potential XNi is the number i
Correspond to the counter N increased in the processing of FIG. 1 by the Newton iteration.

The counter i indicating the number of all nodes is set to 1 (step S31), and it is determined whether each node potential XNi satisfies the convergence condition (step S32). If "YES", XNi is updated as the initial value (X0i) for the converged node of number i (step S35), and step S35 is executed.
The processing is continued from 36.

If "NO", the solution at that time is corrected based on the random number and given as a new initial value. The following random number ε is generated (step S33). ε = 1.2 × {COS ⁻¹ (2 × Y−1)} / π (5) where Y is a uniformly distributed random variable satisfying 0 <Y <1, and ε is 0 １．２1.2. As shown below, XNi × ε is updated as an initial value (X0i) for the node with the number i that does not converge (step S36). X0i = XNi × ε (6)

Further, the correction performed based on the random number may be a calculation in which a random number is added to the solution at that time instead of multiplying the solution at that time by the random number. In this case, the added random number has a value in the range of − (power supply voltage) to + (power supply voltage). As the random variable Y, a distribution other than the uniform distribution can be adopted depending on the application field.

It is determined whether the value of the counter i is equal to or greater than the preset number of all nodes (step S3).
6). If “YES”, the process ends. “NO”
If it is, the value of the counter i is increased by 1 (step S3
7) The process is continued from step S32.

In the process of resetting the node potential, if the convergence condition of the Newton iteration is not satisfied, the value of the node potential that does not converge is multiplied by a random number, and updated as a new initial value to the node potential that does not converge (step S33). And S34). Newton iteration is performed again using the updated initial value of the node potential. This series of operations is called a swing method.

In the swing method, a converged node potential is regarded as a solution, and a non-converged node potential periodically fluctuates near the minimum value of the function f (x). It is intended to avoid the periodic fluctuation of the node potential in a place apart from the minimum value of f (x).

For the swing method to be effective, the following two conditions are assumed. The first assumption is that when the Newton iteration does not converge, the node potentials obtained in the last iteration include a node potential that converges and becomes a solution and a node potential that does not converge and that periodically fluctuates. It is.

The second assumption is that whether or not the convergence condition of the Newton iteration is satisfied changes depending on the initial value given to the variable of the function f (x), and there is independence between node potentials. Even if the initial value of the node potential that does not converge is changed, it does not affect the convergence of the node potential that converges.

Some circuits are composed of circuit blocks having several characteristics, and the first assumption seems to be satisfied relatively well in such circuits.

It is known that a set of initial values that converge has a certain degree of regularity, and that even if one of the initial values is changed, there is an area that does not significantly affect the convergence. It seems that the second assumption is satisfied to some extent.

The swing method is effective for a circuit satisfying both assumptions. However, since the swing method uses random numbers, even a circuit that does not satisfy both assumptions may accidentally converge in a small-scale circuit.

SPICE simulator (NECSPICE V6.
0) Circuit simulation method that does not employ the swing method,
In addition, a circuit simulation method employing the swing method (the simulation method in FIG. 1) was incorporated, and a DC operating point analysis was performed on ten analysis target circuits, and the probability of convergence was evaluated.

[0048]

[Table 1] Table 1 shows the contents of the circuit to be analyzed. Each circuit to be analyzed is composed of ten circuits (circuit numbers 1 to 1) related to the operational amplifier.
0), and the number of nodes, the number of elements, and the number of MOS transistors are different from each other.

[0049]

[Table 2] Table 2 shows the results of the DC operating point analysis. As a result of the DC operating point analysis, there is no swing method, there is a swing method (Nmax = 50),
And three cases with the swing method (Nmax = 100).

Nmax is an upper limit value to be compared with the counter N which is the number of Newton iterations in step S16 of FIG. 1, and 50 and 100 are respectively specified in the method by the swing method. The × in the result item indicates that the convergence condition of the Newton iteration was not satisfied and the number of repetitions of the rocking method exceeded the upper limit. The number of the item of the result indicates the number of repetitions of the rocking method in which the convergence condition of the Newton iteration is satisfied and converged.

The method not using the swing method did not converge in all the circuits to be analyzed, and the method using the swing method converged more than half of the circuits to be analyzed. The swing method has a higher probability of convergence in the DC operating point analysis than the method not based on the swing method.

In the swing method, the larger the circuits (circuit numbers 9 and 10), the lower the convergence in the DC operating point analysis tends to be. In the case of 50, the number of repetitions of the rocking method tends to be slightly larger.

It is considered that the reason for the latter tendency is that the number of Newton repetitions exceeds the upper limit and the Newton repetition is terminated before the periodic fluctuation occurs in the process of calculating the node potential. However, convergence may not be achieved unless Nmax = 50 as in the circuit number 1.

FIG. 4 shows a method (Nmax) according to the swing method shown in Table 2.
= 100) shows the change in the residual of the node potential. The residual of the node potential is a value that is referred to in step 15 in FIG. 1 and step 32 in FIG. 3 to determine the convergence condition.

In the case of the circuit numbers 2, 5, and 8, as the number of repetitions of the swing method increases, the average value of the residuals decreases, indicating that the method based on the swing method worked effectively.

In the case of the circuit number 6, the average value of the residuals is almost constant without depending on the number of repetitions of the swing method, indicating that the method by the swing method acted by chance.

In the case of the circuit numbers 3 and 7, since the number of repetitions of the swing method is 1, it cannot be evaluated whether the method based on the swing method worked.

According to the above embodiment, if the convergence condition is not satisfied, a value obtained by multiplying the value of the variable at that time by a random number is reset as an initial value, and Newton repetition is repeatedly performed. It is possible to increase the probability of satisfying the convergence condition of Newton iteration used in DC operating point analysis for obtaining a node potential of a node.

In the above embodiment, the field of circuit simulation in which calculation is performed using the Newton method has been described. However, the present invention can be applied to other fields such as financial relations in which calculation is performed using the Newton method. it can.

As described above, the present invention has been described based on the preferred embodiment. However, the simulation method and the simulator of the present invention are not limited only to the configuration of the above-described embodiment, and are not limited thereto. Simulation methods and simulators with various modifications and changes from the configuration are also included in the scope of the present invention.

[0061]

As described above, in the simulation method and the simulator according to the present invention, when the convergence condition is not satisfied, a value obtained by multiplying the value of the variable at that time by a random number is reset as an initial value, and Newton iteration is performed. Because it repeats,
It is possible to increase the probability of satisfying the convergence condition of Newton's iteration used in DC operating point analysis for obtaining a node potential of each node of the analysis target circuit.

[Brief description of the drawings]

FIG. 1 is a flowchart illustrating a simulation method according to an embodiment of the present invention.

FIG. 2 shows an application example of the Newton method.

FIG. 3 is a flowchart of a process of setting a node potential in FIG. 1;

FIG. 4 shows a change in the residual of the nodal potential in the method based on the swing method in Table 2 (Nmax = 100).

FIG. 5 is a block diagram of a circuit simulator described in Japanese Patent Application Laid-Open No. 5-342294.

FIG. 6 is an example of an analysis target circuit in which DC operating point analysis is performed by the simulation method of FIG. 5;

[Explanation of symbols]

 81 Analysis condition file 82 Analysis condition reading unit 83 Operating point analysis unit 84 Operating point determination unit 85 Non-convergence node storage unit 86 Convergence / non-convergence analysis result output unit 87 Analysis result file 88 Convergence / non-convergence analysis data 89 Node initial value setting Unit 90 non-convergence node re-analysis control unit

Claims (8)

[Claims] 1. A simulation method for obtaining a solution of a variable using a Newton iteration method from a simultaneous equation having a plurality of variables, wherein the step of giving an initial value to each of the variables and performing a Newton iteration is obtained by the Newton iteration. Analyzing the solution of each of the obtained variables to determine whether the solution of each variable satisfies a predetermined convergence condition. Is given as a new initial value, and for a variable determined not to satisfy the convergence condition, the solution at that time is corrected based on a random number and given as a new initial value; and Performing a Newton iteration on the basis of the value. 2. The simulation method according to claim 1, wherein the random number is generated based on a probability of a uniform distribution. 3. A step of determining whether a convergence condition is satisfied is performed every time a predetermined number of Newton iterations are performed.
The simulation method according to claim 1. 4. The simulation method according to claim 1, wherein when the convergence condition determination step and the new Newton iteration step are performed a predetermined number of times, an error is displayed and the simulation is terminated. 5. The simulation method according to claim 4, wherein a variable satisfying a convergence condition, a solution of the variable at that time, and a variable not satisfying the convergence condition are displayed together with the error display. 6. The simulation method according to claim 1, wherein a variable determined as not satisfying the convergence condition is a new initial value by multiplying a solution at that time by a random number. 7. The simulation method according to claim 1, wherein each of the variables is a voltage or a current of a node in the circuit. 8. A simulator for performing the simulation method according to claim 1.