JPH10162037A - Method and device and storage medium for transition analysis - Google Patents

Abstract

PROBLEM TO BE SOLVED: To shorten the analysis time by correcting the value of a component of a state variable vector corresponding to a component of an evaluation vector according to vibration of the component of the evaluation vector from a certain fixed value wen the component of the evaluation vector varies from the certain fixed value beyond a 3rd set value less than a 2nd set value. SOLUTION: Circuit constitution data and analytic condition data are inputted from a circuit constitution data file and an analytic condition data file (S20). Then, a state variable vector V at a point (t) of time is found (S21). When a potential V(i) meets the condition to be made constant, 0 is substituted in a variable flag FV(i) (S23). When the state variable V(i) is made constant and it has been decided to be a variable, 1 is substituted in the variable flag FV(i) (S24). The state variable vector V is written in a state variable waveform data file (S25). When FV(i)=0 as to while i=0 to n-1, a node current U(i) is calculated and substituted in UB(i) (S27). Lastly, Δt is added to the point (t) of time (S28).

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a transient analysis method and apparatus for simulating a time change of a state variable such as a potential or a current of an electric circuit, and a storage medium storing a program for executing the method.

[0002]

2. Description of the Related Art A transient analysis method is used for efficiently designing and developing a semiconductor integrated circuit. With the recent increase in the degree of integration and scale of semiconductor integrated circuits, the time required for simulation has been increasing, and shortening of the time is required. A transient analysis method proposed by the present inventor (JP-A-8-77215) to meet this demand will be described using a simple circuit example shown in FIG.

In this circuit, circuit elements E01, E03,
E12, E23 and E40 are connected by wiring. As an analysis condition, a known signal is given from the signal source S, and the potential of the node N3 is fixed to 0V. Node N0
The potentials at N4 are V (0) to V (4), respectively, and the sum of the currents flowing into nodes N0 to N4 is U (0), respectively.
To U (4).

The state variable vector V = (V (0), V (1), V (2)) at time t = iΔt, i = 0 to imax
Is obtained as a solution of the transient analysis. Potentials V (3) and V
Since (4) is given as an analysis condition, it is not a component of the state variable vector V to be obtained. Actually, since the number of circuit elements is large, the state variable vector V at each time is obtained by the successive approximation method. Node current vector U = (U
(0), U (1), U (2)) are originally 0, but when the solution of the state variable vector V is obtained by the successive approximation method, iterative processing is performed so that the node current vector U converges to 0. I do. The node current vector U is represented by U = F (V). Here, F (V) is a vector determined by the circuit configuration, and each component is a nonlinear function of all components of the state variable vector V.

In this successive approximation method, j =
Until | U (j) | ≦ εu is satisfied for all of 0 to 2, the state variable vector V is determined by repeatedly performing, for example, the Newton-Raphson method. The state variable vector V at each time point can be obtained in a shorter time as the number of dimensions is lower.

Therefore, the present inventor has proposed that the state variable vector V
When the absolute value of the temporal change is equal to or smaller than the small set value εv for each of the components, the number of dimensions of the state variable vector V is reduced by reducing the number of dimensions of the state variable vector V. In the case where the absolute value of the time change of the component of the node current vector U corresponding to the above exceeds a small set value εu, the component of the corresponding state variable vector V is returned to a variable.

[0007]

According to the above method, the analysis time can be reduced, but the analysis accuracy is lower than when the variables are not converted into constants. The present inventor has discovered that this decrease in accuracy is mainly due to a delay in returning a constant component of the state variable vector V to a variable.

An object of the present invention is to reduce the analysis time by appropriately converting the components of the state variable vector and to convert the constant components of the state variable vector into variables. It is an object of the present invention to provide a transient analysis method and apparatus and a storage medium storing a program for executing the method, which can improve the analysis accuracy by performing the method more appropriately.

[0009]

According to the present invention, a state variable vector V of a circuit at time t is calculated by a successive approximation method, and in the successive approximation method, each component of the state variable vector V is calculated. Iterative processing is performed until it is determined that the evaluation vector U, which includes the corresponding component and has a predetermined relationship with the state variable vector V and should be a constant vector, converges on the constant vector, and converts the state variable vector V A state variable vector calculating step of determining the state variable vector V at time t,
A constant value step of converting the component of the state variable vector V into a constant and excluding the component from the component of the state variable vector V when the displacement is not greater than or equal to the set value εv; When the component of the evaluation vector U deviates from the value before the time Δt by more than the second set value εu, a variable return step of returning the constantized component to the component of the state variable vector V; Is performed for each time point t, and the component of the evaluation vector U corresponding to the constantized component is calculated from the value before the time Δt by the second set value εu When the deviation exceeds the third set value εw below, the state variable vector V corresponding to the component of the evaluation vector U is changed according to the change of the component of the evaluation vector U from the value before the time Δt. Correct the value of the component That correction step, with a.

According to the present invention, by correcting the value of the component of the state variable vector V in the correction step, the delay of the conversion of the component of the constant state variable vector V into a variable is reduced,
This has the effect of improving the accuracy of the solution of the state variable vector V. In the first aspect of the present invention, the third set value εw in the correction step is equal to the second set value εv.

According to the first aspect, when the change of the evaluation vector component is relatively small, the correction of the state variable vector component corresponding to the change is ignored, and the correction is performed only for the one that satisfies the variable return condition. So that
This has the effect of preventing (the amount of improvement in solution accuracy) / (increase in correction calculation time) from being reduced. In the second aspect of the present invention, when the value of the component of the state variable vector V is corrected in the correction step, the correction step is performed again using the corrected state variable vector V.

According to the second aspect, the effect of the correction of the evaluation vector component is propagated to the adjacent node, and the correction is performed more accurately. In the third aspect of the present invention, the state variable vector V corrected in the correction step is used as a solution of the state variable vector. According to the third aspect, there is an effect that the accuracy of the solution of the state variable vector is improved as compared with the case where the state variable vector before correction is used as the solution.

In a fourth aspect of the present invention, the components of the state variable vector V are all node potentials, and the components of the evaluation vector U are all node currents. Component V (i) is
(I) = V (i)-(U (i) -UB (i)) / Gii
Where U (i) is the ith component of the evaluation vector U at time t corresponding to V (i), and UB (i)
Is the ith component of the evaluation vector at time (t-Δt) corresponding to V (i), and Gii is the vector U = F
It is the ith row and the ith column component of the Jacobian function matrix of the vector F (V) in (V). Each component of the vector F (V) is a function of the component of the vector V, and is generally a nonlinear function.

A transient analysis apparatus according to a fifth aspect of the present invention has a computer that executes any one of the above transient analysis methods. In the storage medium according to the sixth aspect of the present invention, a program for executing any one of the above transient analysis methods by a computer is stored.

[0015]

Embodiments of the present invention will be described below with reference to the drawings. [First Embodiment] As shown in FIG. 3, the hardware configuration of the transient analysis apparatus is a general computer system, and a console 10 and an external storage device are connected to a computer 10. The external storage device includes a circuit configuration data file 12 and an analysis condition data file 13
, A state variable waveform data file 14, and a transient analysis program 15.

In the following description, the following variables are used. The state variable vector V, the node current vector U, and their components are the same as described above with reference to FIG. V = (V (0), V (1),..., V (n-1)) A state variable V (j) which is a constant is added to the state variable vector V.
(Constantization component) is not included, and it is assumed that the dimension is k-dimensional (k ≦ n). An n-dimensional one including a constant component is represented by V ′.

V (i): potential of node i at time t as a state variable, i = 0 to n-1 VB (i): potential of node i at time (t−Δt) FV (i) : A variable flag. When '1', it indicates that the state variable V (i) is a variable, and when '0', it indicates that the state variable V (0) is constant.

FA (i): A variable decision flag,
When it is “1”, it indicates that the conversion of the constant state variable V (i) is determined, and when it is “0”, it indicates that this determination is not made. FP: A flag indicating that the variable conversion process is in progress. When "1", the variable conversion process is not completed, and when "0", the variable conversion process is completed.

U = (U (0), U (1),..., U (n−1)) The node current vector U has a constant state variable V
It is assumed that the node current U (j) corresponding to (j) is not included and that it has k dimensions (k ≦ n). The n-dimensional one including the constant component is represented by U ′. U (i): Total current flowing into node i at time t (node current) UB (i): Total current flowing into node i at time (t−Δt) F (V): Each component is vector V , Fk = (F1, F2,..., Fk-1), the components F1, F2,.
Functions (1) to V (k-1), which are generally nonlinear functions, are determined by the circuit configuration, and the vector equation U = F (V) holds. The relationship between U ′ and V ′ corresponding to U = F (V) is represented by U ′ = F ′ (V ′).

G: a Jacobian function matrix of the vector F (V), which is a conductance matrix of k rows and k columns, and whose i-th row and j-th column component is a partial derivative of Fi with respect to V (j).
Fi / ∂V (j). Assuming that the column vector V becomes the column vector V + ΔV after the time Δt, F (V + ΔV) =
The relationship of F (V) + GΔV is established. The conductance matrix of n rows and n columns corresponding to V ′ and U ′ is represented by G ′.

Next, the contents of the transient analysis program executed by the computer 10 will be described with reference to FIGS. FIG. 2 is a detailed flowchart of step 22 in FIG. Hereinafter, the numerical values in parentheses are the step identification numbers in the figure. (20) The circuit configuration data and the analysis condition data are input from the circuit configuration data file 12 and the analysis condition data file 13, respectively. The circuit configuration data is composed of modeled circuit element characteristic data and element connection data. The analysis conditions are known conditions, such as an externally applied potential and a current waveform.

An initial value 1 is assigned to each of the variable flags FV (0) to FV (n-1), and an initial value 0 is assigned to a time point t. (21) As described above, the state variable vector V at the time point t is obtained by using, for example, the Newton-Raphson method. (22) As described later, a constant component of the state variable vector V that satisfies the parameterization condition is returned to a variable. Since there is no constant component at first, it is not variable.

(23) For each of i = 0 to n−1,
When FV (i) = “1”, | V (i) −VB (i) |
If <εv, that is, if the potential V (i) satisfies the constant condition, '0' is substituted for the variable flag FV (i).
Here, εv is a small first set value set in advance. For example, in FIG. 5A, when t = t4, the state variable V
(I) is converted into a constant.

(24) For each of i = 0 to n−1,
If FV (i) = '0' and FA (i) = '1', that is, the state variable V (i) is constant, and
If the variable is determined in step 22, '1' is substituted for the variable flag FV (i). Variable decision flag F
The initialization of A (i) is performed as described later in the next iteration of the loop of steps 21 to 28, that is, in step 22 after Δt.

The step 23 which is a constant processing is placed between the step 22 which is the variable processing and the present step 24. This is because even if the variable is determined in the step 22, it will be described later in the step 22. Step 23 is performed by the potential correction processing.
This is due to the consideration of the case where the constant is used. (25) Write the state variable vector V to the state variable waveform data file 14 in FIG.

(26) If t ≧ te, the process is terminated.
Otherwise, go to step 27. Here, te is the upper limit of the range of the time t, and is set in advance. (27) For each of i = 0 to n−1, FV (i) =
If it is “0”, the node current U is calculated from U ′ = F ′ (V ′)
(I) is calculated (because the node current U does not include the node current U (i), the node current U (i) cannot be calculated from U = F (V)), and this is calculated as UB.
Substitute (i). However, if the node current U (i) has already been calculated in step 224 to be described later in step 22, this U (i) is replaced with UB (i) without calculating the node current U (i) again. ).

This UB (i) is used in the next repetitive processing of the loop of steps 21 to 28, that is, in steps 225 and 226 described later in step 22 after Δt. (28) At is added to the time point t, and the process returns to the step 21. Next, the details of the variable conversion processing in step 22 will be described.

(221) Variable decision flag FA (0)-
The initial value 0 is substituted for FA (n-1). (222) The initial value 0 is substituted into the variable processing flag FP and the node i. (223) FV (i) = '0' and FA (i) = '0'
, That is, a state variable V (i) that is constant
If the variable has not been determined, the process proceeds to step 224; otherwise, the process proceeds to step 227.

(224) The node current U (i) is calculated from U ′ = F ′ (V ′). (225) If | U (i) −UB (i) |> εu, then
That is, if the variable condition is satisfied, the process proceeds to step 226; otherwise, the process proceeds to step 227. Where εu
Is a small second set value set in advance. The value of εu can be set independently of εv in step 23 of FIG.

For example, in FIG. 5B, at t = t7, the state variable V (i) satisfies the variable condition. (226) 1 is substituted into the variable conversion processing flag FP and the variable conversion determination flag FA (i). ΔVi = (U (i) −U
B (i)) / Gii is calculated, and V (i) is subtracted by ΔVi. Here, Gii is a component at the i-th row and the i-th column of the conductance matrix G.

Next, referring to FIG. 4, state variable V (i)
Will be described in this manner. As shown in FIG. 4A, the potential V of the node N1 on one end of the circuit element E12
(1) is a variable, and the circuit elements E12 and E23
Between the potential V (2) of the node N2 and the circuit element E23.
It is assumed that the potential V (3) of the node N3 opposite to the node N2 is constant. Assuming that currents flowing through the circuit elements E12 and E23 are I12 and I23 as shown, U (2) =-I12 + I23.

FIGS. 4B to 4D each show the potential V
FIGS. 4E to 4G show the values of (1) to V (3) at t = t1 and t = t2, respectively.
値 U (3) at t = t1 and t = t2. FIG.
In (B) to (G), the solid line is before correction. Let t = t2 be the current time, and let t = t1 be the time Δt before the current time. Since the potential V (1) has changed from before Δt, the current I12 has also changed, and the node current U (2) has changed from ΔT before ΔU (2) = U (2) −UB (2) = − ΔI12 +
It has changed by ΔI23. Potentials V (2) and V (3)
Does not change from before Δt, so that the change Δ
I23 is 0, and ΔU (2) = − ΔI12.

Since the potential V (2) is constant, ΔV
t, but more precisely, the current change ΔI1
2, the potential V (2) becomes ΔV (2) = − Δ from before Δt.
It is thought that it decreases by I12 / G22, that is, increases by ΔI12 / G22. Therefore, the potential V (2) is calculated as follows: V (2) −ΔV (2) = V (2) − (U (2) −UB
(2)) / G22 is corrected. The dashed line in FIG. 4C shows the state after this correction.

When | U (2) −UB (2) | is relatively small, the correction amount ΔV (2) can be ignored.
In step 225, the variable condition | U (i) -UB (i) |
By performing this correction only on the one that satisfies> εu, it is possible to prevent (amount of improvement in accuracy of solution) / (increase in correction calculation time) from being reduced. By this correction, the potential V
When (2) decreases by ΔV (2), the current I23 increases, so that the node current U (3) decreases before Δt as shown by the dashed line in FIG. 4G, and ΔU (3) ≠ 0 Becomes
That is, the effect of the potential correction is propagated to the adjacent node to promote the current correction. It is conceivable that the current correction corrects the parameterization condition that was not satisfied in step 225 before correction, and the effect of the correction of the potential and the current propagates in the same manner.

By doing so, the delay in converting the constant component of the state variable vector V into a variable is reduced, and the accuracy of the solution of the state variable vector V is improved. FIGS. 6A and 6B show the potentials V (1) and V in FIG.
FIG. 6C shows the change in the correction amount ΔV.
The change of the potential V (2) in the conventional example without considering (i) is shown.

(227) The node i is incremented by one. (228) If i <n, the process returns to step 222, where i =
If n, the process proceeds to step 229. (229) If FP = “1”, that is, step 2
If the potential correction at 26 has been performed for at least one of i = 1 to n−1, the process returns to step 222 to propagate the effect of the correction. Subsequent step 2
In 24, by using the corrected potential V (i),
As described above, the effect of potential correction propagates to the next node,
The current correction of this node is performed.

If FP = “0”, that is, if the propagation of the effect of the correction has ended, the variable conversion processing ends. Note that the effect of reducing the variable delay can be obtained even if the above correction is used only in step 22, that is, only to reduce the variable delay, and the state variable vector V before correction is used in another step.

The following second embodiment assumes that the first embodiment is a limited use of such a correction. [Second Embodiment] FIG. 7 shows a step 29 inserted between steps 22 and 23 of the flow of FIG. 1 in the transient analysis method according to the second embodiment of the present invention.

This step 29 is for using the above-mentioned correction in processes other than step 22. In step 22, if FV (i) = '0' and FA (i) = '1' for each of i = 0 to n-1, ie, the variable of the state variable V (i) If the return to is determined in step 22, the potential V (i) before the correction in step 22 is calculated based on the potential V (i) in step 22.
The potential V (i) is corrected by subtracting the above-mentioned ΔVi.

As a result, the potential V (i) becomes more accurate, and the accuracy of the solution of the state variable vector V is further improved. The present invention also includes various modified examples. For example, the process of step 225 in FIG. 2 is performed by | U (i) -UB
(I) First processing for determining |> εw and | U (i) −UB
(I) The processing is divided into a second processing for judging |> εu, the second setting value εu is set to a setting value larger than the third setting value εw, and the processing of step 226 in FIG.
Is divided into a third process of substituting 1 for
When a positive determination is made in the first process, a fourth process is performed, then a second process is performed, and when a positive determination is made in the second process, a third process is performed, and then the process proceeds to step 227. Step 227 when a negative determination is made in the first processing or the second processing
You may be made to go to. By doing so, the amount of calculation increases, but the correction is performed more accurately, and the effect of reducing the variable delay is improved.

Further, since the current and the potential have a predetermined relationship, the components of the state variable vector V are not limited to the potential, and all or a part of the components of the state variable vector V may be a current. However, this current is a current flowing through the circuit element, and is not a node current which is originally zero. Evaluation vector U
Is not limited to a vector having a node current as a component, and may be any as long as it can determine the convergence of the solution of the state variable vector V at time t, and has a predetermined relationship with the state variable vector V and is essentially a constant vector. Anything should do.

Further, VB (i) in step 23 of FIG.
And UB (i) of steps 225 and 226 of FIG.
It may be at the time point slightly before the time point t, for example, at the time point (t−2Δt).

[Brief description of the drawings]

FIG. 1 is a flowchart illustrating a transient analysis method according to a first embodiment of the present invention.

FIG. 2 is a flowchart showing details of step 22 in FIG. 1;

FIG. 3 is a block diagram illustrating a schematic configuration of a transient analysis device according to the first embodiment of the present invention.

FIG. 4 is a diagram illustrating the conversion of a state variable into a constant;

FIG. 5 is a diagram showing changes in potential and current at a node i, and conversion of state variables into constants and variables.

FIG. 6 is a diagram showing that the conversion of a constant state variable into a variable is performed more appropriately than before.

FIG. 7 is a diagram showing steps inserted in the flow of FIG. 1 in the transient analysis method according to the second embodiment of the present invention.

FIG. 8 is a circuit diagram showing a simple example of an analysis target.

[Explanation of symbols]

 Reference Signs List 10 computer 12 circuit configuration data file 13 analysis condition file 14 state variable waveform file

Claims (7)

[Claims] 1. A state variable vector V of a circuit at a time point t is calculated by a successive approximation method. In the successive approximation method, a component corresponding to each component of the state variable vector V is included. And a state variable vector calculating step of determining the state variable vector V by repeatedly performing the processing until it is determined that the evaluation vector U, which should be a constant vector, converges on the constant vector, When the component of the state variable vector V does not deviate from the value before the time Δt by the first set value εv or more, a constant that converts the component of the state variable vector V into a constant and excludes the component from the component of the state variable vector V When the component of the evaluation vector U at the time point t corresponding to the converted component is shifted from the value before the time Δt by more than the second set value εu, A variable return step of returning the obtained component to the component of the state variable vector V, for each time point t, wherein the time point t is sequentially increased from an initial value. A third component in which the component of the evaluation vector U is equal to or less than the second set value εu from the value before the time Δt.
When the value exceeds the set value εw, the value of the component of the state variable vector V corresponding to the component of the evaluation vector U is changed according to the change of the component of the evaluation vector U from the value before the time Δt. A transient analysis method, comprising: a correcting step of correcting. 2. The third set value εw of the correction step
The transient analysis method according to claim 1, wherein is equal to the second set value εv. 3. When the value of the component of the state variable vector V is corrected in the correcting step, the correcting step is executed again using the corrected state variable vector V. Transient analysis method described. 4. The transient analysis method according to claim 1, wherein the state variable vector V corrected in the correcting step is used as a solution of the state variable vector. 5. The components of the state variable vector V are all node potentials, the components of the evaluation vector U are all node currents, and in the correction step, the i-th component V (i) of the state variable vector V is , V (i) = V (i)-(U (i) -UB
(I)) / Gii, where U (i) is the time t
Is the i-th component of the evaluation vector U corresponding to V (i), and UB (i) is the i-th component of the evaluation vector at time (t−Δt) corresponding to V (i). Gii is the i-th row and the i-th column component of the Jacobi function matrix of the vector F (V) in the vector U = F (V), The Gii is described in any one of Claims 1-4. Transient analysis method. 6. A transient analysis apparatus comprising a computer that executes the transient analysis method according to claim 1. Description: 7. A storage medium storing a program for executing the transient analysis method according to any one of claims 1 to 5 on a computer.