JPH09293092A - Modeling method and simulation method for electronic circuit - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide the modeling method for the electronic circuit which can find the delay time of the electronic circuit fast with high precision. SOLUTION: In a step S10, analog simulation is performed to find the relations (data point) of a delay time Yi to n kinds of parameter Xi and in a step S11, a start data point and an end point are regarded as data points of a model for the delay time; and the gradient ai between adjacent data points is found in a step S12, the absolute value difference bi of the adjacent gradient ai is found in a step S13. In a step S14, the m larger absolute value differences bi of the gradients ai are selected in a step S14 to obtain data points of the model for the delay time and in a step S15, the respective data points are interpolated linearly to form a model f1 (xi ).

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a modeling method for modeling a delay time of an electronic circuit and a simulation method for simulating the electronic circuit.

[0002]

2. Description of the Related Art Conventionally, simulation of an electronic circuit using an information processing device such as a workstation has been used for the purpose of assisting and optimizing the design of the electronic circuit. In such simulation, electronic circuits are modeled, and characteristics such as transient response to an input signal are analyzed for these models. In such analysis, it is necessary to model the delay time of the electronic circuit. The delay time of such electronic circuits is modeled as a function of output load (capacitance) or input transition time. In reality, it is difficult to accurately model the delay time of an electronic circuit, and the amount of calculation during simulation increases, so in an actual simulation,
As shown in FIG. 2, the delay time is approximated by a linear line (linear approximation), or as shown in FIG. 3, the delay time is linearly interpolated (for each predetermined section of the output load (capacity) or the input transition time range). Simulation is performed based on the delay time obtained by non-linear approximation).

In the linear approximation, the data points indicated by black dots in FIG. 2 are approximated by a linear line indicated by a straight line in FIG. 2 and the delay time is obtained as a linear function of the output load (capacitance) or the input transition time. ing. In addition, in the nonlinear approximation as described above, FIG.
Several data points as shown in the figure are obtained, and the delay time is obtained by approximation by linear interpolation between these data points.

[0004]

However, in the above-mentioned linear approximation by the linear line, the error of the delay time obtained in the area where the actual data point is apart from the linear line becomes large. Also in the non-linear approximation, in the region where the change in the slope of the characteristic curve of the delay time is large as compared with the interval of the data points, an error as shown by the diagonal line in FIG. 3 occurs. In the nonlinear approximation, the error can be reduced by reducing the interval between the data points, but when the number of data points is increased, the delay time table becomes larger,
Since the amount of calculation at the time of designing and simulating an electronic circuit increases, the execution time for performing these processes increases.

The present invention has been made in view of the above problems, and an object of the present invention is to provide an electronic circuit modeling method capable of obtaining the delay time of an electronic circuit with high accuracy.

Another object of the present invention is to provide an electronic circuit simulation method capable of performing an electronic circuit simulation with high accuracy.

[0007]

In the method of modeling an electronic circuit according to the present invention, when modeling the delay time of the electronic circuit, first, for example, the output load (capacitance), the input transition time, etc. of the electronic circuit The parameters are changed in n (n: arbitrary) ways, the delay time of the electronic circuit with respect to each parameter is obtained, and the data point having coordinates of each parameter and the delay time corresponding to the parameter is obtained.

Next, using the increment of the delay time with respect to the increment of the parameter between the data points as the slope between the data points, an index representing the change in the slope at each data point is obtained, and the upper m (m <n) of the index is obtained. ) Points are selected, data points corresponding to the index of m points are selected, and linear interpolation is performed between the selected data points to model the delay time of the electronic circuit.

Alternatively, the increment of the delay time with respect to the increment of the parameter between the data points is defined as the slope between the data points,
Data corresponding to the index obtained for each section is obtained by dividing the obtained index into m (m <n) sections, and obtaining the index indicating the change in the slope at each data point. The points are selected and the delay time of the electronic circuit is modeled by linearly interpolating between the selected data points.

The absolute value of the slope difference between each data point and two data points adjacent to this data point may be used as an index, or each data point and its adjacent data point. The absolute value of the difference between the slope of a quadratic curve passing through two data points at this data point and the slope of a similar quadratic curve for data points adjacent to this data point, or each data point It is also possible to use the absolute value of the quadratic differential value at this data point of a quadratic curve that passes through two data points adjacent to the data point.

Further, in the electronic circuit simulation method according to the present invention, the simulation is performed based on the delay time of the electronic circuit modeled by the electronic circuit delay time modeling method according to the present invention.

[0012]

BEST MODE FOR CARRYING OUT THE INVENTION The method for modeling an electronic circuit according to the present invention can be used when a transient response or a frequency response of an electronic circuit is analyzed by a workstation or the like.

As shown in FIG. 1, the simulation apparatus according to the first embodiment of the present invention performs an input unit 1 for inputting an instruction or the like from a user and an operation or the like regarding the operation of an electronic circuit or the like. An arithmetic processing unit 2, a memory 3 in which data, arithmetic programs, etc. are stored by the arithmetic processing unit 2, and a disk device 4 for storing data, arithmetic programs, etc.
Delay time modeling unit 5 for modeling delay time of electronic circuit
And an output unit 6 for outputting simulation results and the like.
And

The simulation apparatus having such a structure operates according to the flowchart shown in FIG. In step S1, the arithmetic processing unit 2 refers to, for example, a database of electronic components registered in the disk device 4 or the like on the basis of a user's instruction or the like supplied from the input unit 1, and a component of an electronic circuit, Input data indicating the input / output terminals, the power supply and their connection. In step S2, the arithmetic processing unit 2 obtains the transfer function (gain) of each component forming the electronic circuit based on the data input in step S1. In step S3,
The arithmetic processing unit 2 models the delay time of the electronic circuit. Then, in step S4, the arithmetic processing unit 2
The characteristics such as the transient response and frequency response of the electronic circuit are analyzed based on the transfer function obtained in step S2, the delay time model obtained in step S3, and the like, and the analysis result is output via the output unit 6.

The modeling of the delay time of the electronic circuit in step S3 of FIG. 4 described above is performed according to the flowchart shown in FIG. First, the arithmetic processing unit 2 performs step S
At 10, analog simulation is performed based on the transfer function of each component obtained in step S2 of FIG.

Generally, the delay time of the electronic circuit is modeled as a function of the output load (capacitance) or the input transition time. Therefore, in this step S10, these parameters (for example, the output load) X _i are first n times different. Then, the change in the delay time Y _i corresponding to this change is measured. As a result, the delay time Y _i increases as the parameter X _i increases.
For example, it changes as shown in FIG. Below, parameter X
_{A set} (X _i , Y _i ) of _i and the delay time Y _i corresponding to this parameter X _i is called a data point.

[0017] In step S11, of these data points, both ends of the data points variance range of the parameter X _i (X _1,
Y ₁ ), (X _n , Y _n ) is a delay time model f1 (X _i ).
Data points P1 and Pn (P6 in the case shown in FIG. 6) of the above, and in the subsequent step S12, the slope a _i between adjacent data points is obtained according to the following equation. a _i = (Y _{i + 1} −Y _i ) / (X _{i + 1} −X _i ) (i = 1, 2, ..., N−2, n−1) (Equation 1)

Then, in step S13, the absolute value difference b _i between the adjacent slopes a _i is calculated according to the following equation. b _i = | a _i −a _i−1 | (i = 2, ..., N−2, n−1) (Equation 2)

By the processing of these steps S12 and S13, as shown in FIG. 7, the inclination a _i and the absolute value difference b _i are obtained for each data point. In determining the slope a _i corresponding to the data points (i) in this way, if the calculated slope a _i based on the data points (i) and the next data point (i + 1), the inclination and a _i data The slope is at an intermediate point between the point (i) and the next data point (i + 1). However, when obtaining the absolute value difference b _i corresponding to the data point (i), the absolute value is calculated based on the slope a _i at the data point (i) and the slope a _i-1 at the previous data point (i-1). Difference b
By finding _i , the absolute value difference b _i at data point (i) can be found.

When the absolute value difference b _i between the adjacent slopes a _i is calculated, the calculated slope a _{i is} calculated in step S14.
From the maximum value of the absolute value difference b _i of m, for example, in the case shown in FIG. 6, four data points (X _i , Y _i ) corresponding to A1, A2, A3, and A4 are selected and a delay time model is selected. f1
Let it be the data point of (X _i ). Here, for example, the parameter X _{i in} FIG. 7 indicating the value corresponding to each point in FIG. 6 is 2.4.
And 4.2, the absolute value difference b _i (X _i ) has the same value, and the corresponding data point is the model f1 (X _i ).
If it is the m-th data point of
Select the data point with the smaller _i .

Further, in step S15, a total of m
Delay time model f by linearly interpolating between +2 data points
1 (X _i ). As a result, the model f1 (X _i ) of the delay time shown by the solid line in FIG. 6 is obtained. The error of the model f1 (X _i ) thus obtained is much smaller than that of the model obtained by linear approximation as shown in FIG. 2, for example.

Further, the model f1 obtained in this way
(X _i) is the point absolute value difference b _i of slope a _i is large, that is, starting from a large change data points the slope a _i, since the selected as the data points of the model, for example, the data points shown in FIG. 3 With the same number of data points as when is set at equal intervals, a model with a significantly smaller error can be created.

Therefore, by using such a model, the error can be significantly reduced without increasing the number of data points, so that the design and simulation of the electronic circuit can be performed at high speed and with high accuracy. .

In the first embodiment described above, the error can be greatly reduced as compared with the linear approximation and the non-linear approximation shown in FIGS. 2 and 3, but step S1 in FIG.
In 2, the slope a _i is obtained from the difference between two adjacent data points and the data point on one side, so the slope a _i will include some error.

Therefore, in the second embodiment, in step S3 of the flow chart shown in FIG. 4, the data point (i) and two data points (i-1) on both sides of the data point (i),
A quadratic curve passing through three points (i + 1) is obtained, and the quadratic curve is differentiated to obtain the slope a _i .

That is, in the second embodiment, as shown in FIG.
The delay time of the electronic circuit is modeled according to the flow chart shown in FIG. First, the arithmetic processing unit 2
In step S21, the above-mentioned step S in FIG.
Similar to 10 to S11, analog simulation is performed to obtain n data points (X _i , Y _i ), and the data points of the start point and the end point are set as the data points of the model f2 (X _i ).

Next, in step S22, three consecutive points (X _i-1 , Y _{i -1} ) in these data (X _i ,
Y _i ), (X _{i + 1} , Y _{i + 1} ) quadratic curve g _i (X _i )
Is calculated, and in the subsequent step S23, this quadratic curve g
(X _i) by differentiating the data points (X _i, Y _i) determining the slope _{a i (= g i '(} X i)) in the. g _i (X _i ) =
If aX _i ² + bX _i + c (a, b, c: constant), the slope a _i becomes 2aX _i + b. Here, since it is not possible to obtain the above-mentioned quadratic curve g _i (X _i ) at the data points (1) and (n) at both ends, the data points (2) and (n−1) next to these quadratic curves g _i (X _i ) cannot be obtained. Quadratic curve g ₂ (X _i ), g
_{Using n-1} (X _i ), the data points (1) of these curves,
Let the slopes g ₂ '(X ₁ ) and g _n-1 ' (X _n ) in ( _n ) be the slopes a _{i at} the data points at both ends.

Alternatively, step S22 and step S
In 23, the slope a _i at the data point (X _i , Y _i ) may be obtained by the following equation. a _i = (Y _{i + 1} −Y _i−1 ) / (X _{i + 1} −X _i−1 ) (i = 2, ..., n−2, n−1) (Equation 3)

When the inclination a _i at each data point (X _i , Y _i ) is obtained in this way, in steps S24 to S26, step S of the flowchart shown in FIG.
Similar to 13 to S15, the absolute value difference b between the adjacent slopes a _i
i (Δg _i '(X _i ) is calculated, and the upper m number from the maximum value of the absolute value difference b _i of the calculated slope a _i , for example, FIGS.
In the case shown in (4), the data points (X _i , Y _i ) corresponding to the four B1, B2, B3, B4 are selected and used as the data points of the delay time model f2 (X _i ) and further, step S26
In, a total of m + 2 data points are linearly interpolated to obtain a delay time model f2 (X _i ). As a result, FIG.
The model f2 (X _i ) of the delay time indicated by the solid line in 0 is obtained. The model f2 (X _i ) shown in FIG. 10 has the model f1 shown in FIG. 6 in the region where X _i is 3 or more.
The error is smaller than (X _i ).

According to the second embodiment, it is possible to model a delay time having a smaller error with limited data points. This model requires more labor to create than the first embodiment, but higher accuracy can be expected. Therefore, by using a model based on such a modeling method, designing and simulation of an electronic circuit can be performed at high speed, and these designing and simulation can be performed with higher accuracy.

In the first and second embodiments described above, FIG.
Step S13 in, in step S24 of FIG. 8, for seeking the absolute value difference b _i by the difference of two adjacent slope a _i (a change in the slope a _i), contains a slight error in the absolute value difference b _i Get lost.

Therefore, in the third embodiment, in step S3 of the flow chart shown in FIG. 4, the second-order differential value of the quadratic curve passing through each data point and two data points on both sides of the data point is obtained, A delay time model f3 (X _i ) is obtained based on the second derivative.

That is, in the third embodiment, as shown in FIG.
According to the flowchart shown in FIG. 1, the delay time of the electronic circuit is modeled. First, in step S31, the arithmetic processing unit 2 performs an analog simulation to perform n data points (X _i , X _i , similar to step S10 to S11 of FIG. 5 and step S21 of FIG. 8 described above).
Y _i ) is obtained, and the data points at the start point and the end point are set to the model f3 (X
_i ) Data points.

Next, in step S32, as shown in FIG.
As in step S22 of, the three consecutive points (X
_A quadratic curve h _i (X _i ) passing through _i−1 , Y _i−1 ), (X _i , Y _i ) and (X _{i + 1} , Y _{i + 1} ) is obtained. Next, step S33
, The quadratic curve h _i (X _i ) is second-order differentiated to change the slope h _i ″ (X _i ) of the slope at the data point (X _i , Y _i ).
Ask for. _{h i (X i) = aX} i 2 + bX i + c (a, b,
c: constant), the rate of change of slope h _i ″ (X _i ) is 2a
(Coefficient of quadratic term).

Alternatively, step S32 and step S
In 33, the slope change rate H ″ (X _i ) may be directly obtained from the data point (X _i , Y _i ) by the following equation: h _i ″ (X _i ) = (Y _{i + 1} + Y _{i − 1−2} × X _i ) / (X _i −X _i−1 ) ² (i = 2, ..., n−2, n−1) (Equation 4)

From the maximum value of the change rate h _i ″ (X _i ) of the slope corresponding to each data point, the top m, for example, FIG.
And in the case shown in FIG. 13, four C1, C2, C3, C
The data points (X _i , Y _i ) corresponding to 4 are selected as the data points of the delay time model f3 (X _i ), and further, in step S36, a total of m + 2 data points are linearly interpolated to obtain the delay time. Model f3 (X _i ). Here, for example, the parameters X _{i in} FIG.
As in the case of 2, the values of the rate of change of slope h _i ″ (X _i ) are the same, and the corresponding data points are m of the model f3 (X _i ).
In the case of the second data point, for example, the data point having the larger parameter X _i is selected.

As a result, the delay time model f3 (X _i ) shown by the solid line in FIG. 13 is obtained. The model f3 (X _i ) shown in FIG. 13 is further reduced in error than the model f2 (X _i ) shown in FIG. 10 according to the second embodiment.

According to the third embodiment, a delay time with a smaller error can be modeled with limited data points. Further, since the quadratic differential value of the quadratic curve is a coefficient of the quadratic term as described above, it becomes known when the quadratic curve is obtained. For example, in the above-described second embodiment, the quadratic curve 1 This can be obtained more easily than the case where the absolute value difference between adjacent primary differential values is obtained after obtaining the secondary differential value. Therefore, according to the third embodiment, it is possible to more easily perform modeling with further improved accuracy. By using such a model, design and simulation of an electronic circuit can be performed at high speed and with high accuracy.

Incidentally, the electronic circuit models f1 (X _i ), f2 (X _i ), f according to the first to third embodiments described above.
In the case of obtaining 3 (X _i ), a region where the change in inclination is large (for example, in FIGS. 7, 10 and 13, a region where X _i is 5 or less).
Although the accuracy of the model is improved overall by preferentially setting the data points of the above as the data points of the model, if the interval of the data points is biased and the accuracy of the area with a small inclination becomes insufficient. There is also. When only a model of such an area having a small inclination is required, it is desired to improve the accuracy of this area.

Therefore, in the fourth embodiment, in step S3 of the flowchart shown in FIG. 4, the data points other than the start point and the end point are divided into m groups for each predetermined section of the parameter X _i , and each group is divided into m groups. Within the above mentioned first
In the model f, the data point having the maximum absolute value difference b _i obtained in the same manner as the example is used as the data point of the section corresponding to the group.
4 (X _i ).

That is, in the fourth embodiment, as shown in FIG.
The delay time of the electronic circuit is modeled according to the flowchart shown in FIG. First, in step S41 to S43, the arithmetic processing unit 2 performs an analog simulation to obtain n data points (X _i , Y _i ) in the same manner as in step S10 to step S14 in FIG. the data points of the end point as data points of the model f4 (X _i), determine the slope a _i between adjacent data points, further, the absolute value difference b _i between adjacent slope a _i.

Next, in step S44, the data points other than the start point and the end point are divided into four groups each having four data points, as shown in FIG. And
The largest absolute value difference b _i among the data points in each group is determined, and the data point corresponding to the determined absolute value difference b _i is determined.

Then, in step S45, step S
A linear interpolation is performed between the data points obtained in 44 to obtain a delay time model f4 (X _i ). As a result, the delay time model f4 (X _i ) shown by the solid line in FIG. 16 is obtained.

In the fourth embodiment, the parameter X _i
Since the maximum value of the absolute value difference b _i is calculated for each predetermined section of and the data point corresponding to this data is used as the data point of the model f4 (X _i ), there is a delay at the data point without bias in the section of the parameter X _i. Time modeling can be done.

For example, in the case where an area having a large change in inclination between data points is concentrated in a specific section, and there is an area having a slight change in inclination other than this area, the first to third embodiments described above are performed. In some cases, it may not be possible to detect a slight change in the tilt in such a region in the form, but this fourth
In the above embodiment, it is possible to detect such a slight change in the inclination.

Therefore, by using such a model, the design and simulation of the electronic circuit can be performed at high speed and with high accuracy.

The present invention is not limited to each of the above-described embodiments. For example, the absolute value difference b _i of the slope a _i of each data point is the same as in the above-mentioned second or third embodiment.
Look, these absolute difference b _i divided to a fourth embodiment and m groups similar, the absolute value difference b _i in each group
The model may be obtained by using the data point having the maximum value as the data point in the section corresponding to the group.

In addition, as in each of the above-described embodiments, the model of the delay time is obtained, and the error between the obtained model and the actually measured delay time is obtained as, for example, the average value of the errors at the respective data points. It is possible to make appropriate changes such as a configuration in which the model with the minimum is finally used.

[0049]

In the method of modeling an electronic circuit according to the present invention, the parameters of the electronic circuit are changed in n (n: arbitrary) ways, the delay time of the electronic circuit for each parameter is calculated, and The data point whose coordinates are the set of delay times corresponding to the parameters is obtained, and the increment of the delay time with respect to the increment of the parameter between each data point is defined as the slope between the data points, and the index indicating the change in the slope at each data point is set. By obtaining the upper m (m <n) points of the index, selecting the data point corresponding to the index of the m point, and linearly interpolating between the selected data points to model the delay time of the electronic circuit. Based on the index, the data point at the position where the inclination changes greatly can be preferentially used for modeling.

Therefore, the accuracy of the model of the delay time of the electronic circuit can be improved without increasing the number of data points. By using such a model of the delay time, the design and simulation of the electronic circuit can be performed at high speed and with high accuracy. Can be done with precision.

Also, the increment of the delay time with respect to the increment of the parameter between each data point is used as the slope between each data point, the index representing the change in the slope at each data point is obtained, and the obtained index is m (m <n). Divide into sections, find the upper point of the index in each section, select the data point corresponding to the index found in each section, and linearly interpolate between the selected data points to model the delay time of the electronic circuit By doing so, it is possible to prevent the positions of the selected data points from being biased and improve the accuracy of the delay time model.

Further, in the electronic circuit simulation method according to the present invention, the simulation can be performed based on the delay time of the electronic circuit modeled by the method for modeling the delay time of the electronic circuit according to the present invention. It is possible to shorten the time required for and to improve the accuracy.

[Brief description of drawings]

FIG. 1 is a block diagram showing a configuration of a simulation apparatus according to a first embodiment of the present invention.

FIG. 2 is a diagram showing an example of a delay time model of an electronic circuit obtained by a conventional linear approximation method.

FIG. 3 is a diagram showing an example of a delay time model of an electronic circuit obtained by a conventional nonlinear approximation method.

FIG. 4 is a flowchart showing a procedure of simulation by the simulation device.

FIG. 5 is a flowchart showing a modeling procedure of an electronic circuit in the simulation procedure.

FIG. 6 is a diagram showing an example of a model of a delay time of the electronic circuit obtained by the procedure for modeling the electronic circuit.

FIG. 7 is a diagram showing an example of calculation results obtained in each step of the modeling procedure.

FIG. 8 is a flowchart showing a modeling procedure of an electronic circuit according to the second embodiment of the present invention.

FIG. 9 is a diagram showing an example of calculation results obtained in each step of the modeling procedure.

FIG. 10 is a diagram showing an example of a model of a delay time of an electronic circuit obtained by the procedure for modeling the electronic circuit.

FIG. 11 is a flowchart showing a process of a main part of a modeling procedure of an electronic circuit according to a third embodiment of the present invention.

FIG. 12 is a diagram showing an example of calculation results obtained in each step of the modeling procedure.

FIG. 13 is a diagram showing an example of a model of a delay time of an electronic circuit obtained by the procedure for modeling the electronic circuit.

FIG. 14 is a flowchart showing a process of a main part of a modeling procedure of an electronic circuit according to a fourth embodiment of the present invention.

FIG. 15 is a diagram showing an example of a calculation result obtained in each step of the modeling procedure.

FIG. 16 is a diagram showing an example of a model of a delay time of an electronic circuit obtained by the procedure for modeling the electronic circuit.

[Explanation of symbols]

X _i parameter, Y _i delay time, f1 (X _i ) to f
4 (X _i ) model

Claims (6)

[Claims] 1. A method for modeling a delay time of an electronic circuit, wherein the parameters of the electronic circuit are changed in n (n: arbitrary) ways, the delay time of the electronic circuit for each parameter is obtained, and , A data point having coordinates of a set of delay times corresponding to the parameter is obtained, and an increment of the delay time with respect to an increment of the parameter between the data points is defined as a slope between the data points, and a change in the above slope at each data point is calculated. The index to be expressed is calculated, the m (m <n) points above the index are calculated, the data point corresponding to the index of the m point is selected, and the delay time of the electronic circuit is linearly interpolated between the selected data points. A method of modeling an electronic circuit, characterized by: 2. A method for modeling a delay time of an electronic circuit, wherein the parameters of the electronic circuit are changed in n (n: arbitrary) ways, and the delay time of the electronic circuit for each parameter is obtained, , A data point having a set of delay times corresponding to the parameter as coordinates, and an increment of the delay time with respect to an increment of the parameter between the data points is defined as a slope between the data points, and a change in the slope at each data point is represented. The index is calculated, the calculated index is divided into m (m <n) sections, the upper points of the index in each section are calculated, and the data point corresponding to the calculated index is selected for each section, and the selected data is selected. A method of modeling an electronic circuit, characterized by linearly interpolating between points to model a delay time of the electronic circuit. 3. The absolute value of the slope difference between each data point and two data points adjacent to the data point is used as the index.
The method for modeling an electronic circuit according to any one of 1. 4. As the index, the slope at each data point of a quadratic curve passing through each data point and two data points adjacent to the data point, and the data points adjacent to each data point The method of modeling an electronic circuit according to claim 1 or 2, wherein the same absolute value of the difference in slope of the quadratic curve is used. 5. The absolute value of a secondary differential value at each data point of a quadratic curve passing through each data point and two data points adjacent to the data point is used as the index. The method of modeling an electronic circuit according to claim 1, wherein 6. The above-mentioned claim 1 or claim 2 or claim 3.
Alternatively, a simulation method for an electronic circuit, characterized in that a simulation is performed based on the delay time of the electronic circuit modeled by the method for modeling the delay time of the electronic circuit according to claim 4 or 5. .