JP2605188B2 - Circuit constant automatic design system and circuit constant optimization method - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a circuit constant automatic design system for automatically determining constants of circuit components of an arbitrary circuit in a state in which the circuit topology is fixed, and a method of optimizing a constant value. Things.

[0002]

2. Description of the Related Art In general, analog electronic circuits have a wide variety of evaluation items for defining their characteristic specifications, such as AC (alternating current), DC (direct current), and transient characteristics. Therefore, it is necessary to consider these characteristics when determining circuit constant values such as a resistance value and a capacitance value.

However, in the current manual-centered analog circuit design, considerable skill is required to optimally determine each circuit constant value in consideration of the total characteristics of AC, DC, and transient. It takes a lot of time to determine the circuit constant value . There are problems such as. Therefore, in order to solve these problems, a system for automatically designing an optimal circuit constant value for a required specification (hereinafter, abbreviated as a circuit constant optimization system) has been desired. For example, "1988
IEICE technical report CAS88-69 “A Tr
-Amplifier Design Utilizing a Circuit Simulator
There is a system indicated by "". Hereinafter, this system will be described with reference to the drawings.

FIG. 8 is a diagram showing the above-mentioned conventional circuit constant optimizing system. This conventional system 1 includes a circuit simulator 2 for analyzing circuit characteristics such as AC, DC, and transient characteristics, and a specification required by a designer. A design program 3 for determining an initial value of a circuit constant upon receiving the signal, and evaluating whether the characteristics analyzed by the circuit simulator 2 satisfy the required specifications ;
And a rule base 4 in which a relationship between circuit characteristics and each circuit constant is described.

Next, the operation will be described with reference to the flowchart of FIG. First, in step s5, the designer provides the design program 3 shown in FIG. 8 with the required specification values such as the operating point of the transistor, the power supply voltage, and the characteristics such as AC, DC, and transient characteristics of the circuit to be optimized. a specification value f _a, the maximum and minimum allowable value f _max of the characteristic specifications, and f _min, a weight coefficient W for distinguishing the importance of each characteristic specification, the request satisfaction S _r of the characteristic specifications Enter Here, the numeric value of the request satisfaction S _r is 0-1 for each characteristic specification, the degree to which must satisfy the characteristics specification inputs a value close to higher 1. In addition, inputs a request satisfaction S _t of the overall characteristics.

Next, in step s6, the above-mentioned step s
The design program 3 calculates the initial values of the circuit constants based on the required specification values input in step 5. When the initial values are calculated, the design program 3 executes a circuit simulation.
In addition to starting the circuit 2, the connection information of the circuit necessary for the circuit simulation is transferred to the circuit simulator 2. Next, at step s7, shea obtaining circuit simulator 2 is AC of the circuit constants optimized circuit, DC, transient characteristics
Perform the simulation .

Next, the flow after step s8 will be described. For simplification of the description, first, the case where there is one input characteristic item will be described. In step s8, the design program 3 determines whether or not each characteristic obtained in step s7 satisfies the specification by determining whether the relationship between the characteristic value f and the degree of satisfaction S is a curve shown in FIG. Evaluation is made using a function S (f) expressed by a curve. This function S
The value of (f) is in the range of 0 to 1 for any characteristic value f, a 1 to become functions when the characteristic value f matches the characteristic specification value f _a.

[0008] This function is the maximum allowable value f of the characteristic specification value.
It is expressed by, for example, the following equation using _max and the minimum allowable value f _min . When f _a ≧ f when S (f) = exp {-K (f a -f) 2 / (f a -f min) 2} ·· (1) f a ≦ f S (f) = exp { −K (f _a −f) ² / (f _max −f _a ) ² } (2) where K is a constant in equations (1) and (2), and
(2) the value of S (f) obtained by the equation when f = f _a S
(F) = 1, and when f → + ∞, S (f) → 0, f →
When −∞, S (f) → 0.

Next, in step s9, the design program 3 calculates the value of S (f) obtained in step s8,
It is determined whether the following expression is satisfied. S (f) ≧ S _r (3) S _r : Demand Satisfaction If Expression (3) is true, the process proceeds to step s11,
The circuit constant value at the time of performing the simulation in step s7 is output as the optimum constant value. On the other hand, if the expression (3) is false, the process proceeds to step s10, and the rule base 4
Change the circuit constant value in accordance with the rules, again, circuit simulation
Ration .

Here, the contents of the rule base 4 are described in advance by a human based on circuit design rules. For example, when designing each constant value of the self-bias amplifier circuit shown in FIG. 11 so as to satisfy three characteristic specifications of the circuit gain G _a , the lower cut-off frequency f _CLa , and the higher cut-off frequency F _CHa. think of. The transistors Q ₁ for simplicity of explanation here is treated as an ideal transistor.

In the case of the circuit shown in FIG. 11, the circuit gain G changes mainly with the values of R _C and R _E. That is, increasing the value of R _C (or value small R _E) circuit gain when increases (increase the value of or R _E) the value of R _C small negative circuit when the gain is reduced. Further, the low-frequency cutoff frequency f _CL mainly changes according to C ₁ , R ₁ , and R _{2. If} the value of C ₁ is increased (or the values of R ₁ and R ₂ are increased), the low-frequency cutoff frequency f _CL is reduced. The frequency f _CL decreases, and conversely, if the frequency f _CL decreases, the lower cut-off frequency f _CL increases. The high-frequency cutoff frequency f _CH is mainly determined by R _C and C _C
The higher the value of C _C (or the larger the value of R _C ), the lower the high-frequency cutoff frequency f _CH becomes, and conversely, the lower the value, the higher the high-frequency cut-off frequency f _CH becomes.

That is, the structure of the rule base 4 is described, for example, as a table shown in FIG. 12 in accordance with the above-described circuit design knowledge. In FIG. 12, G, f _CL , and f _CH are characteristic values of the circuit gain, the lower cut-off frequency, and the higher cut-off frequency obtained in step s7 in FIG. 9, respectively. As described above, the loop of steps s7 → s8 → s10 → s7 is repeated until expression (3) becomes true in step s9. Next, a method of changing the circuit constant value in the course of this repetition will be described in detail.

Now, assume that the requirement satisfaction degree input in step s5 is S _r and the initial value of the element to be optimized is a
(1). Here, the initial value a (1) is calculated in step s6. Further, the characteristic value at the time of the initial value a (1) is defined as f (1), and the satisfaction S (f ₁ ) calculated by the equations (1) and (2) using the characteristic value f ( ₁ ) is It is assumed that it is located at the point A of the satisfaction curve shown in FIG. This point A does not meet the requirements satisfaction S _r, constant value a (1) changes to re circuit in step s7
You need to simulate . Therefore, based on the knowledge that the characteristic value f (1) at the point A is smaller than the characteristic specification value fa, the rule base 4 determines whether to increase or decrease the constant value a (1). For example, if the rule base 4 requests that the constant value a (1) be increased, the next constant value a (2) will be a predetermined amount d ₁ from a (1).
Is determined by the following equation. a (2) = a (1) + d ₁ (4)

Next, the characteristic value at the time of the constant value a (2) is represented by f
Suppose that the satisfaction level S (f ₂ ) calculated by the equations (1) and (2) using this characteristic value is located at the point B of the satisfaction degree curve shown in FIG. This point B does not meet similarly request satisfaction S _r and a point A, the constant value a
(2) is changed and the circuit simulation is performed again in step s7.
Action . Therefore, the next constant value a (3) the previous as well as the value was increased by a predetermined amount d ₁ from a (2), that is determined by the following equation. a (3) = a (2) + d ₁ (5) The above operation is the satisfaction degree S at the i-th constant value a (i).
(F _i ) is greater than the required satisfaction S _r , or the i-th satisfaction S (f _i ) is the i−1-th satisfaction S (f
_i-1 ) .

Here, when the i-th satisfaction S (f _i ) is greater than the required satisfaction S _r , the constant value a (i) at this time is output as the optimum constant value as described above. , I-th satisfaction S (f _i ) is i−1-th satisfaction S
When it is smaller than (fi _-1 ) , for example, as shown in FIG. 13, the characteristic value f (3) at the time of the constant value a (3) is used,
When the satisfaction degree S (f ₃ ) calculated by the equations (1) and (2) is located at the point C of the satisfaction curve, the amount of change of the constant value is made smaller than the previous d ₁ to reduce the constant value. Change as follows: That is, the next constant value a (4) is determined to be larger than the previous constant value a (2) by the predetermined amount d ₂ (<d ₁ ). a (4) = a (2) + d ₂ (6)

As a result, in the example of FIG.
It is assumed that the degree of satisfaction S (f 4) at the time of ( ₄ ) is located at the point D of the degree of satisfaction curve. This D point is the required satisfaction level S
_{Since r} is satisfied, the design program 3 outputs this constant value a (4) as the optimum constant value. Also, a constant value a
(4) When the satisfaction S (f ₄₎ is located at the D _a point 14 at the time of the use of a previous change amount d _2, to determine the next constant value a (5) by the following equation. a (5) = a (4) + d ₂ (7) In the above example, the amount of change in determining the i-th constant value a (i) is reduced from the initial amount of change d ₁ to d _2. ,
The operation is continued up to a predetermined minimum value d _min of the change amount until convergence is reached.

Next, the characteristic item specified in step s5
Will be described. First, step s5
Weight coefficient W of each characteristic specification specified by
As for the characteristic item, it is input in step s5 described above.
The same processing as in the case of one characteristic item is performed. Then the weight
The same processing is performed for the characteristic item whose coefficient W is the second largest.
U. Thus, in the order of the characteristic items in which the weight coefficient
Proceeding to satisfy equation (3), all characteristic items
Is satisfied with the expression (3), the value obtained by the following expression is
Required satisfaction degree S of the comprehensive characteristics input in step s5_t Yo
Is greater or smaller.S _tt = (S ₁ ・ W ₁ + S _Two ・ W _Two + ... + S _n ・ W _n ) / (W ₁ + W _Two + ... + W _n ) ・ ・ ・ ・ ・ (8) where W_i: Weighting factor S for characteristic item i_i: Satisfaction degree of characteristic item i

[0018] If, if an S _tt ≧ S _t, and outputs the last constant value used as the optimum constant value, the program ends. If a S _tt <S _t, is performed again, the characteristics item weight coefficient W has a maximum value, the same process as in one input properties item in step s5 described above, S
it is determined whether the _tt ≧ S _t. This operation continues until convergence.

[0019]

Since the conventional circuit constant optimizing system is configured as described above, it is necessary to find a direction for searching for a constant value in the optimizing process for each circuit to be optimized. There is a problem that a rule base indicating the relationship between the characteristic and the circuit constant must be separately constructed, and the quality of the optimized design is affected by the description contents of the rule base.

Further, the method of searching for a direction in which the value of the degree of satisfaction (degree of satisfying the target specification) increases is in accordance with a rule base provided for each circuit, and the width of change of the constant value is also predetermined. Was set according to the set value
If the initial value is far from the optimum value, it takes much time to reach the optimum value. In addition, since optimization is performed in the order of the characteristic having the largest weight coefficient, an optimal constant design is performed by trade-off between the characteristics in order to improve the overall characteristics (that is, sacrificing the other characteristic in order to improve one characteristic). Is not performed smoothly.

[0021] Moreover, while optimizing operation at the stage of clearing the request satisfaction has a mechanism to end, request satisfaction S _t of request satisfaction S _r and the overall characteristics of each of the above characteristics specification artificial variable Therefore, in the determination of the optimum value, if the characteristic specification value and the required satisfaction are set higher than the capability of the circuit, the optimization operation does not converge, so that the optimum constant is not output, and conversely, it is set low. In such a case, there has been a problem that each constant value converges before becoming a truly optimum constant.

The present invention has been made in order to solve the above problems, and enables optimization of circuit constants for an arbitrary circuit without requiring a rule base for each circuit.
An object of the present invention is to provide a circuit constant automatic design system and a circuit constant optimizing method for automatically designing a constant value that is truly optimal for input specifications at high speed, always considering comprehensive characteristics while making a trade-off between characteristics.

[0023]

According to a first aspect of the present invention, there is provided an automatic circuit constant design system, comprising: a circuit characteristic analyzing means for analyzing a DC characteristic, an AC characteristic, and a transient characteristic of a circuit; For an evaluation function defined using each value to indicate the degree of coincidence between the specification value and each characteristic value obtained from the circuit characteristic analysis means, an element to be determined as a circuit constant in the circuit in the circuit And sensitivity analysis means for analyzing the sensitivity of the evaluation function to a change in the constant value of at least one element, and values required for the analysis by the circuit characteristic analysis means and sensitivity analysis means are set and obtained by the analysis. Control means for searching for an optimal constant by changing the constant value based on the characteristic value and the sensitivity characteristic,
The upper SL sensitivity analyzing means, the change of the constant value for each element
The search direction to the optimal constant, and determine the constant for each element.
After optimization by value change, every two or three elements
Increase the number and perform sensitivity analysis to determine the search direction for the optimal constant.
Determined is intended to constant.

According to a second aspect of the present invention, there is provided an automatic circuit constant design system according to the first aspect of the present invention, wherein the control means of the system according to the first aspect provides a control means for the next constant value in proportion to the magnitude of the sensitivity obtained by the sensitivity analysis means. This is provided with a constant change amount determining means for determining the change amount.

According to a third aspect of the present invention, in the circuit constant optimizing system according to the second aspect, the constant change amount determining means changes the change amount in proportion to the sensitivity. The evaluation function value is checked based on the constant value, and if the evaluation function value is smaller than the previous value, the constant value whose change amount is changed in proportion to the sensitivity is set as the next constant value. If the value becomes larger than the previous value, the constant value based on the amount of change in the sensitivity analysis is used as the next constant value .

According to a fourth aspect of the present invention, there is provided a circuit constant optimizing method according to the first aspect of the present invention, wherein the sensitivity analysis means increases the constant value obtained by increasing the constant value by the finite difference method. If both the sensitivity and the reduced sensitivity obtained by reducing the constant value are analyzed, and the control means sets the evaluation function to satisfy the target specification as the function value increases, the sensitivity function is subject to sensitivity analysis. When both the increasing sensitivity and the decreasing sensitivity are all negative values in all combinations of the constant values, and conversely, if the function value is reduced, the target specification is set to be satisfied.
Similarly, when both the increase sensitivity and the decrease sensitivity are all positive values in the combination of all the constant values to be subjected to the sensitivity analysis, the last constant value used in the sensitivity analysis is determined to be the optimum value. It was done.

[0027]

The circuit constant automatic design system according to the present invention introduces an evaluation function that represents the optimality of all characteristics to be considered and the total characteristics of all the constraints required at the time of circuit constant optimization. When it is set that the degree of optimization is higher as the evaluation function becomes smaller, the minimum value, that is, the optimum value of the circuit constant is found by using the sensitivity analysis of a plurality of elements as well as the sensitivity analysis of each element. The method of determining whether the found constant value is the optimum value, that is, the method of determining whether it is the minimum value of the above evaluation function, is such that when the constant value is R for each circuit constant, the constant value is increased, that is, R + ΔR. The above evaluation function value and the constant value are reduced, that is, R-
Since both the evaluation function value when ΔR is larger than the evaluation function value when the constant value is R, the minimum value of this evaluation function, that is, the optimum value of the circuit constant is determined. Conversely, even when the optimality is set to be higher as the evaluation function becomes larger, the same processing is performed for the maximum value.

Further, since the evaluation function representing the degree of optimality in the present invention includes all the characteristics to be considered in the optimization and all the constraints required at that time, the minimum value (or the maximum value) of the evaluation function is obtained. That is, by finding the optimum value of the circuit constant, a trade-off is automatically made between each characteristic and the constraint condition, and the optimum value of the circuit constant can be obtained so as to improve the overall characteristics of the circuit.

Further, finding the minimum value (or maximum value) of the evaluation function using the sensitivity analysis in the present invention does not require knowledge of the circuit such as a rule base, and optimizes a constant for an arbitrary circuit. Is possible. At this time, conventionally, the sensitivity analysis has been performed for each element, but when optimizing the constant, it may be necessary to change the constants of a plurality of elements at the same time. For example, consider a first-order low-pass filter including a resistor R and a capacitor C. Since the cutoff frequency of the filter is determined by the product of R and C, it is necessary to reduce the capacitance so as not to deteriorate the characteristics of the filter, that is, to reduce the value of the capacitance without changing the cutoff frequency. At the same time, it is necessary to simultaneously change the constants of two elements such that the resistance value is increased. If this constant change is performed by repeating the change for each element twice, the characteristics change will be caused by the first change. Therefore, it cannot be determined that the change is a constant change necessary for optimization. Not done. Therefore, by optimizing circuit constants by sensitivity analysis using a plurality of elements, such as performing sensitivity analysis for each element and then sensitivity analysis for every two elements, knowledge of the circuit is not required and any circuit can be used. On the other hand, constant optimization is possible.

The method for finding the minimum value of the evaluation function according to the present invention does not require an artificial value (for example, satisfaction), automatically determines the minimum value, and always obtains the true circuit constant optimum value. To reach.

When changing the constant value, it is usually safest to use the change amount used in the sensitivity analysis, but this change amount is very small, so that the initial value is optimal. If it is far from the value, it takes time to reach convergence.
Thus, by determining the amount of change of the constant value in proportion to the magnitude of the sensitivity obtained by the sensitivity analysis by the constant change amount determining means (constant change amount determining program), the constant value greatly changes when the sensitivity is large. , The optimum value of the constant can be obtained at high speed.

[0032]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS One embodiment of the present invention will be described below with reference to the drawings. In FIG. 1, a circuit constant optimizing system 1 includes a circuit simulator 2 for analyzing characteristics of a circuit, and a one-element sensitivity analysis program 12 for selecting a circuit constant for each element and performing sensitivity analysis of an evaluation function for each element. A two-element sensitivity analysis program 13 for selecting two elements at a time and performing sensitivity analysis, a three-element sensitivity analysis program 14 for selecting three elements at a time and performing sensitivity analysis, and initializing circuit constants in response to specifications required by a designer. determining the value, the circuit stain
The state characteristic is based on the optimum constant value based on the state characteristic analyzed by the comparator 2 and the sensitivity characteristic analyzed by the one-element sensitivity analysis program 12, the two-element sensitivity analysis program 13, and the three-element sensitivity analysis program 14, respectively. It has a design program 3 for determining whether there is any. FIG. 2 is a block diagram showing another embodiment of the circuit constant optimizing system according to the present invention. In this embodiment, the amount of change in the constant value is determined by the system 1 based on the sensitivity obtained by the sensitivity analysis. It comprises a system 1A having a constant change amount determination program 10. Here, the circuit simulator 2, the sensitivity analysis programs 12 to 14 and the design program 3 in FIG. 1 correspond to the circuit characteristic analysis means, the sensitivity analysis means and the control means, respectively. The constant change amount determining program 10 in FIG. 2 corresponds to constant change amount determining means. In this embodiment, the program 10 and the design program 3 constitute control means.

Next, the operation of the system, that is, the method of optimizing the circuit constants will be described with reference to the flowchart of FIG.

First, in step S5, the designer requests the design program 3 for the required specification values such as the operating point of the transistor and the power supply voltage, and the DC and DC of the circuit to be optimized.
A target value f _ia of each characteristic f _i such as AC and transient characteristics and an allowable boundary value f _ib thereof are input. Next, at step S6, the initial value of the circuit constants, i.e., the initial state is set S ₁ of the circuit. Next, at step S15, and at the same time the initial state S ₁ is set, if the design program 3 passes the circuit connection information required for circuit simulation <br/> to the circuit simulator 2, to start the circuit simulator 2, circuit The value of each characteristic f _{i in} the state S ₁ (referred to as the state characteristic in S ₁ ) is obtained, and the characteristic value f _i is _calculated from the target value f _ia and the allowable boundary value f _ib as follows. The characteristic value bar f _i is made dimensionless by a normalization equation such as an equation (by making each property dimensionless, the degree of coincidence with the specification of each property can be evaluated on the same scale).

[0035]

(Equation 1)

Φ _i (bar f _i ) is introduced as an individual evaluation function indicating how much the characteristic value bar f _i satisfies the target specification. Here, the property of the property f _i , that is, I) a property that must match the target value (hereinafter, abbreviated as a match request). II) The smaller the target value, the better the characteristics
Abbreviated as reduction request). III) The higher the target value, the better the characteristics (hereinafter abbreviated as increase request). The individual evaluation function φ _i is defined separately according to For example, the individual evaluation function φ _i
Is as follows: I) Match request

[0037]

(Equation 2)

II) Request for decrease, III) Request for increase

[0039]

(Equation 3)

These indicate that the smaller the evaluation function value is, the more the circuit satisfies the required specifications.

An evaluation function Φ _j represented by the following equation, for example, is introduced to evaluate the overall characteristics of the circuit using the respective characteristics evaluated by the individual evaluation functions.

[0042]

(Equation 4)

Here, R ₁ , R ₂ ,... Represent circuit constants to be optimized. All the characteristics and constraints to be considered in this constant optimization are included in this evaluation function Φ _j . Thus, in step S15, the circuit constant is set to the initial value, that is,
An evaluation function value Φ ₁ for the initial state S _{1 of the} circuit is calculated.

[0044] Thereafter, in step S16, the initial state small amount [Delta] R _k (where [Delta] R _k each constant value in S ₁ for each element when the R _k are constant positive which depends on the initial value of R _k The sensitivity analysis is performed when the constant value is changed by the amount. That is, R _k + ΔR _k and R _k −Δ for each element.
When R _k and the constant value are respectively changed, step S1
5 and in the same manner using the circuit simulator 2, the evaluation function value _{Φ 1 (R 1, R 2} , ···, R k + ΔR k, ···) and [Phi ₁
(R ₁ , R ₂ ,..., R _k −ΔR _k ,...) Are calculated, and the increase sensitivity S _1k ⁺ and the decrease sensitivity S _1k ⁻ defined by the following equations are calculated using the values. I do. Increase sensitivity S _jk ⁺ = Φ _j (R ₁ , R ₂ ,..., R _k + ΔR _k ,...) −Φ _j (R ₁ , R ₂ ,..., R _k ,. ... (13) decrease in sensitivity ^{_{S jk - = Φ j (R}} 1, R 2, ···, R k -ΔR k, ···) -Φ j (R 1, R 2, · ··, R _k , ...) (14)

Next, in step S17, when the element constant is changed for each element, whether Φ _j does not become smaller than the evaluation function value before the change, that is, whether or not Φ _j is an optimum value for the change of one element Is determined. The determination method is based on S _jk ⁺ and S calculated in step S16.
_jk ^- is when the positive respectively, determines an optimum value the constant value R _k. This is determined for each element k constituting the circuit. Only when it is determined that all the element constants are the optimum values, the process proceeds to the calculation of the element sensitivity characteristics for every two elements (step S18). If at least one of S _jk ⁺ or S _jk ^- is negative,
Sensitivity S _jk therein ^+, S _jk ^- select the smallest of, the process proceeds to step S10.

The operation of the constant change amount determining program in step S10 for the case where the sensitivity is negative in the sensitivity analysis for each element will be described with reference to the flowchart of FIG. Sensitivity S _jk ⁺ selected in step S17, in step S22, S _jk ^- For if S _jk ⁺ smallest to the smallest element _{k R k → R k + ΔR} k * ····· (15) where ΔR _k ^* is a constant variation proportional to the absolute value | S _jk ⁺ | and is represented by ΔR _k ^* = | S _jk ⁺ | · ΔR _k (ΔR _k : a positive fixed amount depending on the initial value of R _k ). You. If S _jk ^- ΔR _k ^* is the smallest when in ^{_{R k → R k -ΔR k *}} ····· (16) where the absolute value | S _jk ^- | a constant amount of change that is proportional to, ΔR _k ^* = | ^- | represented by · ΔR _k S _jk. Calculate the constant value as follows. If the next constant value is determined by the constant change amount represented by the equation (15) or (16), the constant value oscillates and does not converge because the constant change amount is large when the sensitivity near the optimum value is large. There are cases. Here, such an example will be described with reference to FIG. Now, it is assumed that when the value of R _k is r ₀ , it is the B ₀ point. Further, the sensitivity at B ₀ point size of | S ⁰ _jk ⁺ | to. At this time, | S ⁰ _jk ⁺ |
Assuming that the amount of change proportional to is ΔR _B0 ^* , ΔR _B0 ^* = | S ⁰ _jk
⁺ | · ΔR _k (ΔR _k is a positive fixed amount depending on the initial value of R _k ). Then, R _k changes by ΔR _B0 ^* (R _k → R _k
+ ΔR _B0 ^* ) B Suppose that you have come to point ₁ . In this case, the vehicle approaches the optimum point C. Then the size of the sensitivity by B ₁ point | S ¹ _jk ⁺ | to the | S ¹ _jk ⁺ | If the value is greater, R _k
Is ΔR _B1 ^* past point C which is the optimal value (where Δ
R _B1 ^* = | S ¹ _jk ⁺ | · ΔR _k (R _k → R _k + Δ)
R _B1 ^* ) B Comes to point ₂ . B The magnitude of sensitivity at point ₂ |
S ² _jk ⁺ | and put the | S ² _jk ⁺ | case also large R _k value comes B ₃ points from the opposite direction past the point C. When the sensitivity at point B ₃ is high, it also passes point C. In this way, vibrations occur forever around points B ₂ and B ₃ sandwiching point C and do not converge to the optimum value at point C. Steps S23, S24 and S25 are performed to solve such a problem.

Next, in step S23, the evaluation function Φ _j (R ₁ , R ₂ ,..., R _k + ΔR _k ^* ,...) For the constant value obtained by the equation (15) or (16). (17) Φ _j (R ₁ , R ₂ ,..., R _k −ΔR _k ^* ,...) (18) is calculated. The value of the expression (17) or (18) is compared with the value of the previous evaluation function Φ _j (R ₁ , R ₂ ,..., R _k ) (19) (step S24) ). Therefore, when the value of the expression (17) or (18) is smaller than the value of the expression (19), the state of the count constant at the time of the constant value represented by the expression (15) or (16) is set to S ₂ . That is, this constant value is adopted as the next constant value. Conversely, (17) or (1
8) the value (19) if the value is greater than or sensitivity of the magnitude of | S _jk ⁺ | or | S _jk ^- | is the time sensitivity analysis the amount of change in a constant value in step S25 in the case of 1 or less In the above case, the constant value is changed as follows: R _k → R _k + ΔR _k (21) In the above case, R _k → R _k −ΔR _k (21) That is, the constant value based on the amount of change at the time of the sensitivity analysis is adopted as it is as the next constant value. The state of the circuit constant at the time of the constant value of the equation (20) or (21) is defined as S ₂ . Thereafter, steps S15 → S1 in FIG. 3 until the optimum value is determined based on the element sensitivity of one element.
The loop of 6 → S17 → S10 is repeated. Step S1
If it is determined in step 7 that the sensitivity characteristics of each element are the optimum values for all the elements, the process proceeds to the next element sensitivity characteristic calculation of every two elements (step S18).

In step S18, the evaluation function value calculated by changing the constant R _k to R _k + ΔR _k and R _k −ΔR _k one element at a time in
Each evaluation function value is calculated by changing each constant by combining the elements, and using this value, 2 is defined by the following equation.
Calculate the increase and decrease sensitivity of the variables. Where the symbol S _jkl
⁺⁺ represents the sensitivity when the k- th and l- th elements are each increased by a very small amount (a minus sign indicates a decrease). S _jkl ⁺⁺ = Φ _j (R ₁ , R ₂ ,..., R _k + ΔR _k ,..., R _l + ΔR ₁ ,...) −Φ _j (R ₁ , R ₂ ,. R _k ,..., R _l ,...) (22) S _jkl ^{+ −} = Φ _j (R ₁ , R ₂ ,..., R _k + ΔR _{k ,. l} −ΔR _l ,...) −Φ _j (R ₁ , R ₂ ,..., R _k ,..., R _l ,...) (23) S _jkl ^{− +} = _{Φ j (R 1, R 2} , ···, R k -ΔR k, ···, R l + ΔR l, ···) -Φ j (R 1, R 2, ···, R k, · _{··, R l, ···) ·····} (24) S jkl - = Φ j (R 1, R 2, ···, R k -ΔR k, ···, R l -ΔR _l ,...) −Φ _j (R ₁ , R ₂ ,..., R _k ,..., R _l ,...) (25) where ΔR _k and ΔR _l are each depending on the initial value of R _k, R _l It is a positive constant amount.

Next, in step S19, step S
Based on the increase and decrease sensitivity of the two variables calculated in 18,
It is determined whether or not the value is an optimum value in the change of the element. The determination method is S _jkl ⁺⁺ calculated in step S18,
When S _jkl ^+- , S _jkl- ⁺ and S _jkl ^- are each positive,
Set R _k constant values, For the R _l, determines an optimum value. This is determined for all two element combinations of the elements (k, l) constituting the circuit. Only when it is determined that the optimum value is obtained in all the combinations, the process proceeds to the device sensitivity characteristic calculation for every three devices (step S20). If at least one is S _jkl ⁺⁺ , S _jkl ^+- ,
If S _jkl- ⁺ and S _jkl ^- are negative, the one with the smallest sensitivity is selected and the process proceeds to step S10.

The operation of the constant change amount determining program in step S10 in the case where the sensitivity is negative in the sensitivity analysis for each two elements will be described with reference to the flowchart of FIG.
In step S22, the sensitivity S _jkl ⁺⁺ selected in step ^{_{S19, S jkl + -, S}} jkl - + and S _jkl ^- if if S _jkl ⁺⁺ to set the smallest element is smallest R _k of → R _k + ΔR _k ^* , R _l → R _l + ΔR _l ^* (26) where ΔR _k ^* and ΔR _l ^* are constant changes determined in proportion to the absolute value | S _jkl ⁺⁺ | _Yes , ΔR _k ^* = | S _jkl ^{++
_{| · ΔR k, ΔR l *}} = | represented by · ΔR _l | S _jkl ^++. If S _jkl ⁺ _-is smallest R _k → R _k + ΔR _k ^* , R _l → R _l −ΔR _l ^* (27) where ΔR _k ^* and ΔR _l ^* are absolute values | S _jkl ^+- | is a constant change amount determined in proportion to | R _k ^* = | S _jkl ^{+-
_{| · ΔR k, ΔR l *}} = | - | represented by · ΔR _l S _jkl ^+. If S _jkl- ⁺ is smallest R _k → R _k −ΔR _k ^* , R _l → R _l + ΔR _l ^* (28) where ΔR _k ^* and ΔR _l ^* are absolute values | S _jkl- ⁺ | is a constant variation determined in proportion to ΔR _k ^* = | S _jkl- ^{+
_{| · ΔR k, ΔR l *}} = | - | represented by · ΔR _l S _jkl +. If S _jkl ^- is smallest R _k → R _k −ΔR _k ^* , R _l → R _l −ΔR _l ^* (29) where ΔR _k ^* and ΔR _l ^* are absolute values | S _jkl ^- | a constant change amount determined in proportion ^{_{to, ΔR k * = | S jkl}} -
^{_{| · ΔR k, ΔR l *}} = | - | represented by · ΔR _l S _jkl.
As in the case of one element, steps S23, S24, and S25 are performed so that the constant value does not fluctuate near the optimum value.

Next, in step S23, (26)-
Let V be the value of the evaluation function Φ _j at the time of the constant value obtained in any one of the equations (29). V and the value of Φ _j (R ₁ , R ₂ ,..., R _k ,..., R ₁ ,...) (30) are compared. So if V is (30) is smaller than the value of the expression is the any one of (26) to (29), the state of the circuit constant of the time constant values obtained in other words the variation and S _2. That is, this constant value is adopted as the next constant value. If V is is 1 or less (30) when the value is greater than or size of sensitivity Conversely, equal to the amount of change in time of sensitivity analysis the amount of change in a constant value in step S25 in the case R _k → R _k + ΔR _k , R _l → R _l + ΔR _l (31) In the above case, R _k → R _k + ΔR _k , R _l → R ₁ −ΔR _l (32) In the above case, R _k → R _k −ΔR _k , R _l → R _l + ΔR _l ... (33) In the above case, it is fixed as R _k → R _k −ΔR _k , R _l → R _l −ΔR _l. Change the value. That is, a constant value based on the amount of change at the time of the sensitivity analysis is adopted as the next constant value. Then (31) the state of the circuit constant of the time constant value represented by any one of the - (34) and S _2. Thereafter, the loop of the sensitivity characteristic of one element is again performed (step S15 → S16 → S17 → S1).
Enter 0).

If it is determined in step S19 that the sensitivity characteristic of every two elements is the optimum value for all combinations of elements, the process proceeds to the next element sensitivity characteristic calculation of every three elements (step S20). About steps S20 and S21,
The above processing is similarly performed for each combination of three elements.
In step S21, the process ends only when the circuit constant value is determined to be the optimum value for all combinations of three elements, and the last value held by each element is the optimum value of each circuit constant for the target specification. give. This is because, even if each circuit constant value held at the end of the processing is changed by a small amount for each element, every two elements, or every three elements, the evaluation function Φ _j does not decrease any more. That is, the circuit characteristic value f _i
Does not approach the target value f _ia any more. That is, those circuit constant values are optimal values for the target value f _ia .

As described above, according to the circuit constant automatic setting system and the circuit constant optimizing method of each of the above embodiments, the evaluation function is represented by a function having a plurality of characteristics.
In order to improve the overall characteristics, there is an effect that the trade-off between each characteristic is performed smoothly, and since the search direction to the optimum constant is determined by sensitivity analysis, it is possible to search for the search direction as before It does not require a rule base for each circuit.

Further, since sensitivity analysis is performed by simultaneously increasing or decreasing a plurality of elements, a direction which cannot be searched by one element sensitivity analysis is also covered in order to find a search direction for an optimum constant. That is, the sensitivity analysis of a plurality of elements works effectively when the sensitivity analysis of one element fails to reach the optimum constant. Further, in the case of the above embodiment, when the sensitivity analysis of 1, 2, and 3 elements does not find a direction in which the value of the evaluation function is reduced, it is determined that the evaluation function is the optimum value. And no artificial compromise is added to the characterization.

In addition, since the constant change amount is determined by the constant change amount determining program in accordance with the sensitivity, the number of repetitions until convergence is reduced, and the convergence speed is high even when the initial value is far from the optimum value. Then, the optimum value is obtained.
When the amount of change in the constant is determined according to the magnitude of the sensitivity, the convergence may not be achieved, such as when the sensitivity near the optimum value is large. By determining the constant value, convergence is ensured, and an optimum constant value can be obtained.

In the above embodiment, the evaluation function is defined so as to satisfy the target specification as the function value decreases, but the evaluation function is defined so as to satisfy the target specification as the function value increases. Even with this, the same objects and effects as those of the above embodiment can be achieved.

Hereinafter, a case will be described in which the evaluation function is defined such that the larger the function value, the more the target specification is satisfied. Also in this case, it is necessary to normalize each characteristic so that each characteristic can be evaluated in the same dimension. However, here, for simplicity of description, the standardization used in the above embodiment is used. Equation (9) is used. For example the number evaluation function for evaluating the individual characteristics using a bar f _i obtained by the equation (9) gives the following equation. Match request

[0058]

(Equation 5)

Reduction request, increase request

[0060]

(Equation 6)

Equations (35) and (36) are functions that take values from 0 to 1, and are closer to 1 as the characteristic value satisfies the required specifications. Thus, each characteristic is set to 0 to 1
Is basically the same as the evaluation using the satisfaction curve of the conventional system. Next, for evaluating the overall characteristics of the circuit, for example, the expression (1)
Use 2).

Hereinafter, each constant value is determined by sensitivity analysis so as to maximize the evaluation function obtained by Expression (12).
In the above-described embodiment, the sensitivity becomes a negative value among the increasing sensitivity and the decreasing sensitivity calculated by the equations (13) and (14), and the constant value is changed for the element having the smallest sensitivity. ) And (14), the sensitivity becomes a positive value among the increasing sensitivities and the decreasing sensitivities, and the constant value is changed for the element having the highest sensitivity. When the calculated Φ _1k ⁺ and Φ _1k ^- are both larger than Φ ₁ , except for the two points where the above Φ _1k ⁺ and Φ _1k ^- are both judged to be the optimum values when both are smaller than Φ _1. The operation is the same, and the effect by this is the same as that of the above embodiment.

In the above embodiment, when the sensitivity analysis is performed, both the increase sensitivity and the decrease sensitivity are analyzed. However, this operation may be performed on only one of them. For example, a case will be described in which an evaluation function is defined such that the smaller the function value, the more the target specification is satisfied.

Also in this case, the operation can be described with reference to the flowchart of FIG. 3, and the standardization formula for each characteristic, the individual evaluation function formula, and the evaluation function formula for evaluating the overall characteristics are also used in the description of the above embodiment. Equations (9), (10), (11),
The same one as (12) can be used. That is, after the evaluation function [Phi ₁ for the initial state S ₁ of the circuit in step S15 is calculated, the sensitivity analysis to determine the search direction to an optimal value. At this time, first, step S16
Then, the sensitivity when the element to be subjected to the constant design is moved by a small amount ΔR _{k for} each element with respect to the evaluation function Φ is calculated.

That is, when the constant value R _k is R _k + ΔR _k , the evaluation function value obtained by the equation (12) is Φ ₁ (R ₁ , R ₂ ,
.., R _k + ΔR _k ,...), The sensitivity S _1k is obtained by the following equation. S _1k = Φ ₁ (R ₁ , R ₂ ,..., R _k + ΔR _k ,...) −Φ ₁ (R ₁ , R ₂ ,..., R _k ) (37) This equation (37) is equivalent to the increasing sensitivity equation (1 ) used in the above embodiment.
This corresponds to 3). From S _1k (where k = 1, 2,...) Calculated by equation (37) , the one with the largest absolute value is selected. If S _1k > 0, R _k → R _k −ΔR _k (38) If S _1k <0, replace with R _k → R _k + ΔR _k (39) and use the constant value of state S ₂ . This operation is continued until the following equation is satisfied, where Φ _j is the evaluation function in the j-th circuit state. | Φ _j −Φ _j−1 | ≦ TOL (40) where TOL is a permissible value for determination of the optimum value. In the above description, the expression (37) is used in step S16 in the flowchart of FIG. Equations (38) and (39) correspond to the processing in step S10, and equation (40) corresponds to the processing in step S17. After it is determined that the optimum value is obtained in the sensitivity analysis for each element by the equation (40) , the next step S1
In step 8, sensitivity analysis is performed for all combinations of two elements among the elements to be designed. That is, a small amount Δ
Calculate the sensitivity when moving by R _k and ΔR _l .

Now, let the constant value R _k be R _k + ΔR _k , the constant value R _l
When R is defined as R _l + ΔR _l , the evaluation function value obtained by the equation (12) is Φ _j (R ₁ , R ₂ ,..., R _k + ΔR _k ,.
R _l + ΔR _l, ···) and then, the constant value R _k R _k + ΔR _k,
When the constant value R _l is R _l −ΔR _l , the evaluation function value obtained by Expression (12) is Φ _j (R ₁ , R ₂ ,..., R _k + Δ
_{R k, ···, R l -ΔR} l, if ...), sensitivity S
_jkl ⁺⁺ and S _jkl ^{+ −} are obtained by the equations (22) and (23) in the same manner as in the sensitivity calculation of the two elements in the above embodiment. In the above embodiment, the sensitivities S _jkl- ⁺ and S _jkl ^- are also calculated, but are not calculated here. Of the S _jkl ⁺⁺ and S _jkl ⁺ _-obtained by _performing this sensitivity calculation for all combinations of two elements, the one with the largest absolute value is selected, and if | S _jkl ⁺⁺ | _{If jkl} ⁺⁺ <0, the operation of equation (26) of the above embodiment is performed. If | S _jkl ⁺⁺ | is maximum and S _jkl ⁺⁺ > 0, the operation of equation (29) of the above embodiment is performed. If | S _jkl ^+- | is maximum and S _jkl ^+- <0, the operation of the equation (27) of the above-described embodiment is performed. If | S _jkl ^+- | is maximum and S _jkl ^+- > 0, the equation of the above-described embodiment is used. The operation of (28) is performed, and the obtained constant value is used as the constant value of the circuit state S _{j + 1} . This behavior is
As with sensitivity analysis of 1 element, continues until satisfies equation (40), it is determined that the optimum value in sensitivity analysis for each of 2 elements when satisfy equation (40). Thereafter, the process proceeds to the sensitivity analysis for every three elements. In the following processing, S _jkl ⁺⁺ and S _jkl ^{+ −} calculated by the sensitivity analysis for every two elements are _converted to S _jkl ^{+ −} by the sensitivity analysis for every three elements.
Similar processing is performed _{instead of jklm} ⁺⁺⁺ , _Sjklm ^++- , _Sjklm ^+-+ , and _Sjklm ^-++ . As described above, in the above-described embodiment, the case where both the increase sensitivity and the decrease sensitivity were calculated at the time of the sensitivity analysis was described using only one of them. In this case, the search calculation to the optimum value was performed in the above-described embodiment. Since it is reduced by half compared to the example, there is an effect that the analysis time until obtaining the optimum value is short. Further, in this case, since the artificial variable is used for the determination of the optimum value, the accuracy of the obtained optimum value depends on the value of the artificial variable TOL, but the other effects are not changed at all.

On the other hand, in the above embodiment, the amount of increase (or the amount of decrease) of the constant value in the sensitivity analysis is represented by ΔR _k (ΔR _k , ΔR _l when calculating the element sensitivity characteristics of two elements, and three elements each). When calculating the element sensitivity characteristics, ΔR _k , ΔR _l , ΔR
Although the _m), these variation ΔR _k, ΔR _l, the value of [Delta] R _m is not limited to a fixed value, [Delta] R _k depending on the stage of convergence as shown in the flowchart of FIG. 6, for example, [Delta] R _l, [Delta] R The value of _m may be changed. That is, when calculating the element sensitivity characteristic of one element at step S16, firstly, the variation of the constant value is performed in the initial setting value [Delta] R _k, the value of the next [Delta] R _k If this result is determined to the optimum value at step S17 Is reduced, and the element sensitivity characteristics of each element are calculated again in step S16. The value of [Delta] R _k small process of calculating repetitive element sensitivity characteristic continues until less than the minimum value [Delta] R _kmin of [Delta] R _k where the value of [Delta] R _k is predetermined. Hereinafter, in the calculation of the element sensitivity characteristics for each two elements in step S18, ΔR _{k in} the calculation of the element sensitivity characteristics for each element is ΔR _k and ΔR _k.
l, and in the calculation of the element sensitivity characteristics for each of the three elements in step S20, the processing is the same as in the calculation of the element sensitivity characteristics for each of the elements except for the points of change to ΔR _k , ΔR _l, and ΔR _m. It is.

Here, in general, when the amount of change at the time of sensitivity analysis is increased, the speed up to convergence (until an optimum value is obtained) increases, and conversely, when the amount of change is reduced, the accuracy of the obtained optimum value is improved. I do. In the example of FIG. 6, since the value of the amount of change ΔR _k (or ΔR _l , ΔR _m ) is initially increased, the effect that the reaching speed to reach the vicinity of the optimum value is fast, and gradually ΔR _k (Or ΔR ₁ , ΔR _m ) is reduced, so that the accuracy of the obtained optimum value is improved.

FIG. 7 is a flowchart showing another example of changing the amount of change at the time of sensitivity analysis according to the convergence stage. In this case, in the example of FIG. 6, the change amount ΔR _k (or ΔR _l , ΔR
₇ ), the device shown in FIG. 7 first calculates the device sensitivity characteristics of one to three devices with the initial set values ΔR _k , ΔR _l , and ΔR _m , and then calculates ΔR _k , ΔR _l , is that repeating this back to device sensitivity characteristic of each re 1 element by decreasing the value of [Delta] R _m. Other operations are the same as those in the example of FIG. The unique effects achieved in the example of FIG. 7 are the same as those of the example of FIG.

In the embodiments shown in FIGS. 3, 4, 6, and 7, the description has been made on the assumption that the set of constant values to be changed in the sensitivity analysis is a maximum of three elements. In this case, the same operation and effect as those of the above embodiment can be obtained. In addition, an expression other than the expression used in the above embodiment may be used as a normalization expression. It goes without saying that there are various usage forms, such as using an expression other than the expression used in the above embodiment as the evaluation function expression defined to be small (or large).

Further, the sensitivity analysis means of the present invention sets the evaluation function to the minimum (or maximum) in order to obtain the optimum value of the circuit constant.
Is used as the means, but the minimum value of any function,
(Or the maximum value) is obviously effective.

[0072]

As described above, according to the present invention, the characteristics and other constraints to be considered for determining the constant are set to one.
Since the processing is performed in one evaluation function, the trade-off between the characteristics is easy.
Since constants are changed by performing sensitivity analysis using a plurality of elements such as two elements or three elements, knowledge of a special rule base or the like for the circuit is not required, so that the present invention is effective for an arbitrary circuit, and the evaluation function of the evaluation function is Since the minimum value is determined based on the increase sensitivity and the decrease sensitivity, there is an effect that the minimum value can be found with high accuracy. Also optimal
The search direction for the optimal constant to some extent in the early stage of optimization
For this reason, it is necessary to use
High processing by reducing the number of simulations
Can be faster. In other words, there are few parameters to change
If so, the optimal value is reached faster. Also the goal
Increase the number of search directions as the property approaches
Therefore, the design accuracy is high.

Further, since the amount of change is determined by the magnitude of the sensitivity, even when the initial value is far from the optimum value, the convergence is achieved at a high speed, and the time required for the optimization is shortened.

[Brief description of the drawings]

FIG. 1 is a configuration diagram showing a circuit constant automatic design system according to an embodiment of the present invention.

FIG. 2 is a configuration diagram showing a circuit constant automatic design system according to another embodiment of the present invention.

FIG. 3 is a flowchart showing a circuit constant optimizing method by the system of FIGS.

FIG. 4 is a flowchart showing an operation of a constant change amount determination program of FIG. 2;

FIG. 5 is a diagram illustrating a relationship between a constant value and an evaluation function value for explaining an optimization method by the systems of FIGS.

FIG. 6 is a flowchart showing another embodiment of the circuit constant optimizing method of the present invention.

FIG. 7 is a flowchart showing still another embodiment of the circuit constant optimizing method of the present invention.

FIG. 8 is a block diagram showing a conventional circuit constant automatic design system.

FIG. 9 is a flowchart showing a circuit constant optimizing method by the system of FIG. 8;

FIG. 10 is a diagram showing a relationship between characteristic values and satisfaction for explaining an optimization method by the system of FIG. 8;

FIG. 11 is a circuit diagram used to explain a rule-based structure in the system of FIG. 8;

FIG. 12 is a chart used to explain a rule-based structure in the system of FIG. 8;

FIG. 13 is a diagram illustrating a relationship between characteristic values and satisfaction for explaining an optimization method by the system in FIG. 8;

FIG. 14 is a diagram showing a relationship between characteristic values and satisfaction for explaining an optimization method by the system of FIG. 8;

[Explanation of symbols]

1, 1A Automatic circuit constant design system 2 Circuit simulator (circuit characteristic analysis means) 3 Design program (control means) 10 Constant change amount determination program (constant change amount determination means) 12 1-element sensitivity analysis program (sensitivity analysis means) 13 2 Element sensitivity analysis program (sensitivity analysis means) 14 Three-element sensitivity analysis program (sensitivity analysis means)

 ──────────────────────────────────────────────────続 き Continuation of the front page (56) References JP-A-62-226279 (JP, A) JP-A-63-118878 (JP, A)

Claims (4)

(57) [Claims] 1. A circuit characteristic analysis means for analyzing a DC characteristic, an AC characteristic, a transient characteristic, etc. of a circuit, and a match between a target specification value of each circuit characteristic and each characteristic value obtained from said circuit characteristic analysis means. The sensitivity of the evaluation function to a change in the constant value of at least one element among the elements to be determined for the circuit constants in the circuit for the evaluation function defined using each value to represent the degree of The sensitivity analysis means to be analyzed and the values required for the analysis of the circuit characteristic analysis means and the sensitivity analysis means are set, and the optimum constant is changed by changing the constant value based on the characteristic value and the sensitivity characteristic obtained by the analysis. Control means for searching, the sensitivity analysis means
By changing the constant value for each element,
Determine the search direction and optimize by changing the constant value for each element
After that, the sensitivity is increased by increasing the number of elements every 2 or 3 elements.
Circuit constant automatic design system, characterized in that to decide the search direction to the optimum constant analyzed. 2. The method according to claim 1, wherein the control means includes constant change amount determining means for determining a change amount to a next constant value in proportion to the magnitude of the sensitivity obtained by the sensitivity analyzing means. The automatic circuit constant design system according to claim 1. 3. The circuit constant automatic design system according to claim 2, wherein said constant change amount determining means checks an evaluation function value based on a constant value having a change amount changed in proportion to sensitivity. If is smaller than the previous value, the constant value whose change amount is changed in proportion to the sensitivity is set as the next constant value, and if the function value is larger than the previous value , the change amount during sensitivity analysis A circuit constant optimizing method characterized in that a constant value based on (i) is used as a next constant value. 4. The circuit constant automatic design system according to claim 1, wherein the sensitivity analysis means obtains the increased sensitivity and the constant value obtained by increasing the constant value by the finite difference method. If both the reduced sensitivity is analyzed and the control means sets the evaluation function so as to satisfy the target specification as the function value increases, the above increase will occur in all combinations of constant values subject to sensitivity analysis. When both the sensitivity and the reduction sensitivity are all negative values, and conversely, if the function value is set to satisfy the target specification as the function value decreases, the combination of all constant values to be subjected to sensitivity analysis Wherein the last constant value used in the sensitivity analysis is determined to be an optimum value when both the increase sensitivity and the decrease sensitivity both take positive values.