JPH0638089B2 - An electronic computer for determining transient response characteristics of electronic circuits. - Google Patents

Description

Description: TECHNICAL FIELD OF THE INVENTION The present invention relates to an electronic computer for determining a transient response characteristic of an electronic circuit, and more particularly to an electronic computer including a non-linear element having a characteristic that a current characteristic changes smoothly with respect to a terminal voltage. The present invention relates to an electronic computer that determines a transient response characteristic of a circuit.

[Technical Background of the Invention and Problems Thereof] In designing an electronic circuit, the circuit is repeatedly analyzed and modified in the course of designing to finally design a circuit having a desired operation. Therefore, in order to perform efficient circuit design, it is desirable to obtain circuit analysis results at high speed. However, the conventional analysis method is not always sufficient as described below.

That is, the transient response of the electronic circuit is represented by the following non-linear differential equation regarding the current at a certain time t _n , where x is a node voltage vector at a certain time t _n .

First derivative for time t _n Can be approximated using a suitable integration method. For example, in the backward Euler approximation, Is. here, Is.

As a result of this approximation, equation (1) becomes Becomes This equation is a non-linear algebraic equation. Solving this equation physically corresponds to finding the DC operating point of the non-linear circuit. Therefore, the transient response of the electronic circuit can be obtained by finding the DC operating point of the nonlinear circuit corresponding to the equation (3) at each time.

Equation (3) is generalized to be represented by the nonlinear equation system g _i (x) = O, (i = 1, 2, ..., N) (4). However, N is the number of equations.

This equation can usually be solved using the Newton method as shown in FIG. In this Newton method, each non-linear function value ▲ g ^m _i ▼ (i =
1, ..., N) and its first derivative ▲ J ^m _i ▼ (i = 1, ..., N)
Calculate N).

Then, with the function value ▲ g ^m _i ▼ obtained in this iteration,
Linear prediction value from the function value obtained in the previous iteration Convergence is determined using the absolute value of the difference.

Conditions for all nonlinear functions When holds, the iteration of the Newton method ends.
However, ε is an appropriate positive number.

However, in such conventional Newton's method, as described above, ▲ g ^m _i ▼ and ▲ J ^m _i must be used in each iteration.
Since ▼ has to be calculated, the calculation takes a long time, and the circuit design cannot be performed efficiently.

[Object of the Invention] The present invention solves the drawbacks of the conventional method of analyzing an electronic circuit and provides an electronic computer for obtaining the transient response characteristic of the electronic circuit, which can obtain the analysis result of the circuit at high speed. The purpose is.

[Summary of the Invention] The present invention provides a diode, a bipolar transistor, and an MO.
In electronic circuits including non-linear elements such as SFET, the current characteristics of these non-linear elements are made paying attention to the characteristic that they do not change abruptly with respect to the terminal voltage and are smooth. , The current value flowing through the non-linear element, the primary differential coefficient and the secondary differential coefficient of the current value with respect to the terminal voltage of the element, the difference between the terminal voltage obtained by repeating this time and the terminal voltage obtained in the past iteration From the vector and the product of the quadratic differential coefficient of the device current obtained in the past iteration, find the value of the quadratic form consisting of these difference vector and the quadratic differential coefficient, and obtain its absolute value and a certain positive If the convergence of the Newton's method is detected and the convergence is detected by the size relation of the number of, the non-linear function value and the first derivative obtained in the previous iteration are used. Then, the above characteristics are obtained by an electronic computer having a configuration for obtaining the transient response characteristics of the electronic circuit.

[Effect of the Invention] According to the present invention as described above, it is not necessary to calculate the non-linear function value ▲ g ^m _i ▼ and the first derivative ▲ J ^m _i ▼ by calculation in each iteration in the calculation by the Newton method unlike the conventional case. Therefore, the time required for calculation is shortened, and the electronic circuit can be efficiently designed. Moreover, the analysis can be performed with almost the same analysis accuracy as the conventional one.

[Examples of the Invention] The present invention will be described in detail below with reference to Examples.

In the actual electronic circuit analysis, each non-linear equation represented by the equation (4) is composed of a combination of functions representing currents of some non-linear elements. For non-linear elements,
There are diodes, bipolar transistors, MOSFETs, etc., but it has been known by actual measurement that the current characteristics of these elements are smooth without abrupt changes with respect to the terminal voltage.

Non-linear function However, if it is smooth and the change in x is small enough, ▲
g ^m _i ▼ can be approximated by the following equation.

Where ▲ H ^m-1 _i ▼ is the second derivative of g _i (x), It is defined as

Using the approximation of Eq. (7), the vector And 1/2 of the value of the quadratic form consisting of ▲ H ^m-1 _i ▼ , It is possible to judge the convergence of Newton's method by using | Δg _i | ε (10).

In the case of the condition (6) in the conventional Newton method, the function etc. ▲ g ^m _i ▼ had to be calculated in the ^m- _th iteration, but this condition is not necessary. .
A function satisfying this condition was obtained in the previous iteration instead of ▲ g ^m _i ▼. Also, instead of ▲ J ^m _i ▼, ▲ J ^m-1 _i ▼ obtained in the previous repetition can be used to calculate the DC operating point of the circuit. When this condition holds for all functions, the iteration of the Newton method ends, and the transient response characteristic of the electronic circuit can be obtained.

Next, an embodiment of the present invention will be described based on a flowchart for explaining the analysis method by the electronic computer shown in FIG. In the present invention, the transient response characteristic of the electronic circuit is obtained by the electronic computer configured to obtain the transient response characteristic of the electronic circuit.

First, set x ° indicating the initial voltage of the nonlinear element and a certain positive number ε given as the convergence condition value, and set the value of the counter m for counting the number of iterations of the Newton method to 1. To do. Then
The value of a counter i for counting the number of repetitions of N nonlinear functions of is set to 1, and a variable flag n _c representing the number of nonlinear functions that do not satisfy the convergence condition of the Newton method is set to 0. Then, in, it is determined whether or not the value of the counter m for counting the number of iterations of the Newton method is 1. When it is determined that the counter m is not 1 as a result of this determination, To calculate. This means that Δg _i is obtained by the approximate value of the difference between the current values that are linearly predicted based on the nonlinear function values that have not yet been calculated and the past nonlinear function values. Further, by performing | Δg _i | ≦ ε, the approximate value Δg
The absolute value of _i and the convergence condition value ε are compared to determine the magnitude relationship. When it is determined that the absolute value of this approximate value Δg _i is less than or equal to the convergence condition value ε, at Ask for. This is the nonlinear function value ▲ g obtained in the past.
Nonlinear function value from ^m-1 _i ▼ and first-order derivative ▲ J ^m-1 _i ▼ (x ^m −x _m-1 ). Once asked, And ▲ J ^m-1 _i ▼ Apply to ▲ J ^m _i ▼ = ▲ J ^m-1 _i ▼, and consider the nonlinear function value ▲ g ^m _i ▼ and the first derivative ▲ J ^m _i ▼ that should be obtained this time in order to use the value obtained by the previous iteration as it is. To set and execute. In addition, at the counter m
Is determined to be 1 or the absolute value of the approximate value Δg _i is greater than the convergence condition value ε in, the terminal voltage x ^m of the non-linear element and the non-linear element in The non-linear function value ▲ g ^m _i ▼ is obtained from the current value g _i (x _m ) flowing through Calculation, that is, first derivative ▲ J ^m _i ▼, second derivative Calculate. And this second derivative The terminal voltage x ^m used when calculating I will keep it as. Next, at the variable flag n
One is added to _c , and the magnitude relation between the value of the counter i and the number N of nonlinear functions is determined in. As a result of this determination, when it is determined that the value of the counter i is less than or equal to the number N of nonlinear functions, the processes are sequentially repeated from.
When it is determined that the value of the counter i is larger than the number N of the non-linear functions as a result of the determination of, it is determined whether the variable flag n _c is zero. As a result of this determination, when it is determined that the variable flag n _c is not zero, first, The sum of the first-order differential coefficients is set as the first-order differential coefficient as described above, and a value representing each nonlinear function value in a determinant is set as the nonlinear function value. Based on these set the first derivative and the non-linear function value, performs the calculation of linear equations of ^{J m x m + 1 = J} m x m -g m, obtains the terminal voltage of the non-linear element. Then in
After incrementing the counter m by one, the execution is repeated successively. In, when it is determined that the variable flag n _c is zero, it is determined that the variable flag n _c has converged, the terminal voltage of the non-linear element obtained in the previous time is output, and the analysis of the electronic circuit ends.

The filters and ring oscillators shown in Table 1 were specifically analyzed using an electronic computer for calculating the transient response characteristics of the electronic circuit according to the present invention. The analysis time and analysis accuracy at that time are shown in Table 2 and FIG. 3 in comparison with the case where the conventional method is applied.

As is clear from the results shown in Table 2 and FIG.
For a circuit such as a filter whose operating point does not change much, the analysis accuracy is almost the same as the conventional one and the calculation speed can be increased by about 20% compared to the conventional one.

[Brief description of drawings]

FIG. 1 is a flow chart for explaining a conventional analysis method of an electronic circuit, FIG. 2 is a flow chart for explaining an analysis method by an electronic computer of the present invention, and FIG. 3 is a conventional analysis accuracy of the present invention. It is the figure contrasted and shown.

Claims (1)

[Claims] 1. An electronic computer for determining a transient response characteristic of an electronic circuit including a non-linear element having a characteristic in which a current characteristic changes smoothly with respect to a voltage, and means for setting an initial voltage and a convergence condition value of the non-linear element. , A means for setting the first counter for counting the number of iterations of the Newton method to 1, and a value for the second counter for counting the number of nonlinear functions to 1, and a nonlinear function which does not satisfy the convergence condition of the Newton method Variable flag setting means for setting the variable flag representing the number of the counters to zero, first judging means for judging whether or not the value of the first counter is 1, and by this means, the first counter value is 1 If not, the approximate value of the difference between the linearly predicted current values based on the nonlinear function values that have not yet been calculated and the past nonlinear function values is calculated. Therefore, further, the second determination means for comparing the absolute value of the approximate value with the convergence condition value to determine the magnitude relationship, and this means, the absolute value of the approximate value is determined to be less than or equal to the convergence condition value. In this case, the non-linear function value and the first-order differential coefficient obtained in the past are regarded as the non-linear function value and the first-order differential coefficient to be obtained this time, and are set, and the first determination means sets the first counter value to 1 Or when it is determined by the second determining means that the absolute value of the approximate value is larger than the convergence condition value,
After the non-linear function value, the first derivative and the second derivative are calculated based on the current value flowing through the non-linear element and the terminal voltage of this element, and after holding the terminal voltage used when calculating the second derivative , A means for increasing the variable flag by 1, a third judging means for increasing the second counter value by 1 and judging a magnitude relationship between the second counter value and the number of nonlinear functions, The second by means
When it is determined that the counter value of is less than or equal to the number of non-linear functions, the means for repeating the steps from the first determining means to the third determining means, and the second determining means by the second determining means. When it is determined that the counter value is greater than or equal to the number of non-linear functions, fourth determining means for determining whether or not the variable flag is zero, and when the variable flag is not zero by this means, the set nonlinearity is set. A linear equation is calculated based on the function value and the first derivative to obtain the terminal voltage of the nonlinear element, and the first counter is set to 1
The variable flag setting means for sequentially repeating the execution of each means, and when the fourth determination means determines that the variable flag is zero, it is determined that the variable has converged An electronic computer for determining a transient response characteristic of an electronic circuit, characterized in that it has means for outputting a terminal voltage of the element.