Data processing: structural design – modeling – simulation – and em – Modeling by mathematical expression
Reexamination Certificate
1999-01-04
2001-02-20
Teska, Kevin J. (Department: 2763)
Data processing: structural design, modeling, simulation, and em
Modeling by mathematical expression
C716S030000
Reexamination Certificate
active
06192328
ABSTRACT:
BACKGROUND OF THE INVENTION
Field of the Invention
Due to the fact that the integration density of electrical circuits is becoming ever greater (VLSI), it is becoming more and more complex to determine system states of an electrical circuit, for example by means of a circuit simulation. The integration densities attained in modern circuits are already so great that even parasitic effects, for example crosstalk effects between lines which connect the individual components of the electrical circuit to one another, must be considered. The lines are normally modeled as linear components, for example as a sequence of RC elements. If the integration density is high, the additional modeling of lines leads to an increased number of sets of mutually coupled linear components within an electrical circuit, which are in each case coupled to non-linear components of the electrical circuit. Expressed figuratively, this results in “islands” of mutually coupled linear components of an electrical circuit that is to be investigated.
The large number of coupled linear components which are caused, for example, by modeling the parasitic effects in the lines subject the computers that are used in the investigation of the individual electrical circuits to requirements which cannot be satisfied at the moment, even by very high-performance computers.
A so-called eigenvalue solver for determining eigenvalues for a homogeneous differential equation system is known from Booten et al., “A Preconditioned Jacobi-Davidson Method for Solving Large Generalized Eigenvalue Problems,” Report NM-R9414, Centrum voor Wiskunde en Informatica, Netherlands, ISSN-0169-0388 (1994).
The determination of a transfer function for a set of coupled linear components is described in Vlach and Singhal, “Computer Methods for Circuit Analysis and Design,” Van Nostrand Reinhold Company, New York, ISBN-0-442-28108-0 (1983).
A process is known for the approximation of a transfer function for a set of coupled linear components of an electrical circuit, in which only the so-called dominant eigenvalue is considered. See Glashoff and Merten, “Neue Verfahren zur Laufzeitberechnung bei Semi-Custom-Schaltungen,” [New Methods for Delay Time Calculation in Semi-Custom Circuits]; Informatik in der Praxis, Springer, ISBN 3-540-17054-5, p. 13-26 (1986).
A plurality of transfer functions can be determined separately for a set of linear components. The transfer functions thus each describe the response of the set of linear components with respect to two reference connections for the respective transfer function. This is described by Ratzlaff and Pillage, “RICE: Rapid Interconnect Circuit Evaluation Using AWE,” IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, Vol. 13, No. 6, pp. 763-76, June 1994.
The method described by Vlach and Singhal has the disadvantage that, there, only the state of the set of linear components is considered, and only with respect to two connections of the set of linear components to non-linear components. It is not possible to use that method to consider a greater number of connections to further non-linear components.
The method described by Ratzlaff and Pillage has the disadvantage, inter alia, that, although a number of connections of the set of linear components to linear components are considered, these are, however, in each case always only in pairs. On the one hand, therefore, this requires increased computation capacity for carrying out the method and, on the other hand, the accuracy of the results which are achieved by that method is very low.
SUMMARY OF THE INVENTION
It is accordingly an object of the invention to provide a method and configuration for computer-aided determination of a system relationship function, which overcomes the above-mentioned disadvantages of the heretofore-known devices and methods of this general type and which describes a set of coupled linear components of an electrical circuit which has any number of non-linear components and linear components, the set of coupled linear components being coupled to any number of non-linear components, which can be carried out more quickly and whose results provide more accurate statements than the prior art methods about the system state of the set of linear components.
With the foregoing and other objects in view there is provided, in accordance with the invention, a method for computer-aided determination of a system relationship function describing a set of coupled linear components of an electrical circuit with an arbitrary number of non-linear components and linear components, the method which comprises the following steps:
a) defining a differential equation system with equations for a set of coupled linear components;
b) determining a predeterminable number of eigenvalues for a homogeneous differential equation system of the differential equation system;
c) determining an error for the eigenvalues with respect to an error criterion obtained by ignoring all the eigenvalues of the homogeneous differential equation system;
d) determining whether the error is less than a predetermined limit;
e) if the error is not less than the limit, defining further eigenvalues and repeating the method steps b) to d) with the further eigenvalues until the error is less than the limit;
f) if the error is less than the limit, defining the system relationship function from the equations of the differential equation system described by the determined eigenvalues; and
g) outputting the system relationship function describing the set of coupled linear components of the electrical circuit.
In other words, a differential equation system, which represents a state description of the set of coupled linear components, is defined for the set of coupled linear components which is embedded in any number of non-linear components. A given number of eigenvalues are determined for the homogeneous differential equation system of the differential equation system, and an error is defined for the eigenvalues which is caused by ignoring the remaining eigenvalues of the homogeneous differential equation system. If the error is less than a predetermined limit, the system relationship function is produced from those equations of the differential equation system which are described by the determined eigenvalues. However, if the error is greater than the predetermined limit, further eigenvalues are determined for the homogeneous differential equation system, and the error is once again estimated, until the error is less than the limit.
The method achieves a considerable savings in computation time since the individual “islands” of mutually coupled linear components, that is to say the set of coupled linear components, can be calculated quickly and in a simple manner and can then be considered further as a so-called black box, which is described by the system relationship function, for any number of connections to non-linear components in the electrical circuit.
Furthermore, a considerable advantage of the method according to the invention is that it is now possible to determine any number of connections, that is to say connections of the set of coupled linear components to non-linear components or else to further linear components which are ignored in the set, for any reason.
The increased accuracy of the results achieved in the determination of the system relationship function is also a considerable advantage.
Furthermore, the method makes it possible to carry out circuit simulations for circuits with very large scale integration, despite taking into account parasitic effects on lines.
In accordance with an added feature of the invention, the eigenvalues are determined in a sequence of their information content with respect to the error criterion. In other words, it is advantageous if the eigenvalues are determined in values which, with respect to their information content, fall with respect to the error criterion, that is to say in such a manner that eigenvalues with a high information content are determined at the start, and eigenvalues with only a
Feldmann Jörg-Uwe
Kahlert Martin
Wever Utz
Frejd Russell W.
Greenberg Laurence A.
Infineon - Technologies AG
Lerner Herbert L.
Stemer Werner H.
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