Monent computation algorithms in VLSI system

• US 20040098677A1
• Filed: 11/20/2002
• Published: 05/20/2004
• Est. Priority Date: 11/20/2002
• Status: Active Grant

• Current Assignee: Bell Semiconductor, LLC (Hilco Inc. (d/b/a Hilco Global))
• Original Assignee: LSI Logic Corporation (Broadcom, Inc.)
• Inventors: Bhutani, Sandeep, Guo, Weiqing
• Granted Patent: US 7,082,583 B2
• Time in Patent Office: Days
• US Class Current: 716/115
• CPC Class Codes: G06F 30/367 Design verification, e.g. using simulation, simulation program with integrated circuit emphasis [SPICE], direct methods or relaxation methods

Abstract

An improved method for interconnect delay analysis for VLSI circuits reduces a parasitic graph for moment computation by eliminating one or more nodes in the graph. The elimination process is performed based upon the degree of the nodes. By eliminating nodes in this fashion, the computation complexity is significantly reduced. With this elimination process, resistor loops and crossed loops can also be solved. The order in which the nodes are eliminated is optimized using the depth-first-search method on the parasitic graphs, further reducing the computation complexity. The method provides a consistent functional interface, applicable to different circuit model structures. In addition, the method accounts for coupling capacitance between interconnects.

Claims

1. A method for reducing a parasitic graph for an interconnect model circuit, the parasitic graph comprising a plurality of nodes, comprising the steps of:

(a) performing a depth-first-search on the graph;

(b) determining a degree of a deepest node with a smallest degree, wherein the node can have a degree of more than one;

(c) reducing the graph by eliminating the node; and

(d) recursively performing the determining step (b) and the reducing step (c) until the depth-first-search completes.

2. The method of claim 1, wherein the reducing step (c) comprises:

(c1) determining a matrix, wherein each entry of the matrix represents an edge of the graph;

(c2) changing the matrix such that a voltage at the node is no longer coupled to other nodes in the graph; and

(c3) reducing the graph by eliminating the node, wherein the changed matrix represents edges of the reduced graph.

3. The method of claim 1, comprising:

(a1) performing a first depth-first-search on the graph;

(b1) determining the degree for the deepest node with the smallest degree, wherein the node have a degree of one or two;

(c1) reducing the graph by eliminating the node; and

(d1) recursively performing the determining step (b1) and the reducing step (c1) until the first depth-first-search completes.

4. The method of claim 3, further comprising:

(e) determining if nodes with degrees of three or more remain in the reduced graph;

(f) performing a second depth-first-search on the reduced graph, if nodes with degrees of three or more remain in the reduced graph;

(g) determining a degree of another deepest node with a smallest degree, wherein the other node can have a degree of three or more;

(h) further reducing the reduced graph by eliminating the other node; and

(i) recursively performing the determining step (g) and the further reducing step (h) until the second depth-first-search completes.

5. The method of claim 1, further comprising:

(e) determining if the reduced graph has any non-reduced nodes;

(f) marking the reduced graph as completely reduced if there are no non-reduced nodes; and

(g) marking the reduced graph as not completely reduced if there are non-reduced nodes.

6. The method of claim 1, wherein the degree of the node of the graph is a number of edges coupled to the node.

7. A method for reducing a parasitic graph for an interconnect model circuit, the parasitic graph comprising a plurality of nodes, comprising the steps of:

(a) performing a depth-first-search on the graph;

(b) determining a degree of a deepest node with a smallest degree, wherein the node can have a degree of more than one;

(c) reducing the graph by eliminating the node, wherein the reducing comprises;

(c1) determining a matrix, wherein each entry of the matrix represents an edge of the graph,

(c2) changing the matrix such that a voltage at the node is no longer coupled to other nodes in the graph, and

(c3) reducing the graph by eliminating the node, wherein the changed matrix represents edges of the reduced graph; and

(d) recursively performing the determining step (b) and the reducing step (c) until the depth-first-search completes.

8. The method of claim 7, comprising:

(a1) performing a first depth-first-search on the graph;

(b1) determining the degree of the deepest node with the smallest degree, wherein the node can have a degree of one or two;

(c1) reducing the graph by eliminating the node; and

(d1) recursively performing the determining step (b1) and the reducing step (c1) until the first depth-first-search completes.

9. The method of claim 8, further comprising:

(e) determining if nodes with degrees of three or more remain in the reduced graph;

(f) performing a second depth-first-search on the reduced graph, if nodes with degrees of three or more remain in the reduced graph;

(g) determining a degree for another deepest node with a smallest degree, wherein the other node can have a degree of three or more;

(h) further reducing the reduced graph by eliminating the other node; and

(i) recursively performing the determining step (f) and the further reducing step (g) until the second depth-first-search completes.

10. The method of claim 7, further comprising:

(e) determining if the reduced graph has any non-reduced nodes;

(f) marking the reduced graph as completely reduced if there are no non-reduced nodes; and

(g) marking the reduced graph as not completely reduced if there are non-reduced nodes.

11. The method of claim 7, wherein the degree of the node of the graph is a number of edge coupled to the node.

12. A method for reducing a parasitic graph for a interconnect model circuit, he parasitic graph comprising a plurality of nodes, comprising the steps of:

(a) performing a first depth-first-search on the graph;

(b) determining a degree of a deepest node with the smallest degree, wherein the node can have a degree of one or two;

(c) reducing the graph by eliminating the node;

(d) recursively performing the determining step (b) and the reducing step (c) until the first depth-first-search completes;

(e) determining if nodes of degrees of three or more remain in the reduced graph;

(f) performing a second depth-first-search on the reduced graph, if nodes of degrees of three of more remain in the reduced graph;

(g) determining a degree for another deepest node with a smallest degree, wherein the other node can have a degree of three or more;

(h) further reducing the reduced graph by eliminating the other node; and

(i) recursively performing the determining step (g) and the further reducing step (h) until the second depth-first-search completes.

13. A computer readable medium with program instructions for reducing a parasitic graph for an interconnect model circuit, the parasitic graph comprising a plurality of nodes, comprising the instructions for:

(a) performing a depth-first-search on the graph;

(b) determining a degree of a deepest node with a smallest degree, wherein the node can have a degree of more than one;

(c) reducing the graph by eliminating the node; and

(d) recursively performing the determining instruction (b) and the reducing instruction (c) until the depth-first-search completes.

14. A method for calculating moments for an interconnect circuit model, comprising the steps of:

(a) creating at least one parasitic graph for the interconnect circuit model, wherein the at least one parasitic graph comprises a plurality of nodes;

(b) determining if the at least one parasitic graph has been reduced;

(c) reducing the at least one parasitic graph if the at least one parasitic graph has not been reduced, wherein the reducing comprises;

(c1) performing a depth-first-search on the at least one parasitic graph,

(c2) determining a degree of a deepest node with a smallest degree, wherein the node can have a degree of more than one,

(c3) reducing the at least one parasitic graph by eliminating the node, and

(c4) recursively performing the determining step (c2) and the reducing step (c3) until the depth-first-search completes; and

(d) computing moments for the interconnect circuit model utilizing the reduced graph.

15. The method of claim 14, wherein the creating step (a) further comprises:

(a1) setting an initial voltage of each node in the at least one parasitic graph; and

(a2) computing an outgoing current for each node in the at least one parasitic graph.

16. The method of claim 15, wherein the setting step (a1) comprises:

(a1i) setting an aggressor node of the at least one parasitic graph to a first initial voltage, wherein the first initial voltage accounts for coupling capacitance at the aggressor node; and

(a1ii) setting victim nodes of the at least one parasitic graph to a second initial voltage.

17. The method of claim 14, wherein the determining step (b) further comprises:

(b1) updating a current for each node of the at least one parasitic graph if the at least one parasitic graph has been reduced.

18. The method of claim 14, wherein the reducing step (c3) comprises:

(c3i) determining a matrix, wherein each entry of the matrix represents an edge of the at least one parasitic graph;

(c3ii) changing the matrix such that a voltage at the node is no longer coupled to other nodes in the at least one parasitic graph; and

(c3iii) reducing the at least one parasitic graph by eliminating the node, wherein the changed matrix represents edges of the reduced graph.

19. The method of claim 14, wherein the reducing step (c) comprises:

(c1i) performing a first depth-first-search on the at least one parasitic graph;

(c2i) determining the degree for the deepest node with the smallest degree, wherein the node have a degree of one or two;

(c3i) reducing the at least one parasitic graph by eliminating the node; and

(c4i) recursively performing the determining step (c2i) and the reducing step (c3i) until the first depth-first-search completes.

20. The method of claim 19, further comprising:

(c5) determining if nodes with degrees of three or more remain in the reduced graph;

(c6) performing a second depth-first-search on the reduced graph, if nodes with degrees of three or more remain in the reduced graph;

(c7) determining a degree of another deepest node with a smallest degree, wherein the other node can have a degree of three or more;

(c8) further reducing the reduced graph by eliminating the other node; and

(c9) recursively performing the determining step (c7) and the further reducing step (c8) until the second depth-first-search completes.

21. The method of claim 14, wherein the reducing step (c) further comprises:

(c5) determining if the reduced graph has any non-reduced nodes;

(c6) marking the reduced graph as completely reduced if there are no non-reduced nodes; and

(c7) marking the reduced graph as not completely reduced if there are non-reduced nodes.

22. The method of claim 14, wherein the degree of the node of the at least one parasitic graph is a number of edges coupled to the node.

24. The method of claim 14, wherein the computing step (d) comprises:

(d1) determining if the reduced graph has been completely reduced;

(d2) computing moments for non-reduced nodes in the reduced graph using a matrix, if the reduced graph has not been completely reduced, wherein each entry of the matrix represents an edge of the reduced graph; and

(d3) computing moments for reduced nodes in the reduced graph.

25. The method of claim 14, further comprising:

(e) determining if moments for another parasitic graph for the interconnect circuit model are to be computed; and

(f) repeating steps (b)-(d) for the other parasitic graph, if moments for another parasitic graph are to be computed.

26. The method of claim 25, further comprising:

(g) determining if all order of moments for the interconnect circuit model has been computed;

(h) setting an initial voltage of each node of the at least one parasitic graph to a computed moment of a previous moment order, if not all order of moments has been computed; and

(i) recursively repeating steps (b)-(f) until all order of moments for the interconnect circuit model has been computed.

27. A computer readable medium with program instructions for calculating moments for an interconnect circuit model, comprising the instructions for:

(a) creating at least one parasitic graph for the interconnect circuit model, wherein the at least one parasitic graph comprises a plurality of nodes;

(b) determining if the at least one parasitic graph has been reduced;

(c) reducing the at least one parasitic graph if the at least one parasitic graph has not been reduced, wherein the reducing comprises;

(c1) performing a depth-first-search on the at least one parasitic graph,

(c2) determining a degree of a deepest node with a smallest degree, wherein the node can have a degree of more than one,

(c3) reducing the at least one parasitic graph by eliminating the node, and

(c4) recursively performing the determining step (c2) and the reducing step (c3) until the depth-first-search completes; and

(d) computing moments for the interconnect circuit model utilizing the reduced graph.