	US 7,509,243 B2
	Method of determining high-speed VLSI reduced-order interconnect by non-symmetric lanczos algorithm
Chia-Chi Chu, Tao-Yuan (Taiwan); Ming-Hong Lai, Tao-Yuan (Taiwan); and Wu-Shiung Feng, Tao-Yuan (Taiwan)
Assigned to Chang Gung University, Tao-Yuan (Taiwan)
Filed on Jun. 08, 2005, as Appl. No. 11/148,086.
Prior Publication US 2006/0282799 A1, Dec. 14, 2006
Int. Cl. G06F 17/10 (2006.01); G06F 17/50 (2006.01)

U.S. Cl. 703—2 [703/14]

2 Claims

1. A method of determining and building a high-speed VLSI reduced-order interconnect, comprising:

a) accessing an interconnect in VLSI to be analyzed and creating a mathematical model based on electrical parameters including resistance, capacitance, inductance, coupling capacitance, and mutual inductance of the interconnect;

b) feeding an expand frequency point based on a predetermined operating frequency;

c) performing a non-symmetric Lanczos Algorithm;

d) determining an order of reduced model for model reduction based on iteration termination conditions;

e) performing a projection algorithm;

f) creating a reduced system;

g) inputting the reduced system into a signal analyzer for a high-speed and very-large IC interconnect; and

h) analyzing the reduced system and building an interconnect using the reduced system, wherein the model reduction method has a transfer function of the perturbed system equal to the transfer function H(s) of original system, and a transfer function H_Δ(s) of modified nodal analysis expressed as follows:

where, Δ=v_q+1δ_q+1w_q′+v_qβ_q=1w_q=1′, q is the order of reduced model employed the non-symmetric Lanczos Algorithm comprising:

1) inputting a state equation of a target system;

2) selecting an expand frequency point of a reduced system;

3) determining an order of the reduced system;

4) performing the non-symmetric Lanczos Algorithm to create a projection matrix;

5) performing a double projection on state variables by means of the projection matrix to obtain a state equation of the reduced system; and

6) simulating by applying the state equation of the reduced system, while δ_q+1and β_q+1are obtained from computational process of reduced system; and the transfer function H_Δ(s) of perturbed system is equal to transfer function Ĥ(s) of reduced system.