Transient analysis of dispersive VLSI interconnects terminated in nonlinear loads

Abstract

A new algorithm to compute the transient response of a coupled, dispersive multiconductor system terminated in nonlinear loads is presented. The characterization of the multiconductor system is based on full-wave analysis using the spectral-domain approach, rather than the usual TEM approximation. To compute the transient response of such a system, a bilevel waveform relaxation method is used. Waveform relaxation is applied to compute a time-domain solution at the input and output interfaces. The waveforms are then transformed into the frequency domain to compute the updates induced by the multiconductor system and are transformed back to the time domain for the next set of relaxation at the interfaces, Techniques to improve convergence are presented and conditions for convergence are discussed. Examples of ECL, CMOS, and GaAs circuits connected by coupled lines are given for illustration.

Simulation of high-speed interconnects

“…Mixed Frequency/Time Problem: The major difficulty in simulating high-frequency models such as distributed transmission lines is due to the fact that, while described in terms of partial differential equations, they are best represented in the frequency-domain (56). As seen, they do not have a direct representation in the time-domain.…”

“…This demands a generalized method to combine modal results into circuit simulators in terms of a full-wave stamps. References [26]- [29], [56], [74] provide solution techniques and moment generation schemes for such cases.…”

“…The linear multiterminal subnetwork can be characterized in the frequency-domain by its terminal behavior as (56) where is the -parameter matrix of subnetwork , is the vector of terminal voltage nodes that connect the subnetwork to the network , and is the Laplace transform of .…”

“…Let the corresponding residues at different ports be . The original Gilbert's realization will yield Define Next, the realization represented by (131) can be obtained as Unified Transient Simulation: Once a matrix-transfer function describing the multiport interconnect network is obtained, a time-domain realization in the form of state-space equations can be obtained as (132) where and are the vector of terminal currents and voltages of the linear subnetwork [described by (56)]. The differential equations represented by the macromodel (132) can be combined with (55) using the relation as…”

Simulation of high-speed interconnects in a multilayered medium in the presence of incident field

“…In the transverse plane, the total electric field can be written as follows: (4) The line integral of the transverse field between the ground trace and the th trace positioned in the th layer is written as follows: (5) If the reference and the signal traces do not lie in the same layer, the integration in the transverse plane must include the effect of each layer in between. The solution of (5) yields the transverse component of the forcing function in the th layer and at the th conductor position as (6) The longitudinal component of the forcing function can be written in a similar fashion (7) where (8) Since the reference conductor is at the origin of the coordinate system one obtains…”