Harmonic Balance Clock Network Analysis for IC Grids
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Solution Overview
Problem
Current clock network analysis methods for integrated circuits, particularly in clock grid architectures, face computational challenges due to the need for accurate simulation of inductive and distributed transmission-line effects, and are often incompatible with inductive and distributed transmission-line effects, leading to impractical time-domain analysis and reduced-order modeling limitations.
Innovation Solution
A frequency-domain nonlinear Harmonic Balance algorithm is applied to analyze clock networks with grid architectures, focusing on full frequency-dependent transmission line models and direct computation of periodic steady states, reducing the size of the analysis to the number of nonlinear nodes and incorporating frequency-dependent per-unit-length transmission line parameters.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If time-domain analysis is used for clock network analysis, then accurate simulation of inductive and distributed transmission-line effects can be achieved, but computational complexity increases and analysis becomes impractical
Solution Approach 1:
The patent transforms the analysis from time-domain to frequency-domain by applying Harmonic Balance methodology. This parameter change in the mathematical domain allows accurate modeling of inductive and distributed transmission-line effects while reducing computational complexity, as the frequency-domain approach naturally handles periodic steady-state analysis of clock networks.
Solution Approach 2:
The patent replaces the traditional time-domain simulation approach with a frequency-domain Harmonic Balance method. This substitution changes the fundamental mathematical mechanism from time-steving integration to frequency-domain algebraic equations, eliminating the need for complex time-domain transient analysis while maintaining accuracy for periodic clock signals.
2Device complexity
If reduced-order modeling is applied to simplify clock network analysis, then computational complexity is reduced, but accuracy in modeling inductive and distributed transmission-line effects is lost
Solution Approach 1:
The patent uses frequency-domain parameter representation where transmission-line effects are modeled using frequency-dependent per-unit-length parameters. This approach maintains full accuracy of inductive and distributed effects without requiring reduced-order models, as the Harmonic Balance method naturally incorporates frequency-dependent behavior through the nonlinear frequency domain equations.
3Measurement precision
If full frequency-dependent transmission line models are used, then accuracy of clock signal analysis is improved, but computational complexity increases
Solution Approach 1:
The patent substitutes time-domain transient simulation with frequency-domain Harmonic Balance analysis. This replacement allows full frequency-dependent transmission line models to be used efficiently, as the frequency-domain approach directly solves for periodic steady-state without requiring complex time-stepping simulations, thus maintaining accuracy while reducing computational burden.
Data Source
AI summary
A method and system to perform clock network analysis of a clock network of an integrated circuit that includes a grid obtains parameters for each transmission line of the clock network that carries a clock signal between a source of the clock signal and the grid. The method also includes obtaining models of nonlinear components of the clock network, and numerically solving a frequency domain nonlinear Harmonic Balance equation to obtain voltage values at an input and an output of each of the nonlinear components. The number of the voltage values obtained is proportional to the number of the nonlinear components. A physical implementation of the integrated circuit is obtained based on the clock network analysis.