Adaptive Newton-Raphson Iteration for IC Simulation Accuracy
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Solution Overview
Problem
As IC technology shrinks below 90 nm, existing simulation techniques face challenges in accurately simulating large-scale integrated circuits due to the inefficiencies of LU decompositions and the default elimination of Newton-Raphson iterations, which can lead to inaccurate or wrong simulation results.
Innovation Solution
A selective application of Newton-Raphson iterations based on linearity values, where iterations are performed only when the linearity value exceeds a threshold, optimizing the balance between simulation accuracy and performance by determining convergence and applying iterations only when necessary.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If LU decomposition is used for nodal analysis in large-scale circuits, then simulation can be performed, but simulation performance deteriorates due to the large size of the Jacobian matrix
Solution Approach 1:
The circuit is divided into multiple blocks, and the Jacobian matrix is partitioned into sub-matrices corresponding to each block. This segmentation allows for more efficient computation by working with smaller sub-matrices rather than the full large-scale Jacobian matrix, thereby improving simulation performance while maintaining accuracy.
Solution Approach 2:
Different computation strategies are applied to different blocks based on their local characteristics. Linear blocks use direct methods while non-linear blocks use iterative methods. This local differentiation optimizes the overall simulation performance by applying the most efficient method to each specific region of the circuit.
2Productivity
If Newton-Raphson iterations are eliminated to improve performance, then simulation speed increases, but simulation accuracy deteriorates for non-linear devices
Solution Approach 1:
The simulation method dynamically adapts by identifying which blocks are linear and which are non-linear, then applies appropriate iteration strategies to each. This dynamic approach ensures that Newton-Raphson iterations are used only where necessary (non-linear blocks), maintaining accuracy while optimizing speed by skipping iterations in linear blocks.
Solution Approach 2:
The method changes the computation parameter (iteration application) based on the block type. For linear blocks, iterations are disabled; for non-linear blocks, iterations are enabled. This parameter change allows the simulation to achieve both high speed and high accuracy by adapting the computational approach to the specific characteristics of each circuit block.
3Reliability
If Newton-Raphson iterations are applied to all blocks, then simulation accuracy is maintained, but computation time increases due to unnecessary iterations in linear blocks
Solution Approach 1:
Instead of applying Newton-Raphson iterations to all blocks (excessive action), the method applies iterations only to the extent necessary - specifically to non-linear blocks where they are needed for accuracy. This partial action eliminates wasted computation time on linear blocks while maintaining simulation accuracy where required.
Solution Approach 2:
Each block essentially serves itself by having the simulation method automatically identify whether it is linear or non-linear and apply the appropriate computation strategy. This self-service approach allows linear blocks to skip iterations autonomously while non-linear blocks receive the necessary iterative treatment, optimizing overall computation time.
Data Source
AI summary
In accordance with an exemplary simulation technique, an improved selective application of Newton-Raphson iterations can improve accuracy while ensuring good performance. In this method, selectively applying Newton-Raphson iteration in a simulation of a unit of the integrated circuit design can include determining second order effects to define a linearity value. Newton-Raphson iteration is performed when the linearity value is less than a linearity threshold and convergence of the simulation is not achieved.