Circuit Partitioning for Large RC Network Current Analysis
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Solution Overview
Problem
Standard simulation techniques for electromigration verification in VLSI circuits with large RC networks are computationally intensive and expensive due to the need for frequent matrix factorizations, making them impractical for larger circuits.
Innovation Solution
The method involves partitioning the circuit into a non-linear part and a linear part, allowing for separate simulations that reduce the size of the matrix and the number of factorizations required, with the linear part modeled as a single capacitor to preserve total capacitance and current accuracy.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If standard simulation techniques are used for electromigration verification in VLSI circuits with large RC networks, then accurate current analysis is achieved, but computational cost and simulation time become prohibitively expensive
Solution Approach 1:
The circuit is partitioned into two distinct subcircuits: a non-linear subcircuit containing non-linear elements (transistors, diodes, etc.) and a linear subcircuit containing linear elements (resistors, capacitors, inductors). This segmentation allows each subcircuit to be simulated separately using optimized techniques, avoiding the need to factorize the complete large matrix while maintaining accurate current analysis through coupled simulation.
2Reliability
If standard simulation techniques are used for circuits with large RC networks, then complete circuit behavior is captured, but the number of matrix factorizations required becomes computationally prohibitive
Solution Approach 1:
The circuit is divided into non-linear and linear subcircuits that can be simulated separately. The non-linear subcircuit simulation requires fewer matrix factorizations since it contains fewer nodes, while the linear subcircuit can use efficient linear solvers. This segmentation maintains complete circuit behavior accuracy while dramatically reducing the total number of factorizations needed.
Solution Approach 2:
A coupling mechanism is introduced between the two subcircuit simulations to exchange current information at their interface. Currents calculated in the non-linear subcircuit simulation are used as inputs to the linear subcircuit simulation, and vice versa. This intermediary coupling ensures that the complete circuit behavior is accurately captured despite the separate simulations.
3Measurement precision
If the complete circuit is simulated without partitioning, then all circuit interactions are captured, but the matrix size for factorization becomes too large for practical computation
Solution Approach 1:
The complete circuit matrix is segmented into two smaller subcircuits with their own matrices. The non-linear subcircuit matrix is smaller because it excludes the linear RC network nodes, making factorization computationally feasible. The linear subcircuit matrix handles the RC network separately. This segmentation reduces the maximum matrix size while preserving all circuit interactions through the coupling mechanism.
Data Source
AI summary
Improved performance of simulation analysis of a circuit with some non-linear elements and a relatively large network of linear elements may be achieved by systems and methods that partition the circuit so that simulation may be performed on a non-linear part of the circuit in pseudo-isolation of a linear part of the circuit. The non-linear part may include one or more transistors of the circuit and the linear part may comprise an RC network of the circuit. By separating the linear part from the simulation on the non-linear part, the size of a matrix for simulation on the non-linear part may be reduced. Also, a number of factorizations of a matrix for simulation on the linear part may be reduced. Thus, such systems and methods may be used, for example, to determine current in circuits including relatively large RC networks, which may otherwise be computationally prohibitive using standard simulation techniques.