Yield Calculation via Binary Decision Graphs
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Conventional automatic design techniques for analog circuits face significant processing time challenges when calculating the yield based on the domination relationship between sample points, especially as the number of samples increases.
Innovation Solution
The method involves converting performance item values into coordinate values of mesh elements, generating a binary decision graph, and calculating the number of sample points that dominate a given sample point by counting paths in the graph, allowing for efficient yield calculation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional yield calculation methods are used, then yield accuracy is maintained, but processing time increases significantly
Solution Approach 1:
The patent segments the yield calculation process into two distinct phases: an offline phase where the domination relationship matrix is pre-calculated and stored, and an online phase where yield is quickly computed by retrieving pre-stored data. This segmentation allows the computationally intensive matrix calculation to be performed once, while subsequent yield calculations use the pre-processed information, dramatically reducing processing time without sacrificing accuracy.
Solution Approach 2:
The patent performs preliminary calculation and storage of the domination relationship matrix before actual yield calculation is needed. By pre-computing which sample points dominate others and storing this relationship in a matrix structure, the system eliminates the need to re-evaluate domination relationships during yield calculation, thus maintaining measurement precision while significantly reducing the time required for yield computation.
2Quantity of substance
If the number of sample points increases, then yield calculation coverage improves, but processing time increases exponentially
Solution Approach 1:
The patent divides the calculation workload by separating the domination relationship determination (performed once offline) from the yield calculation (performed quickly online). This allows the system to handle large numbers of sample points by pre-processing the complex comparison logic, enabling subsequent yield calculations to scale linearly rather than exponentially with the number of sample points.
Solution Approach 2:
By performing preliminary action to pre-calculate and store the domination relationship matrix, the patent enables the system to efficiently handle increasing numbers of sample points. The offline pre-processing creates a lookup structure that allows online yield calculations to be performed rapidly even as the sample point population grows, thus improving calculation coverage without exponential time penalty.
3Measurement precision
If exhaustive comparison of all sample points is performed, then yield calculation accuracy is ensured, but device complexity increases
Solution Approach 1:
The patent segments the complex exhaustive comparison task into a one-time offline matrix construction phase and a simplified online query phase. The offline phase handles the computational complexity of comparing all sample points, while the online phase simply retrieves pre-computed results, thereby maintaining accuracy while reducing the operational complexity of the yield calculation system.
Solution Approach 2:
The patent creates a copied representation of the domination relationships in the form of a stored matrix, rather than performing direct comparisons each time yield is needed. This copying of the relationship structure allows the system to maintain measurement precision through complete comparison while reducing device complexity by replacing repeated complex operations with simple data retrieval.
Data Source
AI summary
A disclosed method includes: converting, for each sample point, a set of performance item values for a sample point into coordinate values of a mesh element containing the set among plural mesh elements obtained by dividing a space mapped by the performance items; generating a binary decision graph representing a group of the coordinate values of the sample points; calculating the number of sample points including second sample points that dominates a first sample point and the first sample point, by counting the number of paths in the binary decision graph from a root node to a leaf node representing “1” through at least one of certain nodes corresponding to coordinate values that are equal to or less than coordinate values of the first sample point; and calculating a yield of the first sample point by dividing the calculated number by the number of the plural sample points.