Waveform Invariant Node Decomposition for Compact Timing Models
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Solution Overview
Problem
The existing Extracted Timing Model (ETM) methodologies face challenges in efficiently representing circuit paths with advanced technology nodes, as they require more data storage and are runtime-intensive due to the need for precise waveform representation, leading to a significant increase in model size and computational burden.
Innovation Solution
The method identifies a waveform invariant node in a circuit path, allowing the timing model to be decomposed into two components, reducing the number of output slews and delay values by using a uniform waveform beyond the invariant node, thereby reducing the model size and computational complexity without compromising accuracy.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If all slews in an ETM are replaced with waveform samples to accurately characterize input and output waveforms, then the accuracy of the timing model is improved, but the size of the ETM increases dramatically (with a twenty-fold increase or more)
Solution Approach 1:
The circuit path is segmented at the waveform invariant node, dividing the path into two portions. The first portion (from input pin to waveform invariant node) maintains detailed waveform sampling to capture transition characteristics, while the second portion (from waveform invariant node to output pin) uses a uniform representative waveform. This segmentation allows accurate characterization where needed while reducing overall data storage requirements.
Solution Approach 2:
Different regions of the circuit path are assigned different levels of waveform detail based on local characteristics. The waveform invariant node identification determines where detailed sampling is necessary versus where a uniform waveform suffices. This local quality approach ensures high accuracy in regions with significant waveform variation while using simplified representation in regions where waveforms converge.
2Measurement precision
If waveform samples are used instead of discrete slew parameters, then the accuracy of timing analysis is improved, but the runtime for generating the timing model becomes particularly intensive
Solution Approach 1:
The timing model generation process is segmented at the waveform invariant node. Waveform propagation simulation is performed in detail only for the first path portion up to the waveform invariant node, where actual waveform variation occurs. For the second path portion, a uniform representative waveform is used, dramatically reducing the computational runtime while preserving timing analysis accuracy.
Solution Approach 2:
Instead of performing full waveform propagation simulation through the entire circuit path, the method applies partial action by simulating waveforms only up to the waveform invariant node. Beyond this point, a uniform waveform representation is used, reducing computational effort from simulating every segment to simulating only the critical initial segment where waveform characteristics are established.
3Measurement precision
If detailed waveform sampling is used for each circuit path, then the accuracy of the timing model is improved, but the complexity of the timing model increases
Solution Approach 1:
The timing model structure is segmented at the waveform invariant node, creating two distinct components: a first timing arc component for the first path portion with detailed waveform characteristics, and a second timing arc component for the second path portion with uniform waveform characteristics. This segmentation simplifies the overall model complexity by reducing the number of detailed waveform parameters needed while maintaining accuracy in critical regions.
Data Source
AI summary
For a circuit path to be represented in a timing model, a set of propagating waveforms substantially converges through waveform stabilization to a uniform waveform at a waveform invariant node and all pins following. The circuit path is decomposed at the waveform invariant node into first and second portions, which are characterized as first and second timing arcs. In computing output slew and delay values, the first timing arc generation factors only a single output load of the waveform invariant node, and the second timing arc generation factors only the uniform waveform. Similarly, a setup arc employs the uniform waveform rather than multiple clock input waveforms in computing setup/hold values. Simulation of waveform propagation is also simplified by simulating only the uniform waveform for the second portion. Additionally, the first arc may be shared between a plurality of circuit paths which share an input pin and the waveform invariant node.