*From systems to silicon, designers are using simulation to assure higher levels of reliability in their products. The December 2009 release of the Saber products features powerful new capability for performing Worst-Case Analysis on power electronic and multi-domain circuits, taking designers beyond the limitations of traditional WCA techniques.* Why Worst-Case Analysis?

The performance of every system, circuit, and component is inevitably subject to variation – variation due to manufacturing processes, variation due to environmental conditions, and variation due to aging. During the lifetime of a design, combinations of these variations can cause design performance to deviate outside of intended behavior to the point of diminished performance or worse, failure. Fortunately, reliability analysis techniques are available for designers to identify the conditions that cause performance to exceed specified limits. One such technique is Worst-Case Analysis. Worst-Case Analysis (WCA) seeks to determine the combination of design parameter values that causes a performance metric of interest to reach its extreme. By understanding where the worst-case conditions exist, designers can determine whether design performance specifications could possibly be exceeded, and in turn, threaten system reliability.

Traditional WCA Techniques

**Extreme Value Analysis**

One of the most popular techniques for predicting worst-case performance of a circuit is Extreme Value Analysis, or EVA. In most implementations, the EVA method looks for the combination of parameters at their corners that result in the worst case of a given performance measure. Because parameters typically have multiple corners (e.g. typical, minimum, and maximum), designers typically use sensitivity analysis to determine which of these values contributes most to a given worst-case condition. However, the assumption of linearity when calculating parameter sensitivity quickly breaks down for circuits that exhibit nonlinear behavior – often the case as complexity increases.

**RSS**

Another common approach for predicting the worst-case behavior of a circuit is the Root Sum of Squares, or RSS, method. Based on the Central Limit Theorem, the RSS method combines the statistical distributions of several design parameters into a single normal (Gaussian) distribution that characterizes the variability of the performance measure of interest. The worst-case value of the performance measure is then defined as the 3σ (three standard deviations) value of the combined distribution. While the RSS method is a straightforward calculation that does not require simulation, it produces a more optimistic estimate of worst-case performance than EVA produces, missing critical regions of operation. The RSS method also assumes linearity (thus constant parameter sensitivity) across the range of operation and produces less reliable results as circuit complexity increases.

**Monte Carlo Analysis**

Using Monte Carlo Analysis, the variability of circuit performance is evaluated by repeatedly simulating the circuit, and for each iteration randomly selecting parameter values according to their defined statistical distributions. The worst case, found in the tail of the performance distribution, represents a combination of parameters that results in an extreme behavior of the circuit. Monte Carlo Analysis overcomes a limitation of traditional EVA and RSS by considering that a parameter can take any value within its defined distribution (not just the extreme values). Monte Carlo Analysis is useful for identifying a statistical worst-case defined at a prescribed number of standard deviations. However, when looking for the combination of parameters leading to the extreme behavior, the method is computationally inefficient and expensive—often requiring tens of thousands of iterations.

Saber Worst-Case Analysis

Introduced in the D-2009.12 release, Saber Worst-Case Analysis provides designers with powerful capability for predicting the worst-case behavior of power electronic and multi-domain circuits. Saber WCA uses a guided EVA search approach that combines the advantages of traditional WCA methods and the strength of the Saber Simulator to quickly identify parameter combinations from the entire design space that cause extreme worst-case performance, with no limits on design complexity, nonlinear behavior, or combinations of physical domains.

**Saber WCA Advantages** *High quality of results, high confidence* – Saber WCA identifies extreme worst-case conditions to satisfy requirements for establishing performance specifications and assuring system reliability*Easy to use* - An intuitive graphical interface guides the user through the process of setting up and executing Saber WCA tests and documenting results (see Figure 1)*Inherent ability to handle system complexity* – Built on top of the Saber Simulator, Saber WCA is not limited by design complexity and works with any multi-domain design described in MAST or VHDL-AMS*High performance, high efficiency* – Sophisticated search algorithms are tuned to quickly locate regions of worst-case performance across the entire range of operation, in a fraction of the iterations that Monte Carlo techniques require*Enables reuse of tools, models, and methodology* – Saber WCA works seamlessly with existing Saber models and complements Saber’s proven capabilities for achieving Robust Design*Easy to automate and extend* – Saber WCA includes a full API for scripting and customizing tests, search algorithms, and results post-processing

*Figure 1*

Saber WCA – Proven in Production

Particularly as the complexity of electronic systems continues to grow, traditional WCA techniques are limited in their abilities to identify possible worst-case conditions. Saber Worst-Case Analysis overcomes these limitations by providing powerful, efficient, and easy-to-use capability for finding worst-case performance of complex multi-domain circuits.

"The new Saber Worst-Case Analysis tool was instrumental in finding a worst case in our circuit that previous methods had not identified. The WCA tool delivers highly valuable capabilities and is now part of my regular design reliability flow."

*-Leonard Kelly, Sr. Staff Engineer *

Already deployed in automotive, aerospace, defense, and industrial automation applications, Saber Worst-Case Analysis enhances the effectiveness of reliability programs and expands Saber’s offering for achieving a variety of Robust Design goals.

This article was published in the January 2010 Saber eUpdate Newsletter.