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Worst Case Simulation Overview
Worst case simulation analysis is a method that is used in order to predict whether or not a design will satisfy requirements over all component variations. It is a method more applicable then Monte Carlo for electronic simulation.
The fundamental advantage of worst case analysis to Monte Carlo analysis is that is is far more likely to be able to determine circuits that will fail within the constraints of a reasonable number of simulation runs. To obtain a satisfactory estimate of all conditions in a random Monte Carlo requires quite a large number of runs, which in general, takes significant time. Indeed, Monte Carlo can be summed up by, if one hasn't any clue at all what to do, suck it and see.
What is it?
Worst case analysis is a systematic set of simulation runs where all relevant parameters are sequentially set either to their nominal, maximum and minimum values, and nominal, maximum and minimum temperatures. These 3 run types are named:
1 Weak/Slow, usually named either weak or slow.
A nominal/normal model sets all parameters such that the expected
slowest and lowest gain results.
A strong/fast model sets all parameters such that the expected
fastest and largest gain results.
Validity
The goal of worst case analysis is to predict design failure by predicting the worst case signal waveforms. In principle, worst case signals are not identical to signal sets of worst case component runs. It is possible for signals to have their maximum variation at intermediate component values. However, experience shows that it is a very good approximation in most cases.
One argument presented against worst case, is that it is usually too pessimistic, resulting in an "over engineered" product. This is because the probability of all errors conspiring against should be low. In practice, this view is somewhat misguided. For example, it should be appreciated that it is not possible to make the models themselves exact. A worst case model is only an engineering approximation to say, the real 3,4,5... sigma variations. It is far safer to error on the conservative side, than make a prediction based on an inevitable compromised model. If a worst case analysis indicates a failed specification, which appears unsolvable, a more detailed analysis can be performed at that point to determine if the design is still satisfactory.
Method
Models are first partitioned into their main types, that is NPN, PNP, NMOS, PMOS, NJFET, PJFET, R, L, C. All possible combinations of these types are then run. However, in practice, in order to reduce the number of simulation runs R and C are grouped together.
For example, if a design contained NMOS and PMOS, the following sets would be run:
1 weak nmos, weak pmos, weak temp.
2 weak nmos, nominal pmos, weak temp.
3 weak nmos, strong pmos, weak temp.
4 nominal nmos, weak pmos, nominal temp.
5 nominal nmos, nominal pmos, nominal temp.
6 nominal nmos, strong pmos, nominal temp.
7 strong nmos, weak pmos, high temp.
8 strong nmos, nominal pmos, high temp.
9 strong nmos, strong pmos, high temp.
A total of 9 runs. If R/C was included, the number of runs would increase to 27.
Method Evaluation
Consider the Monte Carlo case. This method varies the components randomly. Say, 1.2% for component A, -0.5% for component B, etc, with no guarantee that the maximum or minimum will be included at all. The probability that, say 20 components from 100 will all be within the same band greater than some less than 3 sigma is relatively low, where as in reality, the mechanisms of batch1 supplies, make this event quite likely. That is, batch supply make it more likely for errors to conspire together against the design objective, which Monte Carlo can only predict if a large enough number of runs is performed.
Industry Practice
In I.C. design, a mask set can be $100k, with a fab turnaround time of several months. What manufacture will not do a worst case set of runs prior to ordering the masks:-)
Appendix
1 batch supplies. Components are usually supplied, on reels, from batch manufacturing runs. This results in all components being value grouped somewhere between their published maximum and minimums,
Last updated 27th Aug. 2003
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