# Approaches to circuit analysis

A brief overview of worst case methodologies

When it comes to checking the robustness of hardware designs, there are several possible options to
choose from to perform WCCA (Worst Case Circuit Analysis).

## Different methodologies for different needs

### There are mainly 3 possibilities:

• Extreme value analysis (EVA)
• Root Sum Squared analysis (RSS)
• Monte Carlo analysis (MC)

## These 3 methodologies answer 3 different questions:

Extreme Value Analysis will answer to the following question : is there a risk that the system performance will not be at the required level ? It’s a Yes/No answer : either your worst case is compliant with your requirements, which means that all products will be, either it is not and you know there’s a risk that some products will not be at the required performance level. It’s the way to demonstrate a product’s robustness through calculations. It may be difficult to perform when equations become too complex to handle.

Root Sum Squared analysis will answer another question : considering a bell curve distribution with a given standard deviation for all tolerances, what is the estimation of the standard deviation of the system performance? This will provide an estimate of the performance you can expect, most of the times at 3σ. Using this methodology will enable you to estimate your product’s performance for a defined risk level. It only provides an estimation, as it is based on a series of simplifications (assumes circuit performance variability follows a normal distribution and circuit sensitivities remainconstant over range of parameter variations).

Monte Carlo analysis will answer this question : what could be the performances of some random products? You’ll get as many answers as the number of runs you have in your analysis. This will give you a random example of what might happen if you build a certain number of products. It provides some indications and tendencies, but you won’t have a deterministic view of the robustness of your design. Result distribution will be representative if you know the parameters’ statistical distributions, which is rarely the case.

## Main trends

What we’ve seen is that, for most industries designing critical systems and/or products with high volumes (automotive, aerospace, defense, railway, nuclear power…), the first option is EVA. In some cases, when it’s difficult or even impossible to reach target performances, RSS is applied.

For products with lower criticality and/or volumes (automation, medical devices, energy, …), MC is used most of the time, as risk acceptance on robustness is higher.

For others (consumer electronics, IoT, …), typical performance is generally sufficient.