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Analog SImulation and Variability Analysis for 14nm designs

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Mathematical models speed up circuit design

EU-funded researchers have applied new mathematical methods capable of analysing and predicting electronic circuit behaviour. Reducing the need for long computations and cutting simulation times will help designers bring new innovations to market quicker.

Digital Economy

The ASIVA14 project provided a team of young researchers with the opportunity to develop a number of new mathematical approaches to this challenge. Certain methods were shown to have significant potential for reducing simulation times, and a possible patent was even identified. ‘These methods will be implemented in the commercial software sector, bringing benefits to businesses that will profit from speedier simulation times,’ says project coordinator Professor Wil Schilders from Eindhoven Technical University in the Netherlands. ‘Industry clearly stands to benefit, but we have also generated new insights into certain methodologies that were not known before. This could have an impact on simulations across a range of fields due to the versatility of mathematics - results obtained for one type of application are often readily applicable to many other areas.’ A complex world Across a range of sectors, product design has become so complex that virtual design environments are required. Electronic design automation (EDA) for example is a category of software tools used for designing electronic systems such as integrated circuits and printed circuit boards. Since a modern semiconductor chip can have billions of components, EDA tools have become essential for their design. There is however constant pressure on the electronics industry to come up with new designs much more quickly, and to check these designs for errors and faults at an early design stage. The complexity of modern electronic circuits is such that simulations with cutting edge EDA software can still take many days or even weeks to run. Modern circuits also operate on multiple frequencies – which again complicates the running of simulations – and final performance can be affected by slight imperfections and electromagnetic interference in their embedded environment. ‘To assess variability and uncertainty, so-called Monte Carlo simulations need to be carried out,’ explains Schilders. ‘This means that hundreds of thousands of simulations must be performed. Again, this provides a challenge for mathematicians to come up with methods that considerably speed up the process.’ Mathematical solutions for industry The ASIVA14 project set about addressing these challenges by assigning early stage researchers (ESRs) to carry out specific mathematical tasks. One ESR for example worked on speeding up simulations for particular circuits where more than one frequency is involved. Another worked on speeding up simulations when the parasitic effects of electromagnetism must be taken into account. Finally, another worked on speeding up Monte Carlo simulations. ‘As a result of this project, a method was developed for special types of computational devices that turned out to be between 50 and 100 times faster than current simulation methods,’ says Schilders. ‘These mathematical methods have since been developed and theoretically analysed, and initial results are very promising. There is potential here to speed up simulations considerably.’ The ESR working on parasitic effects also succeeded in testing several mathematical methods with success, leading to a potential patent. For the Monte Carlo simulations, a sophisticated mathematical model was combined with simulations in regions where very rare parameter values occur. As a result, Monte Carlo simulations were speeded up by factors in the order of ten to 100 000. ‘This project has also been successful in helping to bridge the gap between academic mathematics and industrial applications,’ says Schilders. ‘It is important to show that mathematics can help address big industrial challenges.’

Keywords

ASIVA14, ESR, mathematics, industry, electronics, circuits, EDA

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