1. Semi-Symbolic Analysis of Analog and Signal Processing Systems
Carna Radojicic, Florian Schupfer
and Prof. Dr. Christoph Grimm

2. Overview Motivation State of the Art Proposed Solution
Simulation results
Conclusion
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3. Motivation Accurate models -> Increase in model parameters
Process variation -> Parameter deviations
Efficient system analysis and verification methods
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4. Motivation
Verification of analog-mixed signal systems with parameter deviations
Achieving full coverage with small number of simulation runs
Numerical Simulation:
Incomplete coverage
High number of simulation runs
Semi-symbolic simulation:
Complete coverage
for considered parameter space
One simulation run
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5. State of the Art Simulation based techniques
Monte Carlo, Corner Case, Worst Case
Design of Experiments[Rafaila]
Importance sampling[Srinivasan]
Formal verification techniques
Model checking, Equivalence checking
Hybrid verification[Henzinger]
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6. Proposed solution Parameter deviations represented as ranges
using Affine Arithmetic
Semi-symbolic simulation
Guaranteed result inclusion
in one simulation run
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7. Implementation Semi- symbolic simulation on system level – SystemC AMS
Simulation on transistor level
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8. Affine Arithmetic System deviations modeled in intervals
Intervals labeled by symbols
Symbols εi represent interval [-1, 1]
xi is the numerical value which scales the interval
Affine variable consists of nominal value and superimposed intervals
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9. Graphical representations
Range based system response
Signal construction by sub-ranges
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10. I/Q receiver with parameter deviations
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11. Simulation results
The bounds of output signal ranges represent the worst case behavior
The principle for verification
The system meets specification for the worst case -> The specification is satisfied for all values included into the range
Formal verification result obtained inside the range
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12. Simulation results
The specification for the worst case not satisfied -> the system must be refined
To refine the system the sources of uncertainties must be tracked back to their origin to be identified
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13. Conclusion Efficient simulation performance
Pessimistic worst case bounds  single run
Traceable deviations influence
Refinement information/recommendations
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14. Thank You for Your Attention!
Monika Rafaila, Christoph Grimm, Christian Decker, and Georg Pelz. Sequential design of experiments for effective model-based validation of electronic control units. e&i Elektrotechnik und Informationstechnik, 127:164–170, 2010.
R. Srinivasan, Importance sampling - Applications in communications and detection, Springer-Verlag, Berlin, 2002.
Darius Grabowski, Daniel Platte, Lars Hedrich, and Erich Barke. Time Constrained verification of Analog Circuits using Model-Checking Algorithms. Electronic Notes in Theoretical Computer Science (ENTCS), 153(3):37–52, 2006.
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