Abstract
Adapting the supply voltage by using in-situ delay monitors forms a closed-loop control system. The last chapter focused on the in-situ delay monitors (Pre-Error flip-flops) acting as sensors of this system. The following chapter will now deal with the entire control loop. First, we show how the whole system can be analyzed accurately and at the same time efficiently. Subsequently, the Markov chain, which is used to model the AVS system, is explained thoroughly. Describing the voltage adaptation by a Markov model is a beneficial approach, which can be used to evaluate the power saving potential and reliability of the Pre-Error AVS system. In the last section of the chapter, the stability of the AVS control loop is discussed, which has to be ensured for proper system operation.
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- 1.
The Markov model is named after Andrei Markov, who developed his famous theory about stochastic processes in 1906 [56]. Since than the Markov chain has been applied in many scientific fields, like biology [57, 58], information theory [59, 60], finance [61] and even in music for algorithmic composition [62, 63].
- 2.
The pre-error probabilities P pre are again extracted from the SPICE simulation results. For a longer pre-error detection window more transitions are detected as pre-error and P pre increases.
- 3.
The exponential dependence of the sub-threshold leakage current on the drain-source voltage results from drain-induced barrier lowering (DIBL) in short channel devices [66].
- 4.
To ensure proper sampling, the incoming data also has to be kept stable for a minimum amount of time after the triggering edge of the clock (hold time constraint). However, in contrast to the setup-time, the hold-time constraint is relaxed when the supply voltage is scaled. Therefore, the hold time is not considered in the following.
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Wirnshofer, M. (2013). Modeling the AVS Control Loop. In: Variation-Aware Adaptive Voltage Scaling for Digital CMOS Circuits. Springer Series in Advanced Microelectronics, vol 41. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-6196-4_6
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