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Metastability,MTBF,synchronizer & synchronizer failure

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Metastability,MTBF,synchronizer & synchronizer failure

1. 1. METASTABILITY,MTBF, SYNCHRONIZER &SYNCHRONIZER FAILUREPRESENTED BY : SUNIL KUMAR (IMI2012001): VERSHA VARSHNEY(IMI2012010): VIBHOR GUPTA (IMI2012020)
2. 2. CONTENTS 1. INTRODUCTION 2. CASES OF METASTABILITY 3. ILLUSTRATION OF METASTABILITY 4. ENTERING METASTABILITY 5. DURING METASTABILITY 6. INTRODUCTION TO MTBF 7. DERIVATION OF MTBF 8. REFERENCES
3. 3. WHAT IS METASTABILTY Whenever there are setup and hold timeviolations in any flip-flop, it enters in a statewhere its output is unpredictable At the end of metastable state, the flip-flopsettles down to either 1 or 0.
4. 4.  CASES OF METASTABILITY• FOR SYNCHRONOUS SYSTEM-When skew is present• FOR ASYNCHRONOUS SYSEM-Whenever setup and hold time violation occurs.
5. 5. ILLUSTRATION OF METASTABILITY
6. 6. ENTERING METASTABILITYFig:2.Flip –Flops, with four gate delays from D to Q.
7. 7. GRAPH B/W INPUT VOLTAGE AND TIMEFigure 2 :Charts show multiple inputs D, internal clock (CLK2) andmultiple corresponding outputs Q (voltage vs. time). The input edge ismoved in steps of 100ps, 1ps and 0.1fs in the top, middle and bottom
8. 8.  From the graph if we increase thefrequency of input signal then theprobability of system to move inmetastability will increase period of metastability also increased
9. 9. DURING METASTABILITYFig.3 Analog model of a metastable latch
10. 10. •The Analog model result in two first-order differential equations that can becombined into one, as follows:-
11. 11. INTRODUCTION TO MTBF MTBF is Mean time between failure It gives us information on how often a particularelement will fail. It gives the average time interval between twosuccessive failures.
12. 12. EQUATION OF MTBF The MTBF equation isMTBF =Where:S = synchronization periodTw, = flip-flop characteristic constantsFC= clock frequencyFD = average input rate of change
13. 13. DERIVING MTBF EQUATION Clearly, if meta-stability starts with V=VO andends when V=V1, then the time to exit meta-stability is tm:
14. 14.  Probabilistic analysis shows that, given the fact thata latch is metastable at time zero, the probabilitythat it will remain metastable at time t >0 is e-t/τ, which diminishes exponentially fast. The probability of entering metastability, which isthe probability of D‟s having changed within theTW window, is TW/TC =TWFC But D may not change every cycle; if it changes ata rate FD, then the rate of entering metastabilitybecomes Rate =FDFCTW.
15. 15.  P(failure) = p(enter MS) X p(time to exit >S)= XRate(failures) = X The inverse of the failure rate is the meantime between failures (MTBF):MTBF =
16. 16. MTBF EXAMPLE Consider an ASIC designed for a 28-nm high-performance CMOS process. We estimate t =10 ps, TW = 20 ps and FC = 1 GHz. Let’s assume that data changes every 10clock cycles at the input of our flip-flop, andwe allocate one clock cycle for resolution: S =TC. Plug all these into the formula and we obtain4 X 1029 years.
17. 17. REFERENCES R. Ginosar, “Metastability and synchronizers:Atutorial,” IEEE Design Test Comput., vol. 28, pp.23–35, May 2011. S. Lubkin, „„Asynchronous Signals in DigitalComputers,‟‟ Mathematical Tables and OtherAids to Computation (ACM section), vol. 6, no.40, 1952, pp. 238-241. H.J.M. Veendrick, „„The Behavior of Flip-FlopsUsed as Synchronizers and Prediction of TheirFailure Rate,‟‟ IEEE J. Solid-State Circuits, vol.15, no. 2, 1980, pp. 169-176.
18. 18. THANKYOU