1. METASTABILITY
,MTBF, SYNCHRONIZER &
SYNCHRONIZER FAILURE
PRESENTED BY : SUNIL KUMAR (IMI2012001)
: VERSHA VARSHNEY(IMI2012010)
: VIBHOR GUPTA (IMI2012020)

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. WHAT IS METASTABILTY
 Whenever there are setup and hold time
violations in any flip-flop, it enters in a state
where its output is unpredictable
 At the end of metastable state, the flip-flop
settles down to either '1' or '0'.

4.  CASES OF METASTABILITY
• FOR SYNCHRONOUS SYSTEM-
When skew is present
• FOR ASYNCHRONOUS SYSEM-
Whenever setup and hold time violation occurs.

5. ILLUSTRATION OF METASTABILITY

6. ENTERING METASTABILITY
Fig:2.Flip –Flops, with four gate delays from D to Q.

7. GRAPH B/W INPUT VOLTAGE AND TIME
Figure 2 :Charts show multiple inputs D, internal clock (CLK2) and
multiple corresponding outputs Q (voltage vs. time). The input edge is
moved in steps of 100ps, 1ps and 0.1fs in the top, middle and bottom

8.  From the graph if we increase the
frequency of input signal then the
probability of system to move in
metastability will increase
 period of metastability also increased

9. DURING METASTABILITY
Fig.3 Analog model of a metastable latch

10. •The Analog model result in two first-
order differential equations that can be
combined into one, as follows:-

11. INTRODUCTION TO MTBF
 MTBF is Mean time between failure
 It gives us information on how often a particular
element will fail.
 It gives the average time interval between two
successive failures.

12. EQUATION OF MTBF
 The MTBF equation is
MTBF =
Where:
S = synchronization period
Tw, = flip-flop characteristic constants
FC= clock frequency
FD = average input rate of change

13. DERIVING MTBF EQUATION
 Clearly, if meta-stability starts with V=VO and
ends when V=V1, then the time to exit meta-
stability is tm:

14.  Probabilistic analysis shows that, given the fact that
a latch is metastable at time zero, the probability
that it will remain metastable at time t >0 is e-
t/τ, which diminishes exponentially fast.
 The probability of entering metastability, which is
the probability of D‟s having changed within the
TW window, is TW/TC =TWFC
 But D may not change every cycle; if it changes at
a rate FD, then the rate of entering metastability
becomes Rate =FDFCTW.

15.  P(failure) = p(enter MS) X p(time to exit >
S)
= X
Rate(failures) = X
 The inverse of the failure rate is the mean
time between failures (MTBF):
MTBF =

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 10
clock cycles at the input of our flip-flop, and
we allocate one clock cycle for resolution: S =
TC.
 Plug all these into the formula and we obtain
4 X 1029 years.

17. REFERENCES
 R. Ginosar, “Metastability and synchronizers:A
tutorial,” IEEE Design Test Comput., vol. 28, pp.
23–35, May 2011.
 S. Lubkin, „„Asynchronous Signals in Digital
Computers,‟‟ Mathematical Tables and Other
Aids to Computation (ACM section), vol. 6, no.
40, 1952, pp. 238-241.
 H.J.M. Veendrick, „„The Behavior of Flip-Flops
Used as Synchronizers and Prediction of Their
Failure Rate,‟‟ IEEE J. Solid-State Circuits, vol.
15, no. 2, 1980, pp. 169-176.

18. THANKYOU