Metastability Characterization Report for Actel Flash FPGAs
22- 2
v1.0
As mentioned earlier, the aperture represents the likelihood of the flip-flop entering a metastable
state. The aperture is defined as a time window within the clock period. Data transitioning inside
the aperture will cause the flip-flop output settling time to be greater than Tco + Tmet. The aperture
is calculated by recording the number of instances in which the settling time exceeds the specified
Tco + Tmet. The metastability aperture decreases exponentially as the allowed settling time (Tco +
Tmet) increases:
Aperture = To × e
–(Tco + Tmet)/
τ
EQ 22-3
If the data transition occurs within the aperture, the flip-flop will stay metastable beyond the
allocated settling time (Tco + Tmet); and therefore, the second flip-flop would register invalid data
(
Figure 22-1). The probability of an asynchronous data transition is uniformly distributed over the
clock period. Therefore, the probability of a single data transition occurring in the metastable
p = aperture / Tc
EQ 22-4
where Tc is the clock period.
In each clock cycle, the failure occurs if the data transition time is within the aperture. Therefore,
the number of failures in one clock cycle can be derived by
EQ 22-5:
ne = n × p = n × (aperture / Tc)
EQ 22-5
where ne represents the number of errors per clock cycle, and n is the number of data transitions
per clock period (fd / fc).
The number of clock cycles in the operation time (N) is the total time divided by the clock period, or
N = Toperation / Tc
EQ 22-6
Combining EQ 22-5 and EQ 22-6 results in the total number of failures per operation time (Ne): Ne = N × ne = (Toperation / Tc) × (fd / fc) × (aperture / Tc)
EQ 22-7
Since Tc = 1 / fc, EQ 22-7 can be simplified to Ne = Toperation × fd × fc × aperture
EQ 22-8
MTBF is defined as the operation time divided by the number of failures, or
MTBF = 1/ (fd × fc × aperture) = 1/ (T0 × e
–(Tco + Tmet) /
τ × f
d × fc)
EQ 22-9
Figure 22-1 Example of Synchronization Circuit
CLK
DQ
CLK
DQ
fd
fc
Tco
Async Data
Sync Data