DIGITAL LOGIC

# Metastability And Synchronisation

## Flip-flop MTBF

$${\rm MTBF}(t_r) = \frac{e^{ \frac{t_r}{\tau} } } {T_O fa}$$

where:
$$t_r$$ = resolution time (time since clock edge), $$s$$
$$f$$ = sampling clock frequency, $$Hz$$
$$a$$ = asynchronous event frequency, $$Hz$$
$$\tau$$ = flip-flop time constant (this is a function of it's transconductance), $$s$$
$$T_o$$ =

Typical values for a flip-flop inside an ASIC could be: $$t_r = 2.3ns$$, $$\tau = 0.31ns$$, $$T_O = 9.6as$$, $$f = 100MHz$$, and $$a = 1MHz$$, which gives $$\rm MTBF = 20.1days$$.