Difficulty: Hard · Puzzle 6 of 6 · Topic: Digital Logic Puzzles
A synchronizer MTBF is modeled as MTBF proportional to exp(Tresolve/tau). If adding one extra sync flop increases settling time by 2 ns and tau=50 ps, by what factor does MTBF improve?
Compute exp(deltaT/tau) using ratio 2 ns / 50 ps.
1) MTBF ratio = exp((Tnew - Told)/tau) = exp(2 ns / 50 ps).
2) Convert units: 2 ns = 2000 ps.
3) Exponent = 2000/50 = 40.
4) Ratio = e^40 approx 2.35 x 10^17.
5) So one extra stage can massively improve reliability when timing budget allows.Answer: MTBF improves by e^40, approximately 2.35e17 times.
Expecting linear MTBF improvement per extra stage; dependence is exponential.
Why does this argument not guarantee safe transfer of one-cycle pulses?