Additional Synchronizer Stages: Probability Reduction, Not Elimination
Mission-critical systems must handle asynchronous inputs safely without assuming metastability can be entirely avoided. Every logic function operating across multiple clock domains relies on synchronizers to manage the statistical risk of setup and hold violations.
A multi-stage synchronizer receives an asynchronous signal ASYNC_IN. The synchronizer consists of a series of flip-flops clocked at an interval T = 10 time units. The resolution time constant for these specific flip-flops is tau = 0.5 time units.
Calculate the relative reduction in failure probability when increasing the synchronizer depth from two stages to three stages. Evaluate the engineering tradeoffs involved in adding additional stages and determine the mathematical limits of metastability resolution.
Constraints
- Assume the setup and hold time windows are negligible compared to the clock period
T. - The total resolution time available in a synchronizer with N stages is approximately
(N-1) * T. - The probability of a flip-flop remaining metastable decays exponentially over time as
e^(-t/tau).
Topics
Solve this problem
Place the gates, wire them up and watch the signals settle. Every submission runs on the same simulation engine that grades it.
This problem is part of Codiode Pro. The statement above is free to read.
The circuit builder and code editor need a desktop screen. On a phone, read the problem here and open it on a laptop to solve.