MTBF Calculation for 2-FF Synchronizer
Mean Time Between Failures (MTBF) quantifies synchronizer reliability and dictates whether a product will survive in the field or fail unpredictably.
A synchronizer circuit resolves metastable states before an asynchronous signal propagates to downstream logic. The system parameters for a baseline single-stage synchronizer are given as follows: clock frequency f_clk is 100 MHz, asynchronous data toggle rate f_data is 10 MHz, setup/hold window T_w is 1 ns, resolution time constant tau is 0.5 ns, and the available resolution time t_res is 5 ns.
Calculate the base MTBF for the current design. Evaluate the impact of adding an additional synchronization stage to extend t_res by one full clock cycle. Determine if the modified design meets a standard 10-year reliability requirement.
Constraints
- Assume $e \approx 2.718$ for manual estimations.
- 1 year is approximately $3.15 \times 10^7$ seconds.
- The MTBF formula is $MTBF = \frac{e^{t_{res} / \tau}}{f_{clk} \cdot f_{data} \cdot T_w}$.
- Frequencies must be converted to Hz and time to seconds before calculating the denominator.
Topics
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