In the context of Clock Domain Crossing (CDC), Mean Time Between Failures (MTBF) quantifies how often a synchronization failure might occur.

A failure here refers to the case where:

1. A signal crosses from one clock domain to another.
2. The signal becomes metastable in the first-stage flip-flop of a synchronizer.
3. The metastability persists for more than one clock cycle, so when the second-stage flip-flop samples it, the signal remains metastable.

This results in an unstable or undefined output being propagated into the receiving clock domain — potentially causing logic failures.

📉 Interpreting MTBF Values

• Higher MTBF → Better system reliability
  (i.e., longer time between potential failures)

• Lower MTBF → Higher failure frequency
  (i.e., metastability may occur more often)

Thus, designers aim to maximize MTBF to minimize the risk of metastability affecting system behavior.

⚙️ Factors Affecting MTBF

According to Dally and Poulton, the MTBF of a synchronizer circuit depends primarily on:

1. Sample clock frequency (f_clk):

   • How often signals are sampled into the receiving clock domain.
   • Higher sampling frequencies reduce MTBF (failures occur more often).

2. Data change frequency (f_data):

   • How frequently the asynchronous input signal changes.
   • Faster-changing data increases the probability of violating setup/hold times.
     

📊 Design Implications

From the above relationships, we can conclude:

• High-speed designs (with fast clocks and frequent data changes) tend to have shorter MTBF, meaning metastability failures may occur more often.
• Designers can improve MTBF by:
  • Reducing data transition rates across CDC boundaries,
  • Allowing more time for metastability to settle (e.g., adding more synchronizer stages), and
  • Using flip-flops with shorter metastability resolution times.