Question

What is the maximum frequency for Clk in MHz, given the flip-flop and logic gate delays?

• A. \( 100 \) MHz
• B. \( 200 \) MHz
• C. \( 250 \) MHz
• D. \( 500 \) MHz

Hint:

For a synchronous sequential circuit, the maximum clock frequency is determined by the longest combinational delay path between flip-flops plus setup time constraints.

Answer 1

The Correct Option is B

Step 1: Understanding the Timing Parameters.
The given timing parameters from the circuit:
- Setup Time (\( t_s \)) = 2 ns
- Hold Time (\( t_h \)) = 0 ns
- Clock-to-Q Propagation Delay (\( t_{pcq} \)) = 2 ns
- Logic Gate Propagation Delay = 1 ns
Step 2: Compute the Minimum Clock Period.
The minimum clock period for a sequential circuit is given by:
\[ T_{min} = t_{pcq} + t_{pd(logic)} + t_{setup} \]
Substituting values: \[ T_{min} = 2 \text{ ns} + 1 \text{ ns} + 2 \text{ ns} = 5 \text{ ns} \]
Step 3: Compute the Maximum Clock Frequency.
\[ f_{max} = \frac{1}{T_{min}} = \frac{1}{5 \times 10^{-9}} \text{ Hz} \]
\[ f_{max} = 200 \text{ MHz} \]
Thus, the maximum clock frequency is: \[ \mathbf{200} \text{ MHz} \]